Abstract

The phase-only filter (POF) and binary phase-only filter (BPOF) have been shown to have high optical efficiency, good target discrimination, and virtually no sidelobes. We present a simple method of amplitude encoding the signal phase information. These new filters have most of the same advantages of a POF or BPOF so that amplitude modulating spatial light modulators or photographic film can be used.

© 1989 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, 812–816 (1984).
    [CrossRef] [PubMed]
  2. J. L. Horner, J. R. Leger, “Pattern Recognition with Binary Phase-Only Filters,” Appl. Opt. 24, 609–611 (1985).
    [CrossRef] [PubMed]
  3. D. L. Flannery, A. M. Biernacki, J. S. Loomis, S. L. Cartwright, “Real-Time Coherent Correlator Using Binary Magnetooptic Spatial Light Modulators at Input and Fourier Planes,” Appl. Opt. 25, 466 (1986).
    [CrossRef] [PubMed]
  4. Fabricated by Lincoln Laboratory, Lexington, MA 02171.

1986 (1)

1985 (1)

1984 (1)

Biernacki, A. M.

Cartwright, S. L.

Flannery, D. L.

Gianino, P. D.

Horner, J. L.

Leger, J. R.

Loomis, J. S.

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Figures (8)

Fig. 1
Fig. 1

Optical correlation.

Fig. 2
Fig. 2

Amplitude encoding: (a) arbitrary phase signal; (b) binarized phase; (c) equivalent amplitude signal; (d) amplitude encoded phase.

Fig. 3
Fig. 3

Input image.

Fig. 4
Fig. 4

Impulse response: (a) binary phase-only filter; (b) amplitude encoded binary phase-only filter.

Fig. 5
Fig. 5

Computer simulation of correlations. Intensity plots of correlation plane: (a) POF; (b) AE POF; (c) BPOF; (d) AE BPOF.

Fig. 6
Fig. 6

SNR of AE POF vs hard clipping and linear scaling factor (intensity): (a) hard clipped (solid line); (b) linearly scaled (dashed line).

Fig. 7
Fig. 7

Correlation of AE BPOF and image: (a) long exposure time; (b) short exposure time.

Fig. 8
Fig. 8

Scan of correlation peak (10-μm pinhole aperture).

Tables (1)

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Table I Autocorrelation Results (in Intensity)

Equations (14)

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r ( x , y ) = FT 1 { S ( ξ, ν ) · H ( ξ, ν ) } .
H ( ξ, ν ) = FT * { s ( x , y ) } = | S ( ξ, ν ) | exp [ j ϕ ( ξ, ν ) ] ,
H ( ξ, ν ) = 1 · exp [ j ϕ ( ξ, ν ) ] .
H B ( ξ, ν ) = exp [ j ϕ B ( ξ, ν ) ] .
h B ( x , y ) = FT 1 { exp [ j ϕ B ( ξ, ν ) ] } ,
h A ( x , y ) = FT 1 { 1 2 + 1 2 exp [ j ϕ B ( ξ, ν ) ] } ,
h A ( x , y ) = 1 2 δ ( 0 , 0 ) + 1 2 h B ( x , y ) .
r ( x , y ) = FT 1 ( S ( ξ, ν ) · { 1 2 + 1 2 exp [ j ϕ B ( ξ, ν ) ] } ) ,
r ( x , y ) = 1 2 s ( x , y ) + 1 2 r B ( x , y ) .
H A P ( ξ, ν ) = k [ π + ϕ ( ξ, ν ) ] ,
H A P ( ξ, ν ) = 1 2 + ϕ ( ξ, ν ) 2 π .
SNR = I max ( n = 1 N I < 50 % 2 N ) 1 / 2 = I max rms ( I < FWHM ) ,
H A P = k if | ϕ | > k , H A P = ϕ if | ϕ | < k ,
H A P = k ( 1 + ϕ π ) .

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