Abstract

A novel joint transform correlator (JTC) system is presented in which the stored reference image is phase encrypted prior to applying the JTC. The encryption disperses all the trivial correlation peaks in the correlator output. The reference image is encrypted electronically, which simplifies the need for a complex optical setup. The encryption removes the JTC requirement for spatial separation between the reference and the target images in the joint input plane. This efficient use of spatial light modulator space can be used to phase multiplex more reference images so that correlations with multiple reference images can be performed in a single JTC cycle.

© 2010 Optical Society of America

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References

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2006 (1)

1998 (1)

1997 (1)

1996 (1)

1995 (1)

1994 (1)

R. R. Kallman and D. H. Goldstein, “Phase-encoding input image for optical pattern recognition,” Opt. Eng. 33, 1806-1812 (1994).
[CrossRef]

1993 (1)

1991 (1)

O. Perez and M. A. Karim, “Optical enhancements of joint Fourier transform correlator by image subtraction,” Proc. SPIE 1471, 255-264 (1991).
[CrossRef]

1990 (2)

1966 (1)

Awwal, A. A. S.

Ferreira, C.

García, J.

Garcia-Martinez, P.

Goldstein, D. H.

R. R. Kallman and D. H. Goldstein, “Phase-encoding input image for optical pattern recognition,” Opt. Eng. 33, 1806-1812 (1994).
[CrossRef]

Goodman, J.

Hester, C. F.

C. F. Hester and M. G. Temmen, “Phase-phase implementation of optical correlator,” Proc. SPIE 1297, 207-219 (1990).
[CrossRef]

Jahan, S. R.

Javidi, B.

Kallman, R. R.

R. R. Kallman and D. H. Goldstein, “Phase-encoding input image for optical pattern recognition,” Opt. Eng. 33, 1806-1812 (1994).
[CrossRef]

Karim, M. A.

O. Perez and M. A. Karim, “Optical enhancements of joint Fourier transform correlator by image subtraction,” Proc. SPIE 1471, 255-264 (1991).
[CrossRef]

A. A. S. Awwal, M. A. Karim, and S. R. Jahan, “Improved correlation discrimination using an amplitude modulated phase-only filter,” Appl. Opt. 29, 2107 (1990).
[CrossRef] [PubMed]

Lu, G.

Marom, Emanuel

Nomura, T.

Perez, O.

O. Perez and M. A. Karim, “Optical enhancements of joint Fourier transform correlator by image subtraction,” Proc. SPIE 1471, 255-264 (1991).
[CrossRef]

Rubner, A.

Tang, Q.

Temmen, M. G.

C. F. Hester and M. G. Temmen, “Phase-phase implementation of optical correlator,” Proc. SPIE 1297, 207-219 (1990).
[CrossRef]

Weaver, C.

Wu, S.

Yu, F. T. S.

Yu, F. T. S.

Zalevsky, Z.

Zhang, Z.

Appl. Opt. (7)

Opt. Eng. (1)

R. R. Kallman and D. H. Goldstein, “Phase-encoding input image for optical pattern recognition,” Opt. Eng. 33, 1806-1812 (1994).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (2)

O. Perez and M. A. Karim, “Optical enhancements of joint Fourier transform correlator by image subtraction,” Proc. SPIE 1471, 255-264 (1991).
[CrossRef]

C. F. Hester and M. G. Temmen, “Phase-phase implementation of optical correlator,” Proc. SPIE 1297, 207-219 (1990).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Multiple phase-encoded reference JTC.

Fig. 2
Fig. 2

Classical JTC with a single reference image: (a) joint input image contains input on the left and a reference image on the right, (b) correlation output, (c) three-dimensional depiction of the correlation output.

Fig. 3
Fig. 3

Phase-encrypted JTC with a single reference image: (a) test input image, (b) fighter plane phase-encrypted reference image, (c) correlation output after applying the phase function to the JPS, (d) three-dimensional depiction of the correlation output.

Fig. 4
Fig. 4

Phase-encoded reference JTC: (a) reference E image, (b) input test image of letters AEFT, (c) absolute value of the joint image containing the test image and the reference phase-encoded image, (d) correlation intensity, (e) three-dimensional correlation intensity.

Fig. 5
Fig. 5

Normalized correlation intensity for input test AEFT and reference image E using various SLM sizes M: (a)  N = 128 ; (b)  N = 256 ; (c)  N = 512 .

Fig. 6
Fig. 6

(a)–(d) Reference images, (e) test input image AEFT, (f) absolute value of the joint image containing the input test image and the four phase-encoded reference images.

Fig. 7
Fig. 7

Normalized correlation intensity when multiple references are phase encoded. Correlation of reference image (a) A with AEFT, (b) E with AEFT, (c) F with AEFT, (d) T with AEFT.

Tables (1)

Tables Icon

Table 1 Effect of SLM Size on Correlation Output

Equations (18)

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f ( x , y ) = t ( x , y + y 0 ) + r ( x , y y 0 ) ,
F ( u , v ) = T ( u , v ) exp [ j y 0 v ] + R ( u , v ) exp [ j y 0 v ] ,
P ( u , v ) = | R ( u , v ) | 2 + | T ( u , v ) | 2 + R ( u , v ) T * ( u , v ) exp ( j 2 v y 0 ) + R * ( u , v ) T ( u , v ) exp ( j 2 v y 0 ) ,
c ( x , y ) = r ( x , y ) r * ( x , y ) + t ( x , y ) t * ( x , y ) + r ( x , y 2 y 0 ) t * ( x , y 2 y 0 ) + r * ( x , y + 2 y 0 ) t ( x , y + 2 y 0 ) ,
| c ( 0 , 2 y 0 ) | 2 = | r ( x , y ) 2 d x d y | 2 r max 2 .
f ( x , y ) = t ( x , y + y 0 ) + i = 1 N r i ( x , y y i ) .
P ( u , v ) = | T ( u , v ) | 2 + i = 1 n | R i ( u , v ) | 2 + i = 1 n R i ( u , v ) T * ( u , v ) exp ( j 2 v ( y 0 y i ) ) + i = 1 n R i * ( u , v ) T ( u , v ) exp ( j 2 v ( y 0 y i ) ) + i = 1 n k = 1 n i k R i * ( u , v ) R k ( u , v ) exp ( j 2 v ( y i y k ) ) + i = 1 n k = 1 n i k R i ( u , v ) R k * ( u , v ) exp ( j 2 v ( y i y k ) ) .
Φ ( u , v ) = exp [ j ψ ( u , v ) ] ,
f ( x , y ) = t ( x , y ) + r ( x , y ) φ ( x , y ) ,
F ( u , v ) = T ( u , v ) + R ( u , v ) Φ ( u , v ) .
P ( u , v ) = | T ( u , v ) | 2 + | R ( u , v ) | 2 + T ( u , v ) R * ( u , v ) Φ * ( u , v ) + T * ( u , v ) R ( u , v ) Φ ( u , v ) .
P Φ = | T | 2 Φ + | R | 2 Φ + T R * + T * R Φ 2 .
c = r r * φ + t t * φ + t r * + t * r φ φ ,
f = t + i = 1 n r i φ i .
P = | T | 2 + i = 1 n | R i | 2 + i = 1 n R i T * Φ i + i = 1 n R i * T Φ i * + i = 1 n k = 1 n i k R i * R k Φ i * Φ k + i = 1 n k = 1 n i k R i R k * Φ i Φ k * .
P Φ p = | T | 2 Φ p + i = 1 n | R i | 2 Φ p + R p * T + i = 1 n R i T * Φ i Φ p + i = 1 n i p R i * T Φ i * Φ p + i = 1 n k = 1 n i k R i * R k Φ i * Φ k Φ p + i = 1 n k = 1 n i k R i R k * Φ i Φ k * Φ p .
c = t t * φ p + i = 1 n r i r i * φ p + t r p * + i = 1 n r i t * φ p φ p + i = 1 n i p r i * t * φ i * φ p + i = 1 n k = 1 n i k r i * r k φ i * φ k φ p + i = 1 n k = 1 n i k r i r k * φ i φ k * φ p .
SNR = | r 2 d x d y | 2 r max 2 2 M N ( | r 2 d x d y | 2 r max 2 ) .

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