To be published in, "Adaptive Optics for Industry and Medicine", Proceedings of the Second
International Workshop on Adaptive Optics for Industry and Medicine. World Scientific. Ed.
Gordon D. Love
MODAL LIQUID CRYSTAL WAVEFRONT CORRECTORS
GORDON D. LOVE AND ALEXANDER F. NAUMOV
Dept. of Physics and School of Engineering, University of Durham, DH1 3LE U.K.
E-mail: g.d.love@durham.ac.uk
MICHAEL Yu. LOKTEV
P.N. Lebedev Physical Institute Samara Branch, Russian Academy of Sciences,
Novo-Sadovaya Street 221, Samara 443011, Russia
IGOR R. GURALNIK,
Samara State University, Acad. Pavlov Street 1, Samara 443011, Russia
GLEB V. VDOVIN
Electronic Instrumentation, TU Delft, P.O. Box 5031, 2600 GA Delft, The Netherlands
Liquid crystal wavefront correctors have traditionally been used as zonal wavefront
correctors, whereby the influence function is usually piston-only over the area defined by the
device pixels. By applying a distributed voltage across the device, a continuous LC cell may
produce modal wavefront deformations. In this paper we will describe the concept of modal
liquid crystal wavefront correctors, review some of the current results.
1
Introduction
Liquid crystal spatial light modulators (LC-SLMs) are an alternative to the
deformable mirror in an adaptive optics system. They are particularly attractive for
non-astronomical applications where low cost, compactness, and low power
consumption may be more important. Their main drawback is their slew rate, which
is much slower than that for a deformable mirror. There are several papers in these
proceedings describing work using LC-SLMs. They modulate optical path length by
refractive index control, instead of real path length adjustment.
Most LC-SLMs are zonal wavefront correctors. In other words, the device is
addressed via electrodes leading to an actuator (or pixel), and the refractive index is
modulated over an area localised to the size of the pixel. The desired wavefront
shape is built up in a series of steps. These devices are analogous to a segmented
mirror, except that in a mirror the influence function is generally tip-tilt-piston, and
in a LC-SLM the influence function is piston-only. See, for example, references
[2,3] for papers on zonal LC-SLMs. Some authors [1] have noted that these
pixelated structures can give rise to diffraction at the pixel boundaries. This is true
for any zonal wavefront corrector, but the fact that the influence function is piston-
1
To be published in, "Adaptive Optics for Industry and Medicine", Proceedings of the Second
International Workshop on Adaptive Optics for Industry and Medicine. World Scientific. Ed.
Gordon D. Love
only means that the fitting error is larger for a LC-SLM than for a deformable
mirror for a given number of actuators.
In this paper we describe how to produce a LC-SLM with a non-local influence
function. Such devices do not have a pixelated electrode structure, and are
analogous to continuous facesheet mirrors. We proceed by describing the simplest
devices, prisms and lenses, and then describe a full modal LC-SLM wavefront
corrector.
2
Liquid crystal prisms
The simplest type of LC device is a LC prism [4]. An approximately linear phase
ramp is produced by using a single LC cell, and applying a voltage ramp along one
of the electrodes, as shown in the following figure 1.
Figure 1. A liquid crystal prism (or beam deflector) produced using a single LC cell. (a) A voltage ramp
is applied along the top electrode so that there is a maximum voltage (typically 10V rms AC) across the
left hand side of the cell, which linearly decreases to 0V across the right hand side. The corresponding
voltage and phase profiles are shown in (b). The phase profile assumes that the phase shift is a linear
function of voltage, which is only approximately true over a limited range of the LC dynamic range.
In the LC prism, the electrical properties of the actual device have been ignored.
This is acceptable, assuming that the applied frequency is relatively small and the
top electrode resistance is relatively small. In this case the voltage simply falls
linearly across the cell.
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LC lens.
It is possible to use the actual electrical properties of the LC cell produce more
complicated voltage profiles across the device [5]. In this case it is necessary to use
a high resistance top electrode, and higher frequency control voltages, as shown in
figures 2 and 3. The LC cell can be modeled similarly to a transmission line,
whereby there is a distributed resistance (the top electrode), and a distributed
2
To be published in, "Adaptive Optics for Industry and Medicine", Proceedings of the Second
International Workshop on Adaptive Optics for Industry and Medicine. World Scientific. Ed.
Gordon D. Love
capacitance and conductance (produced by
the LC layer). The resulting phase and
voltage profile is shown in figure 4.
Figure 2. A LC lens. This is similar to a LC prism,
except that the top electrode needs to be have much
higher resistance (~M), and a AC voltage is applied
to both ends of the top electrode. (b) and (c) show the
geometries necessary to produce a cylindrical and
circular lens respectively
Figure 3. The electrical equivalent of the LC lens
shown in figure 2. Voltage V is applied to either
end. The series of resistors, R, correspond to the
top electrode, and the series of capacitors and
conductances, C and G, correspond to the LC
layer. Note the similarities with a transmission
line.
The voltage profile across the device is
described by the following second order
partial differential equation,
 2V
V
 RGV ,
t
x
where V, is the voltage, R is the sheet
resistance of the top electrode, and C
and G are the capacitance and
conductance per unit length of the LC
Figure 4. Corresponding voltage a phase profile layer. The above equation is for a 1-d
across a LC lens, using the circuit shown in figure
(cylindrical lens). A similar equation
3. In this case a realistic voltage-phase relationship
applies for the 2-d (circular) lens. A full
was used in the calculation.
solution of the equation is complicated
by the fact that both R and G are functions of the voltage, V. The control of a LC
lens is described in more detail in reference [6].
The following analogy can be used to further understand the principle of a
modal LC lens. Imagine a thin rubber membrane on metal ring. If this membrane is
placed in a liquid and the ring vibrates perpendicularly to the membrane surface,
then the resulting membrane oscillations will be larger at the edge than at the centre.
The amplitude and frequency of the forced oscillations determine the profile of the
membrane. The amplitude of the AC voltage across the lens aperture behaves in a
similar fashion.
2
 RC
3
To be published in, "Adaptive Optics for Industry and Medicine", Proceedings of the Second
International Workshop on Adaptive Optics for Industry and Medicine. World Scientific. Ed.
Gordon D. Love
Figure 5 shows a LC lens placed with its optical axis at 45 0 between crossed
polarizers (equivalent to an interferometric arrangement). The focal length, f, can be
calculated using the following equation,
D 2
f 
,
4
where D is the lens diameter,  is the variation in phase from the centre to the edge
of the lens, and  is the wavelength. The focal lengths produced long due to the
finite stroke of the LC cell. Currently achievable f-ratios are from ~100 to .
Figure 6 shows an example of a LC lens producing an image.
Figure 5. Interferograms (produced by placing the device between crossed polarizers) from a spherical
LC lens, for different values of applied voltage (rms) and frequency.
Figure 6. Example of a LC lens producing an image. (Left) lens off, system adjusted to give a good
focus. (Middle) System mechanically adjusted to induced defocus. (Right) LC Lens turn on to correct for
induced defocus.
Figure 7 shows the PSF from a LC lens compared to an ordinary lens.
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To be published in, "Adaptive Optics for Industry and Medicine", Proceedings of the Second
International Workshop on Adaptive Optics for Industry and Medicine. World Scientific. Ed.
Gordon D. Love
Figure 7. PSFs produced by a LC lens by passing a beam of laser light through a lens, followed by a
CCD camera. The left image shows the scale, where each major unit is 1mm, and the sub-units are
100 m.
A LC lens can obviously be used as a variable focal length lens. It can also be
used as a defocus corrector in an adaptive optics system. By carefully controlling
the applied voltages to a modal LC lens it is possible to produce non-parabolic
phase profiles. For example, we have demonstrated the production of controlled
spherical aberration from +3 up to -4 for  = 632.6 nm. Such a device would be
useful for the correction of spherical aberration.
4
A modal LC wavefront corrector.
How can a modal LC device be used to produce more complicated wavefront
shapes? Figure 8 shows a modal LC wavefront corrector [7]. Individual leads are
inserted through holes in the glass substrate, and make contact with a high
resistance continuous electrode. The dielectric mirror reflects light and means the
device works in reflection mode. Each lead corresponds to an actuator. The impulse
function around each actuator can be controlled by adjusting the applied voltage and
frequency. Figure 9 shows an interferogram from the central area of a 16x16
actuator modal LC device.
Figure 8. A modal LC
wavefront corrector. Each of the
addressing leads leading from
the bottom of the device makes
contact with the continuous high
resistance electrode, through the
dielectric mirror. The impulse
function around each lead can be
controlled by altering the applied
voltage and frequency.
5
To be published in, "Adaptive Optics for Industry and Medicine", Proceedings of the Second
International Workshop on Adaptive Optics for Industry and Medicine. World Scientific. Ed.
Gordon D. Love
Figure 9. Interferogram from the central area of a 16x16 actuator modal LC wavefront corrector. The
applied voltage was 5V rms, at frequencies of 1KHz, 10KHz, and 100KHz, respectively.
5
Conclusion
Modal addressing of LC devices allow a continuous phase profile to be produced.
They have the advantage that the fitting error will be less than a pixelated device for
a given number of actuators. This may mean that LC wavefront correctors can be
produced with a very large number of actuators, and with a very high fill factor
(unity), which is difficult to achieve currently.
References
1. Dayton D.C., Browne S.L., Sandven S.P., Gonglewski, J.D., and Kudryashov,
A.V. Theory and laboratory demonstration on the use of a nematic liquidcrystal phase modulator for controlled turbulence generation and adaptive
optics. Appl. Opt. 37 (1998) pp.5579-5589.
2. Dou R., and Giles M.K. Closed-loop adaptive optics system with a liquid
crystal television as a phase retarder. Opt. Lett. 20 (1995) pp.1583-1585.
3. Love G.D., Wavefront correction and production of Zernike modes with a
liquid crystal SLM. Appl. Opt., 36 (1997) pp. 1517-1524.
4. Love G.D. Major J.V., and Purvis, A., Liquid crystal prisms for tip—tilt
adaptive optics, Opt. Lett. 19 (1994) pp.1170-1172.
5. Naumov A.F., Loktev M.Yu., Guralnik I.R., Vdovin, G., Liquid-crystal
adaptive lenses with modal control, Opt. Lett., 23 (1998) pp. 992-994.
6. Naumov A.F.,
Love G.D.,
Loktev M.Yu.,
Vladimirov F.L.,
Control
optimization of spherical modal liquid crystal lenses, Opt.Express, 4 (1999),
pp.344-352.
7. Naumov A.F. Vdovin G.V., Multichannel LC-based wavefront corrector with
modal influence functions. Opt.Lett., 23 (1998) pp. 1550-1552.
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