Abstract

Experimental results of phase-only circular harmonic filtering implemented in a standard Fourier transform correlator are presented. The filter is a computer generated hologram which contains only the phase information of a single circular harmonic component of the target. The result with simple binary objects bears out the simulation result published earlier [ H. F. Yau and C. C. Chang, Appl. Opt. 28, 2070– 2074 ( 1989)] in that the filter is indeed shift- and rotational-invariant and that the correlation peak is more prominent than that produced by ordinary circular harmonic filtering.

© 1990 Optical Society of America

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References

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  1. Y. N. Hsu, H. H. Arsenault, G. April, “Rotation-Invariant Digital Pattern Recognition Using Circular Harmonic Expansion,” Appl. Opt. 21, 4012–4015 (1982).
    [CrossRef] [PubMed]
  2. Y. N. Hsu, H. H. Arsenault, “Optical Pattern Recognition Using Circular Harmonic Expansion,” Appl. Opt. 21, 4016–4019 (1982).
    [CrossRef] [PubMed]
  3. Y. Sheng, H. H. Arsenault, “Method for Determining Expansion Centers and Predicting Sidelobe Levels for Circular-Harmonic Filters,” J. Opt. Soc. Am. A 4, 1792–1797 (1987).
    [CrossRef]
  4. H. F. Yau, C. C. Chang, “Phase-Only Circular-Harmonic Matched Filtering,” Appl. Opt. 28, 2070–2074 (1989).
    [CrossRef] [PubMed]
  5. C. C. Chang, H. F. Yau, W. Y. Au-Yang, “Rotational and Shift Invariant Pattern Recognition by Pure Phase Circular-Harmonic Matched Filtering,” Proc. Nat. Sci. Counc. R.O.C. Part A 13, 46–51 (1989).
  6. H. H. Arsenault, Y. N. Hsu, “Rotation-Invariant Discrimination Between Almost Similar Objects,” Appl. Opt. 22, 130–132 (1983).
    [CrossRef] [PubMed]
  7. J. Rosen, J. Shamir, “Circular Harmonic Phase, Filter for Efficient Rotation-Invariant Pattern Recognition,” Appl. Opt, 17, 2895–2899 (1988).
    [CrossRef]
  8. L. Leclerc, Y. Sheng, H. H. Arsenault, “Rotation Invariant Phase-Only and Binary Phase-Only Correlation,” Appl. Opt. 28, 1251–1256 (1989).
    [CrossRef] [PubMed]
  9. A. V. Oppenheim, J. S. Lim, “The Importance of Phase Signals,” Proc. IEEE 69, 529–541 (1981).
    [CrossRef]
  10. J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  11. P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695–697 (1984).
    [CrossRef]
  12. H. Becker, W. J. Dallas, “Improving Binary Computer Hologram,” Opt. Commun. 15, 50–53 (1975).
    [CrossRef]
  13. W. L. Anderson, “Particle Identification and Counting,” in Application of Optical Fourier Transform, H. Stark, Ed. (Academic, New York, 1982), p. 95.

1989 (3)

H. F. Yau, C. C. Chang, “Phase-Only Circular-Harmonic Matched Filtering,” Appl. Opt. 28, 2070–2074 (1989).
[CrossRef] [PubMed]

C. C. Chang, H. F. Yau, W. Y. Au-Yang, “Rotational and Shift Invariant Pattern Recognition by Pure Phase Circular-Harmonic Matched Filtering,” Proc. Nat. Sci. Counc. R.O.C. Part A 13, 46–51 (1989).

L. Leclerc, Y. Sheng, H. H. Arsenault, “Rotation Invariant Phase-Only and Binary Phase-Only Correlation,” Appl. Opt. 28, 1251–1256 (1989).
[CrossRef] [PubMed]

1988 (1)

J. Rosen, J. Shamir, “Circular Harmonic Phase, Filter for Efficient Rotation-Invariant Pattern Recognition,” Appl. Opt, 17, 2895–2899 (1988).
[CrossRef]

1987 (1)

Y. Sheng, H. H. Arsenault, “Method for Determining Expansion Centers and Predicting Sidelobe Levels for Circular-Harmonic Filters,” J. Opt. Soc. Am. A 4, 1792–1797 (1987).
[CrossRef]

1984 (2)

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

P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695–697 (1984).
[CrossRef]

1983 (1)

1982 (2)

1981 (1)

A. V. Oppenheim, J. S. Lim, “The Importance of Phase Signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

1975 (1)

H. Becker, W. J. Dallas, “Improving Binary Computer Hologram,” Opt. Commun. 15, 50–53 (1975).
[CrossRef]

Anderson, W. L.

W. L. Anderson, “Particle Identification and Counting,” in Application of Optical Fourier Transform, H. Stark, Ed. (Academic, New York, 1982), p. 95.

April, G.

Arsenault, H. H.

Au-Yang, W. Y.

C. C. Chang, H. F. Yau, W. Y. Au-Yang, “Rotational and Shift Invariant Pattern Recognition by Pure Phase Circular-Harmonic Matched Filtering,” Proc. Nat. Sci. Counc. R.O.C. Part A 13, 46–51 (1989).

Becker, H.

H. Becker, W. J. Dallas, “Improving Binary Computer Hologram,” Opt. Commun. 15, 50–53 (1975).
[CrossRef]

Chang, C. C.

H. F. Yau, C. C. Chang, “Phase-Only Circular-Harmonic Matched Filtering,” Appl. Opt. 28, 2070–2074 (1989).
[CrossRef] [PubMed]

C. C. Chang, H. F. Yau, W. Y. Au-Yang, “Rotational and Shift Invariant Pattern Recognition by Pure Phase Circular-Harmonic Matched Filtering,” Proc. Nat. Sci. Counc. R.O.C. Part A 13, 46–51 (1989).

Dallas, W. J.

H. Becker, W. J. Dallas, “Improving Binary Computer Hologram,” Opt. Commun. 15, 50–53 (1975).
[CrossRef]

Gianino, P. D.

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

P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695–697 (1984).
[CrossRef]

Horner, J. L.

P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695–697 (1984).
[CrossRef]

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

Hsu, Y. N.

Leclerc, L.

Lim, J. S.

A. V. Oppenheim, J. S. Lim, “The Importance of Phase Signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Oppenheim, A. V.

A. V. Oppenheim, J. S. Lim, “The Importance of Phase Signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Rosen, J.

J. Rosen, J. Shamir, “Circular Harmonic Phase, Filter for Efficient Rotation-Invariant Pattern Recognition,” Appl. Opt, 17, 2895–2899 (1988).
[CrossRef]

Shamir, J.

J. Rosen, J. Shamir, “Circular Harmonic Phase, Filter for Efficient Rotation-Invariant Pattern Recognition,” Appl. Opt, 17, 2895–2899 (1988).
[CrossRef]

Sheng, Y.

L. Leclerc, Y. Sheng, H. H. Arsenault, “Rotation Invariant Phase-Only and Binary Phase-Only Correlation,” Appl. Opt. 28, 1251–1256 (1989).
[CrossRef] [PubMed]

Y. Sheng, H. H. Arsenault, “Method for Determining Expansion Centers and Predicting Sidelobe Levels for Circular-Harmonic Filters,” J. Opt. Soc. Am. A 4, 1792–1797 (1987).
[CrossRef]

Yau, H. F.

H. F. Yau, C. C. Chang, “Phase-Only Circular-Harmonic Matched Filtering,” Appl. Opt. 28, 2070–2074 (1989).
[CrossRef] [PubMed]

C. C. Chang, H. F. Yau, W. Y. Au-Yang, “Rotational and Shift Invariant Pattern Recognition by Pure Phase Circular-Harmonic Matched Filtering,” Proc. Nat. Sci. Counc. R.O.C. Part A 13, 46–51 (1989).

Appl. Opt (1)

J. Rosen, J. Shamir, “Circular Harmonic Phase, Filter for Efficient Rotation-Invariant Pattern Recognition,” Appl. Opt, 17, 2895–2899 (1988).
[CrossRef]

Appl. Opt. (6)

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

Y. Sheng, H. H. Arsenault, “Method for Determining Expansion Centers and Predicting Sidelobe Levels for Circular-Harmonic Filters,” J. Opt. Soc. Am. A 4, 1792–1797 (1987).
[CrossRef]

Opt. Commun. (1)

H. Becker, W. J. Dallas, “Improving Binary Computer Hologram,” Opt. Commun. 15, 50–53 (1975).
[CrossRef]

Opt. Eng. (1)

P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695–697 (1984).
[CrossRef]

Proc. IEEE (1)

A. V. Oppenheim, J. S. Lim, “The Importance of Phase Signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Proc. Nat. Sci. Counc. R.O.C. Part A (1)

C. C. Chang, H. F. Yau, W. Y. Au-Yang, “Rotational and Shift Invariant Pattern Recognition by Pure Phase Circular-Harmonic Matched Filtering,” Proc. Nat. Sci. Counc. R.O.C. Part A 13, 46–51 (1989).

Other (1)

W. L. Anderson, “Particle Identification and Counting,” in Application of Optical Fourier Transform, H. Stark, Ed. (Academic, New York, 1982), p. 95.

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Figures (8)

Fig. 1
Fig. 1

Target for the calculation of the POCH filter.

Fig. 2
Fig. 2

Enlargement of the filter.

Fig. 3
Fig. 3

Impulse response of the filter.

Fig. 4
Fig. 4

Intensity distribution in the output plane when the target “cheng” is inserted in the input plane.

Fig. 5
Fig. 5

Experimental result when the target is rotated 90°.

Fig. 6
Fig. 6

Intensity distribution in the output plane when the input consists of the “cheng” target and a nontarget pattern “chung.”

Fig. 7
Fig. 7

Intensity distribution in the output plane when the input consists of two target patterns in three orientations.

Fig. 8
Fig. 8

Optical correlation peak intensities of the first-order POCH filter with the “cheng” target at various rotational orientations.

Tables (2)

Tables Icon

Table I Computer Calculated Correlation Peaks of the Target “Cheng” In Four Orientations with its Various CH Components and POCH Component (m = 1)

Tables Icon

Table II Correlation Peaks of the Target F in Four Orientations with its Various CH Components and POCH Component (m = 1) Obtained in a Coherent Correlator

Equations (16)

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F m ( ξ , η )             and            F m * ( ξ , η ) ,
A 1 = f ( x , y ) f m * ( x , y ) ,
A 2 = f ( - x , - y ) * f m ( - x , - y ) ,
A 1 = 2 π f m ( r ) 2 r d r .
A 2 = f ( x , y ) f m ( - x , - y ) d x d y .
f - m ( x , y ) = f m * ( x , y ) ,
A 2 = exp ( - i m π ) 2 π f - m ( r ) 2 r d r .
A 1 = f ( x , y ) [ f m ( x , y ) ] * ,
A 2 = f ( - x , - y ) * f m ( - x , - y ) ,
f m ( x , y ) = F - 1 { phase part of F m ( ρ , Φ ) } .
F m ( ρ , Φ ) = F m ( ρ ) exp [ i ξ m ( ρ ) ] exp ( i m Φ ) ,
f m ( x , y ) = F - 1 { exp [ i ξ m ( ρ ) + i m Φ ] } .
A 1 = f ( x , y ) f m * ( x , y ) d x d y .
A 1 = F { f } [ F ( f m ) ] * ρ d ρ d Φ = 2 π F m ( ρ ) ρ d ρ .
A 2 = f * ( - x , - y ) f m ( x , y ) d x d y .
A 2 = 2 π F - m ( ρ ) ρ d ρ .

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