Joint transform correlator using an amorphous silicon ferroelectric liquid crystal spatial light modulator

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15 April 1990

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JOINT TRANSFORM CORRELATOR USING AN AMORPHOUS LIQUID CRYSTAL SPATIAL LIGHT MODULATOR David A. JARED,

Kristina

M. JOHNSON

SILICON FERROELECTRIC

and Garret MODDEL

University of Colorado, Optoelectronic Computing Systems Center, Boulder, CO 80309, USA Received

5 July 1989; revised manuscript

received

I 1 December

1989

A joint transform correlator is demonstrated that utilizes a high-speed optically addressed spatial light modulator in the Fourier plane consisting of an hydrogenated amorphous silicon photodiode and a ferroelectric liquid crystal modulator. Results are shown for binary-amplitude modulation using a smectic C* ferroelectric liquid crystal operating at 4600 frame/s, 20: 1 contrast ratio, and 70 lp/mm.

1. Introduction Joint transform correlators [ 1 ] (JTCs) have several features that make them an attractive optical pattern recognition architecture: (i) they are relatively insensitive to optical alignment errors as compared with other Fourier based correlators; (ii) a complex-valued spatial-light-modulator is not required in the Fourier plane; (iii) a priori knowledge of the reference image is not necessary; and (iv) JTCs can be compactly designed. Optical joint transform correlators have been demonstrated with a variety of opto-electronic devices [2-71. In this paper, experimental results of a JTC are described that utilizes a high-speed, optical addressed spatial-light-modulator in the Fourier plane consisting of an amorphous silicon photosensor and a ferroelectric liquid crystal modulator [ 8,9]. 2. Theory of joint transform correlation Consider two images,f(x+x,, y) andg(x-x0, y), in the geometry shown in fig. la. The intensity of the Fourier transform of the two images is I(u, tl) = I ~-lf(x+xo, Y) +g(x--xck Y) 1 I2

= IF(u, v)+G(u,

v)l’

=F(u,

u)F*(u,

+F(u,

v)G*(u, u)+G(u,

0030-401 S/90/$03.50

u)+G(u,

v)G*(u, v) v)F*(u,

v) ,

0 Elsevier Science Publishers

(1)

W

1 Fig. I. The input plane of a JTC (a) consist of two images f (x, y) and g(x, y) shifted by *x0. The output plane (b) consist of three regions: the central region contains the overlapping autocorrelations of the two images; the side regions contain the crosscorrelation between the two images.

where 9 is the Fourier transform operator and capital letters denote the Fourier transform of a function. The output of the joint transform correlator, c(x, y), is given by performing a Fourier transform on the intensity distribution of eq. ( 1 ),

B.V. (North-Holland

)

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c,(.v. j’ )

Write Beam

= F[F(u.

z~)F*(u.

z’)]+-F[G(u.

+.F[F(u.

z?)G*(u, z’)]+.F[G(u.

r,)G*(u, r)] c)F*(u,

P)]

(2) Since images are shifted +.Y,,. the Fourier transforms of the images are

Ci( u. 1’) = G,( u. 11)exp( - 2ni.\;,) .

(3)

where Fc( II, rt) and G,( II. r,) are the Fourier transforms of the unshifted images ( i.e., F, ( u, u) = T//‘( .v, y) ] ). Substituting eq. (3) into eq. (2), gives the following expression for the output of the correlator. c,(.\-, j’) =.r‘(s. j’) *,/Is. j%)+‘y(.\‘. .r) *g(.\-. j’) +,f(s+2so,

j,) *,y(_\-.J’)+1’(.\--2.r,,.

J’)*I:(-Y. j‘) (4)

where * denotes correlation. The output plane geometry of the joint transform correlator is readily given by eq. (4). The output plane is divided into three regions as shown in fig. 1b. The central region corresponds to the first two terms in eq. (4) and contains the overlapping autocorrelations of,f( .y. j,) and R( .Y.j>). The side regions correspond to the last two terms in eq. (4) and contains the cross-correlations of ,f(_u. y) and g(.u. j’). Two-dimensional functions can be correlated with each other using this method. In the optical experiment discussed in this paper, an optically addressed spatial-light-modulator in the Fourier plane is used to produce the intensity distribution.

3. Optically-addressed

spatial light modulator

The structure of the OASLM is shown in fig. 2. The device consists of an hydrogenated amorphous silicon (a-Si : H) photosensor and a FLC modulator. The device is fabricated by depositing a PIN a-Si : H photodiode on a sheet of soda lime glass coated with a transparent conductive oxide (TCO ). The P-layer is boron-doped, and the N-layer is phosphorus-doped. .4 smectic C* FLC (SCE9) [lo] is sandwiched between the a-Si : H thin film and another sheet of TCO coated glass. A rubbed polymer is used on both sub98

G’ass +---I-Read Beam

Fig. 7. Layered modulator.

structure

of the

opucall) addressed

spatial

Ilght

strates to orient the FLC in the [h’- ((1”() I’] surface-stabilized state [ I I 1. The tilt angle of the FLC‘ used is approximately 22.5 This results in a 45 rotation of the optic axis between the two stable states. The thickness of the device was I .7 um. This produced a switchable half-wave plate at the readbeam wavelength of 633 nm. The active area of the device is a 1.27 cm diameter circle. The OASLM exhibits a response time of I55 us. a contrast ratio of 20: 1 and a resolution of 70 lp/mm [9]. The a-Si : H photodiode converts an optical image on the write-beam to a spatially varying electric field across the FLC. The varying electric field induces a spatially varying change in the FLC optic axis. The optical axis is switched between two stable orientations producing a binary-amplitude or binary-phase modulated image depending upon the orientation of the device, polarization state of the read-beam. and the orientation of the analyzing polarizer. The surface-stabilized FLC is switched between stable states by applying an electric field above a given threshold. An electric field of approximately 10 V/urn is needed to switch the FLC. A discussion of the physics of switching surface-stabilized FLCs can be found in refs. [ 11,121. The large refractive index difference of 2.5 at the FLC/a-Si: H interface is used to reflect approximately 20% of the read-beam. The read-beam is amplitude modulated in this study. The intensity of the read-beam is approximately 5 uW/cm’. An AC voltage is applied across the device to bias the photodiode and to erase the recorded image. The 4C voltage is a 4.6 kHz square-wave at +2OV and - 15V

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with a 50% duty cycle. This is well within the response time of the FLC, and provides a short integration period for the photoreceptor. The optical and switching characteristics of the device are discussed in detail in refs. [ 8,9,13 1. 3.1. Binary interferograms Smectic C* FLC modulators are bistable. Depending upon the optical arrangement used, the device can produce a binary-amplitude or binary-phase modulated image. In the JTC, the spatial pattern read from the OASLM will be a binary-threshold version of the actual power spectra. As a result, the output of the JTC will not be a true correlation because of the nonlinearity of the device. The performance of JTCs with threshold nonlinear in the Fourier plane has been discussed by Javidi [ 3,4,14]. The effect of threshold nonlinearities in the Fourier plane on the correlation output is basically similar to those seen with binary-phase-only matched-spatial-filters. The correlation peaks tend to be well localized with a high signal-to-clutter ratio [ 3,4]. However, the response is more sensitive to distortions between the input and reference images and more noise sensitive than conventional matched-spatial-filters [ 15- 18 1.

4. Experiment The optical arrangement of the joint transform correlator used is shown in fig. 3. An argon-ion laser (A= 5 14 nm) is spatially filtered into a slightly di-

verging beam. A diverging beam is used to increase the scale of the Fourier transform to better accommodate the spatial resolution of the OASLM. The beam is passed through a photographic transparency containing the input and reference images. The images are approximately 3 mm x 3 mm with a 0.25 mm spacing between them. The input images are binaryamplitude modulated. A Fourier transform lens cf= 500 mm) is placed as close as possible to the transparency. The quadratic phase term that results from not having the transparency at the focal point does not affect the performance of the correlator since the intensity of the Fourier transform is only of interest. The OASLM is used to record the power spectra of the interfering Fourier transforms. Collimated light from a HeNe laser (,I=633 nm) is used as the read-beam. The intensity of the read-beam is approximately 1 pW/cm2 over the aperture of the OASLM. The reflected read-beam is amplitude modulated by passing it through a polarizing beam-splitter. A second Fourier transform lens u=500 mm) is placed as close as possible to the polarizing beamsplitter. A Fairchild CCD video camera and a Sony video monitor is used to view the correlation plane. A photograph of the output plane showing the autocorrelation of an object is shown in fig. 4a. The output plane for a multiple object recognition problem is shown in fig. 4b. As discussed previously, the central region corresponds to the autocorrelation between the two images, and the regions to the right and left of the central region corresponds to the crosscorrelation between the input and reference images.

HeNe laser

polarizinb beam-splitter

Fig. 3. Optical arrangement

of the joint transform

correlator.

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r

-v-

Fig. 4. Photographs of the images on the Input transparency and the corresponding (a) an autocorrelation and (b) a multi-object recognition task.

5. Discussion

The correlation peaks are visible in both cases. The line that passes through the central region is caused by diffraction off the rubbed polymer used to align the FLC and the zig-zag domain walls in the FLC. The dynamic range of the photoreceptor is 0.4 mW/cm’ to 100 mW/cm’ (i.e., z-three orders-of100

correlation

plane output

from the video mon!tor

fat

magnitude). The dynamic range is determined by the minimum write-beam intensity required to switch the FLC and the maximum write-beam intensity that will not permanently degrade the optical properties of the a-Si : H layer. Depending upon the images used in the recognition problem. the intensity of the Fourier transform can vary over four orders-of-magnitude. This results in only a small region of the FLC

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Fig. 4. (continued).

being modulated. The intensity of the low-frequency components of most Fourier transforms tend to be much larger than the high-frequency components. Thus, the dynamic range of the OASLM tends to produce a low-pass filter that only utilizes the lowfrequency information for pattern recognition. The dynamic range of the Fourier transform can be effectively reduced by using a high-pass aperture stop in the Fourier plane, or by using a random phase plate

immediately after the input transparency. Though a random phase plate will generate a more uniform Fourier transform, the correlator would be shift variant. The limited dynamic range of the OASLM also causes the intensity of the correlation plane to be dependent upon the energy of the input and reference images. Thus, the post-processing algorithm used to analyze the correlation plane must be intensity invariant. 101

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A programmable SLM and/or an optical disk can be used to rapidly input images into the JTC. .4n optical disk correlator with 3000 frames/s has been reported [ 19 1. Such a design could take advantage of the 4600 frames/s rate of the OASLM. However. new correlation plane detection and analysis techniques that can cope with these data rates need to be pursued before real-time. practical systems can be realized using JTCs.

References

[ I ] G.S. Weaver and J.W. Goodman. 1248.

[ 21M.C‘. Hamilton

and B.L. Powers. Optics Lctt. I? (19x7) 549. [ 31 B. Javidi and C.J. Kuo. .Appl. Optics 27 ( IUXX)663. [4] B. Javidi and S.F. Odch. Optical Engineering

A joint transform correlator is demonstrated that utilizes an optically addressed spatial light modulator (OASLM) in the Fourier planes. The OASLM consists of an hydrogenated amorphous silicon photodiode and a ferroelectric liquid crystal modulator. The OASLM allows the joint transform correlator to operate at 4600 frames/s with a contrast ratio of 20: I, and a spatial resolution if 70 lp/mm. Results are shown for binary-amplitude modulation using a smectic c‘* ferroelectric liquid crystal.

Acknowledgements Discussions with Mark Freeman are gratefully appreciated. This work is supported under NSF/ERC grant CDR862228.

27

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[j] J.M. Florence. (Optics Lett. 14 ( 1989) 341. [h] F.T.S. Yuand

6. Conclusions

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