Abstract

Conventionally a detected image is represented by an intensity array owing to the square-law nature of most detectors. However, this does not mean that we have to restrict ourselves to using intensity images for the correlation process. Transforming intensity images into phase images before correlation, which can be easily realized by a phase-modulation spatial light modulator, offers an alternative approach for high-performance pattern recognition. A phase-transformed input joint transform correlator is investigated in detail in terms of pattern discriminability, detection efficiency, and noise robustness. We show that the phase-transformed joint transform correlator has higher pattern discriminability and detection efficiency than the conventional joint transform correlator, and it also offers a better trade-off between the pattern discriminability and noise tolerance. A proof-of-concept experiment is also provided.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. S. Weaver, J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  2. F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
    [CrossRef]
  3. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
    [CrossRef]
  4. F. T. S. Yu, G. Lu, M. Lu, D. Zhao, “Application of position encoding to a complex joint transform correlator,” Appl. Opt. 34, 1386–1388 (1995).
    [CrossRef] [PubMed]
  5. T. H. Barnes, T. Eiju, K. Matsuda, N. Ooyama, “Phase- only modulation using a twisted nematic liquid crystal television,” Appl. Opt. 28, 4845–4852 (1989).
    [CrossRef] [PubMed]
  6. B. A. Kest, M. K. Giles, S. D. Lindell, D. L. Flannery, “Implementation of a ternary phase-amplitude filter using a magneto-optic spatial light modulator,” Appl. Opt. 28, 1044–1046 (1989).
    [CrossRef]
  7. L. J. Hornbeck, “Deformable-mirror spatial light modulators,” in Spatial Light Modulators and Applications III, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1150, 86–102 (1989).
  8. R. Juday, S. E. Monroe, D. A. Gregory, “Optical correlation with phase-encoding and phase filtering,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 149–156 (1987).
  9. C. Hester, M. Temmen, “Phase phase implementation of optical correlator,” in Hybrid Image and Signal Processing II, D. P. Casasent, A. G. Tescher, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1297, 207–219 (1991).
  10. R. R. Kallman, D. H. Goldstein, “Phase-encoding input image for optical pattern recognition,” Opt. Eng. 33, 1806–1812 (1994).
    [CrossRef]
  11. G. Lu, Z. Zhang, F. T. S. Yu, “Phase-encoded input joint transform correlator with improved pattern discriminability,” Opt. Lett. 20, 1307–1309 (1995).
    [CrossRef] [PubMed]
  12. A. Tanone, C. M. Uang, F. T. S. Yu, E. C. Tam, D. A. Gregory, “Effects of the thresholding in joint-transform correlation,” Appl. Opt. 31, 4816–4822 (1992).
    [CrossRef] [PubMed]
  13. Z. Zhang, G. Lu, F. T. S. Yu, “A simple method for measuring phase modulation in LCTV's,” Opt. Eng. 33, 3018–3022 (1994).
    [CrossRef]

1995

1994

R. R. Kallman, D. H. Goldstein, “Phase-encoding input image for optical pattern recognition,” Opt. Eng. 33, 1806–1812 (1994).
[CrossRef]

Z. Zhang, G. Lu, F. T. S. Yu, “A simple method for measuring phase modulation in LCTV's,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

1992

1989

1984

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

1966

1964

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Barnes, T. H.

Eiju, T.

Flannery, D. L.

Giles, M. K.

Goldstein, D. H.

R. R. Kallman, D. H. Goldstein, “Phase-encoding input image for optical pattern recognition,” Opt. Eng. 33, 1806–1812 (1994).
[CrossRef]

Goodman, J. W.

Gregory, D. A.

A. Tanone, C. M. Uang, F. T. S. Yu, E. C. Tam, D. A. Gregory, “Effects of the thresholding in joint-transform correlation,” Appl. Opt. 31, 4816–4822 (1992).
[CrossRef] [PubMed]

R. Juday, S. E. Monroe, D. A. Gregory, “Optical correlation with phase-encoding and phase filtering,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 149–156 (1987).

Hester, C.

C. Hester, M. Temmen, “Phase phase implementation of optical correlator,” in Hybrid Image and Signal Processing II, D. P. Casasent, A. G. Tescher, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1297, 207–219 (1991).

Hornbeck, L. J.

L. J. Hornbeck, “Deformable-mirror spatial light modulators,” in Spatial Light Modulators and Applications III, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1150, 86–102 (1989).

Juday, R.

R. Juday, S. E. Monroe, D. A. Gregory, “Optical correlation with phase-encoding and phase filtering,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 149–156 (1987).

Kallman, R. R.

R. R. Kallman, D. H. Goldstein, “Phase-encoding input image for optical pattern recognition,” Opt. Eng. 33, 1806–1812 (1994).
[CrossRef]

Kest, B. A.

Lindell, S. D.

Lu, G.

Lu, M.

Lu, X. J.

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Matsuda, K.

Monroe, S. E.

R. Juday, S. E. Monroe, D. A. Gregory, “Optical correlation with phase-encoding and phase filtering,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 149–156 (1987).

Ooyama, N.

Tam, E. C.

Tanone, A.

Temmen, M.

C. Hester, M. Temmen, “Phase phase implementation of optical correlator,” in Hybrid Image and Signal Processing II, D. P. Casasent, A. G. Tescher, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1297, 207–219 (1991).

Uang, C. M.

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Weaver, C. S.

Yu, F. T. S.

Zhang, Z.

G. Lu, Z. Zhang, F. T. S. Yu, “Phase-encoded input joint transform correlator with improved pattern discriminability,” Opt. Lett. 20, 1307–1309 (1995).
[CrossRef] [PubMed]

Z. Zhang, G. Lu, F. T. S. Yu, “A simple method for measuring phase modulation in LCTV's,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

Zhao, D.

Appl. Opt.

IEEE Trans. Inf. Theory

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Opt. Commun.

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Opt. Eng.

R. R. Kallman, D. H. Goldstein, “Phase-encoding input image for optical pattern recognition,” Opt. Eng. 33, 1806–1812 (1994).
[CrossRef]

Z. Zhang, G. Lu, F. T. S. Yu, “A simple method for measuring phase modulation in LCTV's,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

Opt. Lett.

Other

L. J. Hornbeck, “Deformable-mirror spatial light modulators,” in Spatial Light Modulators and Applications III, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1150, 86–102 (1989).

R. Juday, S. E. Monroe, D. A. Gregory, “Optical correlation with phase-encoding and phase filtering,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 149–156 (1987).

C. Hester, M. Temmen, “Phase phase implementation of optical correlator,” in Hybrid Image and Signal Processing II, D. P. Casasent, A. G. Tescher, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1297, 207–219 (1991).

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 (13)

Fig. 1
Fig. 1

(a) Intensity to phase mapping and (b) a phase transformation.

Fig. 2
Fig. 2

Input to the JTC.

Fig. 3
Fig. 3

Output cross-correlation distributions, obtained from (a) the CJTC, (b) the PJTC, and (c) the BPJTC.

Fig. 4
Fig. 4

API, CPI, and SCR as a function of the dc block size (N × N) (a) from the CJTC, (b) from the PJTC, (c) and from the BPJTC, where the subscripts C, P, and BP represent the CJTC, the PJTC, and the BPJTC, respectively.

Fig. 5
Fig. 5

Output cross-correlation distributions, obtained from (a) the CJTC with a 65 × 65 dc block, (b) the PJTC with a 41 × 41 dc block, and (c) the BPJTC with a 41 × 41 dc block.

Fig. 6
Fig. 6

Detection efficiency (DE) as a function of the dc block size with t = 2.

Fig. 7
Fig. 7

API and CPI as a function of noise standard deviation σ (out of 255).

Fig. 8
Fig. 8

API and CPI as a function of noise standard deviation σ, obtained from (a) the CJTC with the 65 × 65 dc block and (b) the PJTC and the BPJTC with the 41 × 41 dc block.

Fig. 9
Fig. 9

(a) Noise version (σ = 128) of the input scene shown in Fig. 2 and (b) the output cross-correlation distribution of the PJTC with the 41 × 41 dc block.

Fig. 10
Fig. 10

API and CPI as a function of illumination-variation ratio b.

Fig. 11
Fig. 11

API and CPI as a function of illumination-variation ratio b, obtained from (a) the CJTC with a 65 × 65 dc block and (b) the PJTC and the BPJTC with the 41 × 41 dc block.

Fig. 12
Fig. 12

Hybrid JTC system.

Fig. 13
Fig. 13

Experimental results: (a) the input to the PJTC, (b) the output correlation distribution from the PJTC, (c) the input to the CJTC, and (d) the output correlation distribution from the PJTC.

Equations (30)

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

pf ( x , y ) = exp { j T [ f ( x , y ) ] } ,
T [ f ( x , y ) ] = f ( x , y ) M π ,
T [ f ( x , y ) ] = f ( x , y ) G min G max G min π ,
w f ( x , y ) = { 1 x , y f ( x , y ) ( an object ) 0 x , y f ( x , y ) ,
w r ( x , y ) = { 1 x , y r ( x , y ) ( the reference ) 0 x , y r ( x , y ) ,
w b ( x , y ) = 1 w f ( x + a , y ) w r ( x a , y ) ,
pf ( x + a , y ) + pr ( x a , y ) + b ( x , y ) w b ( x , y ) ,
pf ( x , y ) = exp { j T [ f ( x , y ) ] } w f ( x , y ) ,
pr ( x , y ) = exp [ j ϕ r ( x , y ) ] w r ( x , y ) ,
b ( x , y ) = exp [ j ( x p 0 + y q 0 ) ] .
JTPS = | PF ( p , q ) exp ( jpa ) + PR ( p , q ) exp ( jpa ) + W b ( p p 0 , q q 0 ) | 2 = | PF ( p , q ) | 2 + | PR ( p , q ) | 2 + | W b ( p p 0 , q q 0 ) | 2 + PF ( p , q ) PR * ( p , q ) exp ( j 2 pa ) + PF * ( p , q ) PR ( p , q ) exp ( j 2 pa ) + PF ( p , q ) W b * ( p p 0 , q q 0 ) exp ( jpa ) + PF * ( p , q ) W b ( p p 0 , q q 0 ) exp ( jpa ) + PR ( p , q ) W b * ( p p 0 , q q 0 ) exp ( jpa ) + PR * ( p , q ) W b ( p p 0 , q q 0 ) exp ( jpa ) ,
JTPS | PF ( p , q ) | 2 + | PR ( p , q ) | 2 + PF ( p , q ) PR * ( p , q ) × exp ( j 2 pa ) + PF * ( p , q ) PR ( p , q ) exp ( j 2 pa ) .
C P ( x , y ) = pf ( x , y ) pf * ( x , y ) + pr ( x , y ) pr * ( x , y ) + pf ( x 2 a , y ) pr * ( x , y ) + pf * ( x 2 a , y ) pr ( x , y ) ,
| C P ( ± 2 a , 0 ) | 2 = | pf ( x , y ) pr * ( x , y ) d x d y | 2 = | exp [ j ψ f ( x , y ) ] d x d y | 2 ,
| C P ( ± 2 a , 0 ) | 2 = A r 2 ,
A r 2 | W r r 2 ( x , y ) d x d y | 2 / r max 2 1 ,
SCR = API CPI ,
SCR = A r 2 | exp j { T [ g ( x , y ) ] ϕ r ( x , y ) } d x d y | 2 > 1 ,
B P = | w r exp [ j T ( c ) ] exp [ j ϕ r ( x , y ) ] d x d y | 2 = | w r exp [ j ϕ r ( x , y ) ] d x d y | 2 ,
ϕ r b ( x , y ) = { 0 ϕ r ( x , y ) θ π ϕ r ( x , y ) > θ ,
DE = { API ( SCR t ) SCR > t 0 SCR t ,
| C P ( ± 2 a , 0 ) | 2 = | W r pf n ( x , y ) pr * ( x , y ) d x d y | 2 = | W r exp { j T [ f ( x , y ) + n ( x , y ) ] j ϕ r ( x , y ) } d x d y | 2 .
| C P ( ± 2 a , 0 ) | 2 = | W r exp { j T [ n ( x , y ) ] } d x d y | 2 ,
n 0 ( x , y ) = n ( x , y ) μ , c = π / ( G max G min ) , T [ n 0 ( x , y ) ] = c n 0 ( x , y ) ,
| C P ( ± 2 a , 0 ) | 2 = | exp ( jcn 0 ) A r exp ( n 0 2 / 2 σ 2 ) / σ 2 π d n 0 | 2 = A r 2 exp ( c 2 σ 2 / 2 ) ,
| C BP ( ± 2 a , 0 ) | 2 = k exp ( c 2 σ 2 / 2 ) ,
k = | W r exp { j T [ f ( x , y ) ] j ϕ r b ( x , y ) } d x d y | 2 ,
f c ( x , y ) = { bf ( x , y ) bf ( x , y ) < 255 255 bf ( x , y ) 255 .
| C P ( ± 2 a , 0 ) | 2 = | exp j { T [ f c ( x , y ) ] T [ f ( x , y ) ] } d x d y | 2 ,
| C P ( ± 2 a , 0 ) | 2 = | exp { j T [ f c ( x , y ) ] j ϕ r b ( x , y ) } d x d y | 2 .

Metrics