Abstract

We investigate the performance of the binary joint transform correlator (JTC) in the presence of multiple objects for two types of thresholding that are used to binarize the joint power spectrum. The first method uses the median of the joint power spectrum of the reference image and the input scene as the threshold value. The second method is a two-dimensional thresholding technique used to maximize the light intensity of the correlation peak, and it eliminates the even-order harmonic terms. The correlation performance of the binary JTC is determined for both thresholding methods. The binary JTC output is determined analytically in terms of multiple input targets. The separation requirements of the binary JTC and the conventional JTC in the presence of multiple targets are computed. Computer simulation and experiments are presented for a limited number of multiple-target images to determine the correlation peak-to-sidelobe ratio and the correlation width for both thresholding techniques. In the experiments, a hybrid optical processor with an optically addressed spatial light modulator is used to implement the binary JTC. The results indicate that, using both thresholding methods, the binary JTC produces a large peak-to-sidelobe ratio and a narrow peak for the multiple-target images used in the tests. The two-dimensional threshold function produces better correlation performance compared with the median thresholding.

© 1991 Optical Society of America

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References

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  1. B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989).
    [CrossRef] [PubMed]
  2. B. Javidi, J. L. Horner, “Single SLM joint transform correlator,” Appl. Opt. 28, 1027–1032 (1989).
    [CrossRef] [PubMed]
  3. B. Javidi, “SDF based binary nonlinear correlation,” Appl. Opt. 28, 2490–2493 (1989).
    [CrossRef] [PubMed]
  4. J. C. Kirsch, D. A. Gregory, “Video rate optical correlation using a magnetooptic SLM,” Opt. Eng. 29, 1122–1128 (1990).
    [CrossRef]
  5. K. H. Fielding, J. L. Horner, “1-f Binary joint transform correlator,” Opt. Eng. 29, 1081–1087 (1990).
    [CrossRef]
  6. W. B. Hahn, D. L. Flannery, “Basic design elements of binary joint transform correlator and selected optimization techniques,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 344–356 (1990).
  7. S. K. Rogers, J. D. Kline, M. Kabrisky, J. P. Mills, “New binarization techniques for joint transform correlator,” Opt. Eng. 29, 1088–1093 (1990).
    [CrossRef]
  8. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967).
  9. C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]

1990 (3)

J. C. Kirsch, D. A. Gregory, “Video rate optical correlation using a magnetooptic SLM,” Opt. Eng. 29, 1122–1128 (1990).
[CrossRef]

K. H. Fielding, J. L. Horner, “1-f Binary joint transform correlator,” Opt. Eng. 29, 1081–1087 (1990).
[CrossRef]

S. K. Rogers, J. D. Kline, M. Kabrisky, J. P. Mills, “New binarization techniques for joint transform correlator,” Opt. Eng. 29, 1088–1093 (1990).
[CrossRef]

1989 (3)

1966 (1)

Fielding, K. H.

K. H. Fielding, J. L. Horner, “1-f Binary joint transform correlator,” Opt. Eng. 29, 1081–1087 (1990).
[CrossRef]

Flannery, D. L.

W. B. Hahn, D. L. Flannery, “Basic design elements of binary joint transform correlator and selected optimization techniques,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 344–356 (1990).

Goodman, J. W.

Gregory, D. A.

J. C. Kirsch, D. A. Gregory, “Video rate optical correlation using a magnetooptic SLM,” Opt. Eng. 29, 1122–1128 (1990).
[CrossRef]

Hahn, W. B.

W. B. Hahn, D. L. Flannery, “Basic design elements of binary joint transform correlator and selected optimization techniques,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 344–356 (1990).

Horner, J. L.

K. H. Fielding, J. L. Horner, “1-f Binary joint transform correlator,” Opt. Eng. 29, 1081–1087 (1990).
[CrossRef]

B. Javidi, J. L. Horner, “Single SLM joint transform correlator,” Appl. Opt. 28, 1027–1032 (1989).
[CrossRef] [PubMed]

Javidi, B.

Kabrisky, M.

S. K. Rogers, J. D. Kline, M. Kabrisky, J. P. Mills, “New binarization techniques for joint transform correlator,” Opt. Eng. 29, 1088–1093 (1990).
[CrossRef]

Kirsch, J. C.

J. C. Kirsch, D. A. Gregory, “Video rate optical correlation using a magnetooptic SLM,” Opt. Eng. 29, 1122–1128 (1990).
[CrossRef]

Kline, J. D.

S. K. Rogers, J. D. Kline, M. Kabrisky, J. P. Mills, “New binarization techniques for joint transform correlator,” Opt. Eng. 29, 1088–1093 (1990).
[CrossRef]

Mills, J. P.

S. K. Rogers, J. D. Kline, M. Kabrisky, J. P. Mills, “New binarization techniques for joint transform correlator,” Opt. Eng. 29, 1088–1093 (1990).
[CrossRef]

Rogers, S. K.

S. K. Rogers, J. D. Kline, M. Kabrisky, J. P. Mills, “New binarization techniques for joint transform correlator,” Opt. Eng. 29, 1088–1093 (1990).
[CrossRef]

Weaver, C. S.

Appl. Opt. (4)

Opt. Eng. (3)

S. K. Rogers, J. D. Kline, M. Kabrisky, J. P. Mills, “New binarization techniques for joint transform correlator,” Opt. Eng. 29, 1088–1093 (1990).
[CrossRef]

J. C. Kirsch, D. A. Gregory, “Video rate optical correlation using a magnetooptic SLM,” Opt. Eng. 29, 1122–1128 (1990).
[CrossRef]

K. H. Fielding, J. L. Horner, “1-f Binary joint transform correlator,” Opt. Eng. 29, 1081–1087 (1990).
[CrossRef]

Other (2)

W. B. Hahn, D. L. Flannery, “Basic design elements of binary joint transform correlator and selected optimization techniques,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 344–356 (1990).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967).

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Figures (9)

Fig. 1
Fig. 1

Binary nonlinear JTC.

Fig. 2
Fig. 2

Images used in the tests: (a) reference image and two targets in the scene; (b) reference image and three targets in the scene.

Fig. 3
Fig. 3

Weighting function in the binary JTC using a threshold function for binarization [assuming Fig. 2(b) as the input scene]: (a) weighting function 1/S(α, β); (b) inverse Fourier transform of the weighting function [1/S(α, β)].

Fig. 4
Fig. 4

Block diagram of the computer simulation: (a) classic JTC; (b) binary JTC using a threshold value; (c) binary JTC using the optimum threshold function.

Fig. 5
Fig. 5

Conventional JTC results for two tanks in the scene [Fig. 2(a)].

Fig. 6
Fig. 6

Binary JTC results using the median of the joint power spectrum of the reference image (satisfying the locating condition): (a) correlation results for two tanks in the scene [Fig. 2(a)]; (b) correlation results for three tanks in the scene [Fig. 2(b)].

Fig. 7
Fig. 7

Binary JTC results using the threshold function: (a) correlation results for two tanks in the scene [Fig. 2(a)]; (b) correlation results for three tanks in the scene [Fig. 2(b)].

Fig. 8
Fig. 8

Photographs and 3-D plots of the multiple-target detection of the hybrid binary JTC using the median of the joint power spectrum as the threshold: (a) correlation results for two tanks in the scene [Fig. 2(a)]; (b) correlation results for three tanks in the scene [Fig. 2(b)].

Fig. 9
Fig. 9

Photographs and 3-D plots of the multiple-target detection of hybrid JTC using the threshold function for binarization: (a) correlation results for two tanks in the scene [Fig. 2(a)]; (b) correlation results for three tanks in the scene [Fig. 2(b)].

Tables (4)

Tables Icon

Table I Computer Simulation of the Binary JTC Using the Median of the Joint Power Spectrum as the Threshold

Tables Icon

Table II Computer Simulation of the Binary JTC Using the Threshold Function for Binarization

Tables Icon

Table III Experimental Results of the Hybrid Binary JTC Using the Median of the Joint Power Spectrum as the Threshold

Tables Icon

Table IV Experimental Results of the Hybrid Binary JTC Using the Threshold Function for Binarization

Equations (25)

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E ( α , β ) = | I ( α , β ) | 2 = S 2 ( α , β ) + R 2 ( α , β ) + 2 S ( α , β ) R ( α , β ) cos [ x 0 α + y 0 β + ϕ s ( α , β ) ϕ R ( α , β ) ] ,
g ( α , β ) = 2 x 0 d + υ = 1 H υ [ R ( α , β ) S ( α , β ) ] cos [ υ ( x 0 α + y 0 β ) + υ ϕ s ( α , β ) υ ϕ R ( α , β ) ] ,
R 2 ( α , β ) + S 2 ( α , β ) V T 2 R ( α , β ) S ( α , β ) 1 .
H υ [ R ( α , β ) S ( α , β ) ] = 2 π V sin { υ cos 1 [ R 2 ( α , β ) + S 2 ( α , β ) V T 2 R ( α , β ) S ( α , β ) ] } , d = 1 x ° cos 1 [ R 2 ( α , β ) + S 2 ( α , β ) V T 2 R ( α , β ) S ( α , β ) ] .
g 1 c ( α , β ) = 2 π { 1 [ R 2 ( α , β ) + S 2 ( α , β ) V T 2 R ( α , β ) S ( α , β ) ] 2 } 1 / 2 cos [ x 0 α + y 0 β + ϕ S ( α , β ) ϕ R ( α , β ) ] ,
[ R 2 ( α , β ) + S 2 ( α , β ) V T 2 R ( α , β ) S ( α , β ) ] 2
V T ( α , β ) = R 2 ( α , β ) + S 2 ( α , β ) .
R 1 c ( x 0 , y 0 ) = abs ( 1 2 π 1 π exp { i [ ϕ s ( α , β ) ϕ R ( α , β ) ] } d α d β ) .
H υ = { 0 υ = even , υ > 0 , 2 π υ ( 1 ) υ 1 2 υ = odd , υ > = 1 .
g 1 c ( α , β ) = 2 π cos { ϕ s ( α , β ) [ ϕ R ( α , β ) x 0 α y 0 β ] } .
E 1 ( α , β ) = R ( α , β ) S ( α , β ) cos [ x 0 α + y 0 β + ϕ s ( α , β ) ϕ R ( α , β ) ] .
V T = med { V T ( α , β ) } = med { hist [ E ( α , β ) ] } ,
max ( D s i s j ) < min ( D s i r ) ( i , j = 1 , 2 , , n ) ,
s ( x , y ) = i = 1 n s i ( x x i , y y i ) .
g 1 c ( α , β ) = i = 1 n g 1 c i ( α , β ) ,
g 1 c i ( α , β ) = 2 π 1 S ( α , β ) S i ( α , β ) cos [ ( x 0 x i ) α + ( y 0 y i ) β + ϕ s i ( α , β ) ϕ R ( α , β ) ] ,
S ( α , β ) = { i = 1 n j = 1 n S i ( α , β ) S j ( α , β ) cos [ ( x j x i ) α + ( y j y i ) β + ϕ s i ( α , β ) ϕ s j ( α , β ) ] } 1 / 2 .
g 1 c i ( α , β ) = 2 π 1 S 0 ( α , β ) cos [ ( x 0 x i ) α + ( y 0 y i ) β + ϕ s i ( α , β ) ϕ R ( α , β ) ]
S 0 ( α , β ) = { i = 1 n j = 1 n cos [ ( x j x i ) α + ( y j y i ) β ] } 1 / 2 .
SNR = I ( x p , y q ) [ i = 1 N 1 j = 1 N 2 | n ( x i , y j ) n ( x i , y j ) ¯ | 2 / N 1 N 2 ] 1 / 2 ,
s ( x , y ) = i = 1 n s i ( x x i , y y i ) .
S ( α , β ) exp [ j ϕ s ( α , β ) ] = i = 1 n S i ( α , β ) exp [ j ϕ i ( α , β ) ] exp [ j ( α x i + β y i ) ] ,
tan [ ϕ s ( α , β ) ] = i = 1 n S i ( α , β ) sin [ ϕ i ( α , β ) ( α x i + β y i ) ] i = 1 n S i ( α , β ) cos [ ϕ i ( α , β ) ( α x i + β y i ) ] .
tan { ϕ s ( α , β ) [ ϕ R ( α , β ) α x 0 β y 0 ] } = i = 1 n S i ( α , β ) sin [ α ( x 0 x i ) + β ( y 0 y i ) + ϕ i ( α , β ) ϕ R ( α , β ) ] i = 1 n S i ( α , β ) cos [ α ( x 0 x i ) + β ( y 0 y i ) + ϕ i ( α , β ) ϕ R ( α , β ) ] ,
cos { ϕ s ( α , β ) [ ϕ R ( α , β ) α x 0 β y 0 ] } = 1 [ 1 + ( tan [ tan ϕ s ( α , β ) [ ϕ R ( α , β ) α x 0 β y 0 ] } ) 2 ] 1 / 2 × i = 1 n S i ( α , β ) cos [ α ( x 0 x i ) = + β ( y 0 y i ) + ϕ i ( α , β ) ϕ R ( α , β ) ] { i = 1 n i = 1 n S i ( α , β ) S j ( α , β ) cos [ α ( x j x i ) + β ( y j y i ) + ϕ i ( α , β ) ϕ j ( α , β ) ] } 1 / 2 . ( A 5 )

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