Abstract

We describe a joint Fourier transform image correlator that employs thresholding at both the input plane and the Fourier plane. This suggests using a single binary spatial light modulator (SLM) to read in sequentially the binarized input signal and the binarized Fourier transform interference intensity. The performance of the single SLM joint Fourier transform correlator (JTC) is compared with that of the classical JTC in the areas of correlation peak intensity, peak-to-sidelobe ratio, signal-to-noise ratio (SNR), and correlation width. We show that the single SLM JTC outperforms the classical JTC in all such areas. Using a single binary SLM results in significant reduction in cost, size and complexity of the system.

© 1989 Optical Society of America

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References

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  1. B. Javidi, C. J. Kuo, “Joint Transform Image Correlation Using a Binary Spatial Light Modulator at the Fourier Plane,” Appl. Opt. 27, 663 (1988);J. Opt. Soc. Am. A 4(13), P86 (1987).
    [CrossRef] [PubMed]
  2. B. Javidi et al., “Bipolar Joint Transform Correlation,” Proc. Soc. Photo-Opt. Instrum. Eng. 956, 120 (1988).
  3. B. Javidi, S. F. Odeh, “Multiple Object Identification by Bipolar Joint Transform Correlation,” Opt. Eng. 27, 295 (1988).
    [CrossRef]
  4. C. S. Weaver, J. W. Goodman, “A Technique for Optically Convolving Two Functions,” Appl. Opt. 5, 1248 (1966).
    [CrossRef] [PubMed]
  5. J. E. Rau, “Detection of Differences in Real Distributions,” J. Opt. Soc. Am. 56, 1490 (1966).
    [CrossRef]
  6. J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812 (1984).
    [CrossRef] [PubMed]
  7. J. L. Horner, J. R. Leger, “Pattern Recognition with Binary Phase-Only Filters,” Appl. Opt. 24, 609 (1985).
    [CrossRef] [PubMed]
  8. J. L. Horner, H. O. Bartelt, “Two-Bit Correlation,” Appl. Opt. 24, 2889 (1985).
    [CrossRef] [PubMed]
  9. B. Javidi, D. Gregory, J. L. Horner, “Single Modulator Joint Transform Correlator Architectures,” Appl. Opt. 28, 411 (1989).
    [CrossRef] [PubMed]
  10. J. L. Horner, B. Javidi, “Single SLM Joint Transform Correlator,” Invention Disclosure, date of record 24Feb.1988.
  11. B. Javidi, “Analysis of the Bipolar Joint Transform Optical Correlator,” Proc. Soc. Photo-Opt. Instrum. Eng. 977, 307 (1988).
  12. M. A. Flavin, J. L. Horner, “Amplitude Encoded Phase-Only Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 938, 261 (1988).

1989

1988

B. Javidi et al., “Bipolar Joint Transform Correlation,” Proc. Soc. Photo-Opt. Instrum. Eng. 956, 120 (1988).

B. Javidi, S. F. Odeh, “Multiple Object Identification by Bipolar Joint Transform Correlation,” Opt. Eng. 27, 295 (1988).
[CrossRef]

J. L. Horner, B. Javidi, “Single SLM Joint Transform Correlator,” Invention Disclosure, date of record 24Feb.1988.

B. Javidi, “Analysis of the Bipolar Joint Transform Optical Correlator,” Proc. Soc. Photo-Opt. Instrum. Eng. 977, 307 (1988).

M. A. Flavin, J. L. Horner, “Amplitude Encoded Phase-Only Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 938, 261 (1988).

B. Javidi, C. J. Kuo, “Joint Transform Image Correlation Using a Binary Spatial Light Modulator at the Fourier Plane,” Appl. Opt. 27, 663 (1988);J. Opt. Soc. Am. A 4(13), P86 (1987).
[CrossRef] [PubMed]

1985

1984

1966

Bartelt, H. O.

Flavin, M. A.

M. A. Flavin, J. L. Horner, “Amplitude Encoded Phase-Only Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 938, 261 (1988).

Gianino, P. D.

Goodman, J. W.

Gregory, D.

Horner, J. L.

Javidi, B.

B. Javidi, D. Gregory, J. L. Horner, “Single Modulator Joint Transform Correlator Architectures,” Appl. Opt. 28, 411 (1989).
[CrossRef] [PubMed]

B. Javidi et al., “Bipolar Joint Transform Correlation,” Proc. Soc. Photo-Opt. Instrum. Eng. 956, 120 (1988).

J. L. Horner, B. Javidi, “Single SLM Joint Transform Correlator,” Invention Disclosure, date of record 24Feb.1988.

B. Javidi, “Analysis of the Bipolar Joint Transform Optical Correlator,” Proc. Soc. Photo-Opt. Instrum. Eng. 977, 307 (1988).

B. Javidi, C. J. Kuo, “Joint Transform Image Correlation Using a Binary Spatial Light Modulator at the Fourier Plane,” Appl. Opt. 27, 663 (1988);J. Opt. Soc. Am. A 4(13), P86 (1987).
[CrossRef] [PubMed]

B. Javidi, S. F. Odeh, “Multiple Object Identification by Bipolar Joint Transform Correlation,” Opt. Eng. 27, 295 (1988).
[CrossRef]

Kuo, C. J.

Leger, J. R.

Odeh, S. F.

B. Javidi, S. F. Odeh, “Multiple Object Identification by Bipolar Joint Transform Correlation,” Opt. Eng. 27, 295 (1988).
[CrossRef]

Rau, J. E.

Weaver, C. S.

Appl. Opt.

Invention Disclosure

J. L. Horner, B. Javidi, “Single SLM Joint Transform Correlator,” Invention Disclosure, date of record 24Feb.1988.

J. Opt. Soc. Am.

Opt. Eng.

B. Javidi, S. F. Odeh, “Multiple Object Identification by Bipolar Joint Transform Correlation,” Opt. Eng. 27, 295 (1988).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

B. Javidi et al., “Bipolar Joint Transform Correlation,” Proc. Soc. Photo-Opt. Instrum. Eng. 956, 120 (1988).

B. Javidi, “Analysis of the Bipolar Joint Transform Optical Correlator,” Proc. Soc. Photo-Opt. Instrum. Eng. 977, 307 (1988).

M. A. Flavin, J. L. Horner, “Amplitude Encoded Phase-Only Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 938, 261 (1988).

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Figures (4)

Fig. 1
Fig. 1

(a) Classical joint transform image correlator using an electrically addressed SLM at the Fourier plane. The input SLM can work in either the continuous tone mode or binary mode. The binary JTC operates by binarizing the Fourier transform interference intensity. (b) Single SLM implementation of binary inputs/binary interference intensity JTC.

Fig. 2
Fig. 2

Input signal and the reference signal: (a) continuous and (b) binarized around median of pixel values.

Fig. 3
Fig. 3

(a) Normalized Fourier transform interference intensity for the binarized inputs. (b) Thresholded Fourier transform interference intensity of (a).

Fig. 4
Fig. 4

Correlation results for the input signals of Fig. 2: (a) classical JTC with continuous inputs, (b) classical JTC with binary inputs, (c) JTC with binary Fourier transform interference intensity, (d) Single SLM JTC with binary inputs and binary Fourier transform interference intensity.

Tables (1)

Tables Icon

Table I Correlation Results

Equations (10)

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G ( α, β ) = S 1 ( 2 π λ f α , 2 π λ f β ) exp ( i 2 π λ f x 0 α ) + S 2 ( 2 π λ f α , 2 π λ f β ) exp ( i 2 π λ f x 0 α )   ,
| G ( α , β ) | 2 = | S 1 ( 2 π λ f α , 2 π λ f β ) | 2 + | S 2 ( 2 π λ f α , 2 π λ f β ) | 2 + S 1   ( 2 π λ f α , 2 π λ f β ) S 2 *   ( 2 π λ f α , 2 π λ f β ) exp ( i 2 π λ f 2 x 0 α ) + S 1 *   ( 2 π λ f α , 2 π λ f β ) S 2   ( 2 π λ f α , 2 π λ f β ) exp ( i 2 π λ f 2 x 0 α ) .
g ( x , y ) = R 11 ( x , y ) + R 22 ( x , y ) + R 12 ( x 2 x 0 , y ) + R 21 ( x + 2 x 0 , y ) ,
R i j ( x , y ) = s i ( x x , y y ) s j ( x , y ) d x d y , i , j = 1 , 2.
g b ( x , y ) = R 11 b ( x , y ) + R 22 b ( x , y ) + R 12 b ( x 2 x 0 , y ) + R 21 b ( x + 2 x 0 , y ) .
H ( α , β ) = { + 1 i f | G ( α , β ) | 2 υ t b , 1 otherwise  
g 1 c ( α , β ) = { 2 π 1     [ R 2 ( α , β ) + S 2 ( α , β )     V T 2 R ( α , β ) S ( α , β ) ] 2 × cos [ 2 x 0 α + φ S ( α , β )     φ R ( α , β ) ] , when | R 2 ( α , β ) + S 2 ( α , β )     V T 2 R ( α , β ) S ( α , β ) | V T , 0 ,else .
g 1 a [ R ( α , β ) ] = { 2 V T π R ( α , β ) 1 V T 4 R 2 ( α , β ) cos ( 2 x 0 α ) , 4 R 2 ( α , β ) V T 0 ,else
H b ( α , β ) = { + 1  if | G b ( α , β ) | 2 υ t f 1  otherwise,
SNR = [ R ( x i , y j ) ] max [ i = 1 N i j = 1 N j | n ( x i , y j ) | 2 / N i N j ] 1 / 2 ,

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