Abstract

The design of reduced-resolution filters by multiresolution analysis (MA) or by downsampling is extended to spatial light modulators with fill factors less than one. Analysis shows that the dependence of the zero-order correlation peaks with fill factor varies with target size for both design techniques. Also, a practicable performance improvement is obtained for MA compared with downsampling for small- to medium-sized targets that is greater for larger fill factors. The validity of the analysis is confirmed by simulation. A reduced-resolution optical correlator is constructed, and a comparison of MA and downsampling filters is performed for different-sized targets. The experimental results show good qualitative agreement with the simulation; however, the first-order correlation peaks were found to be greater for the experimental results. A possible reason for this is that the manufacturer’s fill-factor specification might be too large; therefore a new technique for measuring the fill factor is proposed.

© 1998 Optical Society of America

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References

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  1. S. A. Serati, T. K. Ewing, R. A. Serati, K. M. Johnson, and D. M. Simon, “Programmable 128 × 128 ferroelectric-liquid-crystal spatial-light-modulator compact correlator,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE 1959, 55–68 (1993).
    [CrossRef]
  2. S. D. Lindell, “Summary of the Transfer of Optical Processing to Systems: optical pattern recognition program,” in Transition of Optical Processors into Systems 1995, D. P. Casasent, ed., Proc. SPIE 2489, 20–34 (1995).
    [CrossRef]
  3. P. C. Miller, P. Virgo, M. Royce, and S. Angeli, “Evaluation of a laboratory automatic target recognition system: air-to-sea image sequence,” DSTO Rep. TR-0478 (Defence Science and Technology Organisation, Salisbury, Australia, 1997).
  4. R. Caprari, “Memory design for electrically addressed spatial light modulators,” DSTO Rep. RR-0094 (Defence Science and Technology Organisation, Salisbury, Australia, 1997).
  5. G. Gheen, E. Washwell, and C. Huang, “Problems facing optical correlators,” in Optical Information Processing Systems and Architectures IV, B. Javidi, ed., Proc. SPIE 1772, 96–102 (1992).
    [CrossRef]
  6. P. C. Miller, “Multiresolution correlator analysis and filter design,” Appl. Opt. 35, 5790–5810 (1996).
    [CrossRef] [PubMed]
  7. S. P. Kozaitis and W. E. Foor, “Optical correlation using reduced resolution filters,” Opt. Eng. 31, 1929–1935 (1992).
    [CrossRef]
  8. D. L. Flannery and S. C. Gustafson, “Adaptive optical correlation using neural network approaches,” in Optical Pattern Recognition, J. L. Horner and B. Javadi, eds., Vol. CR40 of SPIE Critical Reviews of Optical Science and Technology (SPIE Press, Bellingham, Wash., 1992), pp. 25–45.
  9. P. C. Miller, “Optimum reduced-resolution phase-only filters for extended target recognition,” Opt. Eng. 32, 2890–2898 (1993).
    [CrossRef]
  10. S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Patt. Anal. Mach. Intell. 11, 674–693 (1989).
    [CrossRef]
  11. P. C. Miller, “Reduced-resolution synthetic-discriminant-function design by multiresolution wavelet analysis,” Appl. Opt. 34, 865–878 (1995).
    [CrossRef] [PubMed]
  12. P. D. Gianino and C. L. Woods, “General treatment of spatial light modulator dead-zone effects on optical correlation. I. Computer simulations,” Appl. Opt. 32, 6527–6535 (1993).
    [CrossRef] [PubMed]
  13. J. L. Horner and J. R. Leger, “Pattern recognition with binary phase-only filters,” Appl. Opt. 24, 609–611 (1985).
    [CrossRef] [PubMed]
  14. J. A. Davis, D. M. Cottrell, and R. P. Tiangco “Analysis of the phase-only filter,” in Optical Pattern Recognition VI, D. P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490, 77–87 (1995).
    [CrossRef]
  15. D. J. McKnight, K. M. Johnson, and R. A. Serati, “256 by 256 liquid-crystal-on-silicon spatial light modulator,” Appl. Opt. 33, 2775–2784 (1994).
    [CrossRef] [PubMed]
  16. Ferroelectric liquid-crystal-on-silicon SLM’s are available from Boulder Nonlinear Systems, Inc., 1898 South Flatiron Court, Boulder, Colorado 80301.

1996 (1)

1995 (1)

1994 (1)

1993 (2)

1992 (1)

S. P. Kozaitis and W. E. Foor, “Optical correlation using reduced resolution filters,” Opt. Eng. 31, 1929–1935 (1992).
[CrossRef]

1989 (1)

S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Patt. Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

1985 (1)

Angeli, S.

P. C. Miller, P. Virgo, M. Royce, and S. Angeli, “Evaluation of a laboratory automatic target recognition system: air-to-sea image sequence,” DSTO Rep. TR-0478 (Defence Science and Technology Organisation, Salisbury, Australia, 1997).

Caprari, R.

R. Caprari, “Memory design for electrically addressed spatial light modulators,” DSTO Rep. RR-0094 (Defence Science and Technology Organisation, Salisbury, Australia, 1997).

Cottrell, D. M.

J. A. Davis, D. M. Cottrell, and R. P. Tiangco “Analysis of the phase-only filter,” in Optical Pattern Recognition VI, D. P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490, 77–87 (1995).
[CrossRef]

Davis, J. A.

J. A. Davis, D. M. Cottrell, and R. P. Tiangco “Analysis of the phase-only filter,” in Optical Pattern Recognition VI, D. P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490, 77–87 (1995).
[CrossRef]

Ewing, T. K.

S. A. Serati, T. K. Ewing, R. A. Serati, K. M. Johnson, and D. M. Simon, “Programmable 128 × 128 ferroelectric-liquid-crystal spatial-light-modulator compact correlator,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE 1959, 55–68 (1993).
[CrossRef]

Flannery, D. L.

D. L. Flannery and S. C. Gustafson, “Adaptive optical correlation using neural network approaches,” in Optical Pattern Recognition, J. L. Horner and B. Javadi, eds., Vol. CR40 of SPIE Critical Reviews of Optical Science and Technology (SPIE Press, Bellingham, Wash., 1992), pp. 25–45.

Foor, W. E.

S. P. Kozaitis and W. E. Foor, “Optical correlation using reduced resolution filters,” Opt. Eng. 31, 1929–1935 (1992).
[CrossRef]

Gheen, G.

G. Gheen, E. Washwell, and C. Huang, “Problems facing optical correlators,” in Optical Information Processing Systems and Architectures IV, B. Javidi, ed., Proc. SPIE 1772, 96–102 (1992).
[CrossRef]

Gianino, P. D.

Gustafson, S. C.

D. L. Flannery and S. C. Gustafson, “Adaptive optical correlation using neural network approaches,” in Optical Pattern Recognition, J. L. Horner and B. Javadi, eds., Vol. CR40 of SPIE Critical Reviews of Optical Science and Technology (SPIE Press, Bellingham, Wash., 1992), pp. 25–45.

Horner, J. L.

Huang, C.

G. Gheen, E. Washwell, and C. Huang, “Problems facing optical correlators,” in Optical Information Processing Systems and Architectures IV, B. Javidi, ed., Proc. SPIE 1772, 96–102 (1992).
[CrossRef]

Johnson, K. M.

D. J. McKnight, K. M. Johnson, and R. A. Serati, “256 by 256 liquid-crystal-on-silicon spatial light modulator,” Appl. Opt. 33, 2775–2784 (1994).
[CrossRef] [PubMed]

S. A. Serati, T. K. Ewing, R. A. Serati, K. M. Johnson, and D. M. Simon, “Programmable 128 × 128 ferroelectric-liquid-crystal spatial-light-modulator compact correlator,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE 1959, 55–68 (1993).
[CrossRef]

Kozaitis, S. P.

S. P. Kozaitis and W. E. Foor, “Optical correlation using reduced resolution filters,” Opt. Eng. 31, 1929–1935 (1992).
[CrossRef]

Leger, J. R.

Lindell, S. D.

S. D. Lindell, “Summary of the Transfer of Optical Processing to Systems: optical pattern recognition program,” in Transition of Optical Processors into Systems 1995, D. P. Casasent, ed., Proc. SPIE 2489, 20–34 (1995).
[CrossRef]

Mallat, S. G.

S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Patt. Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

McKnight, D. J.

Miller, P. C.

P. C. Miller, “Multiresolution correlator analysis and filter design,” Appl. Opt. 35, 5790–5810 (1996).
[CrossRef] [PubMed]

P. C. Miller, “Reduced-resolution synthetic-discriminant-function design by multiresolution wavelet analysis,” Appl. Opt. 34, 865–878 (1995).
[CrossRef] [PubMed]

P. C. Miller, “Optimum reduced-resolution phase-only filters for extended target recognition,” Opt. Eng. 32, 2890–2898 (1993).
[CrossRef]

P. C. Miller, P. Virgo, M. Royce, and S. Angeli, “Evaluation of a laboratory automatic target recognition system: air-to-sea image sequence,” DSTO Rep. TR-0478 (Defence Science and Technology Organisation, Salisbury, Australia, 1997).

Royce, M.

P. C. Miller, P. Virgo, M. Royce, and S. Angeli, “Evaluation of a laboratory automatic target recognition system: air-to-sea image sequence,” DSTO Rep. TR-0478 (Defence Science and Technology Organisation, Salisbury, Australia, 1997).

Serati, R. A.

D. J. McKnight, K. M. Johnson, and R. A. Serati, “256 by 256 liquid-crystal-on-silicon spatial light modulator,” Appl. Opt. 33, 2775–2784 (1994).
[CrossRef] [PubMed]

S. A. Serati, T. K. Ewing, R. A. Serati, K. M. Johnson, and D. M. Simon, “Programmable 128 × 128 ferroelectric-liquid-crystal spatial-light-modulator compact correlator,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE 1959, 55–68 (1993).
[CrossRef]

Serati, S. A.

S. A. Serati, T. K. Ewing, R. A. Serati, K. M. Johnson, and D. M. Simon, “Programmable 128 × 128 ferroelectric-liquid-crystal spatial-light-modulator compact correlator,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE 1959, 55–68 (1993).
[CrossRef]

Simon, D. M.

S. A. Serati, T. K. Ewing, R. A. Serati, K. M. Johnson, and D. M. Simon, “Programmable 128 × 128 ferroelectric-liquid-crystal spatial-light-modulator compact correlator,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE 1959, 55–68 (1993).
[CrossRef]

Tiangco, R. P.

J. A. Davis, D. M. Cottrell, and R. P. Tiangco “Analysis of the phase-only filter,” in Optical Pattern Recognition VI, D. P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490, 77–87 (1995).
[CrossRef]

Virgo, P.

P. C. Miller, P. Virgo, M. Royce, and S. Angeli, “Evaluation of a laboratory automatic target recognition system: air-to-sea image sequence,” DSTO Rep. TR-0478 (Defence Science and Technology Organisation, Salisbury, Australia, 1997).

Washwell, E.

G. Gheen, E. Washwell, and C. Huang, “Problems facing optical correlators,” in Optical Information Processing Systems and Architectures IV, B. Javidi, ed., Proc. SPIE 1772, 96–102 (1992).
[CrossRef]

Woods, C. L.

Appl. Opt. (5)

IEEE Trans. Patt. Anal. Mach. Intell. (1)

S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Patt. Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

Opt. Eng. (2)

S. P. Kozaitis and W. E. Foor, “Optical correlation using reduced resolution filters,” Opt. Eng. 31, 1929–1935 (1992).
[CrossRef]

P. C. Miller, “Optimum reduced-resolution phase-only filters for extended target recognition,” Opt. Eng. 32, 2890–2898 (1993).
[CrossRef]

Other (8)

D. L. Flannery and S. C. Gustafson, “Adaptive optical correlation using neural network approaches,” in Optical Pattern Recognition, J. L. Horner and B. Javadi, eds., Vol. CR40 of SPIE Critical Reviews of Optical Science and Technology (SPIE Press, Bellingham, Wash., 1992), pp. 25–45.

J. A. Davis, D. M. Cottrell, and R. P. Tiangco “Analysis of the phase-only filter,” in Optical Pattern Recognition VI, D. P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490, 77–87 (1995).
[CrossRef]

Ferroelectric liquid-crystal-on-silicon SLM’s are available from Boulder Nonlinear Systems, Inc., 1898 South Flatiron Court, Boulder, Colorado 80301.

S. A. Serati, T. K. Ewing, R. A. Serati, K. M. Johnson, and D. M. Simon, “Programmable 128 × 128 ferroelectric-liquid-crystal spatial-light-modulator compact correlator,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE 1959, 55–68 (1993).
[CrossRef]

S. D. Lindell, “Summary of the Transfer of Optical Processing to Systems: optical pattern recognition program,” in Transition of Optical Processors into Systems 1995, D. P. Casasent, ed., Proc. SPIE 2489, 20–34 (1995).
[CrossRef]

P. C. Miller, P. Virgo, M. Royce, and S. Angeli, “Evaluation of a laboratory automatic target recognition system: air-to-sea image sequence,” DSTO Rep. TR-0478 (Defence Science and Technology Organisation, Salisbury, Australia, 1997).

R. Caprari, “Memory design for electrically addressed spatial light modulators,” DSTO Rep. RR-0094 (Defence Science and Technology Organisation, Salisbury, Australia, 1997).

G. Gheen, E. Washwell, and C. Huang, “Problems facing optical correlators,” in Optical Information Processing Systems and Architectures IV, B. Javidi, ed., Proc. SPIE 1772, 96–102 (1992).
[CrossRef]

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Figures (17)

Fig. 1
Fig. 1

Schematic diagram illustrating the SLM pixel structure at a resolution of 2 j and with a pixel fill factor F .

Fig. 2
Fig. 2

Idealized 1-D target s(x) consisting of two edges separated by a distance 2x d .

Fig. 3
Fig. 3

Downsampling technique’s (a) PMF R and (b) PMF I versus x for SLM fill factors of 0.6 (dotted curve), 0.8 (dashed curve), and 1.0 (solid curve). (The same values and corresponding curve formats are used for the fill factor in all subsequent plots.)

Fig. 4
Fig. 4

Modulation of the first order by (a) PMF R and (b) PMF I with F = 0.6, 1.0.

Fig. 5
Fig. 5

Variation of the centered sinc term in the MA impulse response F sinc(x4 F /L) versus x for different fill factors.

Fig. 6
Fig. 6

Variation of the downsampling technique’s zero-order correlation peak C R 0 with the target size x d for different fill factors.

Fig. 7
Fig. 7

Variation of (a) the real C R 1 and (b) the imaginary C I 1 components of the downsampling technique’s first-order correlation peak with a target size x d for different fill factors.

Fig. 8
Fig. 8

Plot illustrating the modulation of the first-order edges by the downsampling PMF R for a large target and with F = 0.6, 1.0. (The edges associated with the different fill factors have been displaced slightly for clarity.)

Fig. 9
Fig. 9

Variation of the MA zero-order correlation peak C R 0 with the target size x d for different fill factors.

Fig. 10
Fig. 10

Variation of (a) the real C R 1 and (b) the imaginary C I 1 components of the MA’s first-order correlation peak with the target size x d for different fill factors.

Fig. 11
Fig. 11

(a) Plot illustrating the modulation of the first-order edges at the points x = L/4 ± x d by the centered sinc function F sinc(x4 F /L) for a large target and with F = 0.6, 1.0. (b) Subsequent modulation of the edges shown in (a) by the offset sinc function sinc[4(x - L/4) F /L].

Fig. 12
Fig. 12

Binarized edge-enhanced synthetic image of the smaller landrover target, LR1.

Fig. 13
Fig. 13

Plots of vertical slices through simulated correlation planes obtained with LR1 and its (a) downsampling and (b) MA filters. The dashed–dotted and solid curves correspond to a flat fill factor of 0.56 and a fill factor of 0.77, respectively. (The solid curves are shifted horizontally for ease of comparison.)

Fig. 14
Fig. 14

Plots corresponding to those in Fig. 13 for LR2 and its (a) downsampling and (b) MA filters.

Fig. 15
Fig. 15

Experimental arrangement for the reduced-resolution optical correlator. The lens combination of L1 and L2 produces a zero-order optical FT matched to the central 64 × 64 of the filter SLM. The combination of L3 and L4 produces a demagnified correlation plane at the CCD. PBS, polarizing beam splitter; WP, wave plate; P, polarizer; f 1 = 100 mm; f 2 = 75 mm; f 3 = 63 mm; f 4 = 50 mm.

Fig. 16
Fig. 16

Plots of vertical slices through corresponding experimental (solid curve) and simulated (dashed–dotted curve) correlation planes obtained with LR1 and its (a) downsampling and (b) MA filters.

Fig. 17
Fig. 17

Plots corresponding to those in Fig. 16 for LR2 and its (a) downsampling and (b) MA filters.

Equations (35)

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s x = n = - 2 j - 1 2 j - 1 - 1   s n δ x - n   L 2 j ,
D S 2 j u = S u n = - 2 j - 1 2 j - 1 - 1   δ u - n   u 0 2 j ,
D SLM 2 j u =  D S 2 j u * rect u - F u 0 / 2 j + 1 F u 0 / 2 j ,
rect x a = 1 when - a 2 x < a 2 0 elsewhere ,
D S 2 j - 2 u = S u n = - 2 j - 3 2 j - 3 - 1   δ u - n   u 0 2 j - 2 .
D SLM 2 j - 2 u =  D S 2 j - 2 u * rect u - F u 0 / 2 j - 1 F u 0 / 2 j - 2 ,
M S 2 j - 2 u = S u     2 j - 2 F u 0 1 / 2 rect u + F u 0 / 2 j - 1 F u 0 / 2 j - 2 × n = - 2 j - 3 2 j - 3 - 1   δ u - n   u 0 2 j - 2 ,
M SLM 2 j - 2 u =  M S 2 j - 2 u * 2 j - 2 F u 0 1 / 2 × rect u - F u 0 / 2 j - 1 F u 0 / 2 j - 2 ,
D h 2 j - 2 x = s - x * L 4 n = -   δ x - n   L 4 × exp i π   4 F L   x 4 F L sinc 4 F L   x ,
M h 2 j - 2 x = s - x * exp - i π   4 F L   x sinc 4 F L   x L 4 n = -   δ x - n   L 4 × exp i π   4 F L   x 4 F L sinc 4 F L   x .
s x = δ x - x d + δ x + x d .
D h 2 j - 2 x = s - x * L 4 n = -   δ x - n   L 4 PMF x ,   F ,
PMF x ,   F = cos π   4 F L   x + i   sin π   4 F L   x × 4 F L sinc 4 F L   x .
M h 2 j - 2 x = L 4 n = -   s - x + n   L 4 * exp - i π   4 F L × x - n   L 4 sinc 4 F L x - n   L 4 × exp i π   4 F L   x 4 F L sinc 4 F L   x ;
M h 2 j - 2 n x = s - x + n   L 4 * exp - π i   4 F L x - n   L 4 × sinc 4 F L x - n   L 4 × exp π i   4 F L   x F sinc x   4 F L ,
M h 2 j - 2 n x = s - x + n   L 4 * PMF n x ,   F ,
PMF n = exp - n π i F sinc 4 F L x - n   L 4 × F sinc x   4 F L .
C R n x d ,   F = s x s - x + n   L 4 * PMF R n x ,   F × n   L 4 2 ,
C R n x d ,   F s x PMF R n n   L 4 - x d ,   F + PMF R n n   L 4 + x d ,   F n   L 4 2 ,
C R n x d ,   F PMF R n n   L 4 - x d ,   F + PMF R n n   L 4 + x d ,   F 2 .
S u = 2   cos π u 2 x d ,
PMF 0 x ,   F = F sinc 2 x   4 F L .
PMF 1 x ,   F = cos π F - i   sin π F × sinc 4 F L x - L 4 × F sinc x   4 F L .
BPOF = 1 if   real H 0 - 1 if   real H < 0 ,
f = Nx p 2 λ ,
D h 2 j - 2 x = FT D SLM 2 j - 2 u .
D h 2 j - 2 x = FT D S 2 j - 2 u * rect u - F u 0 / 2 j - 1 F u 0 / 2 j - 2 = FT D S 2 j - 2 u *   ×   FT rect u - F u 0 / 2 j - 1 F u 0 / 2 j - 2 .
FT D S 2 j - 2 u * = FT S u *   n = - 2 j - 3 2 j - 3 - 1   δ u - n   u 0 2 j - 2 .
S u *   n = - 2 j - 3 2 j - 3 - 1   δ u - n   u 0 2 j - 2 S u * n = -   δ u - n   u 0 2 j - 2 ,
FT D S 2 j - 2 u * = FT S u *   n = -   δ u - n   u 0 2 j - 2 .
D h 2 j - 2 x = s - x * L 4 n = -   δ x - n   L 4 × exp i π   4 F L   x 4 F L sinc x   4 F L ,
M h 2 j - 2 x = FT M SLM 2 j - 2 u .
M h 2 j - 2 x = FT M S 2 j - 2 u * 2 j - 2 F u 0 1 / 2 × rect u - F u 0 / 2 j - 1 F u 0 / 2 j - 2 = FT M S 2 j - 2 u * × FT 2 j - 2 F u 0 1 / 2 rect u - F u 0 / 2 j - 1 F u 0 / 2 j - 2 .
M S 2 j - 2 u * = S u * 2 j - 2 F u 0 1 / 2 rect u + F u 0 / 2 j - 1 F u 0 / 2 j - 2 × n = -   δ u - n   u 0 2 j - 2 .
M h 2 j - 2 x = s - x * exp - π i   4 F L   x sinc x   4 F L L 4 n = -   δ x - n   L 4 exp - π i   4 F L   x 4 F L × sinc x   4 F L .

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