Abstract

A modified form of a composite or multiplexed matched filter has been computer simulated and tested. The modification consists of using only the phase function and setting the amplitude function equal to unity—a so-called phase-only filter (POF). The original filter was D. Casasent's synthetic discriminant function (SDF) filter. The filter and test images were made from actual IR imagery. The results are compared in terms of efficiency, correlation peak height and width, and signal/noise ratio. A binary phase version of the SDF/POF was also tested. Its performance is between the SDF and the SDF/POF.

© 1985 Optical Society of America

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References

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  1. J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812 (1984).
    [CrossRef] [PubMed]
  2. A. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
  3. P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-only Correlation Filter,” Opt. Eng. 23, 695 (1984).
    [CrossRef]
  4. J. L. Horner, “Light Utilization in Optical Correlators,” Appl. Opt. 21, 4511 (1982).
    [CrossRef] [PubMed]
  5. J. R. Leger, S. H. Lee, “Hybrid Optical Processor for Pattern Recognition and Classification Using a Generalized Set of Pattern Functions,” Appl. Opt. 21, 274 (1982).
    [CrossRef] [PubMed]
  6. 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]
  7. C. F. Hester, D. Casasent, “Multivariant Technique for Multiclass Pattern Recognition,” Appl. Opt. 19, 1758 (1980).
    [CrossRef] [PubMed]
  8. H. J. Caulfield, W. T. Maloney, “Improved Discrimination in Optical Character Recognition,” Appl. Opt. 8, 2354 (1969).
    [CrossRef] [PubMed]
  9. We wish to thank J. Riggins, AFATL/DLMI, Eglin AFB, Fla. 32542, for making copies of the SDF filter and individual tank images available to us.
  10. J. Riggins, S. Butler, “Simulation of Synthetic Discriminant Function Optical Implementation,” Opt. Eng. 23, 721 (1984).
    [CrossRef]
  11. The IDL language program is available from Research Systems, Inc., 2021 Albion St., Denver, Colo. 80207.
  12. J. Leger, J. Horner, “Pattern Recognition with Binary Phase-Only Filters,” Appl. Opt. in press 1985.

1984

P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-only Correlation Filter,” Opt. Eng. 23, 695 (1984).
[CrossRef]

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

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

1982

1980

1969

1964

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

Butler, S.

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

Casasent, D.

Caulfield, H. J.

Gianino, P. D.

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

P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-only Correlation Filter,” Opt. Eng. 23, 695 (1984).
[CrossRef]

Hester, C. F.

Horner, J.

J. Leger, J. Horner, “Pattern Recognition with Binary Phase-Only Filters,” Appl. Opt. in press 1985.

Horner, J. L.

Lee, S. H.

Leger, J.

J. Leger, J. Horner, “Pattern Recognition with Binary Phase-Only Filters,” Appl. Opt. in press 1985.

Leger, J. R.

Maloney, W. T.

Riggins, J.

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

VanderLugt, A.

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

Appl. Opt.

IEEE Trans. Inf. Theory

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

Opt. Eng.

P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-only Correlation Filter,” Opt. Eng. 23, 695 (1984).
[CrossRef]

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

Other

The IDL language program is available from Research Systems, Inc., 2021 Albion St., Denver, Colo. 80207.

J. Leger, J. Horner, “Pattern Recognition with Binary Phase-Only Filters,” Appl. Opt. in press 1985.

We wish to thank J. Riggins, AFATL/DLMI, Eglin AFB, Fla. 32542, for making copies of the SDF filter and individual tank images available to us.

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Figures (6)

Fig. 1
Fig. 1

Optical correlator showing the position of the filter plane and the Fourier transform lenses L1 and L2.

Fig. 2
Fig. 2

SDF filter in image space, (b), (c), and (d) The actual IR images of the tank shown at orientation angles of 10°, 20°, and 30°, respectively. These latter three images are designated as T1, T2, and T3, respectively.

Fig. 3
Fig. 3

Correlation response in the output plane for (a) correlation between image T2 and the standard SDF filter, and (b) correlation between image T2 and the SDF/POF. T2 was a member of the SDF training set.

Fig. 4
Fig. 4

Correlation response in the output plane for (a) correlation between image T4 and the standard SDF filter, and (b) correlation between image T4 and the SDF/POF. T4 was not a member of the training set.

Fig. 5
Fig. 5

Representative case showing how a continuous phase curve is quantized to two values, 0 and −π.

Fig. 6
Fig. 6

Correlation response in the output plane for correlation between image T2 and the biphase SDF/POF.

Tables (2)

Tables Icon

Table I Comparative Correlation Results

Tables Icon

Table II Average Change In Comparative Correlation Results

Equations (7)

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g ( x , y ) h * ( x , y ) = 1 [ G ( ξ , η ) · H * ( ξ , η ) ] .
H ( ξ , η ) = | H ( ξ , η ) | exp [ i ϕ ( ξ , η ) ] .
H ϕ ( ξ , η ) = H * · | H | 1 = exp ( i ϕ ) .
η H = η M A | g h * | 2 d x 3 d y 3 A | g | 2 d x 1 d y 1 .
SDF = i a i g i ,
g i SDF = 1 ,
T ¯ 1 4

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