User_Guide_Sept_02_2009 Oslo User Guide

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Optics Software for Layout and Optimization User Guide Lambda Research Corporation 25 Porter Road Littleton, MA 01460 USA Tel: 978-486-0766 Fax: 978-486-0755 support@lambdares.com www.lambdares.com ii COPYRIGHT The OSLO software and User Guide are Copyright © 2009 by Lambda Research Corporation. All rights reserved. This software is provided with a single user license or with a multi-user network license. Each license may only be used by one user and on one computer at a time. The OSLO User Guide contains proprietary information. This information as well as the rest of the User Guide may not be copied in whole or in part, or reproduced by any means, or transmitted in any form without the prior written consent of Lambda Research Corporation. TRADEMARKS OSLO® is a registered trademark of Lambda Research Corporation. TracePro® is a registered trademark of Lambda Research Corporation. Pentium® is a registered trademark of Intel, Inc. UltraEdit™ is a trademark of IDM Computer Solutions, Inc. Windows 95®, Windows 98®, Windows NT®, Windows 2000®, Windows XP®, Windows Vista®, Windows 7®, and Microsoft® are either registered trademarks or trademarks of Microsoft Corporation in the United States and/or other countries. Table of Contents Table of Contents Preface 1 Chapter 1 - Your first OSLO session iii 2 Introduction ........................................................................................... 2 Symbols used in this chapter ............................................................. 2 Running OSLO ..................................................................................... 3 The user interface .................................................................................. 3 Spherical mirror example ...................................................................... 6 Defining the lens system data ........................................................... 6 Defining the lens surface data ........................................................... 7 Drawing the lens in the Autodraw window....................................... 8 Plotting the on axis spot diagram ...................................................... 9 Listing the lens surface data ............................................................ 10 Saving the lens ................................................................................ 11 Changing the aperture ..................................................................... 12 Drawing the lens in the graphics window, with “zooming” ........... 13 Finding the best focal plane ............................................................ 14 Plotting the on axis point spread function (PSF) ............................ 15 Extending the rays in the lens drawing ........................................... 16 Calculating the off axis optical path difference (OPD) ................... 16 Optimizing ...................................................................................... 18 Assessing the final design ............................................................... 20 Listing the data ................................................................................ 20 Exiting the program ........................................................................ 20 Conclusion .......................................................................................... 21 Chapter 2 - Configuring OSLO 22 Introduction ......................................................................................... 22 Toolbar menus .................................................................................... 22 Main window .................................................................................. 22 Text window ................................................................................... 22 Graphics window ............................................................................ 23 The status bar ...................................................................................... 23 Preferences .......................................................................................... 24 Designer name (dsgn) ..................................................................... 24 ISO10110 drawing settings (adr1, adr2, adr3, edcm) ..................... 24 Graphics (gems, gacl, gfwb, glab, grax, gfbw, drra, pens) ............. 25 Graphics alternate mode (gfam) ...................................................... 25 No error boxes (noeb) ..................................................................... 25 Tangent check (tanc on) ...................................................................... 25 Compile CCL ...................................................................................... 26 Chapter 3 - The command line 27 Arithmetic calculations ....................................................................... 27 OSLO commands ................................................................................ 27 Assigning values to predefined variables............................................ 28 Printing ................................................................................................ 29 The history button ............................................................................... 29 Keyboard shortcuts ......................................................................... 29 iv The message area................................................................................. 30 Executing CCL command sequences .................................................. 31 Alphabetic list of system data variables .............................................. 32 Chapter 4 - Lens data entry 34 8 x 30 binoculars: Specification .......................................................... 34 Calculations ......................................................................................... 34 Choosing an eyepiece .......................................................................... 34 Scaling the eyepiece ............................................................................ 36 Choosing a catalog objective............................................................... 36 Combining the objective and the eyepiece .......................................... 38 Surface decenters and tilts ................................................................... 40 Adding a right angle prism .................................................................. 41 Converting the prism to a Porro prism ................................................ 43 Adding a second Porro prism .............................................................. 44 Completing the design ......................................................................... 45 Chapter 5 - Graphical analysis 47 Introduction ......................................................................................... 47 Opening a new graphics window .................................................... 47 Labeling a graphics window ........................................................... 47 Generating a plot ............................................................................. 48 Saving a plot .................................................................................... 48 Cutting and pasting a plot................................................................ 48 Lens drawing ....................................................................................... 49 Drawing a lens in 2D ....................................................................... 49 Drawing a lens in 3D ....................................................................... 51 Drawing a lens in 3D with sliders ................................................... 52 Ray intercept curves analysis .............................................................. 53 Ray analysis (RIC) .......................................................................... 53 Ray intercept curves for 2D field points ......................................... 53 Ray intercept curves report graphic................................................. 54 Chapter 6 - Numerical analysis 56 Introduction ......................................................................................... 56 Finding the edge rays .......................................................................... 56 Graphical estimates ............................................................................. 57 Numerical calculation.......................................................................... 58 From the text window ..................................................................... 58 From the menu headers ................................................................... 58 From the command line (abbreviated) ............................................ 59 By executing in the Edit window .................................................... 60 From the command line (in full) ..................................................... 60 The spreadsheet buffer ........................................................................ 60 Clearing the text window and spreadsheet buffer ........................... 60 Reading from the spreadsheet buffer............................................... 61 Writing to the spreadsheet buffer .................................................... 61 Scrolling the spreadsheet buffer ...................................................... 62 Chapter 7 - Slider-wheel design 63 1:1 wide angle relay ............................................................................ 63 Introduction ..................................................................................... 63 Defining the starting point............................................................... 63 Setting up the starting lens .............................................................. 63 Slider-wheel design with ray intercept curves .................................... 65 Plotting the MTF across the field .................................................... 66 Editing the slider-wheel callback command ................................... 66 Listing of the modified slider-wheel callback CCL ........................ 68 Slider-wheel design using MTF at one frequency .............................. 69 Setting clear apertures ..................................................................... 70 Chapter 8 - Programming 71 Introduction ......................................................................................... 71 Defining a new command: sno............................................................ 71 Structure of a CCL command ............................................................. 73 Search CCL library: scanccl ............................................................... 74 Defining a new command: ctn ............................................................ 74 Initial version of command ............................................................. 74 Version with formatted output ........................................................ 75 Adding the glass name string .......................................................... 76 Adding headers and documentation ................................................ 76 The text window toolbar ..................................................................... 78 Adding the command sno to the toolbar ......................................... 78 Calling sno from the toolbar ........................................................... 79 Defining a new command: xmt ........................................................... 79 Writing a command xmt to print transmittance values ................... 79 Converting xmt printed output to graphics ..................................... 80 Preserving the text window contents .............................................. 81 Scaling and drawing the axes .......................................................... 81 Adding standard plot commands to xmt ......................................... 82 Error handling ................................................................................. 82 Listing of complete command xmt ................................................. 83 The graphics window toolbar .............................................................. 85 Creating a new icon for xmt ............................................................ 85 Adding the xmt icon to the graphics window toolbar ..................... 85 Calling xmt from the toolbar icon ................................................... 86 SCP programming: *triplet ................................................................. 86 Load command file programming ....................................................... 88 Chapter 9 - Optimization 89 Optimizing using Seidel aberrations ................................................... 89 Setting up the starting design .......................................................... 89 Defining the error function ............................................................. 90 Description of the Aberration Operands error function .................. 91 Creating a model glass .................................................................... 92 Defining the optimization variables ................................................ 93 Optimization ................................................................................... 93 Choosing a real glass type............................................................... 94 Final optimization steps .................................................................. 95 Autofocus ........................................................................................ 95 Optimization using finite rays ............................................................. 97 50 mm f/5.6 objective: specification ............................................... 97 Finding a starting design ................................................................. 97 Checking for vignetting in the starting design ................................ 98 Assessing the starting design .......................................................... 99 Defining and validating the error function ...................................... 99 Description of the GENII error function ....................................... 100 Defining the optimization variables .............................................. 101 vi Optimization .................................................................................. 101 Engineering aspects: edge thicknesses .......................................... 102 Slider-wheels with concurrent optimization on MTF ....................... 103 Adjusting lens thicknesses ............................................................ 103 Engineering aspects: ambiguity avoidance ................................... 104 Engineering aspects: testplate fitting ............................................. 105 Rounding air spaces ...................................................................... 106 Adjusting clear apertures ............................................................... 106 Chapter 10 - Tolerances and drawings 108 50 mm f/5.6 objective: specification ............................................. 108 Defining the tolerance error function:”opcb_dmtf” .......................... 108 Defining the compensator ............................................................. 110 Optimizing on the compensator ........................................................ 110 Calculating decenter tolerances ......................................................... 111 Checking tolerance entries ............................................................ 111 Symmetrical tolerances surface calculation ...................................... 111 Updating symmetrical surface tolerances ...................................... 113 Asymmetric tolerances surface calculation ....................................... 113 Updating asymmetric surface tolerances ....................................... 114 Updating asymmetric component tolerances................................. 114 Asymmetric tolerances calculation................................................ 114 Tolerance data listing .................................................................... 115 ISO 10110 component drawing......................................................... 116 Setting element drawing defaults .................................................. 116 Setting element material properties ............................................... 116 Setting element surface properties ................................................ 117 Element drawing ........................................................................... 118 Appendix 1 - Index of lens data commands Appendix 2 - Graphics reference 119 122 Alphabetical index............................................................................. 122 Tabular graphics command reference ............................................... 124 Tabular graphics index ...................................................................... 126 Graphics reference examples............................................................. 128 Preface Since its inception at the Institute of Optics at the University of Rochester, the software written by Doug Sinclair has played a key role in the teaching as well as in the performance of optical design. So OSLO, perhaps more than any other optical design software, shows signs of its origins in a teaching establishment. The flexibility of the user interface, the open source nature of much of the code, the CCL programming language which is very similar to C, and real capability of OSLO-EDU, the free version of OSLO, to carry out real design tasks, make it the ideal choice for the teaching environment. This manual has been written to supplement the current documentation for commercial users of OSLO software. Its second aim is to provide a gentle introduction to the experience of optical design for those who have only just downloaded OSLO-EDU from the internet. The first chapter is written expressly for them. More experienced designers may wish to skip straight to the second chapter. 1 Chapter 1 - Your first OSLO session Introduction This chapter gives a click-by-click description of how OSLO can be used to carry out a very simple task involving synthesis, analysis, and optimization of a spherical concave mirror. It is in general applicable to all editions of OSLO, including OSLO EDU. This means that more advanced facilities, which may only be available in OSLO Standard and Premium editions, are not included. The exercise will demonstrate the two main modes of calculation: • the geometrical approximation, in which light is treated as a ray, or the path of a photon • the physical mode of calculation, in which the light is treated as propagating as a wave front, and the results take account of the effects of diffraction. Symbols used in this chapter A left-click on the mouse is indicated by a white arrow, and a right-click by the box with the word “Right”. If a drop-down menu is selected by a left-click, then it is represented by a black circle and arrow. Step by step instructions are marked with bullet points. Instructions about what to do if things go badly wrong are in italics and labeled HELP! . Right Anything typed from the keyboard (whether as a command or as an entry in a dialog box) is shown in this typeface. Labels and headers in spreadsheets and dialog boxes are given in this typeface. Buttons to be clicked are shown in _gray_. Check-boxes (called “radio buttons” in the documentation) are shown like this: Messages which appear whenever the cursor hovers above an icon are shown in a shaded box. These are known as tooltips. Tooltips Questions and answers, representing a typical dialog between a lens designer and the customer, are given in bold type. 2 Chapter 1 - Your first OSLO session 3 Running OSLO • EITHER click on the shortcut icon on the desktop in the Windows desktop, OR click on Start ►All Programs ► OSLO►OSLO [EDU etc] Edition... OR locate the .exe file in C:\Program Files\OSLO (e.g. osloedu.exe) - in some installations the directory name is Lambda Research\OSLO). • The program opens with an introductory dialog box. Click anywhere in the box to close it. • If a message about re-building the CCL database appears, click on _OK_ • The “Tip of the Day” is a useful tutorial for new users. Click on _Close_. Alternatively it can be suppressed permanently by removing the tick from the box in the bottom left corner. • • The Get_startup_option window opens. Choose the default option: Start a new lens and click on _OK_ • The OSLO main window should now appear, similar in appearance to that shown here. We will now discuss the individual components of this window in detail. The user interface A number of terms are defined here, and given in bold print. At the top of the main window in the blue border is the title bar, which gives the lens identifier, the file name under which the current lens was last saved, and the edition of OSLO currently running. Beneath this lies a row of menu headers, File, Lens, Evaluate, etc, each of which its own drop-down menu has. Many of the program commands can be accessed through these menus. The last of the menu headers is Help which gives access to the on-line documentation. In Windows, this can also be accessed via the F1 key on the keyboard. Below that is a row of icons forming the main window toolbar, Setup Window/Toolbar which give one-click access to the most frequently used control functions. The first of these is the Setup Window/Toolbar icon which gives access to a list of further groups of icons which can be added to the toolbar. Other icons are to Open surface data spreadsheet, Open a new lens, Open an existing lens, Save the current lens, Open the standard text editor, etc. Each icon has a description of its function which pops up as a tooltip when the cursor is placed over the icon. At the bottom of the main window, there is a status bar which can be expanded and customized by the user. This will be described in chapter 2. Running OSLO 4 Your first OSLO session Chapter 1 MAIN WINDOW Title bar Menu headers Toolbar Command line Toolbar Surface data spreadsheet Graphics window Toolbar Text window Status bar The window which opens in the top left hand corner is called the surface data spreadsheet. This is the area where all the properties of the lens and its working conditions are defined. Entering data into this spreadsheet is described in chapter 4. Other spreadsheets are available, but only one spreadsheet can be open at a time. Open surface data spreadsheet HELP! If the surface data spreadsheet does not open, click on the blue lens icon on the left of the toolbar in the main window. Alternatively, select from the Lens menu header the option Surface Data Spreadsheet.... Immediately above the surface data spreadsheet is the command line where OSLO commands are typed. They are executed either by pressing Enter or by clicking on the green tick: Accept pending entry/Close spreadsheet Online documentation for any command may be accessed by typing the command in the command line, and then pressing the yellow question mark beside it. Help for the command/spreadsheet If no command is entered the documentation for any currently open spreadsheet is given. Below the command line there is a message area, and on the right hand end there is the history button. The command line is described in detail in chapter 3. The user interface Chapter 1 - Your first OSLO session 5 There should also be a text window visible. This is where printed output is directed. Along the top of this there lays a toolbar consisting of a row of text labels, which are OSLO commands, executed by clicking. Numerical analysis is described in chapter 6. HELP! If the text window toolbar does not look like the one in the diagram, click on the Setup Window/Toolbar icon in the top left-hand corner of the text window, and select Standard Tools from the menu. Any or all of the toolbar groups may be selected for a text window. Either one or two, but not more, text windows can be shown at a time. Setup Window/Toolbar The user may create additional toolbar entries using the CCL programming language. Detailed instructions of how to do this are given in chapter on programming, chapter 8. Also on the main screen there is at least one graphics window. This has a toolbar consisting of a row of icons. All graphical output is displayed in one of the graphics windows. Graphical analysis is discussed in chapter 5. There is an index of OSLO graphics facilities in Appendix 2 at the end of this book. HELP! If the graphics window toolbar does not look like the Setup Window/Toolbar one in the diagram, click on the Setup Window/Toolbar icon on the left-hand side of the graphics window toolbar, and select Standard Tools from the menu. Only one of the graphics window icon groups may be displayed at a time, but different graphics windows may have different groups. Up to 30 graphics windows may be created and displayed by the user at any one time. Two more may be generated automatically. The user may generate icons in any of the graphics toolbars. This is described in chapter 8. HELP! If you have trouble finding the text window or the graphics window, then from the Window menu header select Tile Windows. Alternatively you can type the command tile into the command line and then either click on the green tick or press (Enter) on the keyboard. The user interface 6 Your first OSLO session Chapter 1 Spherical mirror example The remainder of this chapter will consist of instructions on how to specify a concave spherical mirror of radius 16 mm, and then to assess its on-axis performance at apertures of f/4 and f/2.3. Finally its performance at 18° off axis will be assessed, and the stop position and image radius of curvature optimized to give the best performance over the field of view. For clarity, each section will be prefaced by a question from a “customer,” given in bold type. 2 mm R = 16 8 mm Question: Does a spherical mirror working at f/4 give a “diffraction limited” image at its focus when used with a 2 mm diameter parallel axial beam of green light? Defining the lens system data The working conditions of the lens (such as units, paraxial setup data, wavelengths and field points) are defined by entries in the surface data spreadsheet above the double line. Accept pending entry/Close spreadsheet 6 2 3 1 1 5 1 4 1 On the surface data spreadsheet: 1. Left-click with the mouse on _Draw Off_ to open the Autodraw window The label on the button changes to _Draw On_ while the Autodraw window is active. 2. Add the lens identifier (up to 32 characters): Lens: Spherical Click once on the green tick. mirror HELP! If you were to choose a different name for the lens identifier, and the first word of the name happened to be a valid OSLO command words (such as spe), the name would be Spherical mirror example Chapter 1 - Your first OSLO session rejected and the relevant command executed instead. To avoid this, the title might be enclosed in quotation marks: e.g. “spe”. 7 The default value of Ent beam radius is 1.0 mm, the default primary wavelength is 0.58756 µm (the green helium d-line), and the default units are mm, so for this exercise these do not need to be changed. Also at this stage it is only necessary to assess the mirror on axis, so the field angle does not need to be changed from the default value of 1 milliradian. Defining the lens surface data Turning now to the data below the double line, the first line (labeled OBJ) refers to the object space, numbered 0. A parallel beam is the default condition for a new lens. So the THICKNESS - that is the object distance - is infinity (in OSLO, that means 1020, written 1.0000e+20 lens units). Nothing has to be changed on this line since in the object space a medium (GLASS) of AIR is also the default. The object radius (1.0000e+14) is calculated from the field angle by the program, and is not specified by the user. On the second line for surface 1 (AST): 3. Because the aperture is “f/4” the focal length must be 4 times the beam diameter of 2 mm, and the focal length is half the radius of curvature. Change the RADIUS to a value of-16 (mm). Since this is measured from the surface to its center, a negative radius implies a surface concave to the incoming beam. 4. Click on the gray button next to AIR under GLASS and select Reflect (hatch) (or Reflect - the only difference being the appearance of the drawing). 5. Change the THICKNESS from 0.000000 to: -8 (mm). This is the separation from surface 1 to surface 2. It is negative because after reflection the light travels in the opposite direction to the local z-axis. 6. Once again, click on the green tick ( ) to confirm the changes. Note that for surface 1, the APERTURE RADIUS (1.000000) has AS in the gray box next to it. A means that this surface is the aperture stop. S means that the size of the surface is governed by a “paraxial solve,” which means that it will be adjusted to accommodate (approximately) both axial and off-axis beams without truncation. On the third line, which corresponds to the image (IMS) a RADIUS of 0.0 means that the image is plane. Once again its size is the default - it is adjusted using a “paraxial solve.” The box for the next space (THICKNESS) will used for a defocus value, but is zero at present. The box showing the medium after the image (GLASS) is of course blank. There is no need to close the surface data spreadsheet before starting the next section. Spherical mirror example 8 Your first OSLO session Chapter 1 Drawing the lens in the Autodraw window In the main window: • Click on the Lens menu header to open the menu list shown. • Select the last item, Lens Drawing Conditions ... The Lens Drawing Conditions spreadsheet will appear. This is the spreadsheet where the overall appearance of lens system drawings is determined. In the Lens Drawing Conditions spreadsheet: • After Image space rays: select Draw rays to image surface. • The table at the bottom determines what rays will be displayed. In the column headed Rays type on the first line 11 for the number of rays to be drawn for the first (on axis) field point - for which Frac Y Obj = 0.00000. These rays will be drawn with a green pen. • Leave everything else unchanged, and close with the green tick The Autodraw window should now have the appearance shown in the diagram, provided the surface data spreadsheet is open. HELP! The Autodraw window may be hidden behind one of the others. If this happens to be the case, from the Window menu header select Tile Windows Spherical mirror example . Chapter 1 - Your first OSLO session 9 Plotting the on axis spot diagram A spot diagram is a map of the pattern of rays incident on the image from a single object point, using the “geometrical approximation” which ignores the wave nature of light. • From the Evaluate menu header select: Spot Diagram ►Single spot diagram... • In the Print or plot spot diagram spreadsheet, click on three radio buttons as shown: Plot spot diagram. Plot ray intersection points as: Symbols Show Airy disc in plot: Yes • • Leave the other entries as defaults; the axial (FBY = 0, FBX = 0) is the default so there is no need to use the Set Object Point button. Click on _OK_ The colored symbols in this diagram represent the distribution in the image plane of rays which evenly fill the pupil from a single point on axis. The three colors represent the three default wavelengths. The black circle represents the first minimum of the Airy disc, which is the intensity in the image of a perfect lens of the same aperture, in monochromatic light of the default central wavelength of 0.58756 μm. The most important aspect of the diagram is that all the rays fall within this circle. This is one of the criteria by which the assertion can be made: Answer: Yes, the image quality at the focal point is “diffraction limited” - i.e. limited by the wave nature of light and not by aberrations. HELP! Once again, if you have trouble finding the graphics window, from the Window menu header select Tile Windows or type the command tile into the command line. • Close the surface data spreadsheet by clicking on the green tick . Spherical mirror example 10 Your first OSLO session Chapter 1 Listing the lens surface data • Click on the Len header in the text window to list radii, thicknesses, apertures, glass types and surface notes: *LENS DATA Spherical mirror SRF RADIUS OBJ -AST -16.000000 IMS -- • THICKNESS 1.0000e+20 -8.000000 -- 1.000000 AS GLASS AIR SPE NOTE REFL_HATCH 8.0000e-06 S Click on Rin to list the indices and thermal expansion coefficients: *REFRACTIVE INDICES SRF GLASS/CATALOG 0 AIR 1 REFL_HATCH 2 IMAGE SURFACE • APERTURE RADIUS 1.0000e+14 RN1 1.000000 1.000000 RN2 1.000000 1.000000 RN3 1.000000 1.000000 VNBR --- TCE --- Click on Ape to list apertures and any special apertures. *APERTURES SRF TYPE APERTURE RADIUS 0 SPC 1.0000e+14 1 CMP 1.000000 2 CMP 8.0000e-06 • Click on Wav to give the wavelengths and the spectral weighting factors on each. *WAVELENGTHS CURRENT WV1/WW1 1 0.587560 1.000000 • WV2/WW2 0.486130 1.000000 WV3/WW3 0.656270 1.000000 Click on Pxc to list the focal length and some of the operating conditions. *PARAXIAL CONSTANTS Effective focal length: -8.000000 Numerical aperture: 0.125000 Working F-number: 4.000000 Lagrange invariant: -1.0000e-06 Lateral magnification: Gaussian image height: Petzval radius: -8.0000e-20 8.0000e-06 -8.000000 HELP! There are occasions when the text output gets turned off inadvertently. This is most likely to occur if a CCL command is interrupted before it has had time to complete its task. If nothing appears in the text window when text output is expected, look at the first panel on the status bar at the bottom of the main window. If it reads Text output: Off, right click within the text window, and select the last menu entry: Set Text Output On. Right Spherical mirror example Chapter 1 - Your first OSLO session 11 Saving the lens To create a new folder and save the lens in it: • From the File menu header select Save Lens as ... • Of the two buttons labeled Library Directories at the bottom of the Save Lens As window, click on _Private_ • At the top of the window, click on the icon: Create new folder • Type the name for the new folder: User_Guide and click on _Open_ • Under File name type: spherical_mirror • • • Click on _Save_ to save the lens with the file name spherical_mirror.len Note that OSLO is case insensitive, so this file cannot coexist with another file called, for example, SPHERICAL_MIRROR.len Close the surface data spreadsheet with the green tick The lens will be stored in the private lens directory e.g. C:\Program Files\OSLO\EDU64\private\len in the newly created \User_Guide subdirectory. The file is in ASCII format and contains the following text: // OSLO 6.4 39660 0 16046 LEN NEW "Spherical mirror" -8 2 EBR 1.0 ANG 0.0000572957795 DES "OSLO" UNI 1.0 // SRF 0 AIR TH 1.0e+20 AP 9.9999999995e+13 NXT // SRF 1 RFH RD -16.0 TH -8.0 NXT // SRF 2 AIR WV 0.58756 0.48613 0.65627 WW 1.0 1.0 1.0 END 2 DLRS 3 DLNR 0 11 An explanation of these commands will be found in Appendix 1. Spherical mirror example 12 Your first OSLO session Chapter 1 Changing the aperture Question: If the aperture of the spherical mirror is increased to 3.44 mm is it still “diffraction limited” at the new aperture? • In the surface data spreadsheet increase the entrance beam radius from 1 mm to 1.72 mm. • Confirm with the green tick . Right Now recalculate the spot diagram: • Right-click anywhere inside the graphics window containing the spot diagram plotted previously. • Select Update window using current data: to create the diagram shown at right. Because the aperture has increased, the spot diagram is bigger (because of greater aberrations) and the Airy disc is smaller (it is inversely proportional to the aperture). Most of the rays therefore now lie outside the Airy disc circle. Answer: No, it is far from diffraction limited. Spherical mirror example Chapter 1 - Your first OSLO session 13 Drawing the lens in the graphics window, with “zooming” To draw the lens system in a graphics window: • From the Lens menu header select Lens Drawing ... • ► System Accepting all the defaults click on _OK_ Alternatively, • Click on the first icon in the graphics window standard toolbar for Draw system (2D plan view). • Select Plan View ... To view the paths of rays near the focus at a higher magnification: • On the graphics window, leftclick-and-drag around the focus as shown below. • Left click twice within the graphics window to return to the full frame image. Note that the zooming action will work on all graphics windows except the Autodraw window. Clearly a better focal plane can be chosen, a short distance to the right of the current one. Spherical mirror example 14 Your first OSLO session Chapter 1 Finding the best focal plane Question: At this new aperture, where should the focal plane be chosen to give the best image quality for green light on axis? This can be found most quickly using the “autofocus” facility in the surface data spreadsheet, one of a number of built-in optimization functions. • • Open the surface data spreadsheet. Click on the gray button next to the thickness for the image surface (surface IMS). • Select Autofocus - minimize RMS OPD ... ► On-axis (monochromatic) In this context, RMS OPD refers to the root mean square “optical path difference” (or wave aberration). This autofocus action has the effect of finding the focal plane which minimizes the RMS OPD and entering the necessary displacement as the thickness for the image space. The thickness for the space preceding the image space is left unchanged. Listing the lens data - click on the Len header in the text window - gives the extent of defocus needed: *LENS DATA Spherical mirror f/2.33 SRF RADIUS THICKNESS OBJ -1.0000e+20 APERTURE RADIUS 1.0000e+14 AST -16.000000 -8.000000 1.720000 AS IMS -- 0.023809 0.005127 S The value listed for the defocus, shown as the thickness at the image plane, is 0.023809 mm. To get the actual distance from the mirror to the image it is necessary to add the defocus value to the nominal distance of -8 mm. This is the only case in OSLO where an entry in the thickness column of the surface data spreadsheet for a surface affects the axial position of that surface rather than the surface which follows. Answer: GLASS AIR SPE NOTE REFL_HATCH 0.023809 mm Nominal focus Best focus The best focus at an aperture of f/2.33 is at 7.976 mm from the mirror. Spherical mirror example Chapter 1 - Your first OSLO session 15 Plotting the on axis point spread function (PSF) Question: Is the image “diffraction limited” at the new focal plane? The evaluations carried out hitherto only show approximations to the actual distribution of light in the image of a point source, since a spot diagram takes no account of diffraction. To plot the true distribution of light in the image of a monochromatic point source, that is to say, the point spread function: • From the Evaluate menu header select: Spread Function ►Plot PSF Map/Contour... In the Sprd window which opens: • Click on the radio button Gray scale map • Click on the radio button Monochromatic • Type in 0.01 for the Size of patch on image surface. Click on the radio button: Normalize to peak of PSF • • Click on the radio button: Direct integration • Type in 128 for Number of lines/points in drawing and click on _OK_ Note that the first bright ring around the central maximum can just be seen. Note also the figure at the top of the scale on the right: 0.8123. This figure is called the “Strehl ratio,” which is the intensity at the central peak of the image of a point source, normalized to that of the Airy diffraction pattern of an ideal lens. The Maréchal criterion states that if the Strehl ratio exceeds 0.8, a lens system may be described as “diffraction limited”. Answer: Yes, the image is diffraction limited on axis at the new focal plane. Spherical mirror example 16 Your first OSLO session Chapter 1 Edit Lens Drawing Conditions Extending the rays in the lens drawing • Open the Lens Drawing Conditions spreadsheet by clicking on the icon in the main window toolbar. • After Initial distance enter 16. • Close the spreadsheet with the green tick . Calculating the off axis optical path difference (OPD) Question: What is the maximum OPD at full field for a semi-field angle of 18° (total field angle 36°)? • Open the surface data spreadsheet. • • • • Enter 18.0 degrees as the (semi-field) Field angle Left click on the gray SRF button for surface 1 (AST) to highlight the whole row. Right click to bring up the menu of options. Select Insert before to insert a new surface as surface 1. Right Spherical mirror example Chapter 1 - Your first OSLO session • • 17 Under APERTURE RADIUS for the new surface 1, click on the gray button. Select Aperture stop (A) The aperture stop indication (AST) on the gray button under SRF will now move to surface 1, which at the moment is in contact with surface 2. Note that the aberrations of the rays in the off-axis beam (drawn in blue) are so large that they can easily be seen in the lens drawing. To calculate the optical path difference, or wave aberration, over the whole pupil for three field points (on axis, 0.7 field and full field): • From the Evaluate menu header select: Wavefront ►Report graphic... and in the dialog box which opens: • • • Enter 128 as the Number of lines Select Reference ray intersection Click on _OK_ Note the peak-to-valley figure of 37.05 wavelengths under the map for the full field wave aberration. Answer: The axial performance is better than the standard criterion of a quarter of a wavelength for the diffraction limit, but at full field off axis the maximum OPD is 37 wavelengths. Spherical mirror example 18 Your first OSLO session Chapter 1 Optimizing The aperture stop is the limiting aperture of the axial beam. Its longitudinal position determines the beam which is selected to form the off-axis image, and if the field is large, this can have a significant effect on image quality. Also the image has been assessed only over a plane surface - this is of course the usual convention. For this exercise, however, we will investigate the benefits of allowing the image to become curved. Question: Where should the stop be placed, and what curvature of the image is needed, to obtain the best performance over the whole field? Open the slider wheel spreadsheet The answer to this question will demonstrate slider wheel optimization, one of the most useful features of OSLO. • Close the surface data spreadsheet. • Open the Slider-wheel Setup spreadsheet, by clicking on the icon on the main window header. The entries above the line define the contents of the window(s) which will be displayed during slider-wheel optimization. • Select OPD (optical path difference, another name for wavefront aberration) • Select All points Entries below the line determine which parameters will be adjusted with slider-wheels: • Leave the default of 2 for the Number of sliders (up to 32 can be defined at any one time). • On the first line, enter 1 under Surf and type th in the box under Item. Alternatively click on the box and select Thickness (TH) from the menu of options. • On the second line, enter 3 under Surf and type cv under Item. • Click on the green tick to close the Sliderwheel Setup spreadsheet. The two graphics window which open, GW31 and GW32, Spherical mirror example Chapter 1 - Your first OSLO session 19 are specific to slider-wheel optimization. The scrollbar at the right of each slider wheel track can be used to adjust the step increment of the slider-wheel motion. Changing the step size also has the effect of centralizing the slider-wheel in the track. • Watching the lens drawing in GW 32, and the plots of the optical path difference in GW 31, move the upper slider to the extreme right (th 1 = 10) and the lower slider to the extreme left (cv 3 = -0.1). • Once again, open the Slider-wheel Setup spreadsheet, by clicking on the icon. However this time just close it again immediately. This has the effect of centralizing the two slider-wheels and re-drawing both windows with different scales. Although the OPD graphs give no indication of scale, it can be seen that the performance is much improved. • Repeat the sequence once more until the best result is given. This should be when TH 1 = 16.0 mm and CV 3 = -0.125 mm-1 Answer: The aperture stop must be at the centre of curvature of the mirror, and the image surface must be a sphere with its centre at the aperture stop. Spherical mirror example 20 Your first OSLO session Chapter 1 Assessing the final design To evaluate the optical path difference of the new system, once again: • From the Evaluate menu header select: Wavefront ►Report graphic... and in the dialog box which opens: • • Enter 128 as the Number of lines Select Reference ray intersection Click on _OK_ • The peak-to-valley wave aberration at the edge of the field is less than a quarter wavelength, so the lens is diffraction limited over the whole (curved) field. Listing the data To list the correct prescription of the final design, the image separation needs to be adjusted. In the command line: • SRF TH Enter the command: th 2 -7.976 (note the spaces after th and after 2) 2: -7.976000 • Enter the command: th 3 0;rtg to give the final listing (again note the spaces): SRF 3: TH -*LENS DATA Spherical mirror SRF RADIUS THICKNESS OBJ -- 1.0000e+20 1 -- -- AST -16.000000 IMS -8.000000 • -7.976000 -- APERTURE RADIUS 3.2492e+19 1.720000 S 1.720000 AS SPE AIR AIR Save the current lens REFL_HATCH 2.596719 S Click on the save lens icon in the main toolbar to save the lens. Exiting the program • From the File menu header select Exit. If any more changes have been made a message label will give a warning to save the lens, otherwise those changes will be lost. • GLASS Click on _No_ and the program terminates. Spherical mirror example Chapter 1 - Your first OSLO session 21 Conclusion This introduction shows that OSLO commands can be accessed from the menu headers, from the text window headers, from icons or entered directly into the command line. Commands can also be combined into programs in the languages SCL or CCL, as will be shown in chapter 8. Command names are important for accessing the documentation in the on-line help. Here are some of the commands that have been used (either explicitly or via the menus and icons) in this chapter: file_new Opens a new lens file uoc drl Updates lens drawing conditions pls Plots spot diagram len Lists lens data save Saves lens drl Draws lens auf Autofocus sprd Plots the point spread function lse Opens the surface data spreadsheet rpt_wvf Plots wavefront map at 3 field points swe Opens the slider-wheel spreadsheet th Changes a thickness rtg Lists radii/thicknesses/glass types exit Terminates OSLO. To obtain a full list of commands: • From the Help menu header select OSLO Help F1 • Select the Contents tab and click on Command Reference. The commands are listed in the alphabetic sub-directories shown here. Conclusion Chapter 2 - Configuring OSLO Introduction Some ways in which the user interface can be adapted will be demonstrated in this section,. It is recommended that these are implemented before proceeding with the remainder of the exercises in this user guide. Toolbar menus This section shows how the toolbars in the main window, the text window, and the graphics window may be populated with icons/tools. Main window On first use of the program, bring up the full range of icons into the main window toolbar: • On the left of the main window toolbar, click on the blue and red window Setup Window/Toolbar icon. • In the drop-down menu which appears click on Optimization Tools. • Repeat for all the other items in the menu (not all the toolbars listed will be available in Light or EDU versions) • Click on Set Toolbars/Row... and, if it is not already 3, enter 3. Text window Click on the blue and red window Setup Window/Toolbar icon on the left of the text window header. • In the drop-down menu which appears click on Lens Data Tools. • Repeat for all the other items in the menu. • Click on Set Toolbars/Row... and enter 3 for Maximum number of toolbars on first row. • Click on Switch text windows to open a second text window, if desired. It will have the same toolbar choices as the first. Only two text windows may be opened at a time. 22 Chapter 2 - Configuring OSLO 23 Graphics window Each graphics window supports only a single toolbar, but up to 31 additional graphics windows may be opened, each with its own choice of toolbar. • • From the Window menu header select: Graphics►New In the header of the graphics window which opens, click on the Setup Window/Toolbar icon. • Select one of the toolbar options. • Repeat twice more to open a total of four graphics windows. The current one always has a dark blue bar at the top and an asterisk after the title; the header bars of the others are light blue. The status bar The status bar extends across the bottom of the main window for its full width. The following is a suggestion - there are many other possibilities. • Click twice on the status bar, or from the Window menu header select Status Bar... • Leave the parameters for the first three fields unchanged. • Set the parameters for fields 4 to 8 as follows: 4. Focal length 5. Working F-number 6. Lateral magnification 7. Angular magnification 8. Gaussian image height For each field, click on the tab on the right hand side of the field, and then select the option from the dropdown menu. This facility is especially useful for keeping an eye on paraxial quantities during optimization. • Click on OK to close the window. It is not advisable to set more than eight entries as the status bar is limited to 127 characters. The status bar 24 Configuring OSLO Chapter 2 Preferences Preferences are parameters which control many of the functions of the program operation, regardless of what lens is currently open. Status bar settings and preferences, once set, are preserved after exiting the program. They are stored in a text file called oslo.ini in the directory /private. This may be read with a text editor, but it must not be altered. Preferences may be displayed using the show_preference command - e.g. shp dsgn or incorporated into print statements - e.g. printf("Current lens directory is %s\n",str_pref(cdir)). • Before starting to define preferences, ensure that the surface data spreadsheet is closed. Designer name (dsgn) Several of the graphics windows include a space where the designer’s name is listed. The default for new lenses is OSLO. To change it: • From the File menu header select Preferences►Set Preference... • From the gray list, select Designer • On the prompt Enter string preference type [your_name] (with a maximum of 10 characters, no spaces) into the command line • Click on the green tick. Alternatively, just type stp dsgn “[your_name]” in the command line and click on Note that this will not affect the current lens in storage, but only new the green tick lenses created after the change. ISO10110 drawing settings (adr1, adr2, adr3, edcm) On ISO 10110 drawings there is a space for three lines of standard information, which normally consists of your company’s name and address: • • • • • • From the File menu header select Preferences►Set Preference... Select Address1 Type [your_company_name] (maximum of 36 characters) in the command line under Enter string preference: Alternatively, in the command line type: stp adr1 “your_company_name”. Close with the green tick Similarly for Address2 and Address3 e.g. stp adr2 “your_street_address” stp adr3 “your_town” Commas may be specified instead of decimal points on ISO 10110 drawings: • • • From the File menu header select Preferences►Set Preference... Select Element_drawing_commas Select On under Select Boolean preference: Preferences Chapter 2 - Configuring OSLO 25 Graphics (gems, gacl, gfwb, glab, grax, gfbw, drra, pens) Many of the preferences control the appearance of graphics output. For example, when cutting and pasting graphics into Windows, the scale is generally too big for convenience. A better scale is given if the gems preference is set to On: • • • From the File menu header select Preferences►Set Preference... Select Graphics_emf_sizing Select On under Select boolean preference: Several other graphics preferences are collected together for easy access: • From the File menu header select Preferences ► Preference groups... ►Graphics • Modify the entries in the popup box shown in the illustration as required. • Click on OK. Graphics alternate mode (gfam) If the aspect ratio of exported graphics is reversed (landscape <> portrait) then look to see if gfam on (Graphics_alternate_mode On) has inadvertently been set. If so: • Enter the command: stp gfam off • Close with the green tick No error boxes (noeb) Whenever an error message box appears, it needs to be cleared immediately by clicking on OK. This can be a problem on occasions, such as during slider-wheel optimization. It is possible for the user to suppress these error boxes permanently. If desired: • • • From the File menu header select Preferences►Set Preference... Select No_error_boxes Under Select boolean preference: select On Tangent check (tanc on) • Enter the command tanc on in the command line. This will turn on the facility which permits rays to be drawn to highly aspheric surfaces, such as the one illustrated here. • Close with the green tick Tangent check (tanc on) 26 Configuring OSLO Chapter 2 Compile CCL To avoid potential problems, it is a good idea to compile all CCL files before starting to use the program for serious work. To do this: • • • • From the Tools menu header select Compile CCL ... In response to Select compile access: choose Public. • • Close with the green tick In response to Select compile option: choose All. In response to Enter ccl opts: leave the default entry unchanged - e.g.: -D _OSLO_EDU_ -D _OSLO_LIGHT_ -D OPENGL_GRAPHICS Check that the public CCL directory has compiled without error. • Repeat for the Private directory, or (not for users of OSLO EDU version) click on the icon to “Compile all private CCL”. • Once again confirm that the No errors detected message has appeared in the current text window. If an error message is given, then it will be necessary to correct, suppress or delete the file whose name is shown. For example, the error message: indicates the error occurs on line 9 of the file eval_ctn_Version2.ccl in the private/ccl directory. Further details are given in chapter 8. Compile CCL Chapter 3 - The command line Arithmetic calculations Simple arithmetic expressions can be evaluated with the result given in the message bar. • If the surface data spreadsheet is open, close it by clicking on the green tick • Type cos(30*dr) and close with Enter or the green tick • Enter atan2(sqrt(3),1)/dr . The following table gives all the arithmetical functions available in OSLO EDU: Mathematical: pow (power), exp, log, log10, sqrt, j0, j1 (Bessel functions) Trigonometry (all angles are in radians): sin, cos, tan, asin, acos, atan2 Rounding and limits: Random numbers: fabs, rint, r2int, round, min, max, floor, ceil rand (uniform), grand (Gaussian with zero mean) OSLO commands The main purpose of the command line is to execute OSLO commands. • Enter file_open and close with the green tick • If the message Save changes to current lens file? appears, click on No. 27 28 The command line Chapter 3 • In the Open lens file window which opens, under Library directories at the bottom, click on Private. • Click on trip.len • Click on Open • If the surface data spreadsheet opens, close it with the green tick . Multiple commands are stacked with semicolons. For example, if we require to calculate the “sag” of the first surface of the triplet (that is, the distance measured along the axis from the plane through the axial point to the plane through the edge of the clear aperture): • Enter rtg 1 1;sag 1 6.5 *LENS DATA DEMO TRIPLET SRF RADIUS 1 21.250000 V “sag” THICKNESS APERTURE RADIUS 2.000000 6.500000 K *SURFACE SAG AND SURFACE NORMAL SURFACE 1 Y X Z (SAG) 6.500000 -1.018527 NVL -0.305882 GLASS SPE NOTE SK16 C NVK -- NVM 0.952069 Commands can also be issued in a way that initiates a dialog for subsequent parameters: • Enter sag ? • In the command window, in reply to the prompt Enter surface number: enter 1 • In reply to the prompt Enter y: enter 6.5 • In reply to Enter x: leave the default value 0 • Close with the green tick *SURFACE SAG AND SURFACE NORMAL SURFACE 1 Y X Z (SAG) 6.500000 -1.018527 NVL -0.305882 NVK -- NVM 0.952069 Assigning values to predefined variables Values can be allocated, using the command line, to predefined variables. Predefined variables are a ... h, o ... z (real) i ... n and ii ... nn (integer). Also pre-defined are seven real arrays with indices 0 - 1999, ua[] ... za [] and three string arrays of 256 characters astr, bstr, cstr. There are also two predefined constants, dr (degrees to radians conversion factor), on (=1), off(=0) and pi. All are case-insensitive. Allocations remain until OSLO is closed and restarted. For example we can calculate the z (“sag”) value listed above: • Enter r=21.25;y=6.5;z=r-r*cos(asin(y/r)) Assigning values to predefined variables Chapter 3 - The command line • 29 Enter z. Result = 1.0185269938148 Here the value of z which appears in the message area is the “sag” of the previous example. Take care if you use c, f, o, r or v as they are also OSLO command words. pi is π, but it is also an OSLO command. So do not enter pi on its own, but rather include it in an arithmetic expression. • Enter: +pi Result = 3.1415926535898 Take care when arithmetical calculations are carried out while any spreadsheet is open. The results of calculations will, if valid, be used as the contents of the cell which is currently highlighted. Printing Results of printing appear in the current text window: • Enter: prt At height y sag is z At height 6.500000 sag is 1.018527 For more formal presentation, printed output can be formatted. This command uses the formatted print command printf to print the volume of the “cap” enclosed by surface 1. • Enter: aprintf("Volume=% .3f cu.mm.\n",pi*z**2*(r-z/3)) Volume= 68.149 cu.mm. The first argument is a format string. In it, % .3f is a format specification for the double precision numeric value; the space after the % reserves a space for a minus sign (if any), 3 gives 3 places after the decimal point and f is the conversion character for floating point format. Other characters in a format string are printed unmodified, until the final \n which outputs a new line. The history button Previous commands can be called up, for repeating a command, or correcting it. • Click on the history button at the end of the command line. • Alternatively, press ShiftF4. This is known in the documentation as a keyboard shortcut; some others are listed below. • Enter: prh to list the last 40 entries in the history buffer. Keyboard shortcuts F1 Open the online help Printing 30 Ctrl+N The command line Open a new lens Ctrl+O Open an existing lens Ctrl+S Save the lens in its current file Chapter 3 In the command line, Ctrl+X Cut selected text Ctrl+C Copy selected text Ctrl+V Paste selected text Shift+F4 Show the history buffer Ctrl+PgUp Scroll through the history (Ctrl+PgDn to scroll back) In the text editor, Ctrl+E Execute the selected text Ctrl+G Go to the indicated line number Ctrl+Z Undo the last edit Alt+F3 Find text (F3 to find again) Ctrl+R Replace text (Ctrl-T to replace again) In a spreadsheet, Shift-spacebar Insert a new line before the current line The message area The message area under the command line can be used for formatted output. For example to display a string preference: • Enter: message("Private dir: %s",str_pref(prid)) Private dir: C:\Program Files\OSLO\Prm64\private The message area is where error messages can be printed. The message command also converts error numbers to strings: • Enter: sop 9 0 0 • Click on OK in the error box. • Enter: errno Result = -3152 • Different versions of \OSLO have different error numbers. To decode an error number, enter: message errno Again, click on OK in the error box before proceeding. The message area Chapter 3 - The command line 31 Executing CCL command sequences Valid CCL command sequences which use the pre-defined variables listed above, can be executed within the command line. The total length of the command string must not exceed 255 characters. • Enter: prt lid;for(i=0;i<=ims;i++)prt cv[i] th[i] rn[i][1] with the result: DEMO TRIPLET -1.0000e+20 0.047059 2.000000 -0.006303 6.000000 -0.049383 1.000000 0.051813 6.000000 0.007080 2.000000 -0.057854 42.950000 --- 1.000000 1.620410 1.000000 1.616592 1.000000 1.620410 1.000000 1.000000 Here the count variable, i, is a pre-defined integer. The system data variables lid (the lens identifier), cv[i] (the surface curvature, that is, the reciprocal of the radius), th[i] (the separation from surface i to surface i+1) and rn[i][1] (the refractive index in the space after surface i at the first wavelength) are all examples of system data variables which can either be printed, or used in arithmetic expressions or CCL programs. A list of such variables is given in the next section. A system data variable such as th cannot, however, be changed by a simple variable assignment statement such as th[3]=2.0. An attempt to do this will give the error message: Input error Protected variable ‘th’ may not be changed Rather, it must be changed using the dedicated command which has the same name as the variable. For example: • Enter th 3 1.05;rtg A new image surface may also be defined temporarily in this way: • Enter ims 3;rtg The remaining surfaces are unaffected, but they will be lost unless the lens is restored before the lens is saved again: • Enter ims 7;rtg Other commands can be used to change the lens - e.g. the 10th system note, used as a label in the public lens database: • Enter sno10 TRIPLET;opc sno *CONDITIONS: SYSTEM NOTES 10: TRIPLET A list of lens update commands is given in Appendix 1. Executing CCL command sequences 32 The command line Chapter 3 Alphabetic list of system data variables The following is a partial list of the system data variables. To obtain a complete list of all variables exported from OSLO: • • From the Help menu header select OSLO Help F1 Under the Contents tab select Programming►Accessing Data ►CCL Global Data aac aan ad ae af afo ag agn amo ang ap apchk appksn apspec aptyp as0,as1.. asi asp ast atp avx1 avx2 avx3 avx4 avy1 avy2 avy3 avy4 ax1 ax2 ay1 ay2 bcr ben caa cab cc cca ccb cct cdx cdy cns curwav cv cvdat cvmult special aperture action special aperture angle 4 aspheric coefficient in r 6 aspheric coefficient in r 8 aspheric coefficient in r afocal flag aspheric coefficient in r10 special aperture group aberration mode field angle apertures aperture checking flag aperture pickup surface aperture spec: ebr, nao, etc. aperture type aspheric surf coefficients alternate surf intersection flag aspheric surf type aperture stop surf special aperture type special ap. x vertex 1 special ap. x vertex 2 special ap. x vertex 3 special ap. x vertex 4 special ap. y vertex 1 special ap. y vertex 2 special ap. y vertex 3 special ap. y vertex 4 special ap. ax1 special ap. ax2 special ap. ay1 special ap. ay2 use base coord. for coord tilt and bend flag component aper alpha tilt tol component aper beta tilt tol conic constant component coc alpha tilt tol component coc beta tilt tol conic constant tol component x-decenter tol component y-decenter tol cone slope current wv number (base 1) curvature curvature solve/pickup datum curvature pickup datum Alphabetic list of system data variables cvpksn cvtyp cvx dct dcx dcy dcz des df dfcsn doe dor drw dt dth dwv dxt dzt ebr errno evza fcc fcv fldspec fno frn gc gcs gdt gih glpksn gltyp gmz gnz gor goz gra grb grc grd grpcode grptype gsp gwv hor hv1 hv2 curvature pickup surf curvature type toric curvature decenter tol x decentration (local) y decentration (local) z decentration designer name diffractive surf coefficients diffractive surf pickup diffractive surf type diffraction order surf drawing option decenter-tilt order flag grin step size design wv (diffractive surf) x-decenter tol axial surf shift tol entrance beam radius message nbr for last error image evaluation coord. system Fresnel surf substrate conic Fresnel surf substrate curvature field spec: obh, ang, etc. image space working f-number Fresnel surf flag global coord. ref. surf number global coord. reference surf gradient index medium type Gaussian image height glass pickup surf glass type gradium blank thickness gradium coefficient grating order gradium offset into blank gradium coefficient gradium coefficient gradium coefficient gradium coefficient group code group type grating spacing gradium dispersion data ref. hologram diffraction order hologram obj. real/virtual hologram ref. real/virtual Chapter 3 - The command line hwv hx1 hx2 hy1 hy2 hz1 hz2 ims ims_1 irt ldp lensym lid nao nap nr1 nr2 nr3 nr4 numsap numw nz1 nz2 nz3 nz4 obh pfl pfm pre puk rco rd rdt rdx rfs rn rnt rod rotsym rtf sasd sh ska skb skc sla slb • 33 hologram construction wv hologram object x coord. hologram reference x coord. hologram object y coord. hologram reference y coord. hologram object z coord. hologram reference z coord. image surf number image surf number minus one irregularity tol pen for lens drawings lens symmetry flag lens identifier object space numerical ap. image space numerical ap. grin coefficient in r2 grin coefficient in r4 grin coefficient in z6 8 grin coefficient in z number of special apertures number of wavelengths grin coefficient in z grin coefficient in z2 3 grin coefficient in z 4 grin coefficient in z object height perfect lens focal length perfect lens magnification system pressure (atm) image space axial ray slope coord. return surf number radius of curvature radius tolerance toric radius of curvature reference surf refractive indices refractive index tol extruded surf spec rotational symmetry flag radius from test glass file source astigmatic distance radial spline height Sellmeier gradium coefficient Sellmeier gradium coefficient Sellmeier gradium coefficient Sellmeier gradium coefficient Sellmeier gradium coefficient slc spl splpts spt srftyp ss tat tbt tce tct tem th thdat thmult thpksn1 thpksn2 tht thtyp tir tla tlb tlc tlt toric tox toy toz trr_fbx trr_fby trr_fbz trr_fds trr_fpt trr_fxrf trr_fyrf ttun twl txyc uni varnbr vnt wav wv ww zr zrt Sellmeier gradium coefficient no. of radial spline surf zone number of spline points spherical form tol surf type radial spline slope tla tilt tol tlb tilt tol thermal coefft of expansion tlc tilt tol system temperature (deg C) thickness thickness solve/pickup datum thickness pickup datum thickness pickup surf thickness pickup surf thickness tol thickness type total internal reflection flag tilt about (local) -x axis (degs) tilt about (local) -y axis (degs) tilt about (local) +z axis (degs) tilt tolerance toric type offset of tilt vertex in x offset of tilt vertex in y offset of tilt vertex in z fractional x object coord fractional y object coord. fractional z object coord. field point data field point number reference surf x coord. reference surf y coord. tilt tolerance units tol fringe wavelength couple x to y tols number of mm in current units next variable number Abbe V-number tol current wavelength number wavelengths wavelength weights Zernike phase surf coefficients Zernike srf reference ray trace Also in the online Help facility, under the Contents tab select Programming ► Accessing Data ►Other Data to find the definitions of the following read-only variables: beg_selection fptnbr nbr_pens srfssopen varnbr cfg gfx_window numw ssb wav current_pen glass_name oprnbr surface_note cursnbr lensym raynbr system_note end_selection maxcfg sdsnbr txt_window Alphabetic list of system data variables Chapter 4 - Lens data entry 8 x 30 binoculars: Specification The task which will be used to demonstrate lens data input is the problem of modeling the binoculars shown in the photographs, with 8x magnification, a 30 mm diameter entrance pupil, and a field of 73 mm view of 6°. Measurements give an 103 mm overall length from the front of the objective to the back of the eyepiece of 103 mm. The distance from the 28 mm front objective to the eyepiece mounting plate is 73 mm, and the offset between the optical axis of the objective and the optical axis of the eyepiece is 28 mm. Calculations First of all we will calculate the sizes of the Porro prisms. Since the offset between the two optical axes is 28 mm, the path perpendicular to the axis of the binoculars must be 20mm in each prism. The total glass pass in each prism must therefore be 40mm, and the total glass path in the two prisms (shown here in an opened-out-view) 80 mm. The glass which is most commonly used for prisms in the better quality binoculars is Schott BaK4, which has a refractive index of 1.57. The prism path length of 80 mm will then 80 mm have an “air equivalent” path length of 80/1.57 = 51 mm. This needs to be added to the physical length (103 mm) to give a total air equivalent optical path from back to front 51 mm of 154 mm. Now, making an allowance of 19 mm for the finite thicknesses of both eyepiece and objective gives a path between the principal planes, or equivalent thin lenses, of 135 mm. So, to obtain the desired magnification of x8, the focal lengths required are 120 mm for the objective and 15 mm for the eyepiece. Choosing an eyepiece The eyepiece in most common use in prismatic binoculars is the Kellner. This consists of a plano-convex single element lens, with a cemented doublet near the eye. An eyepiece suitable for this application can be found in the book “Optical Design For Visual Systems” by Bruce H. Walker. Users of OSLO Standard and OSLO Premium: • Close the surface data spreadsheet. • • From the File menu, select Lens database, Select Public. 34 Chapter 4 - Lens data entry 35 • In the window that opens, click on LENS ID and choose Sort Up. • Using the scroll bar on the right find the lens with LENS ID “Kellner Eyepiece” As a check, the designer is shown as bhw/WA, the image surface number is 7. • Click on this line to call up the lens. The aberration curves are drawn automatically, and the listing is given in the text window when Prescription is selected. • Open the surface data spreadsheet, and click on the gray Wavelength button. • Right click to get the choice of pre-defined wavelengths, and select d, F and C respectively for the three wavelengths. • In the text window click on Wav *WAVELENGTHS CURRENT WV1/WW1 1 0.587562 1.000000 WV2/WW2 0.486133 1.000000 WV3/WW3 0.656273 1.000000 Users of OSLO Light and OSLO EDU: • From the menu header, choose File > New lens. • Leave the file name as untitled, leave Custom lens as the option, and enter 6 as the number of surfaces. • Fill in the surface data spreadsheet entries as shown. Check the Efl value to confirm that the data entries are correct. All users: Note that the eyepiece has an object at infinity and an image at a finite distance. In other words, we are tracing the rays from the eye to the intermediate image, in the reverse direction of travel of the light. Surface 1 is defined as the aperture stop. Choosing an eyepiece 36 Lens data entry Chapter 4 Scaling the eyepiece The eyepiece must now be scaled to give the required focal length of 15 mm: • In the surface data spreadsheet, click on Draw Off to open the Autodraw window (at which point Draw Off becomes Draw On). • After Lens: assign a title: Kellner Eyepiece F=15 mm • Right click on any of the surface buttons on the left, and choose Scale Lens►Scale To • Insert 15 (this lens is already specified in the default units of mm). • Click on OK. • List the lens by clicking on Len in the text window. New Focal Length ... *LENS DATA Kellner Eyepiece F=15 mm SRF RADIUS THICKNESS OBJ -5.3552e+19 APERTURE RADIUS 1.9491e+19 AST -- 2.731166 2 3 4 81.934981 7.979289 -10.656903 1.071046 4.284182 11.942157 4.284182 4.284182 4.284182 F4 C BAK2 C AIR 5 6 12.584785 -- 3.213137 4.128880 7.497319 7.497319 BAK2 C AIR IMS -- • -- 1.071046 A GLASS AIR V 5.221347 SPE AIR NOTE Ent Pupil * Save the eyepiece in the private/len/User_guide directory with the name bino_ep.len. Choosing a catalog objective Rather than design an objective from scratch, the task will be to locate a suitable lens in the lens manufacturers’ catalogs provided with the program. The focal length required is about 120 mm. While the entrance pupil diameter is 30 mm, allowance must be made for mounting, say 3 mm on the radius (larger than on an internal lens because of the need to provide a seal against moisture). • Click on the third icon on the main window toolbar, which is the symbol for a new lens. • • In the dialog box which opens, click on OK. • • Change Ent beam radius to 15 mm. In the surface data spreadsheet which opens, after Lens: assign a title (e.g. Objective) Change Field angle to 3 degrees. Scaling the eyepiece Chapter 4 - Lens data entry 37 • Left click on the gray surface button in the first column for surface 2 (IMS) to select the surface. • • Right click. • First, at the bottom of the screen, for Catalog: select NEWPORT-LEN • To find a cemented doublet, click on Cem the button for Lens types Dblts Leave default Sort By EFL. From the drop-down menu, choose the option Insert Catalog Lens... In the window which appears, make the following selections: • • Enter the Central EFL (focal length), 120 mm and +/- Range 5 mm • Enter the Central Dia, 36 mm and +/- Range 5 mm. • • • Click on the only lens listed, with focal length 125 mm, part number NPAC074. • Click on the green tick, and the window will close. Click on the gray button Group at the top of the surface data spreadsheet to show the individual surfaces. Delete the non-functional first surface: Left click on the gray Srf button to select the line, right click on the gray button to create the pull-down menu, and select Delete. The aperture stop indicator (AST) on the surface number button will move to the first surface of the doublet. • Set the image distance to the paraxial image distance by clicking on the gray button in the cell for the thickness of surface number 3 (the back focal distance). Select Solve (S) > Axial ray height, and after Enter solve value type 0. The thickness value becomes 118.249113. An S will appear on the gray button next to this, indicating the presence of a paraxial “solve.” What this means is that as long as the lens is rotationally symmetrical, and paraxial rays are valid (that is, rays which are traced using linear formulae, corresponding to light close to the optical axis), then the distance to the next surface (in this case the image surface) will be adjusted so that the height of the paraxial marginal ray at the next surface is zero - in other words, the image will always be at the paraxial focus. • In the text window, click on Slv to confirm this definition. *SOLVES 3 PY -- • Save the lens in the private/len/User_guide directory with the name bino_obj.len • In the text window, click on Len to list the lens. Choosing a catalog objective 38 Lens data entry *LENS DATA Objective SRF RADIUS OBJ -AST 2 3 87.780000 F -52.752000 F -484.254000 F IMS -- • THICKNESS 1.0000e+20 APERTURE RADIUS 5.2408e+18 9.200000 F 3.200000 F 118.249113 S 19.050000 AF 19.050000 F 19.050000 F -- Chapter 4 GLASS AIR SPE BAFN10 F * SF10 F AIR 6.552484 S Check the lens prescription against the manufacturer’s published catalog. Combining the objective and the eyepiece The first task is to combine objective and eyepiece without the prisms. • Ensure the file with the objective, bino_obj is open. • Open the surface data spreadsheet. • If necessary, click on Draw Off to open the Autodraw window. • Change the title to Objective and eyepiece • Left click on the surface button for the image surface (IMS). This will select surface 4, indicated by a bold surround. • Right click on the gray button IMS, under SRF, to bring up the options menu. • • NOTE Choose Insert Lens File ... In the Merge lens file window, find the eyepiece file bino_ep and click on Open. At this stage, of course, the eyepiece is now the wrong way round. • Select the seven surfaces of the eyepiece and the exit pupil (numbered 4 to IMS) • Right click anywhere in this group. • Select Reverse Combining the objective and the eyepiece Chapter 4 - Lens data entry 39 • Click on Gen at the top of the surface data spreadsheet, and change Evaluation mode to Afocal. This means that ray aberrations will be angular rather than transverse linear. • Change the exit pupil (surface 10) aperture radius to 15/8 • Click on surface 10 Special gray button. Select Surface Note (N) and change the note to Exit pupil. Also under the surface 10 Special button, select Surface control(F) > General Change Surface appearance in lens drawing: to Drawn, and change the Pen number to 4 (i.e. red). • Save the file with the name bino_obj_ep.len • Click on Len in the text window header. *LENS DATA Objective and eyepiece SRF RADIUS THICKNESS OBJ -1.0000e+20 APERTURE RADIUS 5.2408e+18 AST 2 3 87.780000 F -52.752000 F -484.254000 F 9.200000 F 3.200000 F 118.249113 S 4 -- 4.133458 2.616880 AIR 5 6 --12.598736 3.216699 11.955396 7.505630 7.505630 BAK2 C AIR 7 8 9 10.668717 -7.988135 -82.025813 4.288931 1.072233 2.734194 4.288931 4.288931 4.288931 BAK2 C F4 C AIR IMS • -- -- 19.050000 AF 19.050000 F 19.050000 F GLASS AIR 1.875000 SPE NOTE BAFN10 F * SF10 F AIR * Exit Pupil Open the surface data spreadsheet and find the Autodraw window. Combining the objective and the eyepiece 40 Lens data entry Chapter 4 Surface decenters and tilts Before modeling the prisms, we will look at how tilted and decentered surfaces are defined. Y X Z Y Z X TLA Y Y Z Z X X TLB TLC The gray button under Special in the surface data spreadsheet includes the option Coordinates where all this is found. The default sequence is Decenter, then tilt in which case the sequence of displacements is: 1. Decenter by DCX along X axis, by DCY along Y axis, and by DCZ along Z axis, all in system units. 2. Tilt anticlockwise about the new X axis through an angle TLA (degrees) 3. Tilt anticlockwise about the new Y axis through an angle TLB (degrees) 4. Tilt clockwise about the new Z axis through an angle TLC (degrees). The tilts are shown in the diagram above. If the Tilt, then decenter option is chosen, the order is reversed. The effect of decentering or tilting a surface is also to decenter or tilt not only the surface and its local coordinate axes, but also all the subsequent surfaces in the system. To tilt only a component or group of surfaces, on the first surface apply the tilt and select the option Use base coordinate system for coordinate returns to this surface: YES. On the last surface, select Coordinate return: YES and Return to surface: [first surface number]. To tilt a single surface, apply the tilt, then select Coordinate return: YES, Return to surface: [default value, the same surface number] and Use base coordinate system for coordinate returns to this surface: YES. Surface decenters and tilts Chapter 4 - Lens data entry 41 Adding a right angle prism The task is to model a simple 90° prism. The measurement of the external dimensions of the binoculars, allowing 3 mm for the case, suggests that the apex of the first prism (20 mm deep) will be 70 mm behind the front surface of the objective (thickness 12.4 mm), leaving an air space of 70 - 12.4 - 20 = 37.6 mm between the rear of the objective and the prism. • Open the surface data spreadsheet. • Change the lens title to Objective prism eyepiece • Change the thickness for surface 3 to 37.6. The solve flag (S) disappears. • Now add an extra surface before surface 4: Left click on the gray surface button for surface 4, and then either right click on the same button and select Insert before, or use the shortcut Shift-space. Users of OSLO EDU will not be able to add the extra surface to the straight-through binocular, since it will cause the surface count limit (10) to be exceeded. However, starting with the file consisting of the objective alone (bino_obj) the exercise of adding the first prism can proceed as described here. • Change the thickness for the new surface 4 to 10 mm. • Under the gray button in the column labeled Aperture Radius for this surface (surface 4), select Special Aperture Data (X). Leave the Ap Id: as 0. Change the shape to Rectangle, keep the Action as Transmit, leave the Group: as 0, and set the semiaperture dimensions to: Xmin = -10 Xmax = 10 Ymin = -10 Ymax = 10 Angle = 0.0 • Change the medium for surface 4 from air to glass: Click on the gray GLASS button, select Catalog > Schott > N-BAK4. (For some versions of OSLO the current Schott catalog will be in the directory be Schott 2004 rather than Schott). • Select the entire row of surface 4. Then right click, selecting Copy. Otherwise right click on the copy icon on the right of the spreadsheet, shown in the diagram. • Click on the gray surface button for surface 5. Right click and select Paste. Otherwise right click the paste icon. The new surface is added before the one highlighted. • Once more, click on the gray surface button for surface 5, right click and select Paste. • Change the Thickness for surface 5 to -10. Adding a right angle prism 42 • Lens data entry Chapter 4 Under the Aperture Radius gray button for surface 5, select Special Aperture Data and set: Ymin = -14.14 Ymax = 14.14 leaving everything else in this dialog box unchanged. • From the gray button under Glass for surface 5, select Reflect (hatch). • Under Glass for surface 6, type AIR • To change the thickness for surface 6 to an axial ray height solve, click on the gray button next to thickness for surface 6, and select Solve (S) > Axial ray height, and after Enter solve value type 0. • Under Special for surface 5, select Coordinates (C). Set TLA = -45, and Tilt and Bend: Yes. Leave everything else as default. In most cases, tilting a surface rotates the coordinate system of the airspace after that surface, and all subsequent surfaces, through the same angle. However if Tilt and Bend is specified, the rotation is through twice this angle, corresponding to the law of reflection. • In the text window, click on Ape to list the special aperture data for the three surfaces of the prism. *APERTURES SRF TYPE APERTURE RADIUS ... 4 CMP 12.022663 Special Aperture Group 0: 0 ATP Rectangle AAC AX1 -10.000000 AX2 5 CMP CMP --10.000000 AY2 10.000000 Transmit 10.000000 AAN AY1 --14.140000 AY2 14.140000 Transmit 10.000000 AAN AY1 --10.000000 AY2 10.000000 11.157981 Special Aperture Group 0: 0 ATP Rectangle AAC AX1 -10.000000 AX2 • AAN AY1 11.590322 Special Aperture Group 0: 0 ATP Rectangle AAC AX1 -10.000000 AX2 6 Transmit 10.000000 Click on Len to list the lens data. Note that the three solved aperture radius values seen on the top-level spreadsheet for surfaces 4, 5 and 6 remain unchanged by the definition of special apertures (X); these values are ignored. Adding a right angle prism Chapter 4 - Lens data entry 43 *LENS DATA Objective prism eyepiece SRF RADIUS THICKNESS OBJ -1.0000e+20 AST 2 3 87.780000 F -52.752000 F -484.254000 F 4 5 6 APERTURE RADIUS 5.2408e+18 GLASS AIR SPE 9.200000 F 3.200000 F 37.600000 19.050000 AF 19.050000 F 19.050000 F BAFN10 F * SF10 F AIR ---- 10.000000 -10.000000 -67.900739 S 12.022663 SX 11.590322 SX 11.157981 SX N-BAK4 C REFL_HATCH * AIR 7 -- 4.133458 2.616880 AIR 8 9 --12.598736 3.216699 11.955396 7.505630 7.505630 BAK2 C AIR 10 11 12 10.668717 -7.988135 -82.025813 4.288931 1.072233 2.734194 4.288931 4.288931 4.288931 BAK2 C F4 C AIR IMS • -- -- 1.875000 NOTE * Exit Pupil Click on Spe to list the surface notes, the coordinate (tilt) data and the surface tag (pen color etc.) data: *SURFACE NOTES 13 Exit pupil *TILT/DECENTER DATA 5 DT 1 BEN DCX TLA --45.000000 DCY TLB --- DCZ TLC --- *SURFACE TAG DATA 1 LMO ELE (3 surfaces) 13 DRW ON LDP 4 The eyepiece is incorrectly modeled since the signs of all curvatures and thicknesses should be inverted. For the time being, however, we will ignore this and proceed to the next stage. Converting the prism to a Porro prism The Porro prism has two reflecting surfaces at right angles to each other. • Select the entire row of surface 5. Then right click, selecting Copy. • Click on the gray surface button for surface 5. Right click and select Paste. • Using the surface data spreadsheet, change the thickness for surface 5 to -20 mm, and the thickness for surface 6 to 10 mm. • Save with the name bino_porro.len. • In the text window click on Len and Spe. Converting the prism to a Porro prism 44 Lens data entry *LENS DATA Objective prism eyepiece SRF RADIUS THICKNESS OBJ -1.0000e+20 APERTURE RADIUS 5.2408e+18 GLASS AIR 87.780000 F -52.752000 F -484.254000 F 4 5 6 7 ----- 10.000000 -20.000000 10.000000 55.152366 S 8 -- 4.133458 2.616880 AIR 9 10 --12.598736 3.216699 11.955396 7.505630 7.505630 BAK2 C AIR 11 12 13 10.668717 -7.988135 -82.025813 4.288931 1.072233 2.734194 4.288931 4.288931 4.288931 BAK2 C F4 C AIR -- -- 19.050000 AF 19.050000 F 19.050000 F SPE AST 2 3 IMS 9.200000 F 3.200000 F 37.600000 Chapter 4 12.022663 11.590322 10.725639 10.293298 SX SX SX SX NOTE BAFN10 F * SF10 F AIR N-BAK4 C REFL_HATCH * REFL_HATCH * AIR 1.875000 * Exit Pupil *SURFACE NOTES 14 Exit Pupil *TILT/DECENTER DATA 5 DT 1 BEN 6 DT 1 BEN DCX TLA DCX TLA --45.000000 --45.000000 DCY TLB DCY TLB ----- DCZ TLC DCZ TLC ----- *SURFACE TAG DATA 1 LMO ELE (3 surfaces) 14 DRW ON LDP 4 Adding a second Porro prism We will now add the second Porro prism. Note that users of OSLO EDU will have reached the 10-surface limit even without the eyepiece, and will have to delete the objective (surfaces 1 to 3) to complete this section, modifying the surface numbering accordingly. • In the surface data spreadsheet, select surfaces 4-7. • Right click, selecting Copy. • Click on surface 8 to highlight the whole surface, rightclick, and select Paste. • Under Thickness for surface 7, enter 0. This automatically deletes the thickness solve on that surface. • The aperture of surface 12 is not sufficiently large. Convert it to a solved aperture by just setting the Aperture Radius for surface 8 to 0. The solved value (6.552484) replaces it immediately. • Surface 18 is not at the true exit pupil. Click on the gray button under Thickness for surface 17, and select Solves (S) > Chief ray height... and enter 0. Adding a second Porro prism Chapter 4 - Lens data entry 45 Completing the design The model does not include the 90º rotation about the optical axis of the second prism relative to the first. • To rotate the second prism Z axis through an angle of 90°, under Special for surface 8, select Coordinates (C), and set the tilt angle about the z-axis, TLC = 90 (degrees). • Change the lens title to: Binoculars complete. • Save with the file name bino_complete.len • Enter the commands: drl;drr 0;drr 1 to draw in 2 dimensions. The full prescription is obtained by clicking on Len Spe and Ape in the text window. *LENS DATA Binoculars complete SRF RADIUS OBJ -- THICKNESS 1.0000e+20 SPE 87.780000 F -52.752000 F -484.254000 F 4 5 6 7 ----- 10.000000 -20.000000 10.000000 -- 12.022663 11.590322 10.725639 10.293298 SX SX SX SX N-BAK4 C REFL_HATCH * REFL_HATCH * AIR 8 9 10 11 ----- 10.000000 -20.000000 10.000000 29.655619 S 10.293298 9.860957 8.996274 8.563933 SX SX SX SX N-BAK4 C REFL_HATCH * REFL_HATCH * AIR 12 -- 4.133458 13 14 --12.598736 3.216699 11.955396 15 16 17 10.668717 -7.988135 -82.025813 -- 4.288931 1.072233 5.649290 S -- 19.050000 AF 19.050000 F 19.050000 F GLASS AIR AST 2 3 IMS 9.200000 F 3.200000 F 37.600000 APERTURE RADIUS 5.2408e+18 NOTE BAFN10 F * SF10 F AIR 6.552484 S AIR 7.505630 7.505630 BAK2 C AIR 4.288931 4.288931 4.288931 BAK2 C F4 C AIR 1.875000 * Exit Pupil *SURFACE NOTES 18 Exit Pupil *TILT/DECENTER DATA 5 DT 1 BEN 6 DT 1 BEN 8 DT 1 9 10 DT BEN DT BEN 1 1 DCX TLA DCX TLA DCX TLA DCX TLA DCX TLA --45.000000 --45.000000 ----45.000000 --45.000000 DCY TLB DCY TLB DCY TLB DCY TLB DCY TLB ----------- DCZ TLC DCZ TLC DCZ TLC DCZ TLC DCZ TLC -----90.000000 ----- Completing the design 46 Lens data entry Chapter 4 *SURFACE TAG DATA 1 LMO ELE (3 surfaces) 18 DRW ON LDP 4 *APERTURES SRF TYPE APERTURE RADIUS 0 SPC 5.2408e+18 1 FIX 19.050000 2 FIX 19.050000 3 FIX 19.050000 4 CMP 12.022663 Special Aperture Group 0: 0 ATP Rectangle AAC AX1 -10.000000 AX2 5 CMP CMP CMP CMP CMP CMP CMP CMP SPC SPC SPC SPC SPC SPC --14.142136 AY2 14.142136 Transmit 10.000000 AAN AY1 --14.142136 AY2 14.142136 Transmit 10.000000 AAN AY1 --10.000000 AY2 10.000000 Transmit 10.000000 AAN AY1 --10.000000 AY2 10.000000 Transmit 10.000000 AAN AY1 --14.142136 AY2 14.142136 Transmit 10.000000 AAN AY1 --14.142136 AY2 14.142136 Transmit 10.000000 AAN AY1 --10.000000 AY2 10.000000 8.563933 Special Aperture Group 0: 0 ATP Rectangle AAC AX1 -10.000000 AX2 12 13 14 15 16 17 18 AAN AY1 8.996274 Special Aperture Group 0: 0 ATP Rectangle AAC AX1 -10.000000 AX2 11 Transmit 10.000000 9.860957 Special Aperture Group 0: 0 ATP Rectangle AAC AX1 -10.000000 AX2 10 10.000000 10.293298 Special Aperture Group 0: 0 ATP Rectangle AAC AX1 -10.000000 AX2 9 AY2 10.293298 Special Aperture Group 0: 0 ATP Rectangle AAC AX1 -10.000000 AX2 8 --10.000000 10.725639 Special Aperture Group 0: 0 ATP Rectangle AAC AX1 -10.000000 AX2 7 AAN AY1 11.590322 Special Aperture Group 0: 0 ATP Rectangle AAC AX1 -10.000000 AX2 6 Transmit 10.000000 6.552484 7.505630 7.505630 4.288931 4.288931 4.288931 1.875000 Completing the design Chapter 5 - Graphical analysis Introduction In general, the graphics facilities in OSLO are of the most frequently generated using the icons in the toolbars of the individual graphic windows. Some facilities, however, can only be accessed from the menu headers, and some only by calling up CCL commands from the command line. A comprehensive catalog of the graphics facilities will be found in the Graphics Reference in the appendix at the end, together with instructions as to how each may be accessed. In this chapter only lens drawing and ray intercept coordinate reports will be discussed in detail. Opening a new graphics window This exercise shows how a new graphics window can be opened in the top left corner of the main window, just under the command window. • From the main window select the Window menu header. • Choose Graphics > Open and type the following responses into the command window: Enter graphics window number: 0 Enter window width: 320 End to window height: 300 Enter window x: 0 Enter window y: 120 Note that the new window has a dark blue title bar, containing the letters GW 2 *. GW means that it is a graphics window with no updateable content. The * symbol means that it is the current window for graphical output. The coordinate system defines x =0, y = 0 as the top left corner, and the command window covers the area x = 0 to 600, y = 0 to 100. The point x = 960 (1420 for wide screens), y = 710 is the bottom right position which can be seen without scrolling. Labeling a graphics window • From the main window select the Window menu header. • Choose Graphics > Title... and type the following response into the command window: • Enter window title: Colors. The title appears in the blue bar at the top of the window. In practice graphics windows are titled automatically by the graphics command associated with the relevant icon in the graphics window. 47 48 Graphical analysis Chapter 5 Generating a plot • Select the Tools menu header. • Choose Plotting toolkit > Colors and Pens. This executes the CCL command colors, which is stored in the file graph_tools.ccl in the public/ccl directory. It shows the pen numbering used in graphics plots. Notice that the letters in the title bar have now changed to UW, meaning that the graphics window is updateable. Saving a plot • Right click on the window and choose Save As ... • Save the file in any format. The size of the file stored will differ according to the format chosen. For comparison, the file sizes for the Colors and Pens graphic are shown: Windows bitmap BMP 164 kB Compressed bitmap RLE 29 kB HP-GL format HGL 29 kB Windows metafile WMF 118 kB Placeable Windows metafile WMF 118 kB Enhanced Windows metafile EMF 182 kB Cutting and pasting a plot • Right click on the window and choose Copy to Clipboard. • Open a Word document or PowerPoint presentation, right click, and choose Paste. • If there are problems with the size of the image pasted into the new application, look again at the Graphics Preferences in Chapter 2. Introduction Chapter 5 - Graphical analysis 49 Lens drawing Drawing a lens in 2D This exercise will demonstrate some of the 2D drawing options, using the standard triplet lens as an example. • Click on the Open Lens icon in the main window toolbar. • Open the file in the Private directory, trip.len • In the graphics window, click on the Setup Window/Toolbar icon. • Select the Lens Drawing toolbar. • Click on the Draw system (2D) icon. This gives a lens drawing including rays as the default. The corresponding icon in the Standard Tools toolbar gives the option of a 2D (plan) drawing without rays. Various options to enhance this drawing will now be shown. • Click, in the main window toolbar on the icon shown here for Edit Lens Drawing Conditions. • On the fifth line, against Image space rays: select Draw rays to image surface. The button then reads Image srf • From the menu header Select File > Preferences > Preference groups > Graphics... and choose from the menu Use labels on graphics. Select Off. • Open the surface data spreadsheet. • Click on the gray button under Special for surface 7 (IMS). • Select Surface Control (F) > General • On the second line, against Surface appearance in lens drawings: select Drawn. Set the Pen number for surface in lens drawings as 3 (blue). • Close both spreadsheets. • Once again click on the Draw system (2D) icon to draw the lens. • Click again on the icon in the main window toolbar for Edit Lens Drawing Conditions. In the ray drawing table at the foot of the spreadsheet, change the three values of the Frac. Y Obj (FBY) to 0.0, -1.0, +1.0 respectively. Also change the number of rays in the second fan (Rays) from 0 to 3, Min pupil to -0.4, and Max pupil to 0.4. Lens drawing 50 Graphical analysis Chapter 5 In this spreadsheet, for each successive ray fan (where the number of rays plotted is non-zero) the pen colors cycle through the sequence: • • 1. 2. 3. 4. 5. 6. 7. 8. Green Blue Red Light-Blue Orange Violet Yellow Black Close the Edit Lens Drawing Conditions spreadsheet. From the Lens menu header, select Show Operating Conditions .. > Lens Drawing *CONDITIONS: LENS DRAWING Initial distance: -Final distance: -Horizontal view angle: 240 Vertical view angle: 30 First surface to draw: 0 Last surface to draw: 0 X shift of drawing: -Y shift of drawing: -Drawn apertures (solid): Quadrant Image space rays: Image srf Rings in aperture (solid): 3 Spokes in aperture (solid): 4 Number of field points (rays): 3 DXF/IGES file view: Unconverted Draw aperture stop location: Off Hatch back side of reflectors: On Red value for shaded solid: 175 Green value for shaded solid: 185 Blue value for shaded solid: 250 Points for aspheric profile: 41 Autodraw Options: YZ Profile Fpt Frac Y Obj Frac X Obj Rays Min Pupil Max Pupil Offset Fan Wvn Cfg 1 --5 -1.00000 1.00000 -Y 1 0 2 -1.00000 -3 -0.40000 0.40000 -Y 1 0 3 1.00000 -3 -0.40000 0.40000 -Y 1 0 • Draw the lens in two dimensions by clicking on the icon for Draw system (2D). Lens drawing Chapter 5 - Graphical analysis 51 Drawing a lens in 3D • Open the Edit Lens Drawing Conditions spreadsheet again. • On the fifth line, for Apertures: change Quadrant to Full apertures. For Number of ray fans in lens drawings enter 6, then scroll down to enter the three new fans with Frac X Obj = 0.0, -1.0, 1.0 respectively. For the three fans, specify 5, 3 and 3 rays and for the last two fans, change Min pupil to -0.4, and Max pupil to 0.4. • • • Select the radio button for FX for the last three fans. Close the Edit Lens Drawing Conditions spreadsheet. To list these values, from the Lens menu header, select Show Operating Conditions > Lens Drawing. *CONDITIONS: LENS DRAWING Initial distance: -Final distance: -Horizontal view angle: 240 Vertical view angle: 30 First surface to draw: 0 Last surface to draw: 0 X shift of drawing: -Y shift of drawing: -Drawn apertures (solid): Full Image space rays: Image srf Rings in aperture (solid): 3 Spokes in aperture (solid): 4 Number of field points (rays): 6 DXF/IGES file view: Unconverted Draw aperture stop location: Off Hatch back side of reflectors: On Red value for shaded solid: 175 Green value for shaded solid: 185 Blue value for shaded solid: 250 Points for aspheric profile: 41 Autodraw Options: YZ Profile Fpt Frac Y Obj Frac X Obj Rays Min Pupil Max Pupil Offset Fan Wvn Cfg 1 --5 -1.00000 1.00000 -Y 1 0 2 -1.00000 -3 -0.40000 0.40000 -Y 1 0 3 1.00000 -3 -0.40000 0.40000 -Y 1 0 4 --5 -1.00000 1.00000 -X 1 0 5 --1.00000 3 -0.40000 0.40000 -X 1 0 6 -1.00000 3 -0.40000 0.40000 -X 1 0 • Click on the icon for Draw system (3D solid model). Lens drawing 52 Graphical analysis Chapter 5 Drawing a lens in 3D with sliders • Click on the icon for Draw system (3D w/slider) • Select Shaded solid. • It may be necessary to extend the slider bars to make the slider tracks visible. • Adjust the sliders according to the following table: Vertical view angle Horizontal view angle Description 30º 240º Default 30º 330º Isometric 0º 270º Y - Z (2D plan view) 90º 270º X-Z 0º 360º X - Y view from image Lens drawing Example Chapter 5 - Graphical analysis 53 If the lens is saved with a particular 3D view in force, the values of the view angles will be stored with the lens and used in subsequent 3D drawings. The horizontal and vertical view angles may also be set in the Edit Lens Drawing Conditions spreadsheet. Ray intercept curves analysis The importance of these curves for diagnosis of aberration problems cannot be overstated, so a detailed description will be given here of this analysis. The lens used for the graphs in this section is the objective of the binoculars modeled in chapter 3. Ray analysis (RIC) • In the graphics window, click on the Setup Window/Toolbar icon. • Select the Ray Analysis toolbar. • Click on the icon for RIC Plot. This gives a set of curves representing the transverse ray aberrations for the default field point, which is on axis (FBY = 0.0). The left hand graph gives the plot of transverse ray aberrations (DY) in the meridional section (the Y - Z section) at different heights (FY) in the pupil. The right hand graph gives the same information in the orthogonal plane that is, DX as a function of FX. The three curves are colored according to the wavelengths, which, in the visible at least, are representative provided the order in which the wavelengths are defined is middle-short-long corresponding to green-blue-red. If the system is defined as afocal (see under the Gen button in the surface data spreadsheet) the aberrations are angular values DYA and DXA, expressed as direction tangents. Ray intercept curves for 2D field points Users of OSLO EDU and OSLO Light should skip this section • Click on the icon for RIC vs Field Points. This gives the graphs laid out in two dimensions according to the relative field coordinates FBX, FBY. In this case, three graphs are given for the three field points defined for this lens, which are (reading from the bottom) FBY = 0.0 (on axis), FBY = 0.7 and FBY = 1.0 (edge of Ray intercept curves analysis 54 Graphical analysis Chapter 5 field). The left-hand column gives DY as a function of FY, the right-hand column plots DX against FX. Ray intercept curves report graphic • Click on the icon for RIC Report Graphic. This icon also appears on the Standard Tools toolbar. The analysis results are shown as 6 graphs within the same window, plus a 2D lens drawing. 1. The left-hand group (unlabeled) gives the same ray intercept curves for three field points as the ray intercept curves for 2D field points. This set of curves gives the relationship between the ray aberrations and their radial position in the pupil. If more than three wavelengths are specified, up to 12 sets of curves will be drawn, with different symbols as well as different colors to distinguish them. Most of the other information in the report (apart from distortion) can be deduced from these curves. A designer can use these curves as a diagnostic tool to analyze the different types of aberration. This analysis is important, since different aberrations require different measures for their correction. However these graphs do have limitations. For example, they do not indicate the aberrations of rays in the four quadrants between the two orthogonal planes. DY FX FY FBY=1 DY DX FY FX FBY=.7 DY DX FY FX FBY=0 2. The astigmatism curves give the variation of paraxial focus across the field for the meridional section (the Y-Z section, labeled T) and the sagittal section (the X-Z section, labeled S). Results are only shown for the mean wavelength. This curve can be plotted as a stand-alone, either monochromatically or in 3 colors, using the menu header: • Evaluate > Ray fans > Single field point ... • At the top, select Field sags. • Choose either Monochromatic or Polychromatic. • Click on OK. 3. The three curves for longitudinal spherical aberration give the movement of the focal point along the axis for different radii in the pupil, for the axial image point only, corresponding to the three wavelengths. Ray intercept curves analysis DX FBY DZ FY DZ Chapter 5 - Graphical analysis 55 The curves for chromatic focal shift represent the axial beam paraxial longitudinal focal variation with wavelength over the range 0.4 to 0.7 μm - or over a different range if other wavelengths are specified. Alternatively, for OSLO Standard and OSLO Premium users, this curve can be plotted as a standalone, in slightly different format, using the menu header: • Evaluate > Ray fans > Other ray analysis ... • From the menu select Chromatic focal shift... • Enter a wavelength range (or zeros for default). • Wv DZ Click on OK. 4. Longitudinal spherical aberration curves indicate the errors in focus DZ of the axial beam as a function of the pupil height DY. Curves are given for the three specified wavelengths. The graph is plotted on its own via the menu header: • Evaluate > Ray fans > Single field point ... • At the top, choose Longitudinal spherical... • Click on OK. 5. The curve for distortion shows the departure from the paraxial magnification as a function of field height. The distortion graph can be plotted alone in a different format using the menu header: • Evaluate > Ray fans > Single field point ... • At the top, choose Distortion • Choose either Monochromatic or Polychromatic. • Insert a value for the aberration scale (in %). • Click on OK. The plots obtained from OSLO EDU and OSLO Light are different from the one shown here. 6. The curve for lateral color shows the difference between the heights of the red and green rays, and between the blue and green rays, as a function of field height. The graph is not available as a standalone. FY DZ FBY FBY To control all the aberration scales, the RIC report graphic command may be called from the main menu header. • • • From the Evaluate menu header select Other ray analysis>Report Graphic..: Fill in the spreadsheet with the required values. The value of the abscissa scale is omitted as it only applies to graphs where curves are plotted against h-tan U rather than DY. Click on OK. Ray intercept curves analysis Chapter 6 - Numerical analysis Introduction This chapter deals with the text window and the spreadsheet buffer which lies under it. In order to illustrate the methods of numerical analysis, a simple task concerning the demonstration triplet lens supplied with the program will be carried out: For the triplet lens supplied with the program, calculate the transverse ray aberration of the outermost ray transmitted at the edge of the third component at the edge of the field, at the central (green) wavelength. Also estimate the transmittance at the extreme field, as a percentage of the axial transmittance. The transverse ray aberration of an off-axis ray in the meridional section is the distance from the point where this ray intersects the image plane, to the intersection point of the pupil ray. This is shown in the diagram. DY Before we can begin the task we need to locate the edge ray concerned in terms of its relative pupil height coordinate FY. Finding the edge rays • Open the lens in the private directory trip.len. Alternatively it will be found in the public directory as /public/demo/LT/demotrip.len. • In the text window, click on Ape to list the apertures. The indication CHK for surfaces 1 and 6 means that in the ray analysis which follows the rays which lie outside these checked apertures will be obstructed. (Checked clear apertures are indicated by a K in the Clear Aperture Radii column of the surface data spreadsheet). 56 Chapter 6 - Numerical analysis 57 *APERTURES SRF TYPE APERTURE RADIUS 0 SPC 3.6397e+19 1 SPC 6.500000 CHK 2 PKP 6.500000 3 SPC 5.000000 4 SPC 5.000000 5 SPC 6.500000 6 SPC 6.500000 CHK 7 CMP 18.170326 • In the graphics window, click on the Setup Window/Toolbar icon, and select the Lens Drawing menu. • Click on the icon for View Ray Fans (2D) - Interactive. • To define the point in the field as the edge of the field, set the slider-wheel for Frac Y Obj to 1.0, and leave the slider-wheel for Frac X Obj at 0.0. • Adjust the slider-wheels for Min pupil and Max pupil until the extreme rays of the bundle just pass through the first and last surfaces respectively. Note the values of the fractional pupil height for these edge rays: -0.43 and+0.61. The latter is the value of FY needed for this problem. • Instead of this procedure, users of OSLO Standard and OSLO Premium may use a quicker method for carrying out vignetting analysis: • From the Optimize menu header, select: Support routines>Vignetting > Vignetting analysis. • Check Copy vignetting data to field point set? No • Leave the Maximum pupil position to test at 5.0 • Click on OK. *VIGNETTING FACTORS FPT CFG FBY 1 0 -2 0 0.700000 3 0 1.000000 FBX ---- FY1 -1.040001 -0.637293 -0.431105 FY2 1.040001 0.810585 0.612924 FXMAX 1.040001 0.990811 0.901827 Graphical estimates • From the Evaluate menu header select: Ray fans > Single field point ... and, leaving all the default values unchanged, click on Set object point at the foot of the spreadsheet. • In the Set object point spreadsheet, set Fractional coordinates of object point to FBY = 1.00 FBX = 0.00 FBZ = 0.00. • Close both spreadsheets, and note from the graph that the value of the transverse ray aberration required is about -0.015 mm. (To confirm the units, from the Lens menu header, select: Show operating conditions > General) DY at WV 1 for ray at FY = Graphical estimates 58 Numerical analysis Chapter 6 • Click on the Plot report graphics wavefront analysis icon on the standard toolbar to get the pupil maps, and note that the area of the edge-of-field map is about 50% of the area of the on-axis map. So we can conclude that the transverse ray aberration of the edge ray is about DY = -0.015 mm; the transmission at this field point is about 50%. EDGE OF FIELD ON AXIS RELATIVE PUPIL AREAS Numerical calculation From the text window • In the text window, trace the pupil ray (the ray through the centre of the aperture stop) from the edge of the object, by clicking on Chf. • Then to trace a fan of rays in the meridional (Y) section, click on Fan. Set the Minimum coordinate to be -0.43, the Maximum coordinate to be 0.61,and Number of rays to be 2, and leave all other options as default values. • Note the value of DY (transverse ray aberration in lens units) for the edge ray transmitted: *TRACE FAN - FBY RAY FY 1 0.610000 2 -0.430000 • • 1.00, FBX FRAC RFS 0.530358 -0.353777 0.00, FBZ 0.00 DYA DXA -0.071477 -0.052849 -- DY -0.013268 0.055365 DX --- Click on Spd in the text window. Note the value of the per cent weighted ray transmission: *SPOT DIAGRAM - FBY 1.00, FBX 0.00, FBZ 0.00 - POLYCHROMATIC APDIV 17.030000 WAV WEIGHTS: WW1 WW2 WW3 1.000000 1.000000 1.000000 NUMBER OF RAYS TRACED: WV1 WV2 WV3 104 104 104 PER CENT WEIGHTED RAY TRANSMISSION: 44.827586 *SPOT SIZES GEO RMS Y 0.021401 GEO RMS X 0.007555 *WAVEFRONT RS WAVELENGTH 1 PKVAL OPD 2.224692 RMS OPD 0.485250 GEO RMS R 0.022696 DIFFR LIMIT 0.003426 STREHL RATIO RSY 0.091087 -0.004210 CENTY -0.002879 RSX -- CENTX -- RSZ -- The conclusion then is that the transverse ray aberration of the edge ray is: DY = -0.013268 mm, and the transmission at this field point is: 44.8% of the on-axis value, excluding the transmittances of optical materials and coatings. From the menu headers • From the Evaluate menu header select: Ray fans > Single field point ... and choose the Command: Print Y ray-fan. Numerical calculation Chapter 6 - Numerical analysis • 59 Set Minimum fractional y-component of pupil coordinate (FY) = -.43, and Maximum fractional y-component of pupil coordinate (FY) = +.61. Set the Number of rays in fan to the minimum value of 3. • Leaving all the other default values unchanged, do not close the dialog box, but click on Set object point at the foot of the spreadsheet. • In the Set object point spreadsheet, leave the specification as Direct entry Set Fractional coordinates of object point to FBY = 1.00 FBX = 0.00 FBZ = 0.00. • Close the Set object point spreadsheet with the green tick, and click on OK in the Trace fans of rays through lens dialog box: *TRACE FAN - FBY RAY FY 1 0.610000 2 0.090000 3 -0.430000 • • 1.00, FBX FRAC RFS 0.530358 0.075914 -0.353777 0.00, FBZ 0.00 DYA DXA -0.071477 --0.010854 -0.052849 -- DY -0.013268 -0.009257 0.055365 DX ---- DZ ---- From the Evaluate menu header select: Spot diagram > Single spot diagram... Select Spot diagram Data and click on OK (the earlier Set Object Point command is still valid). *SPOT DIAGRAM - FBY 1.00, FBX 0.00, FBZ 0.00 - POLYCHROMATIC APDIV 17.030000 WAV WEIGHTS: WW1 WW2 WW3 1.000000 1.000000 1.000000 NUMBER OF RAYS TRACED: WV1 WV2 WV3 104.000000 104.000000 104.000000 PER CENT WEIGHTED RAY TRANSMISSION: 44.827586 SPOT DIAGRAM SYMMETRY: 1.000000 From the command line (abbreviated) • In the command line, type the following: sop 1 0 0;trf y 2 -.43 .61;spd 200 and click on the green tick, or press Enter on the keyboard. Numerical calculation 60 Numerical analysis *SET OBJECT POINT FBY FBX 1.000000 -FYRF FXRF --YC XC 18.264293 -*TRACE FAN - FBY 1.00, FBX RAY FY FRAC RFS 1 0.610000 0.530358 2 -0.430000 -0.353777 Chapter 6 FBZ -FY FX --YFS XFS -0.911383 -0.096417 0.00, FBZ 0.00 DYA DXA -0.071477 -0.052849 -- OPL REF SPH RAD 65.421390 61.550663 DY -0.013268 0.055365 DX --- *SPOT DIAGRAM - FBY 1.00, FBX 0.00, FBZ 0.00 - POLYCHROMATIC APDIV 200.000000 WAV WEIGHTS: WW1 WW2 WW3 1.000000 1.000000 1.000000 NUMBER OF RAYS TRACED: WV1 WV2 WV3 13820 13712 13868 PER CENT WEIGHTED RAY TRANSMISSION: 43.909889 *SPOT SIZES GEO RMS Y 0.020881 GEO RMS X 0.006382 *WAVEFRONT RS WAVELENGTH 1 PKVAL OPD 2.711822 RMS OPD 0.447068 GEO RMS R 0.021835 DIFFR LIMIT 0.003276 STREHL RATIO RSY 0.060859 -0.005045 CENTY -0.003196 RSX -- CENTX -- RSZ -- The new value for the transmission (43.9%) is more accurate than the earlier result since a finer grid of rays (200 rings, not 17.03, in the pupil) was defined by the spd command. By executing in the Edit window • From the Window menu header select: Editor > Open or click the icon. • Use the history button to call up the last line executed: sop 1 0 0;trf y 2 -.43 .61;spd 200 • • Copy and paste it into the Text editor window. Highlight it with the cursor (or press Ctrl-A), and press Ctrl-E. Results are the same. From the command line (in full) • In the command line, one might perhaps type the following: set_object_point(1.0,0.0,0.0,0.0,0.0,1) trace_fan(y,2,-0.43,0.61) spot_diagram(chr,none,200) These forms of the commands are used to make programs self-documenting. The short forms are more useful for command line entry. The spreadsheet buffer The spreadsheet buffer is an array of numerical storage cells, with 1999 rows numbered as in Microsoft Excel, which underlies each text window. The spreadsheet buffer is used for conveying the results of numerical OSLO calculations to variables in CCL commands, so it is important to understand how it works. Clearing the text window and spreadsheet buffer There are three ways to do this: The spreadsheet buffer Chapter 6 - Numerical analysis 61 • EITHER right click anywhere in the text window and select Clear window and SS buffer • OR, from the Window menu header, select: Text > Reset. • OR, in the command line, Enter twr (or textwin_reset) To clear the spreadsheet buffer without affecting the printed output in the text window: • In the command line, enter sbr (or ssbuf_reset) Reading from the spreadsheet buffer • • • In the text editor window, change the first entry so the whole line looks like this: sbr;sop 1 0 0;trf y 2 -.43 .61;spd 200 Highlight the line with the cursor, and press Ctrl-E. Watching the message area under the command line, click on the text window output to confirm the following spreadsheet cell allocations: *SET OBJECT POINT FBY [ a1 ] FYRF [ a2 ] YC [ a3 ] *TRACE FAN - FBY RAY FY 1 [ a4 ] 2 [ a5 ] FBX [ b1 FXRF [ b2 XC [ b3 ] ] ] 1.00, FBX FRAC RFS [ b4 ] [ b5 ] FBZ c1 FY [ c2 YFS [ c3 [ ] ] ] FX d2 XFS [ d3 [ 0.00, FBZ 0.00 DYA DXA [ c4 ] [ d4 [ c5 ] [ d5 ] ] [ OPL e3 ] ] ] [ [ DY e4 e5 ] ] REF SPH RAD [ f3 ] [ [ DX f4 f5 ] ] *SPOT DIAGRAM - FBY 1.00, FBX 0.00, FBZ 0.00 - POLYCHROMATIC APDIV [ a6 ] WAV WEIGHTS: WW1 WW2 WW3 [ a7 ] [ b7 ] [ c7 ] NUMBER OF RAYS TRACED: WV1 WV2 WV3 13820 13712 13868 PER CENT WEIGHTED RAY TRANSMISSION: [ a8 ] *SPOT SIZES GEO RMS Y [ a9 ] *WAVEFRONT RS WAVELENGTH 1 PKVAL OPD [ a10 ] GEO RMS X [ b9 ] GEO RMS R DIFFR LIMIT [ c9 ] [ d9 ] RMS OPD STREHL RATIO [ b10 ] [ c10 ] RSY [ d10 ] CENTY [ e9 ] CENTX [ f9 ] RSX [ e10 ] RSZ [ f10 ] Note that integers and headers are not included in the spreadsheet buffer. • Click on the two numerical results indicated, and note the cell coordinates and values given in the message area as follows: e4 = -0.0132683238458 a8 = 43.909889270714 Note also that these results are full precision (to 14 digits). Writing to the spreadsheet buffer • In the text editor window, add the command for formatted printing: aprintf("DY = % 6.6f Trans = %4.1f %%\n",e4,a8) giving the following output: The spreadsheet buffer 62 Numerical analysis Chapter 6 DY = -0.013268 Trans = 43.9 % Note that the contents of cells of the spreadsheet buffer can also be accessed using the real array ssb(row, column). For example, e4 becomes ssb(4,5) and a8 becomes ssb(8,1). The command aprintf places the two values in the spreadsheet buffer, still at full precision, even though they are printed with fewer places (6 and 1 respectively) after the decimal point. Note in particular that the cells are filled even if printing is turned off. • Click on these results to confirm this: a11 = -0.0132683238458 b11 = 43.909889270714 Scrolling the spreadsheet buffer This section should be omitted at the first reading, as it describes a feature used only in advanced programming. • Type in the command line: sbrow and press Enter Result = 12 This is the row number of the next row to be written to in the spreadsheet buffer. The command sbr (ssbuf_reset) remaps the spreadsheet row whose number is the first argument, with the row number of the second argument. So to renumber the lines so that any new output is written to row 1 rather than row 12: • In the text editor window, change the first entry so the whole line looks like this: sbr 12 1;sop 1 0 0;trf y 2 -.43 .61;spd 200 • Highlight it with the cursor, and press Ctrl-E. Note that the row numbers are the same as before, but this time the rows which had been previously written are Initial row a-column After After preserved, and numbered up to sbr 12 1 sbr -12 0 numbering Values 1999. 1.000 We can restore the line numbering by using the sbr command with a negative index: • In the command line type: sbr -12 0 The effect of this is illustrated in the table. The next row to be written to (in other words, the value of the read-only variable sbrow) is marked with an asterisk in each case. The spreadsheet buffer 1 2 3 4 5 6 7 8 9 10 11 12* 13 0.000 18.264 0.61 -0.43 200.0 1.000 43.9 .02088 2.71 -0.013268 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 1* 2 1 2 3 4 5 6 7 8 9 10 11 12* 13 Chapter 7 - Slider-wheel design 1:1 wide angle relay Introduction The slider-wheel facility is a powerful tool, which allows the user to control any system variable while watching its effect on any numeric parameter or graphic display. In this chapter there will be an illustration of how slider-wheels alone can be used to complete a design task. The requirement is for a four-element unity magnification relay. The object has a diagonal of 600 mm. The object to image distance is 451 mm. The distortion must be less than 0.1% and the design criterion is that the lowest value over the field of the modulation transfer function at 1.0 cycles/mm must be greater than 0.4. The wavelengths to be used for the MTF calculation are the usual three (0.58756 μm, 0.48613 μm and 0.65627 μm), weighted equally. Defining the starting point Clearly a symmetrical design is called for. In the public lens database (OSLO Standard and Premium only) there is an objective lens designed by Roossinov which will be used as the basis for the design of a relay lens. This has the title ROOSSINOV 56DEGHFOV F/8.3 USP2,516,724. It is nearly symmetrical and it has 13 surfaces. The design below has been adapted and simplified from this for use with all versions of OSLO. Setting up the starting lens • From the menu select File>New lens and choose a custom lens with 5 surfaces. • In the surface data spreadsheet, change the lens title to x1 relay. • Click on the gray button under Aperture Radius for surface 5, and select Aperture Stop (A) to move the aperture stop to surface 5. • Fill in the lens parameters as shown in the diagram below. The values for Aperture Radius may be omitted, as these will be adjusted using aperture radius solves - that is to say, the aperture will be set at the value equal to the arithmetical sum of the paraxial marginal and pupil ray heights. This is such an extreme field angle lens that the results look unrealistic at first, but this can be corrected later. 63 64 Slider wheel design • Chapter 7 In the Setup spreadsheet, enter the Object NA as 0.03 and the Object height as 300 mm. Close the Setup spreadsheet. • Select surfaces 1 to 4, right click and choose Copy. • Select surface 6 (IMS), right click and select Paste • Select surfaces 6 to 9, right click and choose Reverse. • Change the thickness for surface 5 to 0.5 and for surface 9 to 155. • In the Aperture radius column some are already Solves. Change the remaining apertures (surfaces 6 to 9) to Solve (S) by setting them to zero. • Under Radius, click on the gray button for surface 9, choose Minus curvature pickup, and on the prompt Enter pickup source surface, enter 1. Press Enter twice more. Define a similar minus curvature pickup for surface 8 from surface 2, for surface 7 from surface 3 and for surface 6 from surface 4. • Enter the command ctg to list the lens with curvatures: x*LENS DATA x1 relay SRF CURVATURE OBJ -- THICKNESS 155.000000 APERTURE RADIUS 300.000000 GLASS AIR 1 2 0.018182 0.030303 3.000000 50.000000 55.000000 S 33.000000 S F1 C AIR 3 4 0.015873 0.002252 17.000000 0.500000 20.735891 S 8.295530 S SK4 C AIR AST -- 0.500000 7.775659 AS NOTE AIR 6 7 -0.002252 P -0.015873 P 17.000000 50.000000 8.294476 S 20.712585 S SK4 C AIR 8 9 IMS -0.030303 P -0.018182 P -- 3.000000 155.000000 -- 33.000000 S 55.000000 S 300.541968 S F1 C AIR • SPE Click on Gen in the Surface data spreadsheet to open the General conditions spreadsheet. 1:1 wide angle relay Chapter 7 - Slider wheel design • Under Ray aiming mode, select Wide angle mode. • Close the General conditions spreadsheet. • Change the Lens drawing conditions to draw 3 rays for each of the field points FBY = 0, FBY = -1, FBY = +1. 65 The lens drawing should now appear as shown in the diagram. Slider-wheel design with ray intercept curves • Open the Slider-wheel Setup spreadsheet by clicking on the icon in the main window toolbar. • Select Ray-intercept, All points, Number of sliders = 4, and define sliders on surfaces 1,2,3,4 for the curvature (cv). • Close the Slider-wheel Setup spreadsheet. At this point the four sliders and two graphics windows, GW31 and GW 32 should become visible. If not, try using the Tile command, or open and close the Slider-wheel spreadsheet again. • The default step size is too large. Click on the lower scroll button at the right-hand end of each slider-wheel to bring the Step to 1e-05. • Adjust the sliders to improve the performance as far as possible. Once the aberrations are too small to discern at the default aberration plotting scale, reopen the Slider-wheel Setup spreadsheet and close it again immediately. The aberrations will be redrawn with a new scale, and the slider-wheels re-centered in their tracks. The step size will still need to be changed, however. • • If a slider reaches the endstop, change the step to re-center it. Note that the graphics zoom feature works on both windows, and the zoom settings are preserved during slider operation. Slider-wheel design with ray intercept curves 66 Slider wheel design One possible solution, for example, is Chapter 7 CV 1 = 0.018822 (RD 1= 53.130 mm) CV 2 = 0.030683 (RD 2 = 32.591mm) CV 3 = .015523 (RD 3 = 64.420 mm) CV 4 = .002462 (RD 4 = 406.13 mm) Plotting the MTF across the field • From the Evaluate menu header select Transfer Function > MTF vs field • Enter three frequencies in units of cycles per mm: 1.0, 2.0, and 3.0. This plots the modulation transfer function at all points in the field for the three spatial frequencies. In the example shown here, the upper (green) curve, which shhows the MTF at 1 cycle per mm, still falls well below the desired 0.4 level over part of the field of view. Editing the slider-wheel callback command In order to use the slider-wheels to optimize the MTF across the whole field, it will be necessary first to make a small modification to one of the CCL commands in the /private/ccl directory. Some users may prefer to skip this exercise and return to it once the next chapter on programming has been covered. • Open the text editor either by clicking on the icon, from the menu header Window > Editor > Open or typing the command ewo. • In the Text editor window, click on File > Open. • At the bottom of the window which opens, after Library Directories: click on Private. • Of the files which have a green icon (*.ccl files) select my_swcallback.ccl and click on Open. Slider-wheel design with ray intercept curves Chapter 7 - Slider wheel design 67 This file contains a single command cmd Sw_callback(int cblevel, int item, int srf) • Go to line 36 of the file (Ctrl-G or Edit > Goto Line, and enter 36). • After the last break; and before the line default: add the lines: case 14: uda; // User guide break; When typing this entry you must take care that the first line ends with a colon (:), and the second and the third with a semicolon (;). On the second line anything following the // is treated as a comment. • In the text editor window (not the main window) click on File > Save. Compilation should be automatic, and the message in the text window should be: *CCL COMPILATION MESSAGES: No errors detected To explain, if the slider-wheel callback CCL is enabled by the user, then the command Sw_callback is called whenever a slider-wheel is moved. When this happens, the value of the integer argument called Level is passed to the CCL command, where it appears as the integer cblevel. This determines which action to be taken by the callback command. If the sw_callback CCL function is invoked with a value of Level between 1 and 9, that number of cycles of optimization (iterations) is performed. If Level is 11, then the sliderwheel controls field angle, and if Level is 13 it controls entrance beam radius. The option Level = 13 is used in one of the tutorials. As a result of the change, if the sw_callback CCL function is invoked with a value of Level equal to 14, then a single command uda will be executed. This command (update_all in long form) has the effect of updating the graphics in all open updateable windows (i.e. those marked UW). All this occurs within the switch statement, with different outcomes according to the value of cblevel, the switch parameter. The listing of the modified CCL command is given below. Slider-wheel design with ray intercept curves 68 Slider wheel design Chapter 7 Listing of the modified slider-wheel callback CCL /***************************************************************************************** * This file contains some simple callbacks that are used in the documentation examples * * with slider-wheel windows. It is meant to be extended by users as needs arise. The * * callback uses the "cblevel" parameter to designate a particular action. The user then * * enters the appropriate number in the Slider-wheel Setup window in the cell marked * * "Level". The value of "Level" is passed to this command as "cblevel" and determines * * the task to be performed. * /*****************************************************************************************/ #define #define #define #define SW_MAXITERS SW_ANGSLIDER SW_DIFFRACTDBLT SW_EBRSLIDER 10 11 12 13 cmd Sw_callback(int cblevel, int item, int srf) { switch (cblevel) { case SW_ANGSLIDER: stp outp off; ang cc[0]; stp outp on; break; case SW_DIFFRACTDBLT: sprintf(str1,"ocm18%+f\n",-cc[0]); o 4 str1; ite 2; break; case SW_EBRSLIDER: stp outp off; ebr cc[0]; stp outp on; break; case 14: uda;//User guide break; default: if (cblevel > 0 && cblevel < SW_MAXITERS) { ite cblevel; uda; } else { beep; msg("Callback not implemented."); } } }... Slider-wheel design with ray intercept curves Chapter 7 - Slider wheel design 69 Slider-wheel design using MTF at one frequency • Plot the MTF curves at the spatial frequencies of 1, 2, and 3 cycles/mm as before. • Open the slider-wheel spreadsheet. • Set up the slider-wheels as before, but this time click on Enable sw_callback CCL function. • Enter Level as 14. • Enter the Setup name x1_relay and click on the Save setup button. This slider-wheel setup (the slider wheel definitions and the other data) is now saved in a file x1_relay.osw, which is stored in the directory .../private/bin/osw/ • Close the slider-wheel setup spreadsheet. • On each slider-wheel change the step size to 1e-05 as before (these values are not stored in the slider-wheel data). • Adjust the curvatures to maximize the MTF at 1 cycle/mm over the whole field. One possible solution, illustrated here, is: CV 1 = 0.01778 (RD 1= 56.237 mm) CV 2 = 0.03090 (RD 2 = 32.359 mm) CV 3 = .01585 (RD 3 = 63.079 mm) CV 4 = .002312 (RD 4 = 432.48 mm) The smallest MTF value for this design is 0.42. This completes the design ask. This example illustrates in microcosm how even a problem with clearly defined objectives and only 4 variables can have a large number of solutions, all meeting the requirements but differing in subtle ways. Slider-wheel design using MTF at one frequency 70 Slider wheel design Chapter 7 Setting clear apertures The apertures at present are based on paraxial ray “solves.” To complete the design, the clear aperture values must be set in accord with real ray, not paraxial ray, requirements. • From the Optimize menu header select Support routines > Vignetting > Set apertures. • Leaving all the choices as defaults, click on OK. *APERTURES SRF TYPE APERTURE RADIUS 0 SPC 300.000000 1 SPC 44.200000 2 SPC 32.000000 3 SPC 15.800000 4 SPC 8.360000 5 SPC 7.950000 CHK 6 SPC 8.360000 7 SPC 15.800000 8 SPC 32.000000 9 SPC 44.300000 10 CMP 300.550935 • If the slider-wheel spreadsheet is re-opened after the lens is saved, the previous setup will have been deleted from it. It can be retrieved by clicking in the Setup name window and right-clicking on x1_relay.osw from the list presented. • Finally, enter the command pld mon to confirm that the level of distortion in the design is indeed very low. Slider-wheel design using MTF at one frequency Chapter 8 - Programming Introduction This chapter will include the basics of how to create a new command producing textual output, and how to include that command as one of the options in the text window header menu. Next there will be how to create a new graphics command, and how to create an icon for this in one of the graphics window headers. Finally there will be a brief review of the SCP and CMD languages. To illustrate these, it is helpful to have a standard lens in storage. • Click on the icon for Open an existing lens. If the warning message appears ... Save changes to current lens file? Click on No. • At the bottom of the window which opens, after Library Directories: click on Public. • Select demo > edu and then click on demotrip.len. • Click on Open. Defining a new command: sno In the surface data spreadsheet, the button labeled Notes gives access to the first 5 lines of the user-defined commentary which is stored with each lens. This consists of up to 10 lines, but the 6th is reserved for some optimization parameters, and the 10th for the public database lens class. The standard OSLO command for listing the system notes is opc sno. There is no facility for calling this from the text window toolbar. This section shows how a new command, sno, which lists the system notes, can be written. Then the procedure for adding a label Sno to the text window (Standard Tools) toolbar will be given, so that the system notes (up to 10 lines of documentation stored with each lens) can be listed with a single click. • First, try out the command from the keyboard. Type the command opc sno *CONDITIONS: SYSTEM NOTES 1: This Cooke triplet is used throughout the OSLO documentation as an example. 2: It is a minor variation on a lens designed by hand by R. Kingslake (see "Lens 3: Design Fundamentals", pp286-295, Academic Press 1978, ISBN 0-12-408650-1), who 4: used nothing more than a hand calculator! The Cooke triplet was invented by 5: Dennis Taylor in 1893, and is still very widely used as a low-cost objective. 10: COOKE TRIPLET CCL commands are stored in ASCII, and may be created either using the OSLO standard text editor, or using UltraEdit-32® from IDM Computer Solution Inc, or (the least convenient) with Microsoft’s Notepad®. Only the use of the first will be described in this chapter. To create the new command: • If the icon for Open the standard text editor appears on the main window taskbar, click on it. Otherwise from the Window menu header select Editor > Open. Alternatively type the command ewo in the 71 72 Programming Chapter 8 command line, • In the editor window, select File > New and type: cmd sno(void) { operating_conds(sno); } Note that there is no punctuation after (void), and there is a semicolon (;) after the single line command. • Highlight the last three lines with the cursor and press Ctrl-E to check that the program has been entered correctly. • There are only two menu options in the editor window header. Choose File > Save as... , click on the gray button labeled Private at the bottom, and choose File type: CCL files (*.ccl,*.ccx,*.h). • Enter File name eval_sno and click on Save. • Compilation takes place automatically: *CCL COMPILATION MESSAGES: No errors detected should be the message which appears in the text window. • Enter the new command in the command line: sno • In the text editor window, add the documentation as // // Written by [your name] [date] // cmd sno(void) // hlp: // hlp: •

SNO

Prints the system notes.

{ operating_conds(sno); } In the editor window header, (not the main window) click on File > Save. The compilation message will appear again: *CCL COMPILATION MESSAGES: No errors detected Each command definition in the private/ccl directory must be unique, so do not attempt to save the command sno again in a *.ccl file of another name. The error message will be: *CCL COMPILATION MESSAGES: eval_sno2.ccl 2: Duplicate procedure definition and this error will persist until the duplicate procedure definition is removed. Defining a new command: sno Chapter 8 - Programming 73 Structure of a CCL command CCL commands can be created by the user to automate sequences of actions, and to carry out calculations and plots specific to a user’s requirements. They are stored as ASCII text in the directory .../private/ccl (not a sub-directory) and must be compiled before use. The simplest CCL command can have the structure: cmd command_name1() { OSLO_command1; OSLO_command2; ...etc... } This is stored in a file demo_anyfilename.ccl. (Prefixes of user-written command files should ideally be restricted to demo_, eval_, graph_ and optim_). It is compiled using the icon (or, in the case of OSLO EDU where the icon is not displayed) the menu sequence Tools > Compile CCL >Private, or the command ccl. It is executed using the call: command_name For example, the CCL file containing the program; cmd hallo(void) { printf(“Hallo world\n”); } may be stored as my_first.ccl, compiled, and then called using the command: hallo This is described in detail in Help > OSLO Help > Contents > Programming > CCL Programming > Using CCL. With formal parameters, or arguments, the structure of a CCL command might become: real argument_name1; int argument_name2; cmd command_name(real argument_name1,int argument_name2) { OSLO_command1(argument_name1,argument_name2); OSLO_command2(argument_name1,argument_name2); } This is compiled and then executed using (for example) either free format: command_name 1.0 1 or the more formal version, often used within CCL code: command_name(1.0,1); In this case the two global variables argument_name1 and argument_name2 might be used by another CCL command. Structure of a CCL command 74 Programming Chapter 8 Local variables may also be declared. Take, for example, the CCL command: real argument_name1; int argument_name2; cmd command_name(real argument_name1,int argument_name2) { real local_variable1; int local_variable2; local_variable1=3.0; local_variable2=4; print(argument_name1,argument_name2,local_variable1,loca l_variable2); } If this is called using the command command_name 1.0 2 the output is: 1.000000 2 3.000000 4 Search CCL library: scanccl Assume that eval_sno.ccl has been added to the private\ccl directory, as described above. • From the menu header select Tools > Search CCL library ... • Under Directory to browse select the option Private • Select the default option Sort functions by filename and click on OK. ** 8 functions are defined in the private directory:** ** C:\Program Files\OSLO\EDU64\private/ccl/ TYPE ---cmd cmd cmd FCTN NAME ARGUMENTS LINE DEFINITION FILE ----------------- ---- --------------sno 5 eval_sno.ccl sw_callback 15 my_swcallback.ccl int cblevel int item int srf tlex_1 18 dbtutorial.ccl real tl__radius1 real tl__radius2 real tl__refractive_index The new command sno appears as the first entry in the list of function names; also given are the number of lines in the command, and the name of the file in which it was defined. Defining a new command: ctn The next new CCL command is an extension of one which appeared in chapter 3. Initial version of command • From the Window menu header select: Editor > Open, or type the command ewo in the command line, or click on the main window toolbar icon. Search CCL library: scanccl Chapter 8 - Programming 75 • Type in the following line: for(i=0;i<=ims;i++)aprt cv[i] th[i] rn[i][1]; • • Split it into two lines and surround with curly brackets. Highlight the whole window (Ctrl-A) and execute (Ctrl-E). The following appears in the active text window: -0.047059 -0.006303 -0.049383 0.051813 0.007080 -0.057854 -- 1.0000e+20 2.000000 6.000000 1.000000 6.000000 2.000000 42.950000 -- 1.000000 1.620410 1.000000 1.616592 1.000000 1.620410 1.000000 1.000000 • Add a line at the beginning: cmd ctn() • • • • • • In the Text Editor window click on File > Save as...(F12). Ensure first that the bottom window reads Save as type: CCL files. Click on Library Directories Private. For File name type eval_ctn Click on Save. Look in the text window. There should be a message *CCL COMPILATION MESSAGES: No errors detected If the message appears: *CCL COMPILATION MESSAGES: eval_ctn.ccl 2: Duplicate procedure definition then there is already a file with extension .ccl in the private/ccl directory containing the line cmd ctn()Locate it and delete it, or change its extension to .ccx. It may be impossible to do this if file extensions are hidden. If so, it is necessary to change the Windows file viewing settings. Under My Computer > Tools > Folder options > View tab > Advanced Settings > Hide extensions for known file types: Uncheck. If there is another compilation error, check the listing carefully, especially the one semicolon and the three different types of bracket: cmd ctn() { for(i=0;i<=ims;i++) aprt cv[i] th[i] rn[i][1]; } Extra lines and spaces are not a problem. • Once compilation is successful, in the command line enter ctn. The output should be as before. Version with formatted output • Change the aprt print statement to: Defining a new command: ctn 76 Programming Chapter 8 aprintf("%3i %12.8f %9.4g %.6f\n",i,cv[i],th[i],rn[i][1]); Here, each format specification begins with a % sign: The format specifier %3i requires that the integer i is to be printed with a field width of 3, right justified within this width. The format %12.8f gives a minimum field width for cv[i] of 12 characters, with 8 digits printed after the decimal point. The format %9.4g prints th[i] in decimal notation with 4 significant figures, but in exponential form if it is 10000 or more, or less than 0.00001. The format %.6f requires n[i] to be printed with 6 digits after the decimal point, and no minimum field width. • Save and execute, giving: 0 1 2 3 4 5 6 0.00000000 0.04705882 -0.00630318 -0.04938272 0.05181347 0.00707965 -0.05785363 1e+20 1.000000 2 1.620410 6 1.000000 1 1.616592 6 1.000000 2 1.620410 42.95 1.000000 Adding the glass name string Glass name strings are not directly accessible. However, the command get_glass_name(i) copies the name of the glass for the ith surface into a read-only string glass_name (See under Help > OSLO Help > Contents > Programming > Accessing Data > Other Data > Data Functions). • Add an extra pair of curly brackets after the for statement, and insert: get_glass_name(i); • Change the print statement to (on a single line): aprintf("%3i %12.8f %9.4g %.8s %.6f\n" ,i,cv[i],th[i],glass_name,rn[i][1]); The format %.8s requires the glass_name string to be printed with a maximum of 8 characters. • List the complete command: cmd ctn() { print(" SRF CV TH GLASS RN"); for(i=0;i<=ims;i++) { get_glass_name(i); aprintf("%3i %12.8f %9.4g %.8s %.6f\n",i,cv[i],th[i],glass_name,rn[i][1]); } } Adding headers and documentation The following conventions have been established by previous writers of OSLO macros, and they are worth observing: Defining a new command: ctn Chapter 8 - Programming 77 1. Each CCL file opens with a set of three or more comment lines giving the author, date, and any update information. e.g. // // Written by [Your initials] [Date] // 2. All documentation for a CCL command is given in HTML format between the header and the body, commented out and preceded by hlp. For example: // hlp:

Lists curvature, thickness, glass type and refractive index.

3. No default system variables are ever used, so that, for example, the command sequence i=92;ctn;prt i must always give the same result. So declare all variables as local variables within the command: e.g. int i; Of course these can have any name chosen arbitrarily, but by keeping to the default variable names, the Ctrl-E execution of selections of code within the text editor window can still proceed, provided the declaration int i; itself is not highlighted. 4. Commands which give just printed output are echoed, preceded by a star, in upper case. e.g. print(“*CTN”); Making these changes, the final version of the command becomes: The output from a call of the command ctn is: *CTN SRF CV 0 0.00000000 1 0.04705882 2 -0.00630318 3 -0.04938272 4 0.05181347 5 0.00707965 6 -0.05785363 TH GLASS 1e+20 AIR 2 SK16 6 AIR 1 F4 6 AIR 2 SK16 42.95 AIR RN 1.000000 1.620410 1.000000 1.616592 1.000000 1.620410 1.000000 Defining a new command: ctn 78 Programming Chapter 8 The text window toolbar Commands which generate only printed output are by convention placed in the text window toolbar. The format for a text window toolbar is: menu toolbar_number { “Label,tooltip_label” = “command”, “Label2,tooltip_label2” = “command2”, } where the first Label (by convention having only 3 or 4 letters) is what appears on the toolbar, the second, tooltip_label, is more detailed, and only appears in a creamcolored box when the cursor hovers over the first label. The command may be either CCL or OSLO command(s). The toolbar_number is toolbar50 for the Standard Tools text window toolbar. Adding the command sno to the toolbar • Still in the Text Editor window, select File > Open and look in the Private CCL directory. Open the file a_menu.ccl. • (If there is no file private/ccl/a_menu.ccl, open the file /public/ccl/a_menu.ccl, and save it as private/ccl/a_menu.ccl) • Go to line 1339 of this file (Ctrl-G and enter 1339 in the dialog box). This should give the entries for: menu toolbar50 • After the line: “Len,Lens data” = “prt_len”, add the line (note the comma before the comment): “Sno,System note” • Compile again by saving the file: *CCL COMPILATION MESSAGES: No errors detected The text window toolbar = “sno”,//[your initials][date] Chapter 8 - Programming 79 Calling sno from the toolbar • Click on Sno in the text window toolbar. If it is not visible, ensure that the Standard Tools menu has been selected. Once again the output is: *CONDITIONS: SYSTEM NOTES 1: This Cooke triplet is used throughout the OSLO documentation as an example. 2: It is a minor variation on a lens designed by hand by R. Kingslake (see "Lens 3: Design Fundamentals", pp286-295, Academic Press 1978, ISBN 0-12-408650-1), who 4: used nothing more than a hand calculator! The Cooke triplet was invented by 5: Dennis Taylor in 1893, and is still very widely used as a low-cost objective. 10: COOKE TRIPLET Defining a new command: xmt In this exercise a command xmt will be created which plots a graph showing the transmission fal1-off across the field arising from vignetting. (The effect of coatings and of the internal transmission of optical materials, available in OSLO Premium, is not included in this analysis). The command will be modified to prevent errors occurring when no rays are transmitted, or when the chief ray fails. This will demonstrate the use of an error handler. Then a new icon will be created, and placed in the Spot Diagram menu of the graphics window toolbar to enable the new command to be called with a single click. Writing a command xmt to print transmittance values • Open the lens file /public/demo/EDU/ demotrip.len • In the Text Editor window, open a new file and type the following in a single line: sbr;sop 0 0 0;spd 44;sop 1 0 0;spd 44 • Highlight with the cursor, press Ctrl-E and click on the two values of PERCENT WEIGHTED RAY TRANSMISSION (100.00 and 43.324607) which appear in the text window. Note the coordinates of the two spreadsheet cells (a6, a14). • In the text editor, add a second line containing a print command. prt a6,a14; • Highlight both lines and press Ctrl-E to confirm the correct values have been printed. Defining a new command: xmt 80 • Programming Chapter 8 The transmission curve is to be plotted at 50 points over a range of value of FBY from 0.0 to 1.0. Introducing the pre-defined integer i as a variable to count through these points, and we can generate all the results using a for loop: sbr; for(i=0;i<51;i++) { sop i*.02 0 0; spd 44; } To extract the relevant values from the spreadsheet, and print them as a neat table, we must switch off printed output with stp(outp,off) and extract the transmission values from the spreadsheet. The spreadsheet cell number of the transmission value of the (i+1)th field point is a(6+8i) or, as a CCL formula, ssb(6+8*i,1). Introducing the double precision predefined variables x (the value of FBY) and y (the % transmission), we can use these in a print statement to create the necessary table: prt x,y; This statement will produce visible output despite the fact that the preference stp(outp,off); has been called, provided prt and not aprt is used for printing. Predefined variables are used at this stage because the Ctrl-E compilation method is incompatible with either local or global variables. • So change the program to: stp(outp,off); sbr; for(i=0;i<51;i++) { x=i*0.02; sop(x,0,0); spd(44); y=ssb(6+8*i,1); prt(x,y); } stp(outp,on); • Highlight it all and execute with Ctrl-E to generate the entire list of 51 values giving the percentage transmission across the field: -0.020000 0.040000 ...etc 0.960000 0.980000 1.000000 100.000000 100.000000 100.000000 47.120419 45.811518 43.324607 Converting xmt printed output to graphics The text window spreadsheet is used as the vehicle for transferring the printed data into plot commands. • • At the beginning, add the command gwr; (graphic window reset) to clear the window and define the dimensions of the plot area to be in the range x=0 ... 1, y = 0 ... 1. Also before the first calculation, add the plot command, moveto(0,1)- most lenses will have 100% transmission on axis. Defining a new command: xmt x = 1, y = 1 x = 0, y = 0 Chapter 8 - Programming • • • • 81 Add pen(3) to plot in dark blue. Delete the print statement. Insert the main plot command, lineto(x,y/100); where the /100 scales the yvalues to keep them within the range 0 ... 1. At the end, add gshow; to ensure that the plot output is drawn immediately and not held in a buffer. It may still be necessary to click on the window to have the graph drawn in full. stp(outp,off); sbr; gwr; moveto(0,1); pen(3); for(i=0;i<51;i++) { x=i*0.02; sop(x,0,0); spd(44); y=ssb(6+8*i,1); lineto(x,y/100); } stp(outp,on); gshow; Preserving the text window contents • In the second line, replace the sbr command by the two lines: k=sbrow; sbr(k,1); • On the third last line, insert the line: sbr(-k,0); Here k, a predefined integer variable, has been used to keep the value of sbrow, the index of the first unwritten row of the spreadsheet. Scaling and drawing the axes • After the gwr command, add the following commands to re-scale the window as illustrated in the diagram, and to draw the axes around the graph: . window(-0.2,1.2,-35,110); moveto(0,0); lineto(1,0); lineto(1,100); lineto(0,100); lineto(0,0); • • (-0.2, 110) (1.2, 110) (0.0, 100.0) Also change the lineto command to (0.0, 0.0) lineto(x,y) to cover the new range of y from 0 to 100. (-0.2, -35) (1.2, -35) Finally surround the whole procedure with curly brackets, add the line cmd xmt() at the top, and save in file private/ccl/graph_xmt.ccl. Defining a new command: xmt 82 • Programming Chapter 8 Note that up to this point only predefined variables have been used (integers i,k double precision real x,y). Thus it is possible to highlight and execute part of, or the whole command (excluding the cmd xmt() header itself) using Ctrl-E. This is helpful for locating errors. The listing of the command is as follows: cmd xmt() { stp(outp,off); k=sbrow; sbr(k,1); gwr; window(-0.2,1.2,-35,110); moveto(0,0); lineto(1,0); lineto(1,100); lineto(0,100); lineto(0,0); moveto(0,100); pen(3); for(i=0;i<51;i++) { x=i*0.02; sop(x,0,0); spd(44); y=ssb(6+8*i,1); lineto(x,y); } sbr(-k,0); stp(outp,on); gshow; } Adding standard plot commands to xmt • Add the pre-processor command at the top of the file: #include "../../public/ccl/inc/gendefs.h" • This makes it possible to call the two commonly used graphics commands: SAVE_DISPLAY_PREFS; and RESTORE_DISPLAY_PREFS; • Following the convention already established, the captions will drawn using the command sequence: if (char_pref(glab)) draw_title_block(str1,str2,str3); where the code for draw_title_block(str1,str2,str3); can be found in the CCL file public/CCL/graph_tools.ccl Error handling • Open the surface data spreadsheet and change the field angle to 30 degrees. Defining a new command: xmt Chapter 8 - Programming 83 • Call the xmt procedure. The command will fail when the transmission falls to zero with an error message as shown. The remedy is to add an error handling procedure to reset the error flag to zero. This will be called from xmt whenever an error occurs. If a procedure invokes a second procedure, then either the second must precede the first, or it needs to be declared: • Add the line at the top, the prototype declaration (note that this one is followed by a semicolon): cmd xmt_error_handler(); • Declare an integer global variable xmt_err to carry the error status between the prcedures. • • Add the error handler command xmt_error_handler at the end. The error handler can now be called. Before the window command, add the line: install_error_handler("xmt_error_handler"); and at the end add the command to restore the original (default) error handler: install_error_handler("prefs"); By adding the error handling precautions to the plotting routine, it is possible to prevent the execution of the spot diagram command if the chief ray has not been traced successfully and to continue execution of the command with the transmission value set to zero if no rays have been transmitted in the spot diagram. . Listing of complete command xmt • Convert the predefined variables to locally defined variables, i becomes iplt, x becomes xplt, y becomes yplt, and k becomes ssb_row_sav. • • Add comments, documentation, ticks and captions etc as shown below. Save and compile. The whole procedure now looks like this: // // Written by [your name] [date] // #include "../../public/ccl/inc/gendefs.h" int xmt_err;//global variable cmd xmt(void); cmd xmt_error_handler(void); cmd xmt(void) // hlp:

XMT

// hlp:

Plots the fall in transmission as a function of field // hlp: arising from central obstructions and vignetting. It does not // hlp: include the effects of coatings or Fresnel reflections.

// hlp:

This CCL command also illustrates how a custom error // hlp: handler prevents reference ray failures terminating execution // hlp: of a CCL command; by setting errno=0 within the error handler // hlp: it permits continued execution of the CCL command even after // hlp: what would otherwise be a fatal error.

Defining a new command: xmt 84 Programming { static int ssb_row_sav,iplt; static real xplt,yplt; static char str1[80],str2[80],str3[80]; SAVE_DISPLAY_PREFS;//as defined in gendefs.h set_preference(output_text, off);//switches off text output ssb_row_sav = sbrow;//saves row after last row written to in SSB ssbuf_reset(ssb_row_sav, 1);//initialises spreadsheet buffer graphwin_reset;//clears graphics window install_error_handler("xmt_error_handler");// see below window(-0.2, 1.2, -35, 110);//xmin xmax ymin ymax moveto(0, 0);// draw x-axis (range 0...1) lineto(1, 0); for (iplt = 1; iplt <11; iplt++) {moveto(iplt*0.1, 0);//draw x-axis ticks linerel(0, -2);} moverel(-0.2,-10); label("Rel.Obj.Ht.");//label x-axis moveto(0, 0);// draw y-axis (range 0...100) lineto(0, 100); for (iplt = 1; iplt <11; iplt++) { moveto(0,iplt*10);//draw y-axis ticks linerel(-0.02,0.0); } moverel(-0.1,0); label("%s","100%");//label y-axis moveto(0,100);// plot transmission curve pen(2);//green for (iplt = 0; iplt <51; iplt++) { xplt=iplt*0.02;// xplt=Relative object height (FBY) yplt=0; xmt_err=0; set_object_point(xplt,0.0,0.0); if (xmt_err==0)// i.e. If sop succeeded ... { spot_diagram(44); if(xmt_err==0)// .. and spd succeeded ... yplt=ssb(6+8*iplt,1);//..set yplt ... }// ... else yplt remains zero. lineto(xplt,yplt); } message("");// clears message area install_error_handler("prefs");// default - see asyst_ccl.ccl ssbuf_reset(-ssb_row_sav, 0);//restores ss buffer row numbering set_preference(output_text, on);//switches text output back on pen(1);// black if (char_pref(glab))// only if preference graphics_labels ON ... { sprintf(str1,"Field angle %.4f",180*ang/pi); sprintf(str2,"Object height %.6g",obh); sprintf(str3,"TRANSMITTANCE VS FIELD"); draw_title_block(str1,str2,str3);//see public/graph_tools.ccl } gshow;//clears graphics buffer, forces display of graphics RESTORE_DISPLAY_PREFS; } /******** ********* ********* ********* ********* ********* **********/ cmd xmt_error_handler(void) { xmt_err=errno; errno = 0;//clears error to permit CCL execution to continue } Defining a new command: xmt Chapter 8 Chapter 8 - Programming 85 The graphics window toolbar Commands which generate graphical output are generally called from icons on one of the graphics window toolbars. The format for a graphics window toolbar is: menu toolbar_number { “bitmap_file, tooltip_label” ... } = “gwt \”window_title\”; gwe \”command\”;”, where bitmap_file.bmp is the name of a bitmap file containing the icon, and stored in the folder /Prm64/bin/bma. Once again, tooltip_label appears in a cream-colored box when the cursor hovers over the icon. The window_title (up to 48 characters) will appear in the blue title bar of the updatable graphics window. Creating a new icon for xmt • Using the computer file listing facility, locate the redundant blank icon blank1.bmp, which is the first file in the directory /[Prm64]/bin/bma This is a file 16 x 15 pixels (all gray) with a palette of 16 colors, plotted at a resolution of 96 pixels per inch. • • Copy it to the same directory, and rename it an_xmt.bmp If time permits, modify the image pixel by pixel as shown, using a program such as Microsoft Paint®, and store it with the same name. blank1.bmp an_xmt.bmp Adding the xmt icon to the graphics window toolbar In a_menu.ccl, the toolbar number is 34 for the Spot Diagram Analysis graphics window. • Open the Text Editor window, select File > Open and look in the Private CCL directory. Open the file a_menu.ccl. • Locate toolbar 34. Go to line 1241 of this file (Ctrl-G and enter 1241 in the dialog box). On this line (or one nearby) should be the entries for the toolbar menu: menu toolbar34 // Spot Diagram Analysis After the line: "plt_spd_fld,Plot RMS Spot Size/OPD vs. Field" Field\";gwe \"spsopd:spsopd\"", = "gwt \"RMS Spot Size vs. The graphics window toolbar 86 Programming add the following, all on one line (note the comma before the comment): Chapter 8 "an_xmt,Plot transmittance vs. Field" = "gwt \"Transmittance vs. Field\";gwe \"xmt\";", // [your name] [date] • • Save a_menu.ccl. Check that compilation is successful: *CCL COMPILATION MESSAGES: No errors detected Calling xmt from the toolbar icon • Ensure that the lens in store is the standard triplet with 30 degrees as the semi-field angle. • Open a new graphics window. • Click on the Setup Window/Toolbar icon, and select the Spot Diagram menu. • Click on the xmt icon shown above. SCP programming: *triplet SCP (“star command program”) is the old macro language of OSLO, still supported but largely replaced by CCL. An SCP command consists of a text file whose name is the same as the command name, and whose first line is *[cmd_name] without a semicolon. All the other lines are commands ending with semicolons, and the file named cmd_name.scp must be stored in the directory /private/scp. The command is not compiled, so errors are not detected until the commands are executed. To call an SCP command, type *[cmd_name] into the command line. • Open the text editor window. • Click on File > New • Type the following lines: SCP programming: *triplet Chapter 8 - Programming 87 *triplet open len pri len trip.len n; gwo 2 320 300 0 100; rpt_ric ray 0.1 0 1 0.2 0.1 1 .005; gwo 3 320 300 320 100; rpt_tfr 100.0; gwo 4 320 300 640 100; rpt_spd 50 0.0 3 0.2 n; gwo 5 320 300 0 400; rpt_psf “128” 64 chr .25 aut .12 .06; The first line must begin with a * and have no semicolon after it. The first gwo command opens a new graphics window, GW2, which is 320 units wide and 300 high in the top left corner of the window, just under the command window. Three more windows are defined in the same way. • Except for the very first line, the entries may be tested during entry by highlighting them with the cursor and pressing Ctrl-E. • In the text editor window, click on File > Save as ... • Change File type to SCP. • Click on PRIVATE to store the command in /private/scp/ • Enter file name as triplet.scp. The file name must be the same as the command name, and only one command is permitted per file. Note that no compilation takes place, so there is no checking for errors before execution. • This command opens the triplet stored in the private lens directory on installation, and plots the ray intersection coordinates, the MTF, the spot diagram and the point spread function at three field point. Parameters for each of these commands are chosen to suit the lens. • To call this SCP command, type: *triplet including the initial asterisk. Some examples of SCP commands are given in the directory /public/scp. SCP programming: *triplet 88 Programming Chapter 8 Load command file programming This is available only in OSLO Standard and Premium versions. The command lcmd opens a text file and executes the OSLO commands in sequence. Unlike CCL and SCP files, the location of the file is quite arbitrary, so this programming language has the advantage that the files can be stored with the lenses. Semicolons at the end of each line are optional, but including them makes it easier to check the command file while it is being developed, using Ctrl-E in the text editor window. • Open the text editor and type: //triplet [your name] [date] open len pri len trip.len n; gwo 2 320 300 0 100; rpt_ric ray 0.1 0 1 0.2 0.1 1 .005; gwo 3 320 300 320 100; rpt_tfr 100.0; gwo 4 320 300 640 100; rpt_spd 50 0.0 3 0.2 n; gwo 5 320 300 0 400; rpt_psf “128” 64 chr .25 aut .12 .06; • In the text editor window, click on File > Save as ... • Store it as a text file in the private/len directory with type .txt and with the name triplet.cmd. • To execute, type in the command line lcmd,search in the private/len directory for the command file triplet.cmd, and click on Open to execute. Load command file programming Chapter 9 - Optimization Optimizing using Seidel aberrations According to Seidel aberration theory, a thin cemented doublet of a specified pair of glass types (one crown, one flint) may in general be corrected exactly for only two of the three coefficients for primary axial chromatic aberration (PAC), spherical aberration (SA3), and coma (CMA3). Using one real and one fictitious glass, however, an exact solution can always be found. This exercise will show how to find, using Seidel aberrations alone, the nearest glass in the Schott catalog to combine with Schott N-BAK4 making a cemented doublet of a focal length 150 mm, and aperture ratio f/6.3. Setting up the starting design • Open a new lens surface spreadsheet. • Select the image surface. Click on the gray SRF button, right click, and choose Insert catalog lens. • Select the EDMUND catalog, and cemented doublet look for a focal length 150 mm diameter 25 mm. • If +/-1 mm ranges are chosen there is only one result. The Edmund catalog number for this lens is EACH32494. The glass types used in this lens are Schott BK7 for the crown and Schott SF5 for the flint. • Set the entrance beam radius to be 150/2/6.3 mm. • Set the semi field angle to 1°. • Set wavelength weights 1.0 (0.58756μm) 0.4 (0.48613 μm), 0.6 (0.65627 μm). • Delete the extra surface, by clicking on the gray SRF button for surface AST, right click, and choose Delete. • We need to be able to alter surfaces 1 2 and 3. Click on the gray SRF button for surface 1 (AST), right click, and choose Ungroup. • Set the image distance at the paraxial back focal point (under thickness for surface 3, select Solves (S) > Axial ray height > Solve value = 0.0). • Listing the lens at this stage gives: 89 90 Optimization *LENS DATA Doublet f/6.3 150 mm SRF RADIUS THICKNESS OBJ -1.0000e+20 AST 2 3 IMS 91.370000 -66.210000 -197.710000 -- 5.700000 2.200000 146.149598 S -- Chapter 9 APERTURE RADIUS 1.7455e+18 12.500000 A 12.500000 12.500000 GLASS AIR SPE NOTE BK7 C SF5 C AIR 2.618244 S Defining the error function • First, close all open spreadsheets (this is important). • Calculate the angle for the marginal axial ray angle at the image for an f/6.3 beam: Type into the command window 0.5/6.3 and record the result: Result = 0.0793650793651 • From the Optimize menu header, select Generate error function> Aberration operands • Then, in the operands data editor which opens, set non-zero weights for just the four operands listed below: OPERAN D MODE WEIGHT NAME 2 MIN 1.0 PU 5 MIN 1.0 PAC OCM5 9 MIN 1.0 SA3 OCM9 10 MIN 9.0 CMA3 OCM10 DEFINITION OCM2+0.07937 For each operand, the MODE is MIN (minimization) rather than CON (constraint) which is equivalent to an infinite weight. (The latter is rarely of value). The WEIGHT gives the relative importance of each operand, and here coma has (arbitrarily) been given higher weight than the other two aberrations. The NAME is for information only, and has no effect on the optimization process. The DEFINITION is a string OCM followed by the element number of the optimization common matrix, Ocm[], that contains the value of the relevant operand calculated by the optimization CCL callback procedure opcb_abs. This string may include one arithmetical operand and one constant. For example, operand 2, sets the non-zero target value for PU (the axial ray angle in image space) to be equal to -0.07937. The entrance beam radius is fixed, so that, by controlling the value of PU in the image space, the focal length of the lens will be controlled to be at or near 150 mm since the optimization will seek to reduce the operand PU-0.07937 to zero. Of course defining operand 21 (EFL) as OCM21-150.0, and assigning it a non-zero weight, would have had the same effect. Optimizing using Seidel aberrations Chapter 9 - Optimization 91 • Close the operands data editor spreadsheet. If it needs to be opened again press the Edit optimization operands icon. • • Click on the icon to open the optimization conditions spreadsheet. Note the entry for the optimization callback, Command for CCL/SCP operands: opcb_abs • On the bottom line, under Error function value, select Weighted sum of squares. Hence the formula for this error function becomes: Min error fn = 1 * (PU + 0.07973)2 + 1 * (PAC)2 + 1 * (SA3)2 + 9 * (CMA3)2 • Close the optimization conditions spreadsheet. To list the starting value of the error function and its component operands: • In the text window, click on Ope *OPERANDS OP MODE WGT O 2 M 1.000000 O 5 M 1.000000 O 9 M 1.000000 O 10 M 9.000000 ... MIN ERROR FUNCTION: • NAME PU PAC SA3 CMA3 VALUE %CNTRB DEFINITION 4.4317e-06 0.00 OCM2+0.07937 -0.003508 34.19 OCM5 -0.004828 64.76 OCM9 0.000205 1.05 OCM10 3.5988e-05 To print the minimization error function alone, type the command: ope erf MIN ERROR FUNCTION: 3.5988e-05 Description of the Aberration Operands error function The aberration operands error function consists of a set of predefined operands, including paraxial ray heights and angles, and Seidel and Buchdahl aberration coefficients. All the default weights are zero, so that at least one non-zero weight must be specified before it be used. The menu header sequence which generates the error function calls the CCL command opabs_template in file /public/CCL/optim_erfs.ccl. This includes a command: Optimizing using Seidel aberrations 92 Optimization Chapter 9 opt_oprdccl("opcb_abs"); which sets the CCL command opcb_abs (in file /public/CCL/optim_callbaks.ccl) as the optimization callback. This in turn contains CCL code which is called every time the error function is evaluated. This callback command, opcb_abs, outputs the values of Gaussian and Seidel quantities to the text window spreadsheet, and then copies selected values into the Ocm[] matrix. The key lines of the code from the command opcb_abs are listed here: paraxial_trace(); Ocm[2] = ssb(1, 2); // pu chromatic_abers(); Ocm[5] = ssb(2, 1); // pac seidel_abers(); Ocm[9] = ssb(3, 1); // sa3 Ocm[10] = ssb(3, 2); // cma3 The relevant lines of CCL in the opabs_template command, which sets up the operands, are: operands(new); opnbr = 0; opnbr++;o(opnbr, opnbr++;o(opnbr, opnbr++;o(opnbr, opnbr++;o(opnbr, opnbr++;o(opnbr, opnbr++;o(opnbr, opnbr++;o(opnbr, opnbr++;o(opnbr, opnbr++;o(opnbr, opnbr++;o(opnbr, ... end(); ins, ins, ins, ins, ins, ins, ins, ins, ins, ins, "OCM1 ", "OCM2 ", "OCM3 ", "OCM4 ", "OCM5 ", "OCM6 ", "OCM7 ", "OCM8 ", "OCM9 ", "OCM10", 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, "PY"); "PU"); "PYC"); "PUC"); "PAC"); "PLC"); "SAC"); "SLC"); "SA3"); "CMA3"); /* /* /* /* /* /* /* /* /* /* Axial ray height */ Axial ray slope */ Chief ray height */ Chief ray slope */ Primary axial color */ Primary lateral color */ Secondary axial color */ Secondary lateral color */ 3rd-order spherical */ 3rd-order coma*/ Users of OSLO Standard and OSLO Premium do have the facility to define the error function as here described. However they do have a more direct way to define the error function, using predefined operands with self-explanatory names. This obviates the need for a CCL callback. The procedure for this is: • Delete any pre-existing operands using the command sequence: ope new;end • • Open the operand spreadsheet. Add three blank lines and then fill in the entries as shown in the diagram: • Close the operands data editor spreadsheet and click on Ope to list the operands. Creating a model glass Before a glass type can be made variable, it needs to be converted to a “model” glass. Open the lens data spreadsheet. Change the glass at surface 1 from BK7 to N-BAK4 Optimizing using Seidel aberrations Chapter 9 - Optimization 93 • Under GLASS for the second surface, click on the gray button next to SF5 and select Model... (M). • Press Enter three times to accept the default name (GLASS2), refractive index, and Abbe V-value. • Click on Rin to list the refractive indices. Although the model glass is specified only by its refractive index at the d wavelength and Abbe number, the refractive index data for F and C wavelengths remain almost unchanged. Defining the optimization variables • In the surface data spreadsheet, define the variables: Under GLASS for the second surface GLASS2, click on the gray button, and select Variable RN/DN. (The Special Variable RN/DN option is exactly equivalent). Note that although the Abbe number is used to define the dispersion for the model glass it is the OSLO “DN” which is used as a variable. This is a normalized parameter, best visualized in the index-dispersion plot. DN takes a value of 0.0 along the line joining N-FK5 and N-SK16, and a value of 1.0 along the line joining N-FK5 and SF11. Nearly all catalog glasses sit between these two lines, but most of the “normal” glasses tend to cluster about DN = 1.0. • Click on the variables button at the top of the spreadsheet, and put an upper limit of 1.0 for the value of DN, the dispersion parameter for surface 2. Leave the lower limit as 0. • Also set the minimum value of RN surface 2 as 1.48, the index of FK51, and the maximum value 1.85, the index of N-LaSF9, the highest index glass which can be regarded as having reasonable cost and acceptable environmental properties. • Click on “Vary all curvatures”. • Close the variables spreadsheet and the surface data spreadsheet. • Save the lens. The listing is given here: *LENS DATA Doublet f/6.3 150 mm SRF RADIUS THICKNESS OBJ -1.0000e+20 AST 2 3 91.370000 V -66.210000 V -197.710000 V IMS -- 5.700000 2.200000 121.451048 S -- APERTURE RADIUS 1.7455e+18 GLASS AIR 12.500000 A 12.500000 12.500000 N-BAK4 C GLASS2 V AIR SPE NOTE 2.182779 S Optimization • Using the header of the Text window, list the operands (Ope) and the variables (Var). Optimizing using Seidel aberrations 94 Optimization *OPERANDS OP MODE WGT O 1 M -O 2 M 1.000000 O 3 M -O 4 M -O 5 M 1.000000 O 6 M -O 7 M -O 8 M -O 9 M 1.000000 O 10 M 9.000000 .... MIN ERROR FUNCTION: *VARIABLES VB SN CF V 1 2 V 2 3 V 3 4 V 4 3 V 5 3 - • NAME PY PU PYC PUC PAC PLC SAC SLC SA3 CMA3 TYP CV CV CV RN DN Chapter 9 VALUE %CNTRB DEFINITION 1.7764e-15 -- OCM1 -0.015829 2.24 OCM2+0.07937 2.182779 -- OCM3 0.017260 -- OCM4 -0.081694 59.77 OCM5 -0.000343 -- OCM6 -0.053498 -- OCM7 -0.000226 -- OCM8 -0.063974 36.65 OCM9 0.004069 1.33 OCM10 0.011166 MIN ---1.480000 -- MAX ---1.850000 1.000000 DAMPING 1.000000 1.000000 1.000000 1.000000 1.000000 INCR 0.000100 0.000100 0.000100 0.001000 0.001000 VALUE 0.010945 -0.015103 -0.005058 1.672698 0.929017 INCR 0.001000 VALUE 0.998766 Optimize for 10 cycles (Ite). *ITERATE FULL 10 NBR DAMPING MIN ERROR 0 1.0000e-08 0.011166 1 3.792096 0.002771 2 0.002633 6.6051e-06 3 0.000615 2.4247e-07 4 7.8298e-06 1.0315e-12 5 1.2696e-09 2.4261e-19 6 1.2696e-09 1.0128e-25 7 1.2696e-09 1.0075e-31 8 1.269595 8.3919e-32 CON ERROR ---------- PERCENT CHG. 75.179931 99.761674 96.329101 99.999575 99.999976 99.999958 99.999901 16.703389 Choosing a real glass type • Find the DN value of the new glass: var 5 *VARIABLES VB SN CF V 5 2 - • TYP DN MIN -- MAX 1.000000 DAMPING 1.000000 List its refractive indices and Abbe V-value rin 2 2 *REFRACTIVE INDICES SRF GLASS/CATALOG 2 GLASS2 RN1 1.694707 RN2 1.711261 RN3 1.687937 VNBR 29.785506 TCE 82.000000 • Open the surface data spreadsheet. • Click on the gray button for surface 2 glass. • Select FIX and choose the latest Schott catalog (either Schott, or Schott 2004, depending on the edition of OSLO). In any event the glass chosen should be SF-15. • Enter rin 2 2: *REFRACTIVE INDICES SRF GLASS/CATALOG 2 SF15 SCHOTT RN1 1.698952 RN2 1.715461 Optimizing using Seidel aberrations RN3 1.692215 VNBR 30.067619 TCE 79.000000 Chapter 9 - Optimization 95 • Open the glass catalog database. • From the menu header select File >Open database > PUBLIC > glass_schott.cdb (it may be glass_schott2004.cdb in some versions of OSLO) • In the GLASSNAME column, click on SF15. Note that the glass is highlighted in yellow on the n-V diagram. The atmospheric and chemical properties are found in the column labeled ChemCode (10112). These are not bad, but a better glass, the lead- and cadmium-free equivalent is NSF15 with a ChemCode of 10111. • Change the glass for surface 2 to N-SF15: under the gray button for GLASS, select Catalog > Schott and click on N-SF15 - it is not possible to just type in the name to replace a model glass. Final optimization steps Reoptimize with the remaining parameters (the three surface curvatures). • Click on Ite: *ITERATE FULL 10 NBR DAMPING MIN ERROR 0 1.0000e-08 2.7751e-05 1 1.0000e-12 2.7540e-05 2 1.0000e-12 2.7520e-05 3 1.0000e-12 2.7519e-05 4 10.000000 2.7519e-05 CON ERROR ------ PERCENT CHG. 0.759895 0.073851 0.003876 1.0937e-06 Autofocus Refocus to minimize the root mean square axial wave aberration, averaged over the three wavelengths: • Open the surface data spreadsheet. • Under the gray THICKNESS button for surface 4 select Autofocus - minimum RMS OPD > On axis (polychromatic). • Right click on the text window, and choose Clear window and SS buffer. • Click on Len Optimizing using Seidel aberrations 96 Optimization *LENS DATA Doublet f/6.3 150 mm SRF RADIUS THICKNESS OBJ -1.0000e+20 AST 2 3 94.166056 V -67.121889 V -273.328281 V 5.700000 2.200000 146.658952 S IMS -- 0.080939 Chapter 9 APERTURE RADIUS 1.7455e+18 GLASS AIR 12.500000 A 12.500000 12.500000 N-BAK4 C N-SF15 C AIR SPE NOTE 2.639626 S • It is worth combining the distances for surfaces 3 and 4 to avoid confusion: Click on the defocus value. b5 = 0.0809387292198 • In the surface data spreadsheet, set the defocus value (thickness surface 4) to 0. • Also click on the thickness for surface 3, and in the command line add +b5. 146.6589521609103+b5 • Finally, list the lens again: *LENS DATA Doublet f/6.3 150 SRF RADIUS OBJ -AST 94.166056 2 -67.121889 3 -273.328281 IMS -. mm V V V THICKNESS 1.0000e+20 5.700000 2.200000 146.739891 -- APERTURE RADIUS 1.7455e+18 12.500000 A 12.500000 12.500000 2.639626 S Optimizing using Seidel aberrations GLASS SPE AIR N-BAK4 C N-SF15 C AIR NOTE Chapter 9 - Optimization 97 Optimization using finite rays The optimization exercise described in this section will be carried on into the tolerance calculations of the next chapter. Because the starting design is well optimized, the initial choice of error function and weights is not critical. The GENII error function, which is given in all versions of OSLO, will be used for the initial design stages. 50 mm f/5.6 objective: specification Design a triplet objective with a focal length of 50 mm, and a 15º semi-field of view, with aperture f/5.6. Vignetting is not permitted - that is to say, the full diameter beam must pass at all field angles. The final detector will be a photographic film with resolution out to 30 cycles/mm, and an MTF of at least 0.1 is required at this spatial frequency. Distortion is not critical. Only current Schott glass types can be used, and manufacture is to be at Rodenstock, by traditional methods, with dimensions marked on the final drawing in mm. Finding a starting design The most obvious starting point is the standard triplet supplied with the program. The first task is to set it up with the correct field, aperture and wavelength weights and to allow the aperture stop (drawn with a red pen) to move separately, rather than being assigned to an air-glass surface: • Click on the icon for Open an existing lens. • At the bottom of the window which opens, after Library Directories: click on Public. • Select demo > edu and then click on demotrip.len. • Click on Open. • • • Open the surface data spreadsheet. • • • • Click on Notes, delete all 5 lines of notes and replace with your own annotations. Change the lens identifier to 50 mm f/5.6 +/-15deg Click on Wavelength. Define the wavelength weights as 1.0 (.58756) 0.4 (.48613), 0.6 (.65627) and close the wavelength editor. Change the entrance beam radius to 4.5 mm. That is, 50/5.6/2, rounded up. Change the field angle to 15° Click on the gray button for Aperture radius for surface 1, select Not checked. Repeat for surface 6. • • • Click on surface 5. Right click and select Insert before • • Click on the button for Aperture radius for surface 5, and select Aperture stop. Change thickness for surface 4 from 6 to 0.0, and thickness for surface 5 frm 0 to 6.0. Click on the gray button under Special for surface 5 (AST). Optimization using finite rays 98 Optimization Chapter 9 • Select Surface Control (F) > General • On the second line, against Surface appearance in lens drawings: select Drawn. Set the Pen number for surface in lens drawings as 4 (red). • Set all the lens aperture radii to Solve. The aperture pickup on surface 2 vanishes. Checking for vignetting in the starting design In the triplet provided, the ray drawing conditions have been changed to allow for the vignetting. The first need is to restore the off-axis beams drawn to their full diameter. • Click on the Edit Lens Drawing Conditions icon. • In the section which governs rays drawn at the foot of the spreadsheet, change the number of rays for fan No. 2 from 0 to 3. Set the Min Pupil to -1.0 and the Max Pupil to +1.0 for fan No. 3. • Close the Lens Drawing Conditions spreadsheet. • Draw the lens. • Click on Len Wav and Pxc to list the lens. *LENS DATA 50 mm f/5.6 +/-15deg SRF RADIUS THICKNESS OBJ -1.0000e+20 APERTURE RADIUS 2.6795e+19 GLASS AIR 1 2 21.250000 -158.650000 2.000000 6.000000 7.304439 S 6.710505 S SK16 C AIR 3 4 -20.250000 19.300000 1.000000 -- 3.665807 S 3.420953 S F4 C AIR AST -- 6.000000 3.420953 AS AIR 6 7 141.250000 -17.285000 2.000000 42.950000 5.931324 S 6.415576 S SK16 C AIR IMS -- *WAVELENGTHS CURRENT WV1/WW1 1 0.587560 1.000000 -- WV2/WW2 0.486130 0.400000 *PARAXIAL CONSTANTS Effective focal length: Numerical aperture: Working F-number: Lagrange invariant: SPE NOTE * 13.376446 S WV3/WW3 0.656270 0.600000 50.000541 0.089999 5.555616 -1.205771 Optimization using finite rays Lateral magnification: Gaussian image height: Petzval radius: -5.0001e-19 13.397605 -149.381547 Chapter 9 - Optimization 99 Assessing the starting design The diagram above indicates the edge thicknesses of the positive components are far too small for economic manufacture. The center thickness of the negative lens needs increasing as well. And the stop needs to move away from the second surface of the negative lens to allow a plane diaphragm plate to be used. • In the Standard Tools graphics menu, click on the Through-Frequency MTF icon. • Right click in the graphics window, and select Recalculate with new parameters... • Enter Maximum frequency 30 cycles/mm. The resolution, especially in the off-axis points, needs improvement, but otherwise the performance is good. • • Click on the icon for ray intercept curves. Right click in the graphics window, and select Recalculate with new parameters... • Enter a value of 0.03333 mm (the reciprocal of the customer-defined spatial frequency) for the User aberration scale. The transverse aberrations at all wavelengths in the meridional (Y) section off axis particularly need to be reduced. Defining and validating the error function • From the Optimize menu header, select Generate error function > GENII Ray Aberration... • Fill in the entries for a Design frequency of 30 cycles/mm. • Fill in the pupil coordinates on the basis of no vignetting: F1 (on axis) fymax = 1.0 F2 (0.7 field) fymin = -1.0 fymax = 1.0 fx = 1.0 F3 (edge of field) fymin = -1.0 fymax = 1.0 fx = 1.0. • The tolerance on distortion at both F2 and F3 is distol = 10% (in other words, distortion will not be tightly controlled). • Finally click on OK to close the Geniierf spreadsheet. • Type in the command line ope all to list the operands that have been defined by this command. (Operands which begin with an underscore are not listed by clicking on the Ope icon in the text window.) Only the first 13 are listed below. Optimization using finite rays 100 Optimization *OPERANDS OP MODE O 1 M O 2 M O 3 M O 4 M O 5 M O 6 M O 7 M O 8 M O 9 M O 10 M O 11 M O 12 M O 13 M WGT --------1.000000 1.000000 1.000000 1.000000 1.000000 Chapter 9 NAME VALUE %CNTRB DEFINITION _Dy tol 0.005556 -- 0.0055555555556 _2.1 Dy 0.011667 -- 0.0116666666667 _2.8 Dy 0.015556 -- 0.0155555555556 _3 Dy 0.016667 -- 0.0166666666667 _4 Dy 0.022222 -- 0.0222222222222 _up Dy/3 0.283656 -- 0.283655904077 _3.2 up Dy 2.723097 -- 2.72309667914 _uprime -3.5749e-14 -- PU+0.0899990260196 Fnb diff -3.5749e-10 0.00 O8/0.0001 Focus diff 0.704983 0.26 DYY(1,1)/O4 Axial DY 0.035247 0.00 DY(1,2)/O1 Axial OPD -1.189682 0.75 OPD(1,2)/O6 Axial DMD 1.828939 1.78 DMD(1,2)/O6 The first weighted operand controls the focal length rather tightly. In the initial stages of design it is preferable that this be relaxed. So: • Click on the icon for Edit optimization operands. • Change the weight for operand 9 from 1.0 to 0.1. • List the operands, noting in particular any that have contributions above 10%. They are: O O O O O 21 22 24 36 37 M M M M M 1.000000 1.000000 1.000000 1.000000 1.000000 0.7 0.7 0.7 1.0 1.0 OPD DMD OPD OPD DMD U U L U U -5.224602 4.600139 -4.782094 -5.267896 6.020660 15.30 11.86 12.82 15.55 20.31 OCM21/OCM6 OCM22/OCM6 OCM24/OCM6 OCM36/OCM6 OCM37/OCM6 These are respectively, for the 0.7 field point, wave aberration and color for the upper Ysection ray, and wave aberration for the lower ray; also for the full field, wave aberration and color for the upper Y-section ray. These are the same aberrations as the plot above indicates will be causing the greatest reduction in MTF, so the error function has been validated. Note that the initial value for the error function is given on the last line of the operand listing as the root mean square of the weighted contributions: MIN RMS ERROR: 2.434848 Description of the GENII error function The GENII error function provided with all versions of the program is remarkably sparse yet effective. It makes maximum use of the results of ray-tracing from a single marginal ray on axis, and a chief ray and three rays in the pupil for each of two other field angles. The aberrations of these rays constitute the error function. The error function has two weighted operands controlling the Gaussian properties, three to control the axial image formation (transverse ray aberration DY, wave aberration OPD and Conrady chromatic variation in wave aberration DMD for color control), and 13 to control the four rays at each of the off-axis points at FBY = 0.7 and 1.0. This makes a total of 31, leaving the remaining 19 for necessary data storage. Because the dimensions of transverse ray aberrations, wavefront aberrations, longitudinal errors and color are so different, the error function uses scaling factors on each to enable the default value of unity weighting as the starting value for each operand. For example, the basic scaling factor on transverse errors is (6 N)-1 where N is the design spatial frequency. Defining the error function invokes a call to geniierf() (or, for users of OSLO-EDU, geniierf_lt) which is in public/ccl/optim_erfs.ccl. The OSLO EDU version specifies geniiops as a callback, which will be found in public/ccl/optim_callbaks.ccl. More information is available in OSLO Help. Optimization using finite rays Chapter 9 - Optimization 101 Defining the optimization variables • Open the surface data spreadsheet. • Click on the gray button for thickness 2, and select Variable. • Repeat for thicknesses 4, 5, 7. • Click on the Variables button to open the variables spreadsheet. • Click on the Vary all curvatures button. • For variable 2 (thickness 4) set a MIN value of 0.5 mm, leaving all other limits as default. • • • Close the variables spreadsheet. Close the surface data spreadsheet List the optimization variables by clicking on Var: *VARIABLES VB SN CF V 1 2 V 2 4 V 3 5 V 4 7 V 5 1 V 6 2 V 7 3 V 8 4 V 9 6 V 10 7 - TYP TH TH TH TH CV CV CV CV CV CV MIN 0.100000 0.500000 0.100000 0.100000 ------- MAX 1.0000e+04 1.0000e+04 1.0000e+04 1.0000e+04 ------- DAMPING 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 INCR 0.000450 0.000450 0.000450 0.000450 2.2222e-05 2.2222e-05 2.2222e-05 2.2222e-05 2.2222e-05 2.2222e-05 VALUE 6.000000 -* 6.000000 42.950000 0.047059 -0.006303 -0.049383 0.051813 0.007080 -0.057854 There is an asterisk against thickness 4 indicating that the current value of the variable (=0) violates the permitted range. As a result, the error function has increased. • Click on the Ope in the text window. MIN RMS ERROR: 3.772815 Optimization • Two clicks on the Ite button gives the output shown below for this error function. *ITERATE FULL 10 NBR DAMPING MIN ERROR CHG. 0 1.0000e-08 3.772815 1 1.0000e-05 2.061430 2 1.0000e-05 1.548952 3 1.0000e-05 1.326489 4 6.1580e-06 1.295507 5 2.3352e-06 1.292165 6 2.3352e-06 1.292093 7 0.000144 1.292093 *ITERATE FULL 10 NBR DAMPING MIN ERROR CHG. 0 1.0000e-08 1.292093 1 1.0000e-08 1.292093 2 1.0000e-08 1.292093 CON ERROR --------- CON ERROR ---- PERCENT 45.360945 24.860311 14.362182 2.335646 0.257970 0.005549 2.4329e-05 PERCENT --- If warning messages about clear aperture checking appear with OSLO EDU they will not affect the result significantly, although the final error function may differ slightly from the values given here.. Optimization using finite rays 102 Optimization Chapter 9 The performance has improved considerably - the lowest MTF at 30 cycles/mm is 0.6 (for T section at .7 field). The prescription is: *LENS DATA 50 mm f/5.6 +/-15 deg SRF RADIUS THICKNESS OBJ -1.0000e+20 APERTURE RADIUS 2.6795e+19 GLASS AIR 1 2 25.838240 V -103.139037 V 2.000000 6.389728 V 7.591942 S 7.036229 S SK16 C AIR 3 4 -14.888983 V 22.497814 V 1.000000 0.499055 V 3.888863 S 3.683790 S F4 C AIR 3.457640 V 3.568729 AS AIR 2.000000 44.869598 V 5.108018 S 5.633273 S SK16 C AIR AST 6 7 -161.514578 V -13.810731 V IMS -- -- SPE NOTE * 13.373470 S The focal length is 50.05 mm, an error of less than 0.1% so there is no need to increase the weight on operand 9. Engineering aspects: edge thicknesses As this lens is to be made by traditional means, a blank needs to be procured with sufficient extra diameter to allow each component to be centered by edging. The thicknesses of all the lenses need to be increased to improve manufacturing yield. Making an allowance of 3 mm on diameter beyond the largest clear aperture diameter for the mounting (with an extra 1 mm on the front lens to allow for weather-proofing), and a further 2 mm for the blank, the edge thickness of each blank should be about 1.5 mm minimum. To calculate the edge thicknesses of the blanks for the two positive lenses: • From the Lens menu header select Show Auxiliary Data > Edge Thickness. • For component 1, enter surface A =1, surface B = 2. Enter the clear semi-diameter 7.6 mm plus 3 mm = 10.6 mm for the y-height at both surfaces: *DISTANCE FROM SRFA 1 TO SRFB 2 AT YHTA YHTB XHTA XHTB ZSAGA 10.600000 10.600000 --2.274242 IS XDIS YDIS ZDIS GLOBAL DISTANCE ---0.820771 0.820771 ZSAGB -0.546529 The edge thickness given (ZDIS) is -0.82 mm, so the centre thickness for surface 1 needs to be increased by about 2.8 mm to reach the target of 1.5 mm. • eth Repeating for surface A =6, B = 7, enter 5.6+2.5 = 8.1 mm for the y-height at both surfaces. otherwise type the command: 6 7 8.1 8.1 0 0 For this lens, the edge thickness of the blank (ZDIS) is -0.83 mm, so the centre thickness for surface 6 also needs to be increased by about 2.8 mm. The centre thickness of the negative lens (surface 3) is too thin, and should also be increased to 1.5 mm. Rather than making these directly in the spreadsheet, they will be used to illustrate the process whereby adjustments can be made with simultaneous optimisation. Optimization using finite rays Chapter 9 - Optimization 103 Slider-wheels with concurrent optimization on MTF Adjusting lens thicknesses The facility provided by OSLO to carry out slider-wheel optimization on one or more parameters, with a simultaneous callback to optimization on other variables, is a powerful design tool. In this context, note that no parameter adjusted with the slider-wheel bars should be an optimization variable. In the example given here, the slider-wheels will be used to adjust the lens thicknesses 1 for surfaces 1, 3 and 6, while the optimization on the lens curvatures, air spaces and image distance will continue to correct performance during each adjustment. • • • • • • Close the surface data spreadsheet. Open the slider-wheel spreadsheet. Select Ray-intercept curves at All points in the field. Define three sliders for Thickness (TH) 1 Thickness (TH) 3 and Thickness (TH) 6. Select Enable sw_callback CCL function with Level = 9 (This must be in the range from 1 to 9 to trigger the Iter function in the callback command.). Close the slider-wheel setup spreadsheet. The text window, the slider-wheel bar and the two temporary slider-wheel windows, GW31 and GW32, should all be visible. The starting value of the error function is 1.292. Slider-wheels with concurrent optimization on MTF 104 • • • • Optimization Chapter 9 Increase thickness 1 in steps of 0.1 until it reaches 4.0 giving an error function of 1.309. Increase thickness 3 in steps of 0.1 until it reaches 1.5. The error function will be 1.372 Increase thickness 6 until it reaches 3.0; the error function becomes 1.408. Increase thickness 1 to 4.7 and thickness 6 to 4.7, the optimized error function will be 1.480. • Close the slider wheels and list the lens. *LENS DATA 50 mm f/5.6 +/-15 deg SRF RADIUS THICKNESS OBJ -1.0000e+20 APERTURE RADIUS 2.6795e+19 GLASS AIR 1 2 29.485222 V -86.537346 V 4.700000 6.170610 V 8.263805 S 6.982274 S SK16 C AIR 3 4 -15.359048 V 21.674799 V 1.500000 0.498922 V 3.947019 S 3.637632 S F4 C AIR 2.252805 V 3.522903 AS AIR AST 6 7 IMS -77.234402 V -14.489037 V -- 4.700000 44.432412 V -- 4.546980 S 5.759546 S 13.376786 S SPE NOTE * SK16 C AIR • Now to check the edge thicknesses, calculate the edge thickness of the front lens blank at a radius of 8.3+3.0 = 11.3 mm: eth 1 2 11.3 11.3 0 0 giving a value of 1.7 mm. • Also find the edge thickness of the third lens blank at a radius of 5.8+2.5 = 8.3 mm: eth 6 7 8.3 8.3 0 0 which gives 1.6 mm. These are both above the 1.5 mm which is required. For the diagram which shows the blank sizes, the barrel semi-diameters have been rounded upwards to 10 mm, 5.5 mm and 7.5 mm respectively. Engineering aspects: ambiguity avoidance It is extremely hard to tell which of the two surfaces of a nearly equi-concave lens is the steepest. To avoid assembly errors, we will investigate the effect of making the second lens truly equi-concave. • Make the second element equi-concave. Click on the surface 4 gray RADIUS button and select Minus curvature pickup (P)... with Pickup source surface = 3 Pickup constant = 0, Pickup multiplir = 1.0. • Reoptimise. The error function is 1.640. This increase is acceptable. Slider-wheels with concurrent optimization on MTF Chapter 9 - Optimization 105 *LENS DATA 50mm f/5.6 +/-15 deg SRF RADIUS THICKNESS OBJ -1.0000e+20 APERTURE RADIUS 2.6795e+19 GLASS AIR 1 2 26.647695 V -361.254520 V 4.700000 7.067320 V 8.681421 S 7.317984 S SK16 C AIR 3 4 -18.435016 V 18.435016 P 1.500000 0.499751 V 3.907032 S 3.580456 S F4 C AIR 2.398524 V 3.464412 AS AIR 4.700000 43.427580 V 4.577052 S 5.729062 S SK16 C AIR AST 6 7 -42.567801 V -16.089048 V IMS -- -- SPE NOTE * 13.383518 S Engineering aspects: testplate fitting • Select the Rodenstock test glass file: Under the File menu header, select Preferences > Set preference > Test_glass_file and in the command line enter rodenstock.tgl. This refers to an ASCII file rodenstock.tgl in the directory OSLO/Prm64/bin/lmo/ which contains 1446 test glass values. Test glass files for other manufacturers are also available, and the user may create others in the same format if desired. • Open the surface data spreadsheet. • For surface 7 (the shortest radius at 16.09 mm) remove the variable curvature (change to Direct specification). • Hold down the shift key and left-click the mouse twice on the radius. A value 16.0766 will appear as the nearest test glass, with a black box around it. • Click on the green tick to accept this (or shift-left-click to restore the nominal radius). The letter T appears next to the fitted radius. • Press Ite to optimize the remaining variables. • Repeat this sequence for surface 3 - remove the variable, fit the closest test glass, and optimise remaining variables. • Repeat this sequence for surface 6 and then again for surface 2. • Click on Len to list the design. Note the T which appears against each radius which has bees fitted to a test glass. Slider-wheels with concurrent optimization on MTF 106 Optimization *LENS DATA 50 mm f/5.6 +/-15 deg SRF RADIUS THICKNESS OBJ -1.0000e+20 APERTURE RADIUS 2.6795e+19 Chapter 9 GLASS AIR 1 2 26.699200 T -375.820000 T 4.700000 7.098400 V 8.692011 S 7.328991 S SK16 C AIR 3 4 -18.438800 T 18.438800 P 1.500000 0.499794 V 3.907388 S 3.581367 S F4 C AIR 2.384983 V 3.465615 AS AIR 4.700000 43.429946 V 4.572836 S 5.724953 S SK16 C AIR AST 6 7 -42.322100 T -16.076600 T IMS • -- -- SPE NOTE * 13.380875 S Click on Ope in the text window. MIN RMS ERROR: 1.641164 The error function has risen slightly. Rounding air spaces Round the air spaces to avoid giving the impression that they are subject to tight tolerances: • Change thickness 2 to 7.1, delete the variable and re-optimize. • Change thickness 4 to 0.5, delete the variable and re-optimize. • Change thickness 5 to 2.4, delete the variable and re-optimize on the one remaining variable, the focus. • Enter the command: ope erf The error function has risen slightly: MIN RMS ERROR: 1.645251 Adjusting clear apertures • Close the variables spreadsheet and the lens data spreadsheet. • Under the Optimize menu header, select Support routines > Vignetting > Set apertures and in the dialog box change the number of digits to 2. • Click on OK. *APERTURES SRF TYPE APERTURE RADIUS 0 SPC 2.6795e+19 1 SPC 8.500000 CHK 2 SPC 8.500000 3 SPC 4.000000 4 SPC 3.600000 5 SPC 3.500000 CHK 6 SPC 5.500000 7 SPC 5.500000 CHK 8 CMP 13.380786 • Remove the Checked aperture (K) indications from surfaces 1, 5 and 7. • Change the clear aperture surface 4 to 4.0 mm (as this lens is reversible). Slider-wheels with concurrent optimization on MTF Chapter 9 - Optimization 107 • Remove the Pickup (P) from the radius on surface 4, change all the other radii to Direct specification, but leave the variable on the back focal distance (thickness 7). • List the lens: 50 mm f/5.6 +/-15 deg. SRF RADIUS THICKNESS OBJ -1.0000e+20 APERTURE RADIUS 2.6795e+19 GLASS AIR 1 2 26.699200 -375.820000 4.700000 7.100000 8.500000 8.500000 SK16 C AIR 3 4 -18.438800 18.438800 1.500000 0.500000 4.000000 4.000000 F4 C AIR AST -- 2.400000 3.500000 A AIR 6 7 42.322100 -16.076600 4.700000 43.397798 V IMS -- -- 5.500000 5.500000 13.366656 S SPE NOTE * SK16 C AIR * This completes the design of this lens. The next chapter will start from this point as the basis of the tolerance calculation exercise. Slider-wheels with concurrent optimization on MTF Chapter 10 - Tolerances and drawings 50 mm f/5.6 objective: specification For the lens which is the final design of the triplet describes in the previous section, the task is to define the surface and component tolerances which, based on root-sum-of-squares statistics, give an MTF which does not fall below 0.1 at 30 cycles/mm at any of the three field points. The assumption will be made that in production there will be a uniform distribution of errors within the tolerance band, and that a focus adjustment will be carried out on assembly. This will be accomplished using a CCL command which assesses the MTF at 30 cycles/mm in both azimuths at 5 field points across the field - with values of FBY of 0.0, ± 0.7 and ± 1.0. Defining the tolerance error function:”opcb_dmtf” The CCL routine below will calculate the MTF in 2 azimuths at 5 field points, 10 values in all. It will then identify the worst (i.e. lowest) of these, and subtract it from the diffraction limited MTF at the same frequency. The error function consists of a single operand, having this value. Subtracting the lowest MTF from the ideal ensures that, as in all optimization operands, the system with the lowest value of the error function is the best one. The routine here is a “callback” - that is to say, it is evaluated whenever the error function is calculated. It places a single value into the real array ocm[1]. This value is then called using the string OCM1 as the definition of the operand. • Open the text editor and create a new file: // // Written by [your name] [Date] // cmd opcb_dmtf(void) // // // // hlp: hlp: hlp: hlp:

Callback for DMTF (degradation in MTF) optimization. OCM1 is max reduction in MTF below ideal MTF at 5 field points for one spatial frequency. Both X & Y are included on axis, as well as field height FBY both +ve and -ve.

{ static double mtfs[10],diff_lim,mtf_min; static double sf=30.0; //spatial frequency stp outp off; k=sbrow; sbr k 1;//scrolls spread sheet buffer to preserve contents sop(0,0,0); mtf(tfr,chr,y,sf,sf,0); mtf(tfr,chr,x,sf,sf,0); sop(0.7,0,0); mtf(tfr,chr,y,sf,sf,0); mtf(tfr,chr,x,sf,sf,0); sop(-0.7,0,0); mtf(tfr,chr,y,sf,sf,0); mtf(tfr,chr,x,sf,sf,0); 108 Chapter 10 - Tolerances and drawings 109 sop(1,0,0); mtf(tfr,chr,y,sf,sf,0); mtf(tfr,chr,x,sf,sf,0); sop(-1,0,0); mtf(tfr,chr,y,sf,sf,0); mtf(tfr,chr,x,sf,sf,0); diff_lim=d5; if(diff_lim==0) cclabort("Diff limited MTF zero","opcb_dmtf"); mtfs[0]=b5;// mtfs[1]=b8;// mtfs[2]=b14;// mtfs[3]=b17;// mtfs[4]=b23;// mtfs[5]=b26;// mtfs[6]=b32;// mtfs[7]=b35;// mtfs[8]=b41;// mtfs[9]=b44;// Ax AX +7 +7 -7 -7 +1 +1 -1 -1 T S T S T S T S T S mtf_min=1.0; for(i=0;i<10;i++)if(mtfs[i] Print/Plot OTF and in the dialog box select: Monochromatic, Print function, with Maximum frequency = 30 line pairs per mm. In this case the diffraction limit MTF at 30 cycles/mm is 0.86. At the best focus, the nominal value of the worst MTF at 30 cycles/mm is 0.49, giving a value of DMTF for the nominal system of 0.36. If the MTF must remain everywhere above 0.1, the value of DMTF must not increase to more than 0.76. Calculating decenter tolerances As an example we will calculate the effect of decentering the second lens by the minimum amount one can expect from traditional mounting methods: • Open the surface data spread sheet. • Under Special for surface 3, select Coordinates (C). • Enter .075 mm for DCY, and under Use base coordinates for returns to this surface: select Yes. • Under Special for surface 4, select Coordinates (C). • Under Coordinate return: select Yes and under Return to surface: enter 3 • Click on Ope and find the new DMTF value: MIN RMS ERROR: 0.612975 So DMTF has increased from 0.36 to 0.61, an increase of 0.25. This has used more than half the entire tolerance budget of 0.40 on one error, so clearly a specialized mounting method (such as laser centering in the mount) will need to be used to meet the performance target. That being the case, we will assume that all the component decenter tolerances can be regarded as zero, and calculate the budget for the remaining errors. Checking tolerance entries The default tolerance values assigned to each parameter are the ISO10110 values. Because there are two successive air spaces (4 and 5), the tolerance on the first one can be removed. • Click on the Edit Surface Tolerances icon, or select from the menu header Tolerance > Update tolerance data > Surface. • Click on Display all surfaces tolerances: • For surface 4, set TH TOL (thickness tolerance) to 0.0 • Close the surface tolerances data editor. Yes. Symmetrical tolerances surface calculation • From the menu header select Tolerance > User-defined Tolerancing and select Sensitivity and Symmetric perturbations. Calculating decenter tolerances 112 • Tolerances and drawings Chapter 10 A warning message comes up. The error function does not assume rotational symmetry, so click on OK. The sensitivity analysis (which may take one or two minutes) lists 6 power errors, 3 element thicknesses, 2 air spaces, 3 indices and 3 V-values, 17 symmetrical contributions in all. The summary is: WORST CASE CHANGE STANDARD DEVIATION RSS UNIFORM GAUSSIAN UNCOMPENSATED 6.019989 1.659396 0.958053 0.729824 COMPENSATED 3.022531 1.056369 0.609895 0.464604 The change in the error function, with focus compensation, for a uniform distribution of errors within the tolerance band is 0.61 is an indication that the standard tolerances are not acceptable. If we allocate 0.33 of the budget of 0.40 to the symmetrical tolerances, then each tolerance will be allowed 0.33/√17 = 0.08 MTF degradation. • From the menu header select Tolerance > User-defined Tolerancing and select Inverse sensitivity and Symmetric perturbations, enter 0.08 for Change in error function. *INVERSE SENSITIVITY ANALYSIS ERROR FUNCTION FOR NOMINAL SYSTEM: ALLOWED CHANGE IN ERROR FUNCTION: 0.360640 0.080000 POWER ERROR TOLERANCE ALLOWED TOLERANCE SRF UNCOMPENSATED COMPENSATED 1 4.204420 109.362285 2 4.416476 72.560814 3 1.941512 1.807345 4 1.910946 1.747543 6 3.571230 3.882230 7 3.599738 27.941716 These tolerances must be tightened from the ISO10110 values of 10, 10, 5, 5, 10 and 10 fringes to 5 fringes throughout. ELEMENT THICKNESS TOLERANCE ALLOWED TOLERANCE SRF UNCOMPENSATED COMPENSATED 1 0.074299 0.096090 3 0.079866 0.246151 6 0.109412 0.337794 The first one needs to be changed to from the ISO10110 value of 0.2 to 0.1 mm. AIR SPACE TOLERANCE ALLOWED TOLERANCE SRF UNCOMPENSATED COMPENSATED 2 0.079453 0.053990 5 0.035223 0.036388 These must be tightened to 0.05 mm. INDEX OF REFRACTION TOLERANCE ALLOWED TOLERANCE SRF UNCOMPENSATED COMPENSATED 1 0.000460 0.006810 3 0.000381 0.000346 6 0.000376 0.000342 These must all be tightened from .001 to 0.0006 (note that the glass type for lens 1 and for lens 3 are the same, so only one standard of glass need be procured). Symmetrical tolerances surface calculation Chapter 10 - Tolerances and drawings 113 ABBE V-NUMBER ERROR (IN %) TOLERANCE ALLOWED TOLERANCE SRF UNCOMPENSATED COMPENSATED 1 5.230509 20.247082 3 3.291042 12.443420 6 4.223386 14.964191 These can stay at 0.8%. Updating symmetrical surface tolerances • Click on the Edit Surface Tolerances icon, or select from the menu header Tolerance > Update tolerance data > Surface. • Change the tolerances on symmetric form error (PWR FR) at all surfaces to 5 • Change the tolerances on thickness (TH TOL) at surfaces 2 and 5 to 0.05. • Change the tolerance on thickness (TH TOL) at surfaces 1 to 0.1 • Change the tolerances on index (RN TOL) at surfaces 1 3 and 6 to 0.0006. • Close the surface tolerances data editor. • Repeat the sensitivity calculation for symmetrical tolerances: STATISTICAL SUMMARY WORST CASE CHANGE STANDARD DEVIATION RSS UNIFORM GAUSSIAN UNCOMPENSATED 4.548071 COMPENSATOR STATISTICS COMP MEAN TH 7 -0.011420 • 1.271472 0.734085 0.559210 STD DEV 0.099581 COMPENSATED 0.744409 0.472209 0.272630 0.207684 MAX 0.356100 RSS 0.483578 The degradation of 0.27 (less than the 0.33 allowed for) leaves a balance of 0.13 for the asymmetric tolerances. Asymmetric tolerances surface calculation Since the full asymmetrical sensitivity analysis cannot be undertaken with OSLO EDU, the relevant elements of the sensitivity analysis will be calculated separately. There are only two surface errors to be considered. These consist of 6 surface irregularity errors, and 6 surface tilt errors (TLA only), 12 in all. If we allocate the remaining 0.13 of MTF degradation (that is, the budget of 0.4 minus the 0.27 taken up by symmetrical tolerances) to these 12 tolerances, then each contribution is 0.13/√12 = 0.038. • Remove the variable from thickness 7 – focus cannot compensate for asymmetrical errors. • Remove the variable from thickness 7, since focus cannot compensate for asymmetrical errors. • From the menu header select Tolerance > User-defined Tolerancing and select Inverse sensitivity and Irregularity fringes, enter 0.038 for Change in error function. Asymmetric tolerances surface calculation 114 Tolerances and drawings *INVERSE SENSITIVITY ANALYSIS ERROR FUNCTION FOR NOMINAL SYSTEM: ALLOWED CHANGE IN ERROR FUNCTION: Chapter 10 0.360640 0.038000 IRREGULARITY ERROR TOLERANCE ALLOWED TOLERANCE SRF UNCOMPENSATED 1 2.097225 2 2.261429 3 0.816355 4 0.818204 6 1.263006 7 1.188189 The tolerance on both surfaces of the last lens needs to be changed to from the ISO10110 value of 2 fringes to 1 fringe. • From the menu header select Tolerance > User-defined Tolerancing and select Inverse sensitivity and Surface tilt tolerance (TLA), and again enter 0.038 for the Change in error function. *INVERSE SENSITIVITY ANALYSIS ERROR FUNCTION FOR NOMINAL SYSTEM: ALLOWED CHANGE IN ERROR FUNCTION: 0.360640 0.038000 SURFACE TILT TOLERANCE (TLA) ALLOWED TOLERANCE SRF UNCOMPENSATED 1 0.139481 2 0.108784 3 0.145052 4 0.161710 6 0.153277 7 0.110764 All these tilt tolerances must be changed to 0.08 degrees (5 minutes). Updating asymmetric surface tolerances • Click on the Edit Surface Tolerances icon, or select from the menu header Tolerance > Update tolerance data > Surface. • Change the tolerances on irregularity – i.e. asymmetric form error IRR FR - at surfaces 6 and 7 to 1.0 • Change the tolerances on tilt (TA TOL) for all refracting surfaces to 0.1 • Close the surface tolerances data editor. Updating asymmetric component tolerances The decision has already been made to center the components precisely. • Select from the menu header Tolerance > Update tolerance data > Component. • Change the tolerances on centration (DCY) and tilt (ALPHA) to 0.0 Asymmetric tolerances calculation • From the menu header select Tolerance > User-defined Tolerancing and select Sensitivity and Asymmetric perturbations, or type the command: tsn asy. Only the summary data is given here. Asymmetric tolerances surface calculation Chapter 10 - Tolerances and drawings 115 STATISTICAL SUMMARY WORST CASE CHANGE STANDARD DEVIATION RSS UNIFORM GAUSSIAN • UNCOMPENSATED 0.946050 0.308895 0.178341 0.135856 The degradation of 0.18 is a little larger than the 0.13 budget for the asymmetric tolerances, but note that all tolerance calculations subject to the approximations of statistics. Tolerance data listing • From the Lens menu header select Show tolerance data > Surface. *SURFACE TOLERANCES 50 mm f/5.6 +/-15 deg RADIUS RD TOL FRINGES THICKNESS TH TOL SRF CON CNST CC TOL PWR IRR TLC TOL DZ TOL 1 26.6992 -5.00 2.00 4.7000 0.1000 ----- RN TOL GLASS V TOL SK16 0.0006 0.8000 DECEN TILT Y/X A/B -0.0800 -0.0800 2 -375.8200 -5.00 2.00 7.1000 0.0500 AIR --0.0800 ------0.0800 ------------------------------------------------------------------------------3 -18.4388 -5.00 1.00 1.5000 0.1000 F4 0.0006 -0.0800 ----0.8000 -0.0800 4 18.4388 -5.00 1.00 0.5000 -AIR --0.0800 ------0.0800 ------------------------------------------------------------------------------5 ----2.4000 0.0500 AIR ----------------------------------------------------------------------------------------6 42.3221 -5.00 1.00 4.7000 0.2000 SK16 0.0006 -0.0800 ----0.8000 -0.0800 7 -16.0766 -5.00 1.00 43.3859 -AIR --0.0800 ------0.0800 ------------------------------------------------------------------------------8 -------------FRINGE WAVELENGTH: 0.546070 Fringes measured over clear aperture of surface unless indicated. Tilt tolerances are specified in degrees. • From the Lens menu header select Show tolerance data > Component. • All values in this table should be zero. Asymmetric tolerances surface calculation 116 Tolerances and drawings Chapter 10 ISO 10110 component drawing The middle element of the triplet objective will be used to demonstrate this facility. Setting element drawing defaults • From the menu header select Lens > Lens Drawing > Element drawing conditions or type the command: edd • Set RMS surface roughness for ground edges Rq = 2 (microns) medium. • Set RMS surface roughness Rq = 2nm (medium) • Set Surface polishing grade to P3. • Set Coating blemishes to 1 Grade 0.4. (MIL 80-50 equivalent) • Set Long scratches to 1 Width 0.008 mm (MIL 80-50 equivalent) • Set Edge chips: Maximum extent from edge to 1 mm. • Define Coating specification as Single layer MgF2 550 nm. • Close the spreadsheet. Setting element material properties • From the menu header select Lens > Lens Drawing > Element • For Left surface of element select 3 • Fill in: • Part Lens 2 [date] • Drawing title 50 mm f/5.6 • Diameter 11 mm +0.2/-0.2 ISO 10110 component drawing Chapter 10 - Tolerances and drawings 117 • Stress birefringence (0/): 20 • Bubbles and inclusions (1/) Number 1 Grade 0.4 • Striae Class 4. Setting element surface properties • Click on Edit left surface. • Leave most entries unchanged but fill in: • • Click on the green tick to close the spreadsheet. • Click on Edit right surface. • Again fill in: • • Surface imperfections Number 1 Grade 0.4 Surface imperfections Number 1 Grade 0.4 Click on the green tick twice and the drawing appears. ISO 10110 component drawing 118 Tolerances and drawings Element drawing The message appears in the message area: Element drawing is best viewed in a “portrait window” format. ISO 10110 component drawing Chapter 10 Appendix 1 119 Appendix 1 - Index of lens data commands This table gives an alphabetic listing of the principal commands used in lens data input, together with the page numbers in the OSLO Program Reference Issue 6.3 (Autumn 2004 edition). The letter in the second column is the label shown on the gray button in the surface data spreadsheet when the relevant parameter is set. Note that not all of these commands are available in OSLO-EDU. Command ach ad ae af afo ag air al alc amo ang ap apck apn ary as0, as1, etc. asi ast asp ben bry cak cal cam cc cfg cns csd cslv ctf cv cvx dcx dcy dcz del des dlid,dlfd,dlha,dlva, dlfs,dlls,dlap,dlrs, dlnr etc doe F A A A A S S X F A F A A C B B B A A T A C C C D Explanation array chan aspheric aspheric aspheric afocal mode aspheric medium aplanatic slv aplanatic slv abn mode field angle aperture ap checking special ap lens array aspheric alt srf intersec aperture stop aspheric tilt & bend birefringent crystal axis crystal axis crystal axis conic const oonfiguration cone slv delete slv in alt cfgs test glass cv curvature toric decentre decentre decentre srf delete desgr name lens and ray drawing control diffractive Page 65 73 73 73 117 73 53 42 42 118 122 49 117 50 64 75 62 27, 50 73 68 57 57 57 57 72 20 79 41 118 45 40 72 67 67 67 32 118 228 to 245 85 srf drawing ent beam rad drw ebr ec eik end epxy esd fno frn gc gcs gdt gih gla gor grd grp gsp hor idd ims ins itf inv jsd kco kdp ldp len lid lme lmo lse mco mer S E E F C C G D G D D Z I Z D D F M merge_catalog nac Q edge slv eikonal srf end data ray aiming eikonal del F number Fresnel global coord glob ref srf gradient index image height medium grating order gradium group grating spc hologram order zernike image srf srf insert interferogram srf invert polarisation kinoform order kinoform depth srf dwg pen begin data lens identifier module end module begin spreadsheet coating insert lens insert catalog lens non-sequential obj space NA nao im space NA nap Graphics reference 63 28, 121 47 108 119 108 121 62 69 118 97 122 54 85 100 34 85 86 91 27 32 112 33 107 89 89 64 20 35 35 17 105 40 37 109 28, 127 28, 121 120 not nxt obh opdw pfl pfm pi pic pk pre pu puc puk py pyc pzrt raim rco rd rdt rev rfh rfl rfs rod rtf sasd scf scl sdad sdaz sdde sdis skp sle sno1, sno2, etc... spl tce tem th tir tla tlb tlc tox toy toz ucp Appendix 1 N L L S S P S S S S S C T R F T F S F F C C C C C C P surface note next srf object height OPD in waves perfect lens perfect lens marg ray solve chief ray solve pickup sys pressure cv solve cv solve ax ray ang th solve th solve polarization ray trace ray aiming coord return radius test glass rd srf reverse refl & hatch reflection ref srf extrude testglass fit astig distance setup cfg scale srfs ap divisions apodisation diffraction efficiency im space spd skip scale lens system notes spline thermal expans coefficient sys temp thickness tir srf tilt angle tilt angle tilt angle tilt offset tilt offset tilt offset user pickup Index of lens data commands 61 28, 122 118 70 70 41 42 44, 47, 54 120 41 42 121 46 46 56, 120 117 68 40 45 33 53 53 50 63 45 120 21 40 123 123 120 120 62 40 126 82 120 120 46 63 67 67 67 67 67 44 ung uni usd usr utp wod wrsp U U P G ungroup units user sag user trace user pickup Wood lens ref sph posn wavelengths wv1... spectral wts ww1... zoe zrr zrx zrxr A A A A Zernike Zernike Zernike Zernike axis 36 117 110 95, 110 47 99 117 26, 124 26, 124 80 91 91 118 In this table, S refers to solves, C refers to tilt/decenter coordinates, and A refers to aspheric surfaces. Other letters are the flags used in the spreadsheet. A complete listing of the lens data commands is on pages 508 - 514 of the OSLO Program Reference. These commands may be used: 1. In the command window, explicitly, as part of an update process: len upd gto 2 nxt th 1.0 end Note the use of gto, nxt, end. A semicolon has the same effect as nxt. 2. As part of a CCL command: { len upd; gto(3); th(1.0); end; } Note the semicolons at the end of each line. 3. In the command window, as a self-contained command: th 3 1.0 4. This is called “global editing” As part of a lens file: NXT ... TH //SRF 3 1.0 5. Implicitly, when the spreadsheet is updated, as shown here. 121 Appendix 2 - Graphics reference Alphabetical index KEY TO COMMAND REFERENCE (in order of preference) Standard tools Accessed via graphics window toolbar using the icon shown Advanced Analysis Accessed via main window toolbar using the icon shown Tools > Special Accessed via main window menu headers grindex CCL command accessed via the command line Function 2D-waveguide coupling Astigmatism - S & T over field Axial chromatic focal shift CCL example - 4 graphs CCL example - contour CCL example - map CCL example - pen colours CCL example - XY graph Distortion grid plot Distortion at all wavelengths Doublet - slider-wheel design Draw system 2D Draw system 2D Draw system 3D shaded solid Draw system 3D solid Draw system 3D variable view Draw system 3D wire-frame Draw system 3D wire-frame Draw system - conditions Draw system - zoom lens Element drawing Encircled energy - diffraction Encircled energy - geometrical Ensquared energy - diffraction Ensquared energy - geometrical Extended source image Footprint - one field point Footprint profile - all field points Gaussian beam movie Command Reference Icon Tools > Special > 2D - Evaluate > Ray Fans Ray Analysis Tools > Plotting Tools > Plotting Tools > Plotting Tools > Plotting Tools > Plotting - Ray Analysis Evaluate > Ray Fans Tools > Demos - Lens Drawing Standard tools Lens Drawing Lens Drawing Lens Drawing Lens Drawing Standard tools Lens Drawing Lens Drawing Lens Drawing Energy Energy Energy Energy Extended Source Spot Diagram Spot Diagram Tools > Demos 122 - OSLO version All All All All All All All All All All All All All All All All All All All All All All All All All All All Grid e10 d11 h2 h9 b10 c10 d10 d10 b3 e11 h1a1 a1 d1 c1 e1 b1 b1 -h1 a2 b7 e7 c7 f7 e9 e4 f4 g10 Appendix 2 Ghost image movie Glass catalogue n-V map GRIN lens - slider-wheel design GRIN axial index Internal transmittance of glass Incidence angle statistics Lateral chromatic aberration Lateral colour (pri & sec) Longitudinal aberration LSF/KED - diffraction calc LSF/KED - geometrical calc MTF over field - 3 frequencies MTF - one field point MTF square wave - 1 field point MTF - thru frequency report MTF - thru frequency report MTF and spot size thru focus MTF FFT one field point MTF thru focus - one field point MTF thru focus across field MTF thru focus report MTF thru focus report OPD - 2D field points OPD - one field point OPD contour - one field point OPD interferogram OPD map - 2D field points OPD map - one field point OPD map/contour report OPD map/contour report OPD report Optimization ray set Partial coherence - bar image Photometric plot Pixellated image Polarisation map PSF - 2D contour lines PSF - 2D field points PSF - contour PSF - FFT - contour PSF - FFT - one field point 123 Spot Diagram Lens >Glass Catalog Tools > Demos grindex internal_trans iangstat - Ray analysis Evaluate >Ray Fans Evaluate >Ray Fans - Energy Energy MTF MTF MTF MTF Standard tools MTF MTF MTF MTF MTF Standard tools Ray Analysis Ray Analysis Wavefront Wavefront Wavefront Wavefront Wavefront Standard tools Ray Analysis Spot Diagram Advanced Analysis ridemo PSF PSF PSF PSF All All All All All All All All All All All All All All All All All All All All All All All All All - Extended Sources Polarization Evaluate > Spread fn All All All All All All All g4 a9 b11 h11 a3 c11 d7 g7 d6 a6 e6 h5 h5 f6 b6 h6 a7 g6 g6 g2 f2 f3 g3 d3 e3 c3 c3 e2 h4 g9 f11 f9 b8 b9 b5 c5 e5 f5 Graphics reference 124 PSF - one field point PSF - section PSF report PSF report PTF - thru frequency Public lens database Ray analysis - 2D field points Ray analysis - one field point Ray analysis report Ray analysis report Ray analysis SIGMA format Ray bundles 2D Ray bundles 3D Ray bundles movie RMS spot size & RMS OPD Seidel aberration demo Slider-wheel design Spot diagram - 2D field points Spot diagram - one field point Spot diagram - recipolar Spot diagram report Spot diagram report Surface reflected phase Surface reflectivity Surface transmission Surface transmitted phase Thin film uniformity Tolerances - Monte Carlo Triplet - slider-wheel design y-ybar diagram Zoom lens drawing Zoom lens drawing Zoom lens report Appendix 2 PSF PSF PSF Standard tools MTF File> Lens Database Ray Analysis Ray Analysis Ray Analysis Standard tools repsig Graphics reference - Lens Drawing Lens Drawing fieldscan Tools > Demos > Seidel - Standard Tools Spot Diagram Spot Diagram Spot Diagram Spot Diagram Standard tools Polarization Polarization Polarization Polarization Polarization Tolerances Tools > Demos > Triplet Optimize > Support Lens Drawing Zoom Zoom All All All All All All - Spot Diagram Tabular graphics command reference See below. - All All All All All All All All All All All All All - All All d5 g5 a5 a5 c6 h8 d2 c2 b2 b2 g11 f1 g1 h1 d4 f10 c9 a4 b4 c4 h3 h3 f8 d8 e8 g8 c8 -a11 d9 h1 h1 a8 lensdraw 32 plan 1.0 Lens Drawing lensdraw 32 oblique 1.0 Lens Drawing Tools>Demos>Rays Tools>Demos>Rays plo ric2d opd chrshft Ray Analysis Ray Analysis Ray Analysis Ray Analysis Evaluate>Ray Fans Evaluate>Other Ray Evaluate>Ray Fans Evaluate>Ray Fans Evaluate>Other Ray pwf2D pwf map pwf con pwf int drl;ddr Standard Tools Lens Drawing drl wir;ddr Standard Tools Lens Drawing drl sol;ddr Standard Tools Lens Drawing drl shs;ddr Standard Tools Lens Drawing drlrot sol Lens>Lens Drawing Lens>Lens Drawing Lens>Lens Drawing Lens>Lens Drawing dre plr ric2d_ray rpt_ric opd Lens Drawing rpt_ric ray Standard Tools Ray Analysis Ray Analysis Ray Analysis Lens>Lens Drawing Evaluate>Other Ray Evaluate>Ray Fans latshft distplt Lens Drawing fieldscan 1 Ray Analysis Ray Analysis rpt_wvf Standard Tools Wavefront Wavefront Wavefront Wavefront Wavefront rpt_spd Standard Tools Spot Diagram Evaluate>Other Ray Evaluate>Other Ray Evaluate>Wavefront Evaluate>Wavefront Evaluate>Wavefront Evaluate>Wavefront Evaluate>Wavefront Evaluate>Spot Diag spd2d pls recipolar spsopd footprt footpro ghosts mov grst Spot Diagram Spot Diagram Spot Diagram Spot Diagram Spot Diagram Spot Diagram Spot Diagram Spot Diagram Evaluate>Spot Diag Evaluate>Spot Diag Evaluate>Spot Diag Evaluate>Spot Diag Optimize>Support Optimize>Support Optimize>Support Lens>Show Optim rpt_psf Standard Tools PSF psf2d sprd map 0.1 dir PSF sprd con 0.1 fft PSF sprd map 0.1 fft PSF pss chr PSF sprd con 0.1 dir PSF PSF rpt_tfr Standard Tools MTF Evaluate>Spread Fn Evaluate>Spread Fn Evaluate>Spread Fn Evaluate>Spread Fn Evaluate>Spread Fn Evaluate>Spread Fn Evaluate>Spread Fn Evaluate>TransferFn plm tfr fftmtf mtfandptf mtf_fld squaremtf sl_otfspd plm tfo MTF MTF MTF MTF MTF MTF rpt_tfo Standard Tools MTF Evaluate>TransferFn Evaluate>TransferFn Evaluate>TransferFn Evaluate>TransferFn Evaluate>TransferFn Evaluate>TransferFn Evaluate>TransferFn fcurv prq chr psq chr pdl bth ple geo ped pgl bth zdrl MTF Energy Analysis Energy Analysis Energy Analysis Energy Analysis Energy Analysis Energy Analysis Zoom Evaluate>TransferFn Evaluate>Energy Dis Evaluate>Energy Dis Evaluate>Energy Dis Evaluate>Energy Dis Evaluate>Energy Dis Evaluate>Energy Dis Lens>Lens Drawing zrpt polstate thunf surfprop rfl surfprop tns surfprop phr surfprop pht dblib_open Zoom Polarization Polarization Polarization Polarization Polarization Polarization Evaluate>Pol Evaluate>Pol Evaluate>Pol Evaluate>Pol Evaluate>Pol Evaluate>Pol File>Lens Database open cdb pub "." "glass_...cdb"; pgq chr 64; sfg xy chr sliderwheel _design yybar source ppi mon gplot_kit _sample ExtendedSources xsource “3barh.ima” ExtendedSources Lens>Glass Catalogs Evaluate>Spread Fn Optimize>SliderW Optimize>Support Source>View extnd Source>Pixellated gplot_sample fill_contour _sample colors wvra sl_3rd Tools> Plotting Toolkit gplot2d _sample Tools>Plotting TKit Tools>Plotting TKit Tools> Plotting Toolkit Tools>Special>2D waveguide Tools>Demos>Seidel sl_trp gradium demo pla chr plf chr pld chr ridemo repsig iangstat Tools>Demos>Triplet Tools>Demos>Grad Evaluate>Ray Fans Evaluate>Ray Fans Evaluate>Ray Fans a b c d e f g h 125 MTF Source>Partial Coh. Tools>Demos>Gauss 3 4 5 6 7 8 AdvancedAnalysis show_movie gbmovie fab 2 9 Tools>Plotting TKit sl_doublet 10 Tools>Demos>Doub 11 126 Appendix 2 Tabular graphics index Draw system 2D Draw system 3D Draw system 3D wire-frame solid YZ Element drawing Ray analysis report Ray analysis - one field point* ISO 10110 Lateral chromatic Distortion grid plot OPD map/contour aberration rpt Spot diagram Spot diagram Spot diagram 2D field points 1 field point* recipolar Point spread PSF PSF - contour function report 2D field points MTF - 1 field MTF 1 field point Phase - thru point* (FFT calc)* frequency* MTF thru focus Encircled energy Ensquared en. across field (diffraction calc) (diffraction calc) Zoom lens Polarisation map Thin film uniformity report Glass catalogue PSF Slider wheel design n-V map 2D contour lines CCL example CCL example CCL example XY graph contour map Triplet slider wheel GRIN lens slider Longitudinal design wheel design aberration a b c Graphics reference Draw system 3D shaded solid Ray analysis 2D field points OPD map - 2D field points RMS spot size & OPD over field PSF map - one field point MTF over field - 3 frequencies LSF & KED (diffraction calc) Surface reflectivity Draw system variable view OPD report Ray fans 2D Ray fans 3D for Ray fans movi vignetting for vignetting OPD OPD Axial chromati focal shift 1 field point* 2D field points OPD map - 1 field OPD contour - 1 OPD Spot diagram point* field point* interferogram report Footprint of beam - Footprint profiles - Ghost image movie Optimisation ra 1 field point all field points patterns PSF contour (FFT PSF map PSF MTF calc)r (FFT calc) section thru frequency MTF - square MTF & spot size MTF through focus MTF through foc wave 1 field pt* report 1 field pt* through focus Encircled energy Ensquared en. LSF & KED Zoom lens drawi (geometrical calc) (geometrical calc) (geometrical calc) Surface Surface Surface Public lens database transmission reflected phase transmitted phase y-ybar diagram Extended source Pixellated image Partial coherence CCL example image bar image 4 graphs CCL example 2D-waveguide Seidel aberration Gaussian beam Doublet slider coupling demo movie wheel design pen colours Astigmatism - S & Distortion Photometric plot Ray analysis Incidence angl T over field SIGMA format statistics at 3 wavelengths d e f g h Appendix 2 127 The 88 examples of OSLO graphics shown in the table below represent almost the full range of graphics output available to users of OSLO Premium version. Brief descriptions of each graphic example are given above. The routes for accessing these graphics are listed in the tabular command reference with the following format: OSLO commands These are given in short form only. They can be typed as shown, and they are also useful as an index to the HELP facility. Standard Tools These refer to the groups of icons called up from the top left corner of any graphics window ExtendedSources These refer to the groups of icons called up from the top left corner of the main window. Evaluate>Spread Fn These show how most of the graphs can be created from menu headers. * Graphs indicated are for one field point only, and they can give results only on axis if accessed via the icons. To plot individual graphs for other field points, either issue the set object point command and then use the command line (for example sop 1 0 0;plr), or work through the menu headers. Graphics reference 128 Appendix 2 Graphics reference examples 1 2 3 4 5 6 7 Graphics reference Appendix 2 129 8 9 10 11 a b c d e Graphics reference f g h

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