Abstract

A spatial filtering technique is proposed to sharpen the correlation peak for a joint transform correlator (JTC) by using the inverse reference power spectrum. Ways of handling the pole problems are discussed under various noise conditions. The minimum mean-square-error method is used to locate the optimum bias value and to estimate threshold level as applied to eradicate the poles. Applications to multitarget recognition and spectral fringe binarization are also studied. Computer-simulated results show that the compensated JTC performs better than the conventional JTC.

© 1993 Optical Society of America

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References

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1990 (4)

1989 (3)

1987 (1)

1984 (1)

F. T. S. Yu, X. J. Lu, “A realtime programmable joint transform correlator,” Opt. Commun. 52, 10–20 (1984).
[CrossRef]

1982 (1)

1966 (1)

Bunch, R. M.

J. A. Davis, E. A. Merrill, D. M. Cotrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Cheng, F.

Cotrell, D. M.

J. A. Davis, E. A. Merrill, D. M. Cotrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Davis, J. A.

J. A. Davis, E. A. Merrill, D. M. Cotrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Ersoy, O. K.

Florence, J. M.

Goodman, J. W.

Gregory, D. A.

Hassebrook, L.

Hendrix, C.

Horner, J. L.

Jutamulia, S.

Kumar, B. V. K. V.

Lin, T. W.

Lu, X. J.

F. T. S. Yu, X. J. Lu, “A realtime programmable joint transform correlator,” Opt. Commun. 52, 10–20 (1984).
[CrossRef]

Merrill, E. A.

J. A. Davis, E. A. Merrill, D. M. Cotrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Mu, G-G.

Nagata, T.

Shi, W.

Sun, Y.

Wang, Z-Q.

Weaver, C. S.

Yu, F. T. S.

Zeng, M.

Appl. Opt. (6)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

F. T. S. Yu, X. J. Lu, “A realtime programmable joint transform correlator,” Opt. Commun. 52, 10–20 (1984).
[CrossRef]

Opt. Eng. (1)

J. A. Davis, E. A. Merrill, D. M. Cotrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Opt. Lett. (2)

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Figures (9)

Fig. 1
Fig. 1

Optical JTC.

Fig. 2
Fig. 2

(a) Input object and reference functions, (b) correlation output produced by a CJTC, (c) correlation output produced by a BICF JTC.

Fig. 3
Fig. 3

(a) Input object cluttered by a shuttle image, (b) correlation output produced by a CJTC, (c) correlation output produced by a TICF JTC.

Fig. 4
Fig. 4

(a) Input object embedded in additive white Gaussian noise, (b) correlation output produced by a CJTC, (c) correlation output produced by a TICF JTC, (d) correlation output produced by a MMSE ICF JTC.

Fig. 5
Fig. 5

(a) Multiobject and multireference functions, (b) correlation output produced by a CJTC, (c) correlation output produced by a TICF JTC.

Fig. 6
Fig. 6

(a) PBR as a function of MMSE bias ratio, (b) PBR as a function of a TICF threshold ratio.

Fig. 7
Fig. 7

(a) PBR as a function of input SNR, (b) PDE as a function of input SNR.

Fig. 8
Fig. 8

(a) PBR as a function of binarization threshold ratio, (b) PDE as a function of binarization threshold ratio, (c) PBR after TICF compensation, (d) PDE after TICF compensation.

Fig. 9
Fig. 9

(a) PBR as a function of TICF threshold ratio for fringe binarization, (b) PDE as a function of TICF threshold ratio for fringe binarization.

Equations (17)

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t ( x , y ) = f ( x - b , y ) + f ( x + b , y ) ,
T ( p , q ) = F ( p , q ) exp ( - j b p ) + F ( p , q ) exp ( j b p ) ,
T 2 = ( 2 F 2 ) + ( F 2 ) exp ( - 2 j b p ) + ( F 2 ) exp ( 2 j b p ) .
T 2 H = ( 2 F 2 H ) + ( F 2 H ) × exp ( - 2 j b p ) + ( F 2 H ) exp ( 2 j b p ) .
F 2 H ( p , q ) = k             or equivalently             H ( p , q ) = k F 2 ,
H ( p , q ) = { 1 , V T F ( p , q ) 2 0 , V T > F ( p , q ) 2 .
min F 2 H - k 2 .
H = k / ( F 2 + a ) ,
min F * ( F + N ) H - k 2 ,
min a k F * ( F + N ) F 2 + a - k 2 = min a k F * N - a F 2 + a 2 ,
min a - + - + F * N - a 2 ( F 2 + a ) 2 d p d q = min a - + - + F 2 N 2 + a 2 ( F 2 + a ) 2 d p d q .
d d a - + - + F 2 N 2 + a 2 ( F 2 + a ) 2 d p d q = - + - + F 2 ( N 2 - a ) ( F 2 + a ) 3 d p d q = 0 .
a = γ σ 2 ,
H ( p , q ) = Σ k i / F i ( p , q ) 2 ,
T 2 H = 4 F 1 cos ( b p ) + F 2 cos ( b p ) 2 H .
2 { F 1 2 cos ( 2 b p ) + F 2 2 cos ( 2 b q ) } ( k 1 / F 1 2 + k 2 / F 2 2 ) = 2 { ( k 1 + k 2 F 2 2 / F 1 2 ) cos ( 2 b p ) + ( k 2 + k 1 F 1 2 / F 2 2 ) cos ( 2 b q ) } .
Δ % = 100 ( P auto - P cross ) / P auto ,

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