Abstract

Experiments are provided to investigate nonlinear joint transform correlator sensitivity to scaling and rotation changes of input objects for various degrees of nonlinearity applied to the joint power spectrum. The experimental results for the images used here show that a severe nonlinear transformation of the joint power spectrum increases the sensitivity of the correlation peak intensity to scaling and rotation changes of input objects. However, the correlation peak-to-sidelobe ratio of the nonlinear joint transform correlator remains higher than the linear joint transform correlator. These experiments indicate that, in the presence of input signal rotation or scale changes, the performance of the nonlinear joint transform correlator may be better than the linear joint transform correlator. The effect of the modulation transfer function of the spatial light modulator on the nonlinear joint transform correlator performance in the presence of multiple input targets is discussed.

© 1992 Optical Society of America

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References

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  1. B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989).
  2. B. Javidi, J. Wang, Q. Tang, “Multiple-object binary joint transform correlation using multiple level threshold crossing,” Appl. Opt. 30, 4234–4244 (1991).
  3. B. Javidi, Q. Tang, D. A. Gregory, T. Hudson, “Experiments on nonlinear joint transform correlators using an optically addressed SLM in the Fourier plane,” Appl. Opt. 30, 1772–1776 (1991).
  4. B. Javidi, “Comparison between the nonlinear joint transform correlator and the nonlinear matched filter based correlator,” Opt. Eng. 29, 1013–1020 (1990).
  5. B. Javidi, J. L. Horner, “Single SLM joint transform correlator,” Appl. Opt. 28, 1027–1032 (1989).
  6. K. H. Fielding, J. L. Horner, “1-f binary joint correlator,” Opt. Eng. 29, 1081–1087 (1990).
  7. W. B. Hahn, D. L. Flannery, “Basic design elements of the binary joint transform correlator,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 344–356 (1990).
  8. A. VanderLugt, F. B. Rotz, “The use of film nonlinearities in optical spatial filtering,” Appl. Opt. 9, 215–222 (1970).
  9. A. Kozma, “Photographic recording of spatially modulated coherent light,” J. Opt. Soc. Am. 56, 428–432 (1966).
  10. C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
  11. W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. Casasent, H. B. Brown, B. V. Markevitch, “Application of the liquid crystal light valve to real time optical data processing,” Opt. Eng. 17, 371–384 (1978).
  12. J. L. Horner, “Metrics for assessing pattern recognition performance,” Appl. Opt. 31, 165–166 (1992). The PSR used in our paper is the same as the signal-to-noise ratio SNR1 defined in Horner’s paper.
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1966).
  14. B. Javidi, G. Zhang, “Experiments on nonlinearly transformed matched filters,” 31, 934–938 (1992).

1992

1991

1990

B. Javidi, “Comparison between the nonlinear joint transform correlator and the nonlinear matched filter based correlator,” Opt. Eng. 29, 1013–1020 (1990).

K. H. Fielding, J. L. Horner, “1-f binary joint correlator,” Opt. Eng. 29, 1081–1087 (1990).

1989

1978

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. Casasent, H. B. Brown, B. V. Markevitch, “Application of the liquid crystal light valve to real time optical data processing,” Opt. Eng. 17, 371–384 (1978).

1970

1966

Bleha, W. P.

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. Casasent, H. B. Brown, B. V. Markevitch, “Application of the liquid crystal light valve to real time optical data processing,” Opt. Eng. 17, 371–384 (1978).

Brown, H. B.

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. Casasent, H. B. Brown, B. V. Markevitch, “Application of the liquid crystal light valve to real time optical data processing,” Opt. Eng. 17, 371–384 (1978).

Casasent, D.

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. Casasent, H. B. Brown, B. V. Markevitch, “Application of the liquid crystal light valve to real time optical data processing,” Opt. Eng. 17, 371–384 (1978).

Fielding, K. H.

K. H. Fielding, J. L. Horner, “1-f binary joint correlator,” Opt. Eng. 29, 1081–1087 (1990).

Flannery, D. L.

W. B. Hahn, D. L. Flannery, “Basic design elements of the binary joint transform correlator,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 344–356 (1990).

Goodman, J. W.

Gregory, D. A.

Grinberg, J.

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. Casasent, H. B. Brown, B. V. Markevitch, “Application of the liquid crystal light valve to real time optical data processing,” Opt. Eng. 17, 371–384 (1978).

Hahn, W. B.

W. B. Hahn, D. L. Flannery, “Basic design elements of the binary joint transform correlator,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 344–356 (1990).

Horner, J. L.

Hudson, T.

Javidi, B.

Kozma, A.

Lipton, L. T.

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. Casasent, H. B. Brown, B. V. Markevitch, “Application of the liquid crystal light valve to real time optical data processing,” Opt. Eng. 17, 371–384 (1978).

Markevitch, B. V.

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. Casasent, H. B. Brown, B. V. Markevitch, “Application of the liquid crystal light valve to real time optical data processing,” Opt. Eng. 17, 371–384 (1978).

Reif, P. G.

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. Casasent, H. B. Brown, B. V. Markevitch, “Application of the liquid crystal light valve to real time optical data processing,” Opt. Eng. 17, 371–384 (1978).

Rotz, F. B.

Tang, Q.

VanderLugt, A.

Wang, J.

Weaver, C. S.

Wiener-Avnear, E.

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. Casasent, H. B. Brown, B. V. Markevitch, “Application of the liquid crystal light valve to real time optical data processing,” Opt. Eng. 17, 371–384 (1978).

Zhang, G.

B. Javidi, G. Zhang, “Experiments on nonlinearly transformed matched filters,” 31, 934–938 (1992).

Appl. Opt.

J. Opt. Soc. Am.

Opt. Eng.

B. Javidi, “Comparison between the nonlinear joint transform correlator and the nonlinear matched filter based correlator,” Opt. Eng. 29, 1013–1020 (1990).

K. H. Fielding, J. L. Horner, “1-f binary joint correlator,” Opt. Eng. 29, 1081–1087 (1990).

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. Casasent, H. B. Brown, B. V. Markevitch, “Application of the liquid crystal light valve to real time optical data processing,” Opt. Eng. 17, 371–384 (1978).

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1966).

B. Javidi, G. Zhang, “Experiments on nonlinearly transformed matched filters,” 31, 934–938 (1992).

W. B. Hahn, D. L. Flannery, “Basic design elements of the binary joint transform correlator,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 344–356 (1990).

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Figures (14)

Fig. 1
Fig. 1

Nonlinear JTC that uses LCLV at the Fourier plane.

Fig. 2
Fig. 2

Image used in the correlation tests. The tank is the reference image.

Fig. 3
Fig. 3

Input–output (I/O) characteristics of the LCLV for three different power supply frequencies applied to the LCLV. The bias supply voltage is 10 V rms.

Fig. 4
Fig. 4

Variations in the normalized correlation peak intensity versus the scale factor of the input signal. Circles correspond to the 200-Hz curve, stars correspond to the 120-Hz curve, and crosses correspond to the 60-Hz curve: (a) correlation of the tank and the tank, without scene noise, (b) correlation of the tank and the tank in the input scene noise.

Fig. 5
Fig. 5

Variations in the correlation PSR versus the scale factor of the input signal. Circles correspond to the 200-Hz curve, stars correspond to the 120-Hz curve, and crosses correspond to the 60-Hz curve: (a) correlation of the tank and the tank without scene noise, (b) correlation of the tank and the tank in the input scene noise.

Fig. 6
Fig. 6

Photographs of the nonlinear JTC output of the tank and the tank without scene noise for no rotational or scale changes of the input image. The 3-D plots of the correlation signals also are shown in the bottom figures. The 3-D plots are normalized to a maximum value of unity. The dc terms are not shown in the 3-D plots: (a) the LCLV is operating along the 60-Hz curve, (b) the LCLV is operating along the 200-Hz curve.

Fig. 7
Fig. 7

Photographs of the nonlinear JTC output of the tank and the tank without scene noise for a scaling change of 1.05. The 3-D plots of the correlation signals also are shown in the bottom figures. The 3-D plots are normalized to a maximum value of unity. The dc terms are not shown in the 3-D plots: (a) the LCLV is operating along the 60-Hz curve, (b) the LCLV is operating along the 200-Hz curve.

Fig. 8
Fig. 8

Variations in the normalized correlation peak intensity versus the rotation factor of the input signal. Circles correspond to the 200-Hz curve, stars correspond to the 120-Hz curve, and crosses correspond to the 60-Hz curve: (a) correlation of the tank and the tank without scene noise, (b) correlation of the tank and the tank in the input scene noise.

Fig. 9
Fig. 9

Variations in the correlation PSR versus the rotation factor of the input signal. Circles correspond to the 200-Hz curve, stars correspond to the 120-Hz curve, and crosses correspond to the 60-Hz curve: (a) correlation of the tank and the tank without scene noise, (b) Correlation of the tank and the tank in the input scene noise.

Fig. 10
Fig. 10

Photographs of the nonlinear JTC output of the tank and the tank without noise for a rotational change of 2 deg. The 3-D plots of the correlation signals are also shown. The 3-D plots are normalized to a maximum value of units. The dc terms are not shown in 3-D plots: (a) the LCLV is operating along the 60-Hz curve, (b) the LCLV is operating along the 200-Hz curve.

Fig. 11
Fig. 11

MTF of the LCLV used in the experiments.

Fig. 12
Fig. 12

Normalized correlation peak intensity versus the separation of the input objects.

Fig. 13
Fig. 13

Reference object and input targets for a multiobject nonlinear JTC experiment. The reference object is denoted by r, and the input targets are denoted by s1, s2, and s3.

Fig. 14
Fig. 14

Photograph of the nonlinear JTC output of the tank and the input scene with three tanks (see Fig. 13). The 3-D plot of the nonlinear JTC output also is shown in the lower figure. The correlations between the reference object and the input targets are denoted by rsi, and the correlations between the input targets are denoted by sisj.

Equations (7)

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E ( α , β ) = S 2 ( α , β ) + R 2 ( α , β ) + 2 S ( α , β ) R ( α , β ) × cos [ 2 x 0 α + ϕ S ( α , β ) - ϕ R ( α , β ) ] ,
g ( E ) = ν = 0 H ν [ R ( α , β ) , S ( α , β ) ] × cos [ 2 ν x 0 α + ν ϕ S ( α , β ) - ν ϕ R ( α , β ) ] ,
H ν [ R ( α , β ) , S ( α , β ) ] = ν 2 π ( i ) ν G ( ω ) exp { i ω [ R 2 ( α , β ) + S 2 ( α , β ) ] } × J ν [ 2 ω R ( α , β ) S ( α , β ) ] d ω .
PSR = [ I ( x i , y j ) ] max i N 1 j N 2 n ( x i , y j ) / N 1 N 2 ,
2 x 0 ½ ( L r + 3 L s ) ,
E ( α , β ) = S 2 ( α , β ) + R 2 ( α , β ) + 2 S ( α , β ) R ( α , β ) M ( 2 x 0 λ f , 0 ) × cos [ 2 x 0 α + ϕ S ( α , β ) - ϕ R ( α , β ) ] ,
max ( D s i s j ) < min ( D s i r ) ,             ( i , j = 1 , 2 , , n ) ,

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