Abstract

Phase extraction pattern recognition is a special case of nonlinear matched filtering. The phase extraction procedure is executed on the input function’s Fourier transform as well as on the filter function’s Fourier transform, both of which are manipulated for correlation purposes. This novel process is examined theoretically, by computer simulations and laboratory experiments. The implementation of a coherent electro-optical phase extraction pattern recognition system demonstrates the advantages of this new approach.

© 1992 Optical Society of America

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References

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  1. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 130–145 (1969).
  2. A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
    [CrossRef]
  3. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  4. T. Nomura, K. Itoh, K. Matsuoka, Y. Ichioka, “Binary Fourier phase-only correlation,” Opt. Lett. 15, 810–811 (1990).
    [CrossRef] [PubMed]
  5. O. K. Ersoy, M. Zeng, “Nonlinear matched filtering,” J. Opt. Soc. Am. A 6, 636–648 (1989).
    [CrossRef]
  6. O. K. Ersoy, Y. Yoon, N. Keshava, D. Zimmerman, “Nonlinear matched filtering,” Opt. Eng. 29, 1002–1012 (1990).
    [CrossRef]
  7. B. Javidi, C. J. Kuo, S. F. Odeh, “Comparison of bipolar joint transform image correlators and phase only matched filter correlator,” in Digital and Optical Shape Representation and Pattern Recognition, R. D. Juday, ed., Proc. Soc. Photo-Opt. Instrum. Eng.938, 66–75 (1988).
  8. B. Javidi, J. Wang, “Binary nonlinear joint transform correlation with median and subset thresholding,” Appl. Opt. 30, 967–976 (1991).
    [CrossRef] [PubMed]
  9. 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]
  10. W. Hahn, D. Flannery, “Basic design elements of binary joint-transform correlation and selected optimization techniques.” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 344–356 (1990).
  11. J. L. Horner, “Light utilization in optical correlators,” Appl. Opt. 21, 4511–4514 (1982).
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  12. B. Kumar, Z. Bahri, “Efficient algorithm for designing a ternary valued filter yielding maximum signal-to-noise ratio,” Appl. Opt. 28, 1919–1925 (1989).
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  13. 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).
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  14. B. V. K. Vijaya Kumar, W. Shi, C. Hendrix, “Phase-only filters with maximally sharp correlation peaks,” Opt. Lett. 15, 807–809 (1990).
    [CrossRef]
  15. D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).
    [CrossRef]
  16. The CUE-2 is an image processing system based on a personal computer manufactured by Galai Laboratories, Industrial Zone, Migdal Haemek, Israel.
  17. T. Kotzer, J. Rosen, J. Shamir, “Phase extraction pattern recognition,” in Optical Society of America 1990 Annual Meeting, Vol. 15 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 225.
  18. B. R. Brown, A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 160–168 (1969).
    [CrossRef]

1991 (1)

1990 (3)

1989 (3)

1988 (1)

1984 (2)

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
[CrossRef] [PubMed]

1982 (1)

1981 (1)

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

1969 (2)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 130–145 (1969).

B. R. Brown, A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 160–168 (1969).
[CrossRef]

Bahri, Z.

Brown, B. R.

B. R. Brown, A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 160–168 (1969).
[CrossRef]

Cheng, F.

Ersoy, O. K.

O. K. Ersoy, Y. Yoon, N. Keshava, D. Zimmerman, “Nonlinear matched filtering,” Opt. Eng. 29, 1002–1012 (1990).
[CrossRef]

O. K. Ersoy, M. Zeng, “Nonlinear matched filtering,” J. Opt. Soc. Am. A 6, 636–648 (1989).
[CrossRef]

Flannery, D.

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

Flannery, D. L.

Gianino, P. D.

Gregory, D. A.

Hahn, W.

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

Hendrix, C.

Horner, J. L.

Ichioka, Y.

Itoh, K.

Javidi, B.

B. Javidi, J. Wang, “Binary nonlinear joint transform correlation with median and subset thresholding,” Appl. Opt. 30, 967–976 (1991).
[CrossRef] [PubMed]

B. Javidi, C. J. Kuo, S. F. Odeh, “Comparison of bipolar joint transform image correlators and phase only matched filter correlator,” in Digital and Optical Shape Representation and Pattern Recognition, R. D. Juday, ed., Proc. Soc. Photo-Opt. Instrum. Eng.938, 66–75 (1988).

Keshava, N.

O. K. Ersoy, Y. Yoon, N. Keshava, D. Zimmerman, “Nonlinear matched filtering,” Opt. Eng. 29, 1002–1012 (1990).
[CrossRef]

Kotzer, T.

T. Kotzer, J. Rosen, J. Shamir, “Phase extraction pattern recognition,” in Optical Society of America 1990 Annual Meeting, Vol. 15 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 225.

Kumar, B.

Kuo, C. J.

B. Javidi, C. J. Kuo, S. F. Odeh, “Comparison of bipolar joint transform image correlators and phase only matched filter correlator,” in Digital and Optical Shape Representation and Pattern Recognition, R. D. Juday, ed., Proc. Soc. Photo-Opt. Instrum. Eng.938, 66–75 (1988).

Lim, J. S.

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Lohmann, A. W.

B. R. Brown, A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 160–168 (1969).
[CrossRef]

Loomis, J. S.

Matsuoka, K.

Milkovich, M. E.

Nagata, T.

Nomura, T.

Odeh, S. F.

B. Javidi, C. J. Kuo, S. F. Odeh, “Comparison of bipolar joint transform image correlators and phase only matched filter correlator,” in Digital and Optical Shape Representation and Pattern Recognition, R. D. Juday, ed., Proc. Soc. Photo-Opt. Instrum. Eng.938, 66–75 (1988).

Oppenheim, A. V.

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Rosen, J.

T. Kotzer, J. Rosen, J. Shamir, “Phase extraction pattern recognition,” in Optical Society of America 1990 Annual Meeting, Vol. 15 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 225.

Shamir, J.

T. Kotzer, J. Rosen, J. Shamir, “Phase extraction pattern recognition,” in Optical Society of America 1990 Annual Meeting, Vol. 15 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 225.

Shi, W.

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 130–145 (1969).

Venkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Vijaya Kumar, B. V. K.

Wang, J.

Yoon, Y.

O. K. Ersoy, Y. Yoon, N. Keshava, D. Zimmerman, “Nonlinear matched filtering,” Opt. Eng. 29, 1002–1012 (1990).
[CrossRef]

Yu, F. T. S.

Zeng, M.

Zimmerman, D.

O. K. Ersoy, Y. Yoon, N. Keshava, D. Zimmerman, “Nonlinear matched filtering,” Opt. Eng. 29, 1002–1012 (1990).
[CrossRef]

Appl. Opt. (6)

IBM J. Res. Dev. (1)

B. R. Brown, A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 160–168 (1969).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 130–145 (1969).

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

O. K. Ersoy, Y. Yoon, N. Keshava, D. Zimmerman, “Nonlinear matched filtering,” Opt. Eng. 29, 1002–1012 (1990).
[CrossRef]

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Opt. Lett. (2)

Proc. IEEE (1)

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Other (4)

B. Javidi, C. J. Kuo, S. F. Odeh, “Comparison of bipolar joint transform image correlators and phase only matched filter correlator,” in Digital and Optical Shape Representation and Pattern Recognition, R. D. Juday, ed., Proc. Soc. Photo-Opt. Instrum. Eng.938, 66–75 (1988).

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

The CUE-2 is an image processing system based on a personal computer manufactured by Galai Laboratories, Industrial Zone, Migdal Haemek, Israel.

T. Kotzer, J. Rosen, J. Shamir, “Phase extraction pattern recognition,” in Optical Society of America 1990 Annual Meeting, Vol. 15 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 225.

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Figures (16)

Fig. 1
Fig. 1

Block diagram of the symmetric NL correlation: FT and IFT denote the Fourier transform and its inverse, respectively; q(x, y) and p(x, y) are the input and filter functions; Nl is a point nonlinearity.

Fig. 2
Fig. 2

(a) Input distribution; (b) intensity distribution over the correlation plane.

Fig. 3
Fig. 3

Three input distributions used in the simulations.

Fig. 4
Fig. 4

Correlation plane with a POF, matched to P, produced by a linear correlator: (a) Fig. 3(a) as the input, (b) Fig. 3(b) as the input.

Fig. 5
Fig. 5

Same as Fig. 4 but with the phase extraction correlator.

Fig. 6
Fig. 6

Same as Fig. 5(a) but with F as the filter function.

Fig. 7
Fig. 7

Figure 3(c) as the input for correlation with P: (a) conventional POF, (b) phase extraction correlator.

Fig. 8
Fig. 8

Output correlation plane with an adaptive NL correlator with Fig. 3(b) as the input.

Fig. 9
Fig. 9

Electro-optical implementation of Fig. 1.

Fig. 10
Fig. 10

(a) The FT of T′(u, υ). (b) FT of W′(u, υ), the output correlation plane. The orders where the desired correlations were obtained are marked.

Fig. 11
Fig. 11

The 2f laboratory setup executing the same process as in Fig. 9 in three cycles.

Fig. 12
Fig. 12

(a) Binarized interference pattern of the POF matched to the letter P, T′(u, υ). (b) Binarized interference pattern of the input (also a single letter P) S′(u, υ). (c) W′, the product of S′ and T′. (d) FT of W′ with the transverse cross section of the (1, 1) correlation peak.

Fig. 13
Fig. 13

(a) W′ with Fig. 3(a) as the input and P as the filter. (b) The FT of W′ (the dimensions of the added white border are approximately the size of the input plane). (c) Cross section of the section corresponding to the letters P and F in (b).

Fig. 14
Fig. 14

As in Fig. 13 but with F as the filter.

Fig. 15
Fig. 15

(a) FT of W′ obtained with Fig. 3(b) as the input and P as the filter. (b) Cross section of (a).

Fig. 16
Fig. 16

Alternative realization of the NL correlator of Fig. 1.

Tables (2)

Tables Icon

Table I Normalized Merit Factorsa

Tables Icon

Table II Correlation Response (in Arbitrary Units) at ±x0, ±bx0 to Four Identical Objects Centered at −bx0, −x0, x0, bx0 with the Phase Extraction Pattern Recognition Systema

Equations (44)

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R ( u , υ ) = | R ( u , υ ) | exp [ j φ ( u , υ ) ] ,
N l { R ( u , υ ) } = | R ( u , υ ) | l exp [ j φ ( u , υ ) ] ; 0 l 1 .
Q ( u , υ ) = F { q ( x , y ) } = A 0 q ( x , y ) exp [ j 2 π ( u x + υ y ) ] d x d y ,
Q ( u , υ ) = exp [ j φ Q ( u , υ ) ] .
P ( u , υ ) = F { p ( x , y ) } ,
P ( u , υ ) = N l = 0 { P ( u , υ ) } ,
G ( u , υ ) = Q ( u , υ ) P ( u , υ ) ,
C ( x , y ) = F 1 { G ( u , υ ) } = exp [ j φ Q ( u , υ ) ] exp [ j φ P ( u , υ ) ] exp [ j 2 π ( u x + υ y ) ] d u d υ .
q ( x , y ) = a ( x + x 0 , y + y 0 ) ,
p ( x , y ) = a ( x , y ) .
C ( x , y ) = δ ( x + x 0 , y + y 0 ) .
q ( x , y ) = a ( x + x 0 , y + y 0 ) + a ( x + x 1 , y + y 1 ) ,
p ( x , y ) = a ( x , y ) .
F { a ( x , y ) } = A ( u , υ ) = | A ( u , υ ) | exp [ j φ ( u , υ ) ]
Q ( u , υ ) = | A ( u , υ ) | exp [ j φ ( u , υ ) ] × { exp [ j 2 π ( u x 0 + υ y 0 ) ] + exp [ j 2 π ( u x 1 + υ y 1 ) ] } .
2 x 2 = x 0 x 1 , 2 y 2 = y 0 y 1 ,
Q ( u , υ ) = 2 | A ( u , υ ) | exp [ j φ ( u , υ ) ] × exp { j 2 π [ u ( x 1 + x 2 ) + υ ( y 1 + y 2 ) ] } cos [ 2 π ( u x 2 + υ y 2 ) ] ,
G ( u , υ ) = N l = 0 { Q ( u , υ ) } P ( u , υ ) = exp { j 2 π [ u ( x 1 + x 2 ) + υ ( y 1 + y 2 ) ] } sgn { cos [ 2 π ( u x 2 + υ y 2 ) ] } .
sgn { cos [ 2 π ( u x 2 + υ y 2 ) ] } = 4 π k = 1 a k cos { [ 2 k 1 ] [ 2 π ( u x 2 + υ y 2 ) ] } ,
C ( x , y ) = 2 π ( δ { [ x + ( x 1 + 2 x 2 ) ] δ [ y + ( y 1 + 2 y 2 ) ] + δ ( x + x 1 ) δ ( y + y 1 ) + k = 2 a k [ δ [ x x 1 x 2 ( 2 k 1 ) x 2 ] δ [ y y 1 y 2 ( 2 k 1 ) y 2 ] + δ [ x x 1 x 2 + ( 2 k 1 ) x 2 ] δ [ y y 1 y 2 + ( 2 k 1 ) y 2 ] } ) .
C ( x , y ) = 2 π ( δ ( x + x 0 ) δ ( y + y 0 ) + δ ( x + x 1 ) δ ( y + y 1 ) + k = 2 a k { δ [ x x 1 x 2 ( 2 k 1 ) x 2 ] δ [ y y 1 y 2 ( 2 k 1 ) y 2 ] + δ [ x x 1 x 2 + ( 2 k 1 ) x 2 ] δ [ y y 1 y 2 + ( 2 k 1 ) y 2 ] } ) .
I C ( x , y ) δ ( x + x 0 ) δ ( y + y 0 ) + δ ( x + x 1 ) δ ( y + y 1 ) + k = 2 a k 2 { δ [ x x 1 x 2 ( 2 k 1 ) x 2 ] δ [ y y 1 y 2 ( 2 k 1 ) y 2 ] + δ [ x x 1 x 2 + ( 2 k 1 ) x 2 ] δ [ y y 1 y 2 + ( 2 k 1 ) y 2 ] } .
q ( x ) = n = 1 4 δ [ x ( 2 n 5 ) x 0 ] ,
F { q ( x ) } = i = 1 4 exp ( j x i 2 π u ) = sin ( 8 π u x 0 ) sin ( 2 π u x 0 ) .
N t { R ( u , υ ) } = { exp [ j φ R ( u , υ ) ] if | R ( u , υ ) | t ( u , υ ) , 0 otherwise ,
t ( u , υ ) = μ | F { p ( x , y ) } | max [ | F { p ( x , y ) } | ] , 0 μ < 1 .
F { n = N 2 N 2 a ( x 2 n x 0 ) } = A ( u ) sin ( 2 π N x 0 u ) sin ( 2 π x 0 u ) .
n = rect ( u n 2 x 0 a ) ,
sin ( π N x 0 a ) sin ( π x 0 a ) = μ N .
n = δ ( x 2 n x 0 ) sinc ( a x π ) .
T ( u , υ ) = | A | 2 + | P ( u , υ ) | 2 + 2 | A | | P ( u , υ ) | cos [ 2 πα u + Φ P ( u , υ ) ] ,
α = sin ( θ ) λ ,
Φ P ( u , υ ) = arg { P ( u , υ ) } .
T ( u , υ ) = { 1 if T ( u , υ ) < | A | 2 + | P ( u , υ ) | 2 1 otherwise ,
T ( u , υ ) = sgn { cos [ 2 πα u + Φ P ( u , υ ) ] }
T ( u , υ ) = n = , n odd 2 n π ( 1 ) ( n 1 ) 2 exp { j n [ 2 πα u + Φ P ( u , υ ) ] } .
S ( u , υ ) = sgn { cos [ 2 πα υ + Φ Q ( u , υ ) ] } .
S ( u , υ ) = n = , n odd 2 n π ( 1 ) ( n 1 ) 2 exp { j n [ 2 πα υ + Φ Q ( u , υ ) ] } .
4 π 2 exp { j [ 2 πα u + 2 πα υ + Φ P ( u , υ ) + Φ Q ( u , υ ) ] }
4 π 2 exp { + j [ 2 πα u + 2 πα υ + Φ P ( u , υ ) + Φ Q ( u , υ ) ] }
η = ( s π ) 4 n = m = m , n odd | 2 n π 2 m π | 2 = ( 1 . 03 × s 4 ) % ,
s = { 2 if the thresholding operation results are bipolar ( 1 and l ) as in this paper , 1 if the thresholding operation results are unipolar ( 1 and 0 ) .
N l { Q ( u , υ ) } = Q ( u , υ ) = | Q ( u , υ ) | l exp [ j φ Q ( u , υ ) ] ; N l { P ( u , υ ) } = P ( u , υ ) = | P ( u , υ ) | l exp [ j φ P ( u , υ ) ] ;
N l { Q ( u , υ ) } N l { P ( u , υ ) } = N l { Q ( u , υ ) P ( u , υ ) } .

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