Abstract

An iterative technique has been used to improve the design and performance of the binary phase version of a tandem-component correlation filter. The results are compared to a regular matched filter, a phase-only filter (POF), and a binary phase POF, in terms of optical efficiency, SNR, and peak correlation intensity.

© 1985 Optical Society of America

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References

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  1. H. O. Bartelt, “Computer-Generated Holographic Component with Optimum Light Efficiency,” Appl. Opt. 23, 1499 (1984).
    [CrossRef] [PubMed]
  2. H. O. Bartelt, “Applications of the Tandem Component Filter a Holographic Element with Optimum Light Efficiency,” Appl. Opt.24, 15Nov. in press (1985).
    [CrossRef] [PubMed]
  3. J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812 (1984).
    [CrossRef] [PubMed]
  4. D. Pape, “Phase-Only Matched Filtering using a Membrane Spatial Light Modulator,” Bull. Am. Phys. Soc. 28, No. 9, Paper FD-10 (Nov.1983).
  5. D. Psaltis, E. Paek, S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulation,” Opt. Eng. 23, 698 (1984).
    [CrossRef]
  6. A. B. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
  7. J. Riggins, S. Butler, “Simulation of Synthetic Discriminant Function Optical Implementation,” Opt. Eng. 23, 721 (1984).
    [CrossRef]
  8. J. R. Fienup, “Reconstruction and Synthesis Applications of an Iterative Algorithm,” Proc. Soc. Photo-Opt. Instrum. Eng. 373, 147 (1981).
  9. H. J. Caulfield, “Role of the Horner Efficiency in the Optimization of Spatial Filters for Optical Pattern Recognition,” Appl. Opt. 21, 4391 (1982).
    [CrossRef] [PubMed]
  10. J. L. Horner, J. R. Leger, “Pattern Recognition with Binary Phase-Only Filters,” Appl. Opt. 24, 609 (1985).
    [CrossRef] [PubMed]
  11. A. Kozma, D. L. Kelly, “Spatial Filtering for Detection of Signals Submerged in Noise,” Appl. Opt. 4, 387 (1965).
    [CrossRef]

1985 (1)

1984 (4)

J. Riggins, S. Butler, “Simulation of Synthetic Discriminant Function Optical Implementation,” Opt. Eng. 23, 721 (1984).
[CrossRef]

H. O. Bartelt, “Computer-Generated Holographic Component with Optimum Light Efficiency,” Appl. Opt. 23, 1499 (1984).
[CrossRef] [PubMed]

J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812 (1984).
[CrossRef] [PubMed]

D. Psaltis, E. Paek, S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulation,” Opt. Eng. 23, 698 (1984).
[CrossRef]

1983 (1)

D. Pape, “Phase-Only Matched Filtering using a Membrane Spatial Light Modulator,” Bull. Am. Phys. Soc. 28, No. 9, Paper FD-10 (Nov.1983).

1982 (1)

1981 (1)

J. R. Fienup, “Reconstruction and Synthesis Applications of an Iterative Algorithm,” Proc. Soc. Photo-Opt. Instrum. Eng. 373, 147 (1981).

1965 (1)

1964 (1)

A. B. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).

Bartelt, H. O.

H. O. Bartelt, “Computer-Generated Holographic Component with Optimum Light Efficiency,” Appl. Opt. 23, 1499 (1984).
[CrossRef] [PubMed]

H. O. Bartelt, “Applications of the Tandem Component Filter a Holographic Element with Optimum Light Efficiency,” Appl. Opt.24, 15Nov. in press (1985).
[CrossRef] [PubMed]

Butler, S.

J. Riggins, S. Butler, “Simulation of Synthetic Discriminant Function Optical Implementation,” Opt. Eng. 23, 721 (1984).
[CrossRef]

Caulfield, H. J.

Fienup, J. R.

J. R. Fienup, “Reconstruction and Synthesis Applications of an Iterative Algorithm,” Proc. Soc. Photo-Opt. Instrum. Eng. 373, 147 (1981).

Gianino, P. D.

Horner, J. L.

Kelly, D. L.

Kozma, A.

Leger, J. R.

Paek, E.

D. Psaltis, E. Paek, S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulation,” Opt. Eng. 23, 698 (1984).
[CrossRef]

Pape, D.

D. Pape, “Phase-Only Matched Filtering using a Membrane Spatial Light Modulator,” Bull. Am. Phys. Soc. 28, No. 9, Paper FD-10 (Nov.1983).

Psaltis, D.

D. Psaltis, E. Paek, S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulation,” Opt. Eng. 23, 698 (1984).
[CrossRef]

Riggins, J.

J. Riggins, S. Butler, “Simulation of Synthetic Discriminant Function Optical Implementation,” Opt. Eng. 23, 721 (1984).
[CrossRef]

VanderLugt, A. B.

A. B. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).

Venkatesh, S.

D. Psaltis, E. Paek, S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulation,” Opt. Eng. 23, 698 (1984).
[CrossRef]

Appl. Opt. (5)

Bull. Am. Phys. Soc. (1)

D. Pape, “Phase-Only Matched Filtering using a Membrane Spatial Light Modulator,” Bull. Am. Phys. Soc. 28, No. 9, Paper FD-10 (Nov.1983).

IEEE Trans. Inf. Theory (1)

A. B. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).

Opt. Eng. (2)

J. Riggins, S. Butler, “Simulation of Synthetic Discriminant Function Optical Implementation,” Opt. Eng. 23, 721 (1984).
[CrossRef]

D. Psaltis, E. Paek, S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulation,” Opt. Eng. 23, 698 (1984).
[CrossRef]

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

J. R. Fienup, “Reconstruction and Synthesis Applications of an Iterative Algorithm,” Proc. Soc. Photo-Opt. Instrum. Eng. 373, 147 (1981).

Other (1)

H. O. Bartelt, “Applications of the Tandem Component Filter a Holographic Element with Optimum Light Efficiency,” Appl. Opt.24, 15Nov. in press (1985).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Basic correlation-type optical system employing the TC filter components f1 and F2. The focal length of each lens L is f.

Fig. 2
Fig. 2

Diagram of iteration scheme used to compute the TC filter. Dashed boxes represent overcompensated iteration modification.

Fig. 3
Fig. 3

Input test image used in the various autocorrelation tests.

Fig. 4
Fig. 4

Correlation operations with various types of filter: (a) matched filter; (b) continuous phase TC filter; (c) binary phase TC filter; (d) optimized binary phase TC filter.

Fig. 5
Fig. 5

Progress of binarized uncompensated iterations for TC filter: relative MS error vs number of iterations.

Fig. 6
Fig. 6

Convergence of relative MS error using overcompensation algorithm for binary TC filter.

Tables (1)

Tables Icon

Table I Light Efficiency, SNR, and Peak Intensity for the Various Types of Correlation Filters

Equations (9)

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G ( ν ) = | FT { f 1 ( x ) } | .
F 2 ( ν ) = exp [ i ϕ 2 ( ν ) ] ,
FT { f 1 } = | G ( ν ) | exp [ i ϕ 1 ( ν ) ] ,
ϕ 2 ( ν ) = ψ ( ν ) ϕ 1 ( ν ) .
i = U i / U ¯ 1 ,
U i + 1 = 1 . 0 k i ,
η H = η M A | g h | 2 d x / A | g | 2 d x ,
η H = A i | u i | 2 / A i | u i | 2 ,
SNR = u i / [ A A i | u i | 2 / ( N A N A ) ] 1 / 2 ,

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