Abstract

An algorithm is provided for treating nonwhite additive noise in determining regions of support for phase-only filters, binary phase-only filters, and complex ternary matched filters. It is analytically shown to be optimal in the signal-to-noise ratio sense. It extends earlier research that assumed white noise.

© 1991 Optical Society of America

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References

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  1. A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
    [CrossRef]
  2. J. L. Horner, P. D. Gianino, Appl. Opt. 21, 812 (1984).
    [CrossRef]
  3. D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).
  4. F. M. Dickey, B. D. Hansche, Appl. Opt. 28, 1611 (1989).
    [CrossRef] [PubMed]
  5. B. V. K. Vijaya Kumar, Z. Bahri, Appl. Opt. 28, 250 (1989).
    [CrossRef]
  6. B. V. K. Vijaya Kumar, Z. Bahri, Appl. Opt. 28, 1919 (1989).
    [CrossRef]
  7. F. M. Dickey, B. V. K. Vijaya Kumar, L. A. Romero, J. M. Connelly, Opt. Eng. 29, 994 (1990).
    [CrossRef]
  8. D. Flannery, Proc. Soc. Photo-Opt. Instrum. Eng. 1297, 194 (1990).
  9. B. V. K. Vijaya Kumar, W. Shi, C. Hendrix, Opt. Comput. Process. 1, 29 (1991).
  10. M. W. Farn, J. W. Goodman, Appl. Opt. 27, 4431 (1988).
    [CrossRef] [PubMed]

1991 (1)

B. V. K. Vijaya Kumar, W. Shi, C. Hendrix, Opt. Comput. Process. 1, 29 (1991).

1990 (2)

F. M. Dickey, B. V. K. Vijaya Kumar, L. A. Romero, J. M. Connelly, Opt. Eng. 29, 994 (1990).
[CrossRef]

D. Flannery, Proc. Soc. Photo-Opt. Instrum. Eng. 1297, 194 (1990).

1989 (3)

1988 (1)

1984 (2)

J. L. Horner, P. D. Gianino, Appl. Opt. 21, 812 (1984).
[CrossRef]

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

1964 (1)

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

Bahri, Z.

Connelly, J. M.

F. M. Dickey, B. V. K. Vijaya Kumar, L. A. Romero, J. M. Connelly, Opt. Eng. 29, 994 (1990).
[CrossRef]

Dickey, F. M.

F. M. Dickey, B. V. K. Vijaya Kumar, L. A. Romero, J. M. Connelly, Opt. Eng. 29, 994 (1990).
[CrossRef]

F. M. Dickey, B. D. Hansche, Appl. Opt. 28, 1611 (1989).
[CrossRef] [PubMed]

Farn, M. W.

Flannery, D.

D. Flannery, Proc. Soc. Photo-Opt. Instrum. Eng. 1297, 194 (1990).

Gianino, P. D.

J. L. Horner, P. D. Gianino, Appl. Opt. 21, 812 (1984).
[CrossRef]

Goodman, J. W.

Hansche, B. D.

Hendrix, C.

B. V. K. Vijaya Kumar, W. Shi, C. Hendrix, Opt. Comput. Process. 1, 29 (1991).

Horner, J. L.

J. L. Horner, P. D. Gianino, Appl. Opt. 21, 812 (1984).
[CrossRef]

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

Romero, L. A.

F. M. Dickey, B. V. K. Vijaya Kumar, L. A. Romero, J. M. Connelly, Opt. Eng. 29, 994 (1990).
[CrossRef]

Shi, W.

B. V. K. Vijaya Kumar, W. Shi, C. Hendrix, Opt. Comput. Process. 1, 29 (1991).

VanderLugt, A.

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

Venkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

Vijaya Kumar, B. V. K.

B. V. K. Vijaya Kumar, W. Shi, C. Hendrix, Opt. Comput. Process. 1, 29 (1991).

F. M. Dickey, B. V. K. Vijaya Kumar, L. A. Romero, J. M. Connelly, Opt. Eng. 29, 994 (1990).
[CrossRef]

B. V. K. Vijaya Kumar, Z. Bahri, Appl. Opt. 28, 1919 (1989).
[CrossRef]

B. V. K. Vijaya Kumar, Z. Bahri, Appl. Opt. 28, 250 (1989).
[CrossRef]

Appl. Opt. (5)

IEEE Trans. Inf. Theory (1)

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

Opt. Comput. Process. (1)

B. V. K. Vijaya Kumar, W. Shi, C. Hendrix, Opt. Comput. Process. 1, 29 (1991).

Opt. Eng. (2)

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

F. M. Dickey, B. V. K. Vijaya Kumar, L. A. Romero, J. M. Connelly, Opt. Eng. 29, 994 (1990).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

D. Flannery, Proc. Soc. Photo-Opt. Instrum. Eng. 1297, 194 (1990).

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Equations (17)

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SNR = | E [ c ( 0 ) ] | 2 / var [ c ( 0 ) ] = | S ( u ) H ( u ) d u | 2 / P n ( u ) | H ( u ) | 2 d u ,
SNR = | R S ( u ) H ( u ) d u | 2 / R P n ( u ) | H ( u ) | 2 d u .
SNR POF ( R ) = [ R | S ( u ) | d u ] 2 / R P n ( u ) d u .
SNR POF ( R ) = ( k R | S k | ) 2 / k R P n k ,
z i = x i / y i , i = 1 , 2 , , N
z 1 z 2 z 3 z N > 0 .
η ( R ) = ( i R x i ) 2 / i R y i ,
R POF * = { i : ( | S i | / P n i ) T } ,
H ( u ) = { sgn [ S β R ( u ) ] u R 0 u R ,
S β ( u ) = S ( u ) e j β .
SNR BPOF ( R ) = [ R | S β R ( u ) | d u ] 2 / R P n ( u ) d u .
H CTMF ( u ) = H 1 ( u ) j H 2 ( u ) ,
H 1 ( u ) = { sgn [ S β R ( u ) ] u R 1 0 u R 1 ,
H 2 ( u ) = { sgn [ S β I ( u ) ] u R 2 0 u R 2 .
SNR CTMF ( R 1 , R 2 , ) = [ R 1 | S β R ( u ) | d u + R 2 | S β I ( u ) | d u ] 2 R 1 P n ( u ) d u + R 2 P n ( u ) d u .
x i = | S β R ( i Δ u ) | , x i + N = | S β I ( i Δ u ) | , y i = P n ( i Δ u ) , y i + N = P n ( i Δ u ) , i = 1 , 2 ,…, N .
R CTMF * = { i : ( x i / y i ) T } ,

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