Abstract

From image processing work, we know that the phase information is significantly more important than amplitude information in preserving the features of a visual scene. Is the same true in the case of a matched filter? From previous work [ J. L. Horner, Appl. Opt. 21, 4511( 1982)], we know that a pure phase correlation filter can have an optical efficiency of 100% in an optical correlation system. We examine this relationship between phase and amplitude in the case of alphanumeric characters, with and without noise, using a computer simulation. We compare the phase-only and amplitude-only filters to the classical matched filter using the criteria of discrimination, correlation peak, and optical efficiency. Three-dimensional plots of the autocorrelation and cross-correlation functions are presented and discussed.

© 1984 Optical Society of America

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References

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  1. A. V. Oppenheim, J. S. Lim, Proc. IEEE 69, 529 (1981).
    [CrossRef]
  2. L. Lesem, P. Hirsch, J. Jordon, IBM J. Res. Dev. 13, 150 (1969).
    [CrossRef]
  3. A. Levi, H. Stark, J. Opt. Soc. Am. 73, 810 (1983).
    [CrossRef]
  4. J. L. Horner, Appl. Opt. 21, 4511 (1982).
    [CrossRef] [PubMed]
  5. A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
    [CrossRef]
  6. H. J. Caulfield, Appl. Opt. 21, 4391 (1982).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. J. R. Leger, S. H. Lee, Appl. Opt. 21, 274 (1982).
    [CrossRef] [PubMed]
  9. H. J. Caulfield, M. H. Weinberg, Appl. Opt. 21, 1699 (1982).
    [CrossRef] [PubMed]
  10. The 3-D plots were generated by software provided by the National Center for Atmospheric Research and modified by P. Fougere, A. F. Geophysical Laboratory.
  11. C. E. Thomas, Appl. Opt. 7, 517 (1968).
    [CrossRef] [PubMed]

1983

1982

1981

A. V. Oppenheim, J. S. Lim, Proc. IEEE 69, 529 (1981).
[CrossRef]

1980

1969

L. Lesem, P. Hirsch, J. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

1968

1964

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

Casasent, D.

Caulfield, H. J.

Fougere, P.

The 3-D plots were generated by software provided by the National Center for Atmospheric Research and modified by P. Fougere, A. F. Geophysical Laboratory.

Hester, C. F.

Hirsch, P.

L. Lesem, P. Hirsch, J. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Horner, J. L.

Jordon, J.

L. Lesem, P. Hirsch, J. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Lee, S. H.

Leger, J. R.

Lesem, L.

L. Lesem, P. Hirsch, J. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Levi, A.

Lim, J. S.

A. V. Oppenheim, J. S. Lim, Proc. IEEE 69, 529 (1981).
[CrossRef]

Oppenheim, A. V.

A. V. Oppenheim, J. S. Lim, Proc. IEEE 69, 529 (1981).
[CrossRef]

Stark, H.

Thomas, C. E.

VanderLugt, A.

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

Weinberg, M. H.

Appl. Opt.

IBM J. Res. Dev.

L. Lesem, P. Hirsch, J. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

IEEE Trans. Inf. Theory

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

J. Opt. Soc. Am.

Proc. IEEE

A. V. Oppenheim, J. S. Lim, Proc. IEEE 69, 529 (1981).
[CrossRef]

Other

The 3-D plots were generated by software provided by the National Center for Atmospheric Research and modified by P. Fougere, A. F. Geophysical Laboratory.

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Figures (8)

Fig. 1
Fig. 1

Letters O and G used in correlation experiment. Numbers refer to points on the 90 × 90 input plane of the FFT. The letter O contains 356 points of unit height; the letter G 355 points.

Fig. 2
Fig. 2

Autocorrelation |gg*|2 using classical matched filter (full phase and amplitude).

Fig. 3
Fig. 3

Autocorrelation with phase-only filter g g ϕ * 2.

Fig. 4
Fig. 4

Autocorrelation with amplitude-only filter g g A * 2.

Fig. 5
Fig. 5

Autocorrelation |gg*|2, SNR = 1, classical matched filter.

Fig. 6
Fig. 6

Autocorrelation g g ϕ * 2, SNR = 1, phase-only filter.

Fig. 7
Fig. 7

Autocorrelation g g A * 2, SNR = 1, amplitude-only filter.

Fig. 8
Fig. 8

Comparison of autocorrelation outputs for the phase-only and classical matched filters with SNR = 4.

Tables (2)

Tables Icon

Table I Correlation Results for Noise-Free Inputsa

Tables Icon

Table II Correlation Results for the Signal with Additive Noisea

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

η H = η · f ( x , y ) g * ( x , y ) 2 d x d y f ( x , y ) 2 d x d y ,
R i j = F - 1 [ F i ( ω ) · F i * ( ω ) ]
F i ( ω ) = F [ f i ( x ) ] ,
F ( ω ) = A ( ω ) exp [ i ϕ ( ω ) ] .
F ϕ ( ω ) = exp [ i ϕ ( ω ) ]
F A ( ω ) = A ( ω ) .

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