Abstract

Synthesizing a Fresnel zone plate inside a Vander Lugt matched filter (MF) results in a lensless matched filter (LLMF) that is space-invariant from the point of view of vignetting apertures. In practice the unfocused output components of the LLMF do not degrade its SNR. A LLMF displacement appears as a combined shift of its filter and lens components. The third-order holographic aberrations of the MF and LLMF, and particularly their root-mean-square astigmatisms, are compared via computer-generated plots.

© 1976 Optical Society of America

Full Article  |  PDF Article

Errata

Marc J. Bage and Michael P. Beddoes, "Lensless matched filter: operating principle, sensitivity to spectrum shift, and third-order holographic aberrations; erratum," Appl. Opt. 16, 1143-1143 (1977)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-16-5-1143

References

  • View by:
  • |
  • |
  • |

  1. A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
  2. M. Tréheux, Applications de l’Holographie, J. Ch. Vienot, Ed. (Université de Besançon, Besançon, 1970), p. 13-3.
  3. A. Vander Lugt, Appl. Opt. 5, 1760 (1966).
  4. H. H. Arsenault, N. Brousseau, J. Opt. Soc. Am. 63, 555 (1973).
  5. N. Brousseau, H. H. Arsenault, Appl. Opt. 14, 1679 (1975).
  6. N. Douklias, J. Shamir, Appl. Opt. 12, 364 (1973).
  7. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  8. M. Bage, M. Beddoes, “Minimization of the Volume Effect in Parallel Matched Filtering,” Appl. Opt. 15, 2632 (1976).
  9. S. Lowenthal, Opt. Acta 12, 261 (1965).
  10. M. Bage, M. Beddoes, J. Opt. Soc. Am. 63, 1306 (1973).
  11. A. Vander Lugt, Proc. IEEE 54, 1055 (1966).
  12. A. Vander Lugt, SPIE Proc. Developments in Holography 25, 117 (1971).
  13. D. Gabor, Opt. Acta 16, 519 (1969).
  14. S. Ragnarsson, Phys. Scr. 2, 145 (1970).
  15. W. T. Maloney, Appl. Opt. 10, 2127 (1971).
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 176.
  17. M. J. Bage, “Coherent Lensless Matched Filter and an Application to Geometrical Feature Extraction in Character Recognition,” Ph.D. dissertation, U. of British Columbia, Vancouver, B.C. (1975).
  18. A. Vander Lugt, Appl. Opt. 6, 1221 (1967).
  19. M. Sayar et al., Isr. J. Technol. 9, 289 (1971).
  20. A. Dickinson, B. M. Watrasiewicz, Opt. Laser Technol. 3, 229 (1971).
  21. K. Singh, P. C. Gupta, Appl. Opt. 14, 2940 (1975).
  22. J. T. Thomasson, SPIE Proc. Pattern Recognition Studies 18, 3 (1969).
  23. Ref. 17, Chap. 4.
  24. G. Winzer, N. Douklias, AGARD Conference Proceedings No. 94: Artificial Intelligence (A9ARD, London, 1971), pp. 21-1, 21-12.
  25. G. Groh, Opt. Commun. 1, 454 (1970).
  26. R. A. Binns et al., Appl. Opt. 7, 1047 (1968).
  27. Ref. 17, Sec. 6.3.2.
  28. R. W. Meier, J. Opt. Soc. Am.55, 987 (1965).
  29. Ref. 17, Chap. 5.
  30. S. Lowenthal, Y. Belvaux, C. R. Acad. Sci. Paris B. 262, 413 (1966).
  31. D. J. Raso, J. Opt. Soc. Am. 58, 432 (1968).
  32. Ref. 17, Chap. 6.
  33. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 463.

1976

1975

1973

1971

A. Vander Lugt, SPIE Proc. Developments in Holography 25, 117 (1971).

W. T. Maloney, Appl. Opt. 10, 2127 (1971).

M. Sayar et al., Isr. J. Technol. 9, 289 (1971).

A. Dickinson, B. M. Watrasiewicz, Opt. Laser Technol. 3, 229 (1971).

1970

S. Ragnarsson, Phys. Scr. 2, 145 (1970).

G. Groh, Opt. Commun. 1, 454 (1970).

1969

J. T. Thomasson, SPIE Proc. Pattern Recognition Studies 18, 3 (1969).

D. Gabor, Opt. Acta 16, 519 (1969).

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

1968

1967

1966

A. Vander Lugt, Appl. Opt. 5, 1760 (1966).

A. Vander Lugt, Proc. IEEE 54, 1055 (1966).

S. Lowenthal, Y. Belvaux, C. R. Acad. Sci. Paris B. 262, 413 (1966).

1965

R. W. Meier, J. Opt. Soc. Am.55, 987 (1965).

S. Lowenthal, Opt. Acta 12, 261 (1965).

1964

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).

Arsenault, H. H.

Bage, M.

Bage, M. J.

M. J. Bage, “Coherent Lensless Matched Filter and an Application to Geometrical Feature Extraction in Character Recognition,” Ph.D. dissertation, U. of British Columbia, Vancouver, B.C. (1975).

Beddoes, M.

Belvaux, Y.

S. Lowenthal, Y. Belvaux, C. R. Acad. Sci. Paris B. 262, 413 (1966).

Binns, R. A.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 463.

Brousseau, N.

Dickinson, A.

A. Dickinson, B. M. Watrasiewicz, Opt. Laser Technol. 3, 229 (1971).

Douklias, N.

N. Douklias, J. Shamir, Appl. Opt. 12, 364 (1973).

G. Winzer, N. Douklias, AGARD Conference Proceedings No. 94: Artificial Intelligence (A9ARD, London, 1971), pp. 21-1, 21-12.

Gabor, D.

D. Gabor, Opt. Acta 16, 519 (1969).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 176.

Groh, G.

G. Groh, Opt. Commun. 1, 454 (1970).

Gupta, P. C.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Lowenthal, S.

S. Lowenthal, Y. Belvaux, C. R. Acad. Sci. Paris B. 262, 413 (1966).

S. Lowenthal, Opt. Acta 12, 261 (1965).

Maloney, W. T.

Meier, R. W.

R. W. Meier, J. Opt. Soc. Am.55, 987 (1965).

Ragnarsson, S.

S. Ragnarsson, Phys. Scr. 2, 145 (1970).

Raso, D. J.

Sayar, M.

M. Sayar et al., Isr. J. Technol. 9, 289 (1971).

Shamir, J.

Singh, K.

Thomasson, J. T.

J. T. Thomasson, SPIE Proc. Pattern Recognition Studies 18, 3 (1969).

Tréheux, M.

M. Tréheux, Applications de l’Holographie, J. Ch. Vienot, Ed. (Université de Besançon, Besançon, 1970), p. 13-3.

Vander Lugt, A.

A. Vander Lugt, SPIE Proc. Developments in Holography 25, 117 (1971).

A. Vander Lugt, Appl. Opt. 6, 1221 (1967).

A. Vander Lugt, Proc. IEEE 54, 1055 (1966).

A. Vander Lugt, Appl. Opt. 5, 1760 (1966).

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).

Watrasiewicz, B. M.

A. Dickinson, B. M. Watrasiewicz, Opt. Laser Technol. 3, 229 (1971).

Winzer, G.

G. Winzer, N. Douklias, AGARD Conference Proceedings No. 94: Artificial Intelligence (A9ARD, London, 1971), pp. 21-1, 21-12.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 463.

Appl. Opt.

Bell Syst. Tech. J.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

C. R. Acad. Sci. Paris B.

S. Lowenthal, Y. Belvaux, C. R. Acad. Sci. Paris B. 262, 413 (1966).

IEEE Trans. Inf. Theory

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).

Isr. J. Technol.

M. Sayar et al., Isr. J. Technol. 9, 289 (1971).

J. Opt. Soc. Am.

M. Bage, M. Beddoes, J. Opt. Soc. Am. 63, 1306 (1973).

H. H. Arsenault, N. Brousseau, J. Opt. Soc. Am. 63, 555 (1973).

D. J. Raso, J. Opt. Soc. Am. 58, 432 (1968).

R. W. Meier, J. Opt. Soc. Am.55, 987 (1965).

Opt. Acta

S. Lowenthal, Opt. Acta 12, 261 (1965).

D. Gabor, Opt. Acta 16, 519 (1969).

Opt. Commun.

G. Groh, Opt. Commun. 1, 454 (1970).

Opt. Laser Technol.

A. Dickinson, B. M. Watrasiewicz, Opt. Laser Technol. 3, 229 (1971).

Phys. Scr.

S. Ragnarsson, Phys. Scr. 2, 145 (1970).

Proc. IEEE

A. Vander Lugt, Proc. IEEE 54, 1055 (1966).

SPIE Proc. Developments in Holography

A. Vander Lugt, SPIE Proc. Developments in Holography 25, 117 (1971).

SPIE Proc. Pattern Recognition Studies

J. T. Thomasson, SPIE Proc. Pattern Recognition Studies 18, 3 (1969).

Other

Ref. 17, Chap. 4.

G. Winzer, N. Douklias, AGARD Conference Proceedings No. 94: Artificial Intelligence (A9ARD, London, 1971), pp. 21-1, 21-12.

Ref. 17, Chap. 5.

Ref. 17, Sec. 6.3.2.

Ref. 17, Chap. 6.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 463.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 176.

M. J. Bage, “Coherent Lensless Matched Filter and an Application to Geometrical Feature Extraction in Character Recognition,” Ph.D. dissertation, U. of British Columbia, Vancouver, B.C. (1975).

M. Tréheux, Applications de l’Holographie, J. Ch. Vienot, Ed. (Université de Besançon, Besançon, 1970), p. 13-3.

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 (8)

Fig. 1
Fig. 1

MF-2: (a) space-invariant recording system; (b) filtering system.

Fig. 2
Fig. 2

LLMF: recording system.

Fig. 3
Fig. 3

LLMF: filtering system.

Fig. 4
Fig. 4

Actual and asymptotic characteristics of the MF and LLMF. Transverse displacement (Δu) and signal size (2a) that reduce the output intensity to a fraction M of its value at Δu = 0. (α = 1, δ = ±1, λ = 632.8 nm, Dt = 500 mm).

Fig. 5
Fig. 5

Theoretical and experimental variations of the output intensity vs the transverse displacement of the LLMF.

Fig. 6
Fig. 6

Autocorrelation of G when the transverse displacement Au of the readout spectrum is (a) 0 μm, (b) 180 μm.

Fig. 7
Fig. 7

Loci of the readout signal positions that yield the same autocorrelation intensity: (a) MF-2, (b) LLMF-1.

Fig. 8
Fig. 8

Space variance of the rms aberration σw/2π in λ/1000. Field curvature and distortion are assumed null. (a) MF-2: α = δ = 1. (b) LLMF-1: α = −δ = 1. (c) LLMF-2: α = δ = 0.33.

Tables (1)

Tables Icon

Table I Minimum Intensity at Diffraction Focus of Different Filters

Equations (62)

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

o ( u ) = ψ ( u ; d s ) S ( ξ ) ,
d s D s - 1 ,
ξ u d s / λ ,
k 2 π / λ ,
ψ ( u ; d s ) exp ( j k 2 d s u 2 ) .
r ( u ) = ψ ( u - D r D r x r ; d r ) ,
d r D r - 1
r ( u ) = ψ ( u ; d r ) exp ( - j k d r x r u ) .
τ ( u ) = I ( u ) = o ( u ) + r ( u ) 2 .
τ ( u ) = 1 + S ( ξ ) 2 + τ + 1 ( u ) + τ + 1 * ( u ) ,
τ + 1 ( u ) ψ * ( u ; d s - d r ) S * ( ξ ) exp ( - j k d r x r u ) .
c ( u ) = ψ ( u ; d t ) T ( ξ α - 1 ) ,
d t D t - 1
ξ u d t / λ .
ξ α - 1 = ξ .
α = D s / D t = d t / d s .
c ( u ) τ ( u ) = ψ ( u ; d t ) T ( ξ ) [ 1 + S ( ξ ) 2 ] + ψ ( u ; d t - d s + d r ) T ( ξ ) S * ( ξ ) exp ( - j k d r x r u ) + ψ ( u ; d t + d s - d r ) T ( ξ ) S ( ξ ) exp ( + j k d r x r u ) .
O ( m ) = c ( m ) τ ( m ) * ψ ( m ; d o ) ,
d o D o - 1 .
O ( m ) = O 01 ( m ) + O 02 ( m ) + O + 1 ( m ) + O - 1 ( m ) ,
O 01 ( m ) P h ψ ( u ; d t + d o ) T ( ξ ) S ( ξ ) 2 exp ( - j k d o u m ) d u ,
O 02 ( m ) P h ψ ( u ; d t + d o ) T ( ξ ) exp ( j k d o u m ) d u ,
O + 1 ( m ) P h ψ ( u ; d t + d o + d r - d s ) T ( ξ ) S * ( ξ ) exp [ j k u × ( m d o - d r x r ) ] d u ,
O - 1 ( m ) P h ψ ( u ; d t + d o + d s - d r ) T ( ξ ) S ( ξ ) exp [ j k u × ( m d o + d r x r ) ] d u .
d o = d s - d t - d r
O + 1 ( m ) = C st ( d o d s m - d r d s x r ) ,
C st ( m ) P s s * ( x + m ) t ( x ) d x .
β d o / d s = D s / D o ,
δ d r / d s = D s / D r .
m o δ β - 1 x r ,
O + 1 ( m o ) = C st ( o ) .
1 D s - 1 D r = 1 D t + 1 D o .
F h ( 1 D s - 1 D r ) - 1 .
D o = - D t < 0.
1 = α + β + δ .
Δ ξ Δ u d s λ - 1
τ + 1 Δ ( u ) τ + 1 ( u - Δ u ) = ψ * [ u - Δ u ; d s ( 1 - δ ) ] × S * ( ξ - Δ ξ ) exp [ - j k d s δ ( u - Δ u ) x r ] .
O + 1 ( m ) = P h ψ ( u ; d t + d o - d s + d r ) T ( ξ ) S * ( ξ - Δ ξ ) × exp { j k d s u [ m β - δ x r + ( 1 - δ ) Δ u ] } d u .
O + 1 ( m ) = P s s * ( x ) t [ x + ( 1 - δ ) Δ u + m β - δ x r ] exp ( - j 2 π Δ ξ x ) d x .
O + 1 ( m o ) = P s s * ( x ) t [ x + ( 1 - δ ) Δ u ] exp ( - j 2 π Δ ξ x ) d x .
s ( x ) t ( x ) = 1 x < a , = 0 elsewhere .
O + 1 ( m o ) = sin π Δ u 2 a λ D s [ 1 - ( 1 - δ ) Δ u 2 a ] π Δ u 2 a λ D s             0 < Δ u 2 a < 1 1 - δ , = 0             elsewhere .
O + 1 ( m o ) large 2 a sinc π Δ u 2 a λ D s ,
sinc x x - 1 sin x .
O + 1 ( m o ) small 2 a 1 - ( 1 - δ ) Δ u 2 a             0 < Δ u 2 a < 1 1 - δ = 0 elsewhere.
log Δ u small 2 a = log 2 a + log ( 1 - M 1 - δ ) ,
log Δ u large 2 a = - log 2 a + log ( M L λ D s / π ) ,
sinc 2 M L = M .
2 a T = ( M L λ D s ( 1 - δ ) π ( 1 - M ) ) 1 / 2 .
O + 1 ( m o ) = P s s * ( x ) t ( x ) exp ( - j 2 π Δ ξ x ) d x .
s ( x ) t ( x ) = 1             W s - w s 2 < x < W s + w s 2 = 0 elsewhere .
O + 1 ( m o ) = sinc ( π Δ ξ w s ) cos ( π W s Δ ξ ) .
O + 1 ( m o ) cos ( π W s Δ ξ ) ,             Δ ξ < 1 2 W s .
W ( ρ , θ ) = 2 π ( ρ λ ) [ 1 8 ( ρ α D t ) 3 S A - 1 2 ( ρ α D t ) 2 ( C x cos θ + C y sin θ ) - 1 2 ( ρ α D t ) ( A x x cos 2 θ + A y y sin 2 θ + 2 A x y sin θ cos θ ) + 1 4 ( ρ α D t ) F C - 1 2 ( D x cos θ + D y sin θ ) ] ,
S A ( α 3 + β 3 + δ 3 - 1 ) = - 3 ( α + δ ) ( 1 - δ ) ( 1 - α ) ,
C l θ l t ( α 2 - β 2 ) - θ l s ( 1 - β 2 ) + θ l r ( δ 2 - β 2 ) ; ( l = x , y ) ,
A k l θ k t θ l t α - θ k s θ l s + θ k r θ l r δ + β ( θ k t - θ k s + θ k r ) × ( θ l t - θ l s + θ l r ) ; ( k , l = x , y ) ,
F C A x x + A y y ,
D l θ l t ( θ l t 2 + θ k t 2 ) - θ l s ( θ l s 2 + θ k s 2 ) + θ l r ( θ l r 2 + θ k r 2 ) - ( θ l t - θ l s + θ l r ) [ ( θ k t - θ k s + θ k r ) 2 + ( θ l t - θ l s + θ l r ) 2 ] ; ( k , l = x , y but k l ) ,
θ l i l i D i with l = x or y and i = r , s , t .
σ w ( R h ) { E [ W 2 ( ρ , θ ) ] - E 2 [ W ( ρ , θ ) ] } 1 / 2 ,
I ( x o , y o , D o ) = 1 - σ w 2 .

Metrics