Abstract

A method of amplitude-compensated matched filtering is presented. This yields much better discrimination and a sharper autocorrelation peak compared with the classical matched spatial filter and the phase-only one. By computer simulation in the case of alphanumeric characters, it is concluded that, although the phase information is significantly more important, in the case of a matched filter, the amplitude is important too. Three-dimensional graphs of autocorrelation and cross-correlation are also provided.

© 1988 Optical Society of America

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References

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  1. A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 529 (1981).
    [CrossRef]
  2. J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812 (1984).
    [CrossRef] [PubMed]
  3. F. T. S. Yu, Optical Information Processing (Wiley-Interscience, New York, 1983), pp. 198–202.
  4. S. M. Arnold, “Electron Beam Fabrication of Computer Generated Hologram,” Opt. Eng. 24, 803 (1985).
    [CrossRef]

1985 (1)

S. M. Arnold, “Electron Beam Fabrication of Computer Generated Hologram,” Opt. Eng. 24, 803 (1985).
[CrossRef]

1984 (1)

1981 (1)

A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 529 (1981).
[CrossRef]

Arnold, S. M.

S. M. Arnold, “Electron Beam Fabrication of Computer Generated Hologram,” Opt. Eng. 24, 803 (1985).
[CrossRef]

Gianino, P. D.

Horner, J. L.

Lim, J. S.

A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 529 (1981).
[CrossRef]

Oppenheim, A. V.

A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 529 (1981).
[CrossRef]

Yu, F. T. S.

F. T. S. Yu, Optical Information Processing (Wiley-Interscience, New York, 1983), pp. 198–202.

Appl. Opt. (1)

Opt. Eng. (1)

S. M. Arnold, “Electron Beam Fabrication of Computer Generated Hologram,” Opt. Eng. 24, 803 (1985).
[CrossRef]

Proc. IEEE (1)

A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 529 (1981).
[CrossRef]

Other (1)

F. T. S. Yu, Optical Information Processing (Wiley-Interscience, New York, 1983), pp. 198–202.

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Figures (4)

Fig. 1
Fig. 1

Autocorrelations (a) |GG|2 with classical filter, (b) |GGP|2 with phase-only filter.

Fig. 2
Fig. 2

Autocorrelation |GGA|2 with amplitude-compensated filter.

Fig. 3
Fig. 3

Cross-correlations (a) |OG|2 with classical filter; (b) |OGP|2 with phase-only filter.

Fig. 4
Fig. 4

Cross-correlation |OGA|2 with amplitude-compensated filter.

Tables (1)

Tables Icon

Table I Correlation Results with Three Kinds of Matched Filter

Equations (7)

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F c ( p , q ) = A 1 F * ( p , q ) = A 1 F ( p , q ) exp [ - i ϕ ( p , q ) ] ,
F p ( p , q ) = exp [ - i ϕ ( p , q ) ] .
F c ( p , q ) = A 1 F ( p , q ) 2 ,
F p ( p , q ) = F ( p , q ) .
F a ( p , q ) = A 2 / F ( p , q ) = A 2 exp [ - i ϕ ( p , q ) ] / F ( p , q ) ,
F a ( p , q ) = { F 0 exp [ - i ϕ ( p , q ) ] / F ( p , q ) ,             [ F ( p , q ) > F 0 ] exp [ - i ϕ ( p , q ) ] ,             [ F ( p , q ) < F 0 ] ,
Δ = G G 2 - G O 2 G G 2 .

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