Abstract

We show that configurations based on joint-power-spectrum correlators can provide not only classical matched filtering but also phase-only or inverse filtering. General, simple, and powerful means that extend the capabilities of classical joint-transform correlator systems are proposed. Moreover, inverse filtering with joint-transform correlators exhibits not only high peak sharpness but also high light efficiency, unlike inverse filtering with frequency–plane correlators, for which these two quantities are inversely related.

© 1993 Optical Society of America

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References

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1993 (1)

K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
[CrossRef]

1990 (1)

1989 (1)

1984 (1)

1982 (1)

1967 (1)

G. W. Stroke, R. G. Zech, Phys. Lett. A 25, 89 (1967).
[CrossRef]

1966 (1)

1964 (1)

A. VanderLugt, IEEE Trans. Inform. Theory IT-10, 139 (1964).
[CrossRef]

Gianino, P. D.

Goodman, J. W.

Hassebrook, L.

Horner, J. L.

Javidi, B.

Johnson, K. M.

K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
[CrossRef]

McKnight, D. J.

K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
[CrossRef]

Oppenheim, A. V.

A. V. Oppenheim, A. S. Willsky, I. T. Young, Signals and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1983), Chap. 4, p. 211.

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. (McGraw-Hill, New York, 1984), Chap. 10, pp. 298–300.

Stroke, G. W.

G. W. Stroke, R. G. Zech, Phys. Lett. A 25, 89 (1967).
[CrossRef]

Underwood, I.

K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
[CrossRef]

VanderLugt, A.

A. VanderLugt, IEEE Trans. Inform. Theory IT-10, 139 (1964).
[CrossRef]

Vijaya Kumar, B. V. K.

Weaver, C. S.

Willsky, A. S.

A. V. Oppenheim, A. S. Willsky, I. T. Young, Signals and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1983), Chap. 4, p. 211.

Young, I. T.

A. V. Oppenheim, A. S. Willsky, I. T. Young, Signals and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1983), Chap. 4, p. 211.

Zech, R. G.

G. W. Stroke, R. G. Zech, Phys. Lett. A 25, 89 (1967).
[CrossRef]

Appl. Opt. (5)

IEEE J. Quantum Electron. (1)

K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
[CrossRef]

IEEE Trans. Inform. Theory (1)

A. VanderLugt, IEEE Trans. Inform. Theory IT-10, 139 (1964).
[CrossRef]

Phys. Lett. A (1)

G. W. Stroke, R. G. Zech, Phys. Lett. A 25, 89 (1967).
[CrossRef]

Other (2)

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. (McGraw-Hill, New York, 1984), Chap. 10, pp. 298–300.

A. V. Oppenheim, A. S. Willsky, I. T. Young, Signals and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1983), Chap. 4, p. 211.

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Figures (1)

Fig. 1
Fig. 1

Fractional-power JTC setup, with a computer interface. Toggle at 1, classical JTC (matched filtering); toggle at 2, computer processing for JTC-based phase-only or inverse filtering. SLM's, spatial light modulators.

Equations (13)

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C FPF ( p ) ( u , v ) = | R ( u , v ) | p 1 R * ( u , v ) S ( u , v ) .
I ( u , v ) = | R | 2 + | S | 2 + R * S exp ( i 2 ϕ ) + R S * exp ( i 2 ϕ ) .
I ( t ) ( u , v ) = | R | 2 + | S | 2 | R | t + | R | t R * S exp ( i 2 ϕ ) + | R | t R S * exp ( i 2 ϕ ) .
C ( t ) ( u , v ) = | R ( u , v ) | t R * ( u , v ) S ( u , v ) ,
SNR = | E [ c ( t ) ( 0 , 0 ) ] | 2 var [ c ( t ) ( 0 , 0 ) ] ,
SNR = [ | R ( u , v ) | 2 t d u d v ] 2 N 0 | R ( u , v ) | 2 2 t d u d v ,
| R ( u , v ) | 2 t d u d v | R ( u , v ) | 2 2 t d u d v = | R ( u , v ) | 2 t ln [ | R ( u , v ) | ] d u d v | R ( u , v ) | 2 2 t ln [ | R ( u , v ) | ] d u d v .
PCE = | c ( t ) ( 0 , 0 ) | 2 P c ,
PCE = [ | R ( u , v ) | 2 t d u d v ] 2 | R ( u , v ) | 4 2 t d u d v ,
| c ( t ) ( x , y ) | = function ( t ) | | R ( u , v ) | 2 t × exp [ i 2 π ( u x + v y ) ] d u d v | function ( t ) | R ( u , v ) | 2 t d u d v = c ( t ) ( 0 , 0 ) ,
η = | C ( t ) ( u , v ) | 2 ,
I ( t ) ( u , v ) = [ | R ( u , v ) | | R ( u , v ) | max ] 2 t 1 2 { 1 + cos [ 2 ϕ ( u ) ] } .
η = 1 6 [ | R ( u , v ) | | R ( u , v ) | max ] 4 2 t .

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