Abstract

Each pixel of a spatial light modulator (SLM) consists of a phase- or amplitude-modulating area (the active zone) within an inactive area (the dead zone). Here we study optical correlators that contain input and filter SLM’s whose dead zones are opaque. Computer simulations and analytical calculations are carried out for these correlators when a phase-only, a binary phase-only, or a classical matched filter is written on the filter SLM. The correlation signal-to-noise ratio for a particular filter is independent of a dead zone since its energy throughput is proportional to its peak correlation intensity.

© 1992 Optical Society of America

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References

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  1. B. Javidi, D. Gregory, J. L. Horner, “Single modulator joint transform correlator architectures,” Appl. Opt. 28, 411–413 (1989).
  2. B. Javidi, J. L. Horner, “Single spatial light modulator joint transform correlator,” Appl. Opt. 28, 1027–1032 (1989).
  3. P. D. Gianino, J. L. Horner, C. L. Woods, “Effects of SLM transmissive dead zones on optical correlation,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed. Proc. Soc. Photo-Opt. Instrum. Eng.1347, 240–246 (1990).
  4. D. Psaltis, E. Paek, S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).
  5. J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization on the output of the joint Fourier transform correlator,” in Spatial Light Modulators and Their Applications, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990) pp. 16–19; Opt. Eng. 29, 1094–1100 (1990).
  6. G. Gheen, E. Washwell, D. Armitage, “The effect of filter pixellation on optical correlation,” in Spatial Light Modulators and Their Applications, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 161–164.
  7. A. Vanderlugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  8. J. Horner, C. Makekau, “Two-focal-length optical correlator,” Appl. Opt. 28, 5199–5201 (1989).
  9. M. Flavin, J. Horner, “Correlation experiments with a binary phase-only filter implemented on a quartz substrate,” Opt. Eng. 28, 470–473 (1989).
  10. H. J. Caulfield, “Role of the Horner efficiency in the optimization of spatial filters for optical pattern recognition,” Appl. Opt. 21, 4391–4392 (1982).

1989 (4)

1984 (1)

D. Psaltis, E. Paek, S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

1982 (1)

1964 (1)

A. Vanderlugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Armitage, D.

G. Gheen, E. Washwell, D. Armitage, “The effect of filter pixellation on optical correlation,” in Spatial Light Modulators and Their Applications, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 161–164.

Bunch, R. M.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization on the output of the joint Fourier transform correlator,” in Spatial Light Modulators and Their Applications, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990) pp. 16–19; Opt. Eng. 29, 1094–1100 (1990).

Caulfield, H. J.

Cottrell, D. M.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization on the output of the joint Fourier transform correlator,” in Spatial Light Modulators and Their Applications, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990) pp. 16–19; Opt. Eng. 29, 1094–1100 (1990).

Davis, J. A.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization on the output of the joint Fourier transform correlator,” in Spatial Light Modulators and Their Applications, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990) pp. 16–19; Opt. Eng. 29, 1094–1100 (1990).

Flavin, M.

M. Flavin, J. Horner, “Correlation experiments with a binary phase-only filter implemented on a quartz substrate,” Opt. Eng. 28, 470–473 (1989).

Gheen, G.

G. Gheen, E. Washwell, D. Armitage, “The effect of filter pixellation on optical correlation,” in Spatial Light Modulators and Their Applications, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 161–164.

Gianino, P. D.

P. D. Gianino, J. L. Horner, C. L. Woods, “Effects of SLM transmissive dead zones on optical correlation,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed. Proc. Soc. Photo-Opt. Instrum. Eng.1347, 240–246 (1990).

Gregory, D.

Horner, J.

M. Flavin, J. Horner, “Correlation experiments with a binary phase-only filter implemented on a quartz substrate,” Opt. Eng. 28, 470–473 (1989).

J. Horner, C. Makekau, “Two-focal-length optical correlator,” Appl. Opt. 28, 5199–5201 (1989).

Horner, J. L.

B. Javidi, D. Gregory, J. L. Horner, “Single modulator joint transform correlator architectures,” Appl. Opt. 28, 411–413 (1989).

B. Javidi, J. L. Horner, “Single spatial light modulator joint transform correlator,” Appl. Opt. 28, 1027–1032 (1989).

P. D. Gianino, J. L. Horner, C. L. Woods, “Effects of SLM transmissive dead zones on optical correlation,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed. Proc. Soc. Photo-Opt. Instrum. Eng.1347, 240–246 (1990).

Javidi, B.

Makekau, C.

Merrill, E. A.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization on the output of the joint Fourier transform correlator,” in Spatial Light Modulators and Their Applications, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990) pp. 16–19; Opt. Eng. 29, 1094–1100 (1990).

Paek, E.

D. Psaltis, E. Paek, S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

Psaltis, D.

D. Psaltis, E. Paek, S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

Vanderlugt, A.

A. Vanderlugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Venkatesh, S.

D. Psaltis, E. Paek, S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

Washwell, E.

G. Gheen, E. Washwell, D. Armitage, “The effect of filter pixellation on optical correlation,” in Spatial Light Modulators and Their Applications, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 161–164.

Woods, C. L.

P. D. Gianino, J. L. Horner, C. L. Woods, “Effects of SLM transmissive dead zones on optical correlation,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed. Proc. Soc. Photo-Opt. Instrum. Eng.1347, 240–246 (1990).

Appl. Opt. (4)

IEEE Trans. Inf. Theory (1)

A. Vanderlugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Opt. Eng. (2)

M. Flavin, J. Horner, “Correlation experiments with a binary phase-only filter implemented on a quartz substrate,” Opt. Eng. 28, 470–473 (1989).

D. Psaltis, E. Paek, S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

Other (3)

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization on the output of the joint Fourier transform correlator,” in Spatial Light Modulators and Their Applications, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990) pp. 16–19; Opt. Eng. 29, 1094–1100 (1990).

G. Gheen, E. Washwell, D. Armitage, “The effect of filter pixellation on optical correlation,” in Spatial Light Modulators and Their Applications, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 161–164.

P. D. Gianino, J. L. Horner, C. L. Woods, “Effects of SLM transmissive dead zones on optical correlation,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed. Proc. Soc. Photo-Opt. Instrum. Eng.1347, 240–246 (1990).

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Figures (11)

Fig. 1
Fig. 1

An example of how dead zone points (Z′) are filled in for an array of 16 sample points (N = 4). These arrays are considered to have dead zone areas, which are given by (Z′/N2) × 100% of (a) 12.5%, (b) 37.5%, (c) 56.3%, (d) 68.8%, (e) 81.3%. X indicates zeros, and ● are nonzeros.

Fig. 2
Fig. 2

Block diagram showing the sequence of simulation operations that are followed to calculate the 64 × 64 point correlation: FFT, fast Fourier transform; pts, points.

Fig. 3
Fig. 3

Correlation SNR versus ODZ area (in %) for case A, with four different samplings for each filter.

Fig. 4
Fig. 4

Correlation SNR versus ODZ area (in percent) for cases A, B, and C, in which N1 = N2 = 4. The abscissa Z i refers to Z1 = Z2 for case A, Z1 for case B, and Z2 for case C.

Fig. 5
Fig. 5

Correlation peak intensities versus sampling number for case A with all three filters and two different dead zone areas. The values of I p are in arbitrary units.

Fig. 6
Fig. 6

Normalized peak correlation intensities versus ODZ area (in percent) for the same three cases as in Fig. 4.

Fig. 7
Fig. 7

Energy throughput efficiency E (in percent) versus the ODZ area (in percent) for cases B and C with all three filters. E is the percentage of the incident light that is recorded at the correlator detector.

Fig. 8
Fig. 8

Percentages of input energy that are blocked, masked, and incident on various planes versus ODZ area (in percent) for case A with a POF.

Fig. 9
Fig. 9

Same as Fig. 8 but with a BPOF.

Fig. 10
Fig. 10

Same as Fig. 8 but with a CMF.

Fig. 11
Fig. 11

Representative diagram showing a pixel of dimensions c x and c y with an active zone (which is represented by the raised portion) of dimensions b x and b y . The remaining area (the non-raised portion) is the dead zone.

Tables (2)

Tables Icon

Table II Normalized Correlation Peak Intensitiesa

Equations (7)

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SNR = k max [ j = 1 n T k j 2 ( < 0.5 k max ) n T ] 1 / 2 ,
w ( x 1 ) = { [ n = - δ ( x 1 - n c x ) s ( x 1 ) ] rect ( x 1 b x ) } rect ( x 1 L x ) .
W ( ξ 2 ) = ( { [ ( 1 c x ) n = - δ ( ξ 2 - n c x ) S ( ξ 2 ) ] b x × sinc ( b x ξ 2 ) } L x sinc ( L x ξ 2 ) ) rect ( c x ξ 2 ) ,
W ( ξ 2 ) b x L x c x rect ( c x ξ 2 ) [ S ( ξ 2 ) sinc ( L x ξ 2 ) ] .
G ( ξ 2 ) = [ m = - δ ( ξ 2 - m M c x ) F * ( ξ 2 ) ] rect ( h x L x ξ 2 e x ) .
k ( x 3 ) = ( b x e x c x h x ) ( { [ s ( x 3 ) 1 b x rect ( x 3 b x ) ] rect ( x 3 L x ) } [ f * ( - x 3 ) sinc ( e x x 3 h x L x ) ] ) 1 c x sinc ( x 3 c x ) .
k ( x 3 , y 3 , b , c , e / h ) = ( 1 - Z 1 ) ( 1 - Z 2 ) q ( x 3 , y 3 , b , c , e / h ) ,

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