Abstract

In Part I we present an approximate mathematical analysis and exact computer simulations for optical correlation in correlators having pixellated spatial light modulators with transmissive (or reflective) dead zones in both the input and filter planes. We show that the correlation amplitude consists of four terms: a true correlation plus three different types of noise terms originating from the transmissive dead zones in both spatial light modulators; we describe the role that each of these terms plays in the correlation process. We calculate peak intensity, signal-to-noise ratio, and energy throughput efficiency as a function of dead-zone area in both spatial light modulators using either phase-only or matched filters. We utilize a dc block in the filter plane for noise reduction. We also use a filter reference image smaller than the input spatial light modulator size to reduce false correlation peaks. We discuss the effects of fabricating a filter from a filter reference image whose center has been offset from optic axis. In Part II [Appl. Opt. 32, 6536 (1993)] we present a general analytical treatment of our model that can justify the simulation results of Part I. This analysis is applicable even to mixed cases of opaque and transmissive dead zones.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. D. Gianino, C. L. Woods, “Effects of spatial light modulator opaque dead zones on optical correlation,” Appl. Opt. 31, 4025–4033 (1992).
    [CrossRef] [PubMed]
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, pp. 174–177.
  3. M. A. Flavin, J. L. Horner, “Amplitude encoded phase-only filters,” Appl. Opt. 28, 1692–1696 (1989).
    [CrossRef] [PubMed]
  4. F. T. S. Yu, F. Cheng, T. Nagata, D. A. Gregory, “Effects of fringe binarization of multiobject joint transform correlation,” Appl. Opt. 28, 2988–2990 (1989).
    [CrossRef] [PubMed]
  5. B. Javidi, J. L. Horner, “Multifunction nonlinear signal processor: deconvolution and correlation,” Opt. Eng. 28, 837–843 (1989).
  6. J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
    [CrossRef]
  7. J. E. Cravatt, M. K. Giles, “An improved model of the TI deformable mirror device,” in Advances in Optical Information Processing IV, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1296, 110–124 (1990).
  8. M. Giles, J. Taylor, N. Grijalva, B. Gioannini, “Optical image correlation usinga deformable mirror device: a feasibility study,” in Acousto-Optic, Electro-Optic, and Magneto-Optic Devices and Applications, J. A. Lucero, ed., Proc. Soc. Photo-Opt. Instrum. Eng.753, 72–81 (1987).
  9. B. D. Bock, T. A. Crow, M. K. Giles, “Design considerations for miniature optical correlation systems that use pixelated input and filter transducers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 297–309 (1990).
  10. P. D. Gianino, J. L. Horner, C. L. Woods, “Effects of SLM transmissive dead zones on optical correlation,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 240–246 (1990).
  11. D. L. Flannery, J. S. Loomis, M. E. Milkovich, “Transform-ratio ternary phase-amplitude filter formulation for improved correlation discrimination,” Appl. Opt. 27, 4079–4083 (1988).
    [CrossRef] [PubMed]
  12. K. H. Fielding, J. L. Horner, “1-f binary joint transform correlator,” Opt. Eng. 29, 1081–1087 (1990).
    [CrossRef]
  13. B. V. K. Vijaya Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
    [CrossRef]
  14. M. A. Flavin, J. L. Horner, “Amplitude encoded binary phase-only filters,” in Digital and Optical Shape Representation and Pattern Recognition, R. D. Juday, ed., Proc. Soc. Photo-Opt. Instrum. Eng.938, 261–265 (1988).
  15. J. D. Downie, M. B. Reid, “Mapping considerations for optimal binary correlation filters,” Appl. Opt. 29, 5235–5241 (1990).
    [CrossRef] [PubMed]
  16. J. Khoury, J. Kane, C. L. Woods, P. D. Gianino, “Edge enhancement techniques for improving the performance of binary phase-only filter pattern recognition devices,” Opt. Eng. (to be published).
  17. D. L. Flannery, J. S. Loomis, M. E. Milkovich, “Design elements of binary phase-only correlation filters,” Appl. Opt. 27, 4231–4235 (1988).
    [CrossRef] [PubMed]

1992 (1)

1990 (4)

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

B. V. K. Vijaya Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
[CrossRef]

J. D. Downie, M. B. Reid, “Mapping considerations for optimal binary correlation filters,” Appl. Opt. 29, 5235–5241 (1990).
[CrossRef] [PubMed]

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

1989 (3)

1988 (2)

Bock, B. D.

B. D. Bock, T. A. Crow, M. K. Giles, “Design considerations for miniature optical correlation systems that use pixelated input and filter transducers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 297–309 (1990).

Bunch, R. M.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Cheng, F.

Cottrell, D. M.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Cravatt, J. E.

J. E. Cravatt, M. K. Giles, “An improved model of the TI deformable mirror device,” in Advances in Optical Information Processing IV, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1296, 110–124 (1990).

Crow, T. A.

B. D. Bock, T. A. Crow, M. K. Giles, “Design considerations for miniature optical correlation systems that use pixelated input and filter transducers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 297–309 (1990).

Davis, J. A.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Downie, J. D.

Fielding, K. H.

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

Flannery, D. L.

Flavin, M. A.

M. A. Flavin, J. L. Horner, “Amplitude encoded phase-only filters,” Appl. Opt. 28, 1692–1696 (1989).
[CrossRef] [PubMed]

M. A. Flavin, J. L. Horner, “Amplitude encoded binary phase-only filters,” in Digital and Optical Shape Representation and Pattern Recognition, R. D. Juday, ed., Proc. Soc. Photo-Opt. Instrum. Eng.938, 261–265 (1988).

Gianino, P. D.

P. D. Gianino, C. L. Woods, “Effects of spatial light modulator opaque dead zones on optical correlation,” Appl. Opt. 31, 4025–4033 (1992).
[CrossRef] [PubMed]

P. D. Gianino, J. L. Horner, C. L. Woods, “Effects of SLM transmissive dead zones on optical correlation,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 240–246 (1990).

J. Khoury, J. Kane, C. L. Woods, P. D. Gianino, “Edge enhancement techniques for improving the performance of binary phase-only filter pattern recognition devices,” Opt. Eng. (to be published).

Giles, M.

M. Giles, J. Taylor, N. Grijalva, B. Gioannini, “Optical image correlation usinga deformable mirror device: a feasibility study,” in Acousto-Optic, Electro-Optic, and Magneto-Optic Devices and Applications, J. A. Lucero, ed., Proc. Soc. Photo-Opt. Instrum. Eng.753, 72–81 (1987).

Giles, M. K.

J. E. Cravatt, M. K. Giles, “An improved model of the TI deformable mirror device,” in Advances in Optical Information Processing IV, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1296, 110–124 (1990).

B. D. Bock, T. A. Crow, M. K. Giles, “Design considerations for miniature optical correlation systems that use pixelated input and filter transducers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 297–309 (1990).

Gioannini, B.

M. Giles, J. Taylor, N. Grijalva, B. Gioannini, “Optical image correlation usinga deformable mirror device: a feasibility study,” in Acousto-Optic, Electro-Optic, and Magneto-Optic Devices and Applications, J. A. Lucero, ed., Proc. Soc. Photo-Opt. Instrum. Eng.753, 72–81 (1987).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, pp. 174–177.

Gregory, D. A.

Grijalva, N.

M. Giles, J. Taylor, N. Grijalva, B. Gioannini, “Optical image correlation usinga deformable mirror device: a feasibility study,” in Acousto-Optic, Electro-Optic, and Magneto-Optic Devices and Applications, J. A. Lucero, ed., Proc. Soc. Photo-Opt. Instrum. Eng.753, 72–81 (1987).

Hassebrook, L.

Horner, J. L.

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

M. A. Flavin, J. L. Horner, “Amplitude encoded phase-only filters,” Appl. Opt. 28, 1692–1696 (1989).
[CrossRef] [PubMed]

B. Javidi, J. L. Horner, “Multifunction nonlinear signal processor: deconvolution and correlation,” Opt. Eng. 28, 837–843 (1989).

M. A. Flavin, J. L. Horner, “Amplitude encoded binary phase-only filters,” in Digital and Optical Shape Representation and Pattern Recognition, R. D. Juday, ed., Proc. Soc. Photo-Opt. Instrum. Eng.938, 261–265 (1988).

P. D. Gianino, J. L. Horner, C. L. Woods, “Effects of SLM transmissive dead zones on optical correlation,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 240–246 (1990).

Javidi, B.

B. Javidi, J. L. Horner, “Multifunction nonlinear signal processor: deconvolution and correlation,” Opt. Eng. 28, 837–843 (1989).

Kane, J.

J. Khoury, J. Kane, C. L. Woods, P. D. Gianino, “Edge enhancement techniques for improving the performance of binary phase-only filter pattern recognition devices,” Opt. Eng. (to be published).

Khoury, J.

J. Khoury, J. Kane, C. L. Woods, P. D. Gianino, “Edge enhancement techniques for improving the performance of binary phase-only filter pattern recognition devices,” Opt. Eng. (to be published).

Loomis, J. S.

Merrill, E. A.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Milkovich, M. E.

Nagata, T.

Reid, M. B.

Taylor, J.

M. Giles, J. Taylor, N. Grijalva, B. Gioannini, “Optical image correlation usinga deformable mirror device: a feasibility study,” in Acousto-Optic, Electro-Optic, and Magneto-Optic Devices and Applications, J. A. Lucero, ed., Proc. Soc. Photo-Opt. Instrum. Eng.753, 72–81 (1987).

Vijaya Kumar, B. V. K.

Woods, C. L.

P. D. Gianino, C. L. Woods, “Effects of spatial light modulator opaque dead zones on optical correlation,” Appl. Opt. 31, 4025–4033 (1992).
[CrossRef] [PubMed]

P. D. Gianino, J. L. Horner, C. L. Woods, “Effects of SLM transmissive dead zones on optical correlation,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 240–246 (1990).

J. Khoury, J. Kane, C. L. Woods, P. D. Gianino, “Edge enhancement techniques for improving the performance of binary phase-only filter pattern recognition devices,” Opt. Eng. (to be published).

Yu, F. T. S.

Appl. Opt. (7)

Opt. Eng. (3)

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

B. Javidi, J. L. Horner, “Multifunction nonlinear signal processor: deconvolution and correlation,” Opt. Eng. 28, 837–843 (1989).

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Other (7)

J. E. Cravatt, M. K. Giles, “An improved model of the TI deformable mirror device,” in Advances in Optical Information Processing IV, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1296, 110–124 (1990).

M. Giles, J. Taylor, N. Grijalva, B. Gioannini, “Optical image correlation usinga deformable mirror device: a feasibility study,” in Acousto-Optic, Electro-Optic, and Magneto-Optic Devices and Applications, J. A. Lucero, ed., Proc. Soc. Photo-Opt. Instrum. Eng.753, 72–81 (1987).

B. D. Bock, T. A. Crow, M. K. Giles, “Design considerations for miniature optical correlation systems that use pixelated input and filter transducers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 297–309 (1990).

P. D. Gianino, J. L. Horner, C. L. Woods, “Effects of SLM transmissive dead zones on optical correlation,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 240–246 (1990).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, pp. 174–177.

J. Khoury, J. Kane, C. L. Woods, P. D. Gianino, “Edge enhancement techniques for improving the performance of binary phase-only filter pattern recognition devices,” Opt. Eng. (to be published).

M. A. Flavin, J. L. Horner, “Amplitude encoded binary phase-only filters,” in Digital and Optical Shape Representation and Pattern Recognition, R. D. Juday, ed., Proc. Soc. Photo-Opt. Instrum. Eng.938, 261–265 (1988).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Diagram of a typical pixel of dimensions c x , c y in SLM1. The active zone in the center has dimensions b x , b y . The shaded area corresponds to the transmissive (or reflective) dead zone.

Fig. 2
Fig. 2

Normalized correlation-peak intensity I p (dashed curves) versus transmissive dead-zone area (in percent) for Case A with a one-pixel dc block inserted in the filter plane. The calculated values are indicated by solid squares. The solid curves are for the corresponding opaque dead-zone mode with no dc block included. The dotted curves give the normalized maximum intensities of those subsidiary peaks higher than I p . Their calculated values are indicated by solid circles.

Fig. 3
Fig. 3

Same as Fig. 2, except for Case B.

Fig. 4
Fig. 4

Same as Fig. 2 except for Case C.

Fig. 5
Fig. 5

Correlation SNR versus transmissive dead-zone area (in percent) with each of the three filters for Cases A, B, and C. The dotted portions of each curve refer to the condition when a subsidiary peak is higher in amplitude than the correlation peak. The vertical bars on the right indicate the SNR variations for each filter under opaque dead-zone conditions and no dc block.

Fig. 6
Fig. 6

Representative three-dimensional pattern for a correlator having a BPOF, a one-pixel dc block and no TDZ in SLM2, and a TDZ of 44% in SLM1 (Case B). The reference image is one half as large as, and is centered within, the input SLM. The SNR is 6.4.

Tables (4)

Tables Icon

Table 1 Transmissive Dead-Zone Cases Studied

Tables Icon

Table 2 Comparison of Signal-to-Noise Ratio and Peak Intensity for Transmissive Dead Zone with and without a One-Pixel dc Blocka

Tables Icon

Table 3 Comparison of Signal-to-Nolse Ratio and Peak Intensity for Transmissive Dead Zone (with One-Pixel dc Block) Relative to Opaque Dead Zone,

Tables Icon

Table 4 Energy Partitioning (%) throughout Correlator with a Phase-Only Filter and a One-Pixeldc Blocka

Equations (10)

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

Z 1 = 1 - b x b y / c x c y ,
Z 2 = 1 - e x e y / h x h y ,
Signal ( SLM 1 ) ~ [ ( 1 - Z 1 ) s + Z 1 ] r x r y ,
Signal ( SLM 2 ) ~ [ ( 1 - Z 2 ) F * + Z 2 ] Q ξ Q η T dc .
k T = k c + k s + k R + k FR .
k c ~ ( 1 - Z 1 ) ( 1 - Z 2 ) ( s f * ) t dc ,
k s ~ ( 1 - Z 1 ) Z 2 s t dc ,
k R ~ Z 1 Z 2 r x r y t dc ,
k FR ~ Z 1 ( 1 - Z 2 ) ( r x r y f * ) t dc ,
SNR = ( k c ) max / { j = 1 n T ( k T ) j 2 [ < 0.5 ( k c ) max ] / n T } 1 / 2 .

Metrics