Spectrometer Wavelength Calibration Instructions

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Calibrating the Wavelength of the Spectrometer
The following describes how to calibrate the wavelength of your spectrometer. Though each spectrometer is
calibrated before it leaves Ocean Optics, the wavelength for all spectrometers will drift slightly as a function of
time and environmental conditions.
You are going to be solving the following equation, which shows that the relationship between pixel number
and wavelength is a third-order polynomial . . .

λp = I + C1 p + C2 p2 + C3 p3
. . . where λ is the wavelength of pixel p, I is the wavelength of pixel 0, C1 is the first coefficient (nm/pixel),
C2 is the second coefficient (nm/pixel2), and C3 is the third coefficient (nm/pixel3). You will be calculating the
value for I and the three Cs.

Setting Up
To re-calibrate the wavelength of your spectrometer, you will need the following:
! A light source that produces spectral lines. Ocean Optics’ HG-1 Mercury-Argon lamp is ideal for this
purpose. If you do not have an HG-1, you will need a spectral line source that produces several (at least
4-6) spectral lines in the wavelength region of your spectrometer.
! Your spectrometer.
! An optical fiber (for spectrometers without a built-in slit, a 50-µm fiber works best).
! Either a spreadsheet program (Excel or Quattro Pro, for example) or a calculator that performs third-order
linear regressions. If you are using Microsoft Excel, choose Tools | Add-Ins and check AnalysisToolPak
and AnalysisToolPak-VBA.

Calibrating the Wavelength
of your Spectrometer
1.

2.

3.

After placing OOIBase32 into Scope Mode, take a spectrum of your light source. Adjust the integration
time -- or the A/D card conversion frequency -- until there are several peaks on the display screen that are
not off-scale.
Move the cursor to one of the peaks and carefully position it so that it is at the point of maximum intensity.
Record the pixel number that is displayed in the status bar (located beneath the graph). Repeat this step for
all of the peaks in your spectrum.
Using your spreadsheet, create a table like the one shown on the next page.
! In the first column, place the exact or true wavelength of the spectral lines that you used. Most
calibration line sources come with a wavelength calibration sheet. If you do not have a wavelength
calibration sheet for your light source, you can probably find the wavelengths for your spectral lines
(assuming that they are being produced by pure elements) in a Chemistry or Physics textbook or
handbook, such as the CRC Handbook of Chemistry and Physics.
! In the second column of this worksheet, place the observed pixel number.
! In the third column, calculate the pixel number squared.
! In the fourth column, calculate the pixel number cubed.

-1-

Calibrating the Wavelength of the Spectrometer

Independent
Variable

True
Wavelength
(nm)
253.65
296.73
302.15
313.16
334.15
365.02
404.66
407.78
435.84
546.07
576.96
579.07
696.54
706.72
727.29
738.40
751.47

4.

5.

Dependent
Variables

Pixel #

Pixel # 2

175
296
312
342
402
490
604
613
694
1022
1116
1122
1491
1523
1590
1627
1669

30625
87616
97344
116964
161604
240100
364816
375769
481636
1044484
1245456
1258884
2223081
2319529
2528100
2647129
2785561

Values computed from
the regression output

Pixel # 3

Predicted
Wavelength

Difference

5359375
25934336
30371328
40001688
64964808
117649000
220348864
230346397
334255384
1067462648
1389928896
1412467848
3314613771
3532642667
4019679000
4306878883
4649101309

253.56
296.72
302.40
313.02
334.19
365.05
404.67
407.78
435.65
546.13
577.05
579.01
696.70
706.62
727.24
738.53
751.27

0.09
0.01
-0.25
0.13
-0.05
-0.04
-0.01
0.00
0.19
-0.06
-0.09
0.06
-0.15
0.10
0.06
-0.13
0.19

Now you are ready to calculate the wavelength calibration coefficients.In your spreadsheet program, find the
functions to perform linear regressions.
-- if using Quattro Pro, look under Tools | Advanced Math
-- if using Excel, look under Tools | Data Analysis
Select the true wavelength as the dependent variable (Y). Select the pixel number, pixel number squared and
the pixel number cubed as the independent variables (X). After you execute the regression, an output similar
to the one shown below is obtained.
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations

0.999999831
0.999999663
0.999999607
0.125540214
22
intercept

Intercept
X Variable 1
X Variable 2
X Variable 3

Coefficents
190.473993
0.36263983
-1.174416E-05
-2.523787E-09

Standard Error
0.369047536
0.001684745
8.35279E-07
2.656608E-10

first coefficient

second coefficient

third coefficient

6.

7.
8.

The numbers of importance are indicated in the above figure. You will need to record the Intercept as well as
the First, Second, and Third Coefficients. Also, look at the value for R squared. It should be very close to 1. If
it is not, you have probably assigned one of your wavelengths incorrectly.
Select Spectrometer | Configure from the menu and choose the Wavelength Calibration page to update
the wavelength coefficients within OOIBase32.
Repeat this process for each channel in your setup.

-2-



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