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Liquid Crystal Spatial Light Modulators in Optical
Metrology
(Invited Paper)
Claas Falldorf, Christoph von Kopylow,
and Ralf B. Bergmann
BIAS - Bremer Institut f¨
ur
Angewandte Strahltechnik GmbH
Klagenfurter Str.2
28359 Bremen, Germany
Email: falldorf@bias.de
Abstract—We provide an overview over recent applications
of electronically adressed liquid crystal spatial light modulators
(SLM) in the field of optical metrology. Three particular examples
are considered: A shear interferometer, a setup for phase retrieval
from a set of intensity measurements and a digital holographic
sensor which allows for the electronic adaption of the reference
wave.
I. INTRODUCTION
Liquid crystal spatial light modulators are electro-optical
devices which can change the lateral distribution of their
complex transmittance depending on either electrical [1] or
optical [2] external signals. Throughout this publication we
will focus on electrically addressed ones, which are organized
in a rectangular grid of individual liquid crystal cells, i.e. their
structure is comparable to that of a CCD camera. What adds to
the benefits of SLMs is their birefringence, i.e. the refractive
index of each individual cell can be controlled along the slow
axis, whereas the refractive index of the respective fast axis
remains unchanged at all. Due to this property, SLMs can be
used to manipulate either solely the lateral phase distribution
of the incident light [3] or phase coupled with intensity [4] by
adding a polarizer for example.
SLMs have originally been designed as inexpensive display
devices for commercial applications, such as rear projection
television systems, front projection home theaters or head
mounted devices for gaming. However, throughout the past
decades a number of groups started to use them as tools for
scientific purposes. Whereas early applications were mostly
focused on optical processing [5], [6], holographic projection
[7] and adaptive optics [8], [9], currently a limited, yet
growing number of developments is to be observed in the field
of optical metrology. Here, the main benefits of employing
SLMs are apparent: They offer a high degree of flexibility,
fast switching times and good reproducibility. Even better,
all these advantages come along without the requirement of
mechanically moving parts.
Perhaps the most common practical applications in op-
tical metrology are systems for fringe projection and optical
tweezing in microscopy [10]. Yet, the technical progress of
available devices in the past decade has led to a number of new
approaches in fields such as comparative digital holography
[11], microscopy [12], shear interferometry [13], [14], wave
front sensing [15], and phase retrieval [16].
Throughout the following sections, we present three partic-
ular examples on how liquid crystal SLMs may be employed
to improve already existing techniques in optical metrology
with regard to robustness, measurement time and flexibility.
II. EXAMPLES OF AP PLI CATI ON
A. Shear Interferometer
The shear interferometer illustrated by Fig. 1 is arranged in
a classical 4f-configuration. It images any wave field incident
in the input plane {~u}across the sensor domain {~x}and
takes advantage of the birefringence of the reflective liquid
crystal SLM in the corresponding Fourier domain {~v}[17].
To describe its functionality, let us assume that the incident
wave field is linearly polarized and that the half wave plate
is adjusted to set the state of polarization to 45◦with respect
to the fast axis of the SLM. In this case, it is convenient and
means no loss of generality to regard the incident light as
being composed of two orthogonally and linearly polarized
wave fields, where the individual polarization states coincide
with the birefringent axes of the device. By passing the SLM
the phase of the wave field being incident on the slow axis will
be shifted by ∆φ(~v)according to the electrically addressed
distribution, whereas the phase of the wave field corresponding
to the fast axis will remain unchanged.
Consider for example the special case of a blaze grating
being generated by the modulator, where the corresponding
phase distribution is given by ∆φB= 2π~g ·~v and ~g is the
grating vector. In this situation, one of the wave fields will
be diffracted by the grating and one will be reflected by the
modulator. Thus, after being transformed into the plane of
the sensor, the wave fields share the same complex amplitude
U(~x)but will be separated by a lateral shift ~s =λf~g, where
fis the focal length of the lenses and λis the wavelength of
the light. To observe interference, the analyzer is adjusted to
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Fig. 1. 4f-configuration with an SLM in the corresponding Fourier domain.
45◦with respect to the fast axis of the SLM. The intensity
distribution IS(~x) = |U(~x) + U(~x +~s)|2of the resulting
interference pattern in the sensor plane equals that of a shear
interferometer with the shear given by ~s. In this configuration
both, direction and magnitude of the shear can be selected
respectively by the grating vector ~g of the blaze grating.
The great benefit of this approach is that it offers a high
degree of flexibility, reproducibility and robustness without the
need for mechanically moving parts. In addition, phase shifting
techniques may be applied by changing the global phase of the
displayed blaze grating for consecutive measurements. Hence,
no particular phase shifting device is required.
Figure 2a shows a commercially available system based on
the presented configuration which was developed by BIAS.
Figure 2b depicts a typical result from the field of non
destructive testing. A bonded panel made from carbon fibre
laminate has been investigated from the flat frontside by means
of thermal loading. The figure shows the corresponding phase
difference in units of radians. The aim of the measurement
was to screen out potential detachments on the corresponding
backside which is shown by the embedded figure.
B. Phase Retrieval
The 4f-arrangement depicted by Fig. 1 can be further
employed to realize phase retrieval from a set of intensity
measurements, if the half wave plate and the polarizer are
removed and the light incident in the input plane ~u is assumed
to be linearly polarized in the direction of the slow axis of
the SLM. In this case, the SLM may be used to modulate
the light in the Fourier domain with the transfer function of
propagation. Thus a sequence of intensity distributions of the
same wave field in various propagation states can be captured
across a common sensor plane without the requirement of any
mechanical alignment throughout the measurement process.
The acquired intensities can be subjected to well established,
iterative phase retrieval algorithms in order to recover the
lateral phase distribution of the investigated wave field [18].
In comparison to the state of art, the camera sensor is not
mechanically shifted. Therefore, this approach significantly
reduces the measurement time to less than a second and
consequently allows for the investigation of quasi static scenes.
Experimental results are given by Fig. 3. A speckle field was
Fig. 2. a) Shear interferometer and b) obtained results indicate no detachment.
generated by means of a diffuser in the input plane of the 4f-
configuration. The size of the speckle effect was adjusted using
an aperture in the Fourier domain. Ten intensity distributions
have been acquired in order to retrieve the resulting phase
distribution shown by Fig. 3a. To compare the results, the wave
field in the sensor domain was superposed by a reference wave
and standard interferometric techniques were used to obtain
the phase as well. The difference between the measured results
is given by Fig. 3b in units of radians and indicates great
agreement with a standard deviation of only σ= 2.2%.
C. Virtual Lensless Fourier Holography
The digital holographic sensor presented by Fig. 4 was
developed within the frame of the EU project Real 3D.
The reference wave emerges from a fibre tip and can be
manipulated by means of the SLM, which is used to maintain
the regime of lensless Fourier holography for various object
positions. In lensless Fourier holography, the reference wave
is configured to emerge from a plane directly in front of the
object. The advantages of that scheme are that the band of the
recorded signal is minimized and a simple Fourier transform
reconstructs the object in focus [19].
As a proof of principle, two holograms of a set of
Lego R
bricks have been captured with the SLM generating
different complex transmittances. The distance between the
scene and the sensor was 231mm, while the distance between
the fibre tip and the camera sensor was 176mm. Therefore,
by default the sensor is not in lensless Fourier configuration.
In Fig. 5a the modulus of the Fourier transform of the
first hologram is shown. While capturing this hologram, the
Fig. 3. a) Result obtained by phase retrieval, b) comparison to interferometry.
Fig. 4. Digital holographic sensor with adaptive reference wave (left: photo
of the system; right: corresponding layout).
complex transmittance generated by the SLM was set to a
constant, i.e. apart from its phase shifting capabilities the SLM
acted as a simple mirror. Consequently, the reconstructed scene
is seriously blurred and parts of the blurred objects appear as
aliased frequencies at the right border. In Fig. 5b the modulus
of the Fourier transform of the second recorded hologram is
shown. In this case, the SLM was programmed to generate a
chirp like complex transmittance of which the central part is
depicted by the embedded figure. Yet, the scene appears to
be in focus, indicating that the system is in lensless Fourier
configuration. Furthermore, adding a blazed grating to the
chirp like distribution will adapt the sensor to lateral shifts
of the object as well. The result of this approach may be
best described by the idea of a virtual source point in the
reconstruction volume which can be shifted around in space.
III. CONCLUSION
We have shown that liquid crystal SLMs are valuable tools
in the field of optical metrology. The main benefit associated
with these devices is their high degree of flexibility, which
comes along without the requirement of moving parts. Yet, a
number of potential applications may be restricted by the small
space-bandwidth product associated with currently available
systems. However, by extrapolating the technical progress of
the past decade, it is expected that in a few years SLMs
could be employed as dynamic computer generated holograms
(CGH). This will even increase their relevance for optical
Fig. 5. Fourier transform (modulus) of a hologram captured a) with and b)
without adapted reference wave (inset: phase distribution of the SLM).
metrology by enabling their application to fields typical for
CGH, such as aspheric lens testing.
ACK NOWL ED GME NT
We thank T. Meeser, M. Agour, R. Klattenhoff and E.
Kamau for support with the experiments. Furthermore, we are
grateful to the Deutsche Forschungsgemeinschaft (DFG) for
supporting this work within project B5 of the collaborative
research center SFB 747 and project WeSer. This research
received funding from the ECs 7th Framework Programme
FP7/20072013 under grant agreement no. 216105 (Real3D).
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