Physik Instrumente PI TEC66 Kinematics Of Multi Axis Tip Tilt Systems

PI-TEC66-Kinematics-of-Multi-Axis-TipTilt-Systems Piezo Positioning Systems with Parallel Kinematics

User Manual: Physik Instrumente Piezo Positioning Systems with Parallel Kinematics

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Kinematics of Multi-Axis Tip/Tilt Systems
Piezo tip/tilt mirror systems from PI are based on parallel kinematics with a single movable
platform for all directions of motion. The systems achieve a higher linearity than can be
attained by switching two single-axis systems in succession, as is the case with galva-
noscanners, for example, and therefore, are very compact.
Horse head nebula
(Photo: Brian Lula)
Arrangement of the actuators of a tripod piezo drive
The tilt angle and
the travel in Z are
calcu lated using the
follow ing formulas:
θY = 2A –
θX =
Z =
A, B, C is the linear
displacement of the
relevant actuators.
(B+C)
2a
(B-C)
b
(A+B+C)
3
Principle of a tilt system with
differential piezo drive
Tip/Tilt System with Differential Piezo Drive
(Tetrapod)
The platform is driven by two pairs of piezo
actuators located in 90° angles to one another.
Four actuators are controlled differentially in
pairs, depending on the tilt direction. The tilt
axes θX and θY are arranged orthogonally so
that a coordinate transformation is not neces-
sary.
This concludes in an excellent stability in linear
and angular positioning for a wide tempera-
ture range.
Just as the tripod, the differential version guar-
antees an optimum angular stability over a
large temperature range. For position con-
trolled versions, the differential evaluation of
two sensors per axis provides an improved
linearity and resolution.
θY
θX
Piezo-actuated tip/tilt mirrors and platforms
are suitable both for highly dynamic operation,
such as tracking, scanning, image stabilization,
elimination of drift and vibration, and for static
positioning of optical systems and samples.
They allow for an optical beam deflection up
to 100 mrad, extremely short response times
from milliseconds to microseconds and reso-
lutions down to nanoradians.
PI offers a large range from compact systems
for laser beam steering up to large units used
for astronomy.
Tip/Tilt System with Tripod Piezo Drive
The platform is driven by three piezo actuators
that are located in 120° angles to one another.
By means of coordinate transformation, the
motion can be split among the different actua-
tors.
In addition to tilting, the platform may also be
used linearly in Z direction, which is important,
for example, for correcting optical path lengths
(phase shifters).
Piezo
Piezo
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Dynamics of a Piezo Tip/Tilt Mirror
The maximum operating frequency of a piezo
tip/tilt system strongly depends on its mecha-
nical resonant frequency. The properties
of amplifier, controller and sensor are also
important. To estimate the effective resonant
frequency of the system – a combination of
platform and mirror – it is necessary to calcu-
late the moment of inertia of the mirror sub-
strate first.
IM = m
[
2R2 + H2
12 +
(
H
2+ T
)
2
]
Moment of inertia of a rectangular mirror:
IM = m
[
L2 + H2
12
+
(
H
2
+ T
)
2
]
with:
m = mirror weight [g]
IM = moment of inertia of a mirror
[g × mm²]
L = mirror length orthogonally to tilt axis
[mm]
H = mirror thickness [mm]
T = distance of pivot point to platform surface
(see technical data of individual models)
[mm]
R = mirror radius [mm]
Moment of inertia of a rotationally symmetric
mirror:
The resonant frequency of the system is calcu-
lated with resonant frequency of the platform
(see technical data) and moment of inertia of
the mirror substrate using the following for-
mula:
Resonant frequency of a piezo tip/tilt system
with mirror
with:
f' = resonant frequency of platform with mir-
ror [Hz]
f0 = resonant frequency of platform without
mirror [Hz]
I0 = moment of inertia of platform (see techni-
cal data) [g × mm²]]
IM = moment of inertia of mirror
[g × mm²]
f ' = m f0
1 + IM/I0
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TEC66 Kinematics of Multi-Axis Tip/Tilt Systems 10/2017 Subject to change without notice. © Physik Instrumente (PI) GmbH & Co. KG 2017
© Physik Instrumente (PI) GmbH & Co. KG
All contents, including texts, graphics, data etc., as well as their layout,
are subject to copyright and other protective laws. Any copying, modi-
fication or redistribution in whole or in parts is subject to a written
permission of PI.
Although the information in this document has been compiled with
the greatest care, errors cannot be ruled out completely. Therefore,
we cannot guarantee for the information being complete, correct and
up to date. Illustrations may differ from the original and are not bind-
ing. PI reserves the right to supplement or change the information
provided without prior notice.
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MOTION | POSITIONING
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