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Optical correlation by use of partial phase-only
modulation with VGA liquid-crystal displays
Ignasi Labastida, Arturo Carnicer, Estela Martı´n-Badosa, Santiago Vallmitjana, and
Ignacio Juvells
The development of liquid-crystal panels for use in commercial equipment has been aimed at improving
the pixel resolution and the display efficiency. These improvements have led to a reduction in the
thickness of such devices, among other outcomes, that involves a loss in phase modulation. We propose
a modification of the classical phase-only filter to permit displays in VGA liquid-crystal panels with a
constant amplitude modulation and less than a 2 phase modulation. The method was tested experi-
mentally in an optical setup. © 2000 Optical Society of America
OCIS codes: 200.4740, 100.4550, 120.5060, 230.3720.
1. Introduction
Liquid-crystal displays 共LCD’s兲 that have been re-
moved from commercial video projectors are com-
monly used as spatial light modulators in hybrid
optoelectronic setups for optical correlation.
1,2
The
development of these liquid-crystal panels has fo-
cused on increasing their pixel resolution through a
reduction in the panels’ thickness and in their pixel
pitch. For optical setup design purposes the pixel-
pitch decrease is an advantage because it involves a
reduction in the total length of the setup. However,
some such devices are not thick enough to achieve a
phase modulation of 2 rad.
To display a phase-only filter 共POF兲 on LCD’s, we
demonstrate that the same correlation results can be
obtained if the absolute value of the phase is taken.
For that purpose, we require an operating curve with
a constant amplitude modulation and at least a -rad
phase modulation when the maximum number of
gray levels available is used. Other authors have
tried to overcome the limited phase modulation of the
LCD by means of different approaches, e.g., changing
the operating wavelength of the setup
3
or using a
double-pass configuration.
4
We used two LCD’s removed from a commercial
VGA video projector. With these devices, we did not
obtain the desired configuration with linearly polar-
ized light. But, as was pointed out in Refs. 5–7, we
achieved a suitable operating curve with elliptically
polarized light. We built a converging VanderLugt
correlator with two LCD’s to validate the method.
Optical correlations were obtained with the modified
POF displayed on a LCD in an elliptically polarized
light configuration.
2. Liquid-Crystal Display Characterization
The characterization of the liquid-crystal panels is
focused mainly on the way in which these devices
modulate light, depending on the gray level assigned
to each pixel. Generally, amplitude and phase mod-
ulation are coupled in the sense that both the ampli-
tude and the phase of light passing through spatial
light modulators are modified. However, it is possi-
ble to find some operational conditions under which
one characteristic remains mainly constant, whereas
the other one changes considerably. These are
called the amplitude-mostly configuration and the
phase-mostly 共PM兲 configuration,
6,8
respectively.
There is also a third configuration that often is used
because of its high values of contrast: the high-
contrast 共HC兲 configuration.
6
Although it intro-
duces an important phase modulation, the contrast
ratio is much higher than that obtained by use of an
amplitude-mostly mode. On the other hand, using a
PM configuration with a high constant transmittance
maximizes the light efficiency of the optical arrange-
ment because light absorption is minimal.
When placing a LCD between two polarizers dif-
The authors are with the Departament de Fı´sica Aplicada i
O
`
ptica, Universitat de Barcelona, Avinguda Diagonal 647, E08028
Barcelona, Spain. I. Labastida’s e-mail address is nasi@optica.
ub.es.
Received 10 May 1999; revised manuscript received 2 August
1999.
0003-6935兾00兾050766-04$15.00兾0
© 2000 Optical Society of America
766 APPLIED OPTICS 兾 Vol. 39, No. 5 兾 10 February 2000
ferent configurations can be obtained, depending on
the voltage applied and the orientation angles of the
polarizers. The voltage applied depends on the gray
level assigned to each pixel and on the position of the
potentiometer controls, which regulate brightness,
contrast, and color, of the video projector. These
controls have to be set in a compromise position when
a single video projector addresses two LCD’s, and the
curve search has to be carried out by rotation of the
polarizers. This limitation reduces the acquisition
of different operating curves.
In our study two LCD’s that were removed from a
commercially available VGA Epson video projector
共Model EMP-3000兲 were characterized to find a HC
configuration for the input device and a PM one for
the filter. The characterization consists of deter-
mining how the LCD modulates the amplitude and
the phase of the light. The amplitude modulation is
the square root of the ratio between the intensities
before and after the light passes through the panel.
The phase modulation is obtained with an interfero-
metric procedure that is based on the measurement
of the relative phase shift between several pairs of
gray values displayed on the LCD when it is placed in
one arm of a Mach–Zehnder interferometer.
5,9
We show two interesting resultant configurations:
The first 共Fig. 1兲 corresponds to a HC mode in which
the device transmittance 共amplitude squared兲 in-
creases with the gray level and reaches a normalized
maximum value of 1 for a gray level of 255. The
contrast of the modulator is approximately 125:1,
which is high enough to display the input image.
The second 共Fig. 2兲 exhibits the best PM operating
curve. It is not advisable to use configuration 2 to
display a POF for several reasons: 共i兲 The phase
modulation reaches only 1.6 rad. 共ii兲 The ampli-
tude modulation is not constant 共the minimum value
of the amplitude modulation is approximately 43% of
the maximum amplitude obtained兲. 共iii兲 If we use
only the 关0–兴 range, the transmittance is too low to
yield good correlation results, and we lose bandwidth
共104 gray levels兲.
Both curves 共Figs. 1 and 2兲 were obtained by use of
linearly polarized light at the input and the output of
the LCD’s. Nevertheless, if we use elliptically polar-
ized light instead it is possible to achieve a configu-
ration with just phase modulation.
5
To obtain a suitable phase-only configuration with
elliptically polarized light, we have to substitute the
two linear polarizers that are at the input and the
output sides of the LCD by two pairs of linear polar-
izers plus a 兾4 plate. The fast axes of these plates
must be oriented parallel to the corresponding mo-
lecular directors at each side of the panel. The input
polarizer has to be rotated by an angle from the fast
axis of the input plate, whereas the output polarizer
must be oriented at an angle ⫺ relative to the fast
axis of the output plate.
7
For such conditions, we found an angle of ⫽35°
for which the operating curve 共Fig. 3兲 makes use of
the 256 gray levels available, producing phase mod-
ulation and a constant transmittance. Although
with this operational mode the phase modulation
reaches only rad, we show in Section 3 a way to
overcome this drawback for correlation purposes.
3. Implementation of Phase-Only Filters with 关0–兴
Modulation
We observed that our devices can operate in a phase-
only modulation configuration in the range 关0–兴
with constant amplitude and by use of the entire
dynamic range of the image. For such conditions,
we show that it is possible to achieve the same cor-
relations as were obtained with an ordinary POF.
10
However, with this 关0–兴 curve it would be possible to
implement binary masks by use of the points that
correspond to the 0 and the modulations. Let
h共x, y兲 be the reference to detect, and let H共u, v兲⫽
Fig. 1. HC operating curve. Re, real; Im, imaginary.
Fig. 2. Phase-mostly operating curve.
10 February 2000 兾 Vol. 39, No. 5 兾 APPLIED OPTICS 767
兩H共u, v兲兩exp关⫺i共u, v兲兴 be its Fourier transform.
The POF is defined as H
POF
共u, v兲⫽exp关⫺i共u, v兲兴.
We then introduce the phase-only filter 共-POF兲 as
H
-POF
共u, v兲 ⫽ exp关⫺i兩共u, v兲兩兴
⫽ cos关共u, v兲兴 ⫺ i兩sin关共u, v兲兴兩, (1)
The function f 共x兲⫽兩sin共x兲兩 can be written as a Fou-
rier series, as follows:
兩sin共x兲兩 ⫽
2
⫺
4
冋
1
3
cos共2x兲 ⫹
1
15
cos共4x兲
⫹
1
35
cos共6x兲 ⫹ ...
册
, (2)
and therefore the phase codified in the filter can be
written as
exp关⫺i兩共u, v兲兩兴 ⫽ cos关共u, v兲兴 ⫺
2i
⫹
4i
3
⫻ cos关2共u, v兲兴 ⫹ .... (3)
To avoid the diffraction of all the terms superimposed
on the zero order, we introduce a linear phase shift
into the expression for the filter:
exp关⫺i兩共u, v兲 ⫹ 2au兩兴
⫽ cos关共u, v兲 ⫹ 2au兴 ⫺
2i
⫹
4i
3
⫻ cos关2共u, v兲 ⫹ 2共2a兲u兴 ⫹ .... (4)
By analyzing Eq. 共4兲, we can obtain information about
the filter reconstruction. Using the -POF, we have
an on-axis constant term, and symmetrically ar-
ranged from it at a distance of x ⫽⫾a are the phase-
only reconstructions of the reference. These images
have conjugated phases. There are also higher-
order harmonics with decreasing energy at the points
x ⫽⫾2a, ⫾4a, ⫾6a, . . . . Therefore it is expected
that we will find the correlation and the convolution
between the scene and the target situated symmet-
rically from the reconstruction of the scene.
4. Optical Results
To test our method experimentally, we built an opti-
cal setup that is based on the converging VanderLugt
correlator, which is a modification of the classical 4f
architecture,
11
because of its versatility in modifying
the scale of the Fourier transform without a change
in either the lenses or the distances between them.
Two LCD’s are used to display the images: one at
the input plane and the other at the Fourier plane.
Fig. 3. LCD 关0–兴 phase-only modulation operating curve.
Fig. 4. Correlation between the scene and the smallest satellite.
768 APPLIED OPTICS 兾 Vol. 39, No. 5 兾 10 February 2000
A VGA card stores a 24-bit red–green–blue image of
640 ⫻ 480 pixels. The red and the blue channels
yield the information corresponding to the filter and
the scene, respectively, whereas the green channel
remains at zero. The VGA card is connected to the
video projector, and the signals are sent to the red
and the blue panels.
The input image used in the experiments com-
prises three satellites of different sizes. The original
scene is 512 ⫻ 512 pixels and 8 bits兾pixel 共256 gray
levels兲. By adding zero-valued points and losing
some rows, we have an image displayed on the LCD
that is 640 ⫻ 480 pixels to adapt its size to the VGA
resolution. On the right-hand side of Fig. 4, we
show the significant area of the scene. The input
image is displayed on the first LCD in the HC con-
figuration, whereas the filter is displayed on the sec-
ond LCD with the 关0–兴 phase-only modulation
operating curve.
The -POF of the target was computed with the
phase introduced to the scene by the HC configura-
tion of the first LCD taken into account. Figure 4
shows the optical correlation between the scene and
the smallest satellite by use of the -POF matched to
it.
5. Conclusions
We have proposed a method for displaying a POF on
a LCD with a less than 2-rad phase modulation.
By using elliptically polarized light, we have achieved
a configuration with constant amplitude modulation
and rad in phase modulation. We have designed a
filter to be displayed in that configuration to obtain
the same correlation results that would be obtained
with the classical POF. Experimental results have
been obtained in a converging VanderLugt correlator
that verify the method.
This study was supported by the CICYT 共Comisio´n
Interministerial de Ciencia y Tecnologı´a兲 under
project TAP97-0454.
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