Abstract

Experimental and theoretical results describing matched filter selectivity for a particular class of signal as obtained, for example, in holographic velocimetry are reviewed. An experiment showing noise rejection is described for filters having both low and high ratios of signal to reference beam. The data presented are for transmissive signals. Best results are obtained using high ratio filters and high contrast signals. Extension to signals derived from diffusely reflecting material objects is treated. By utilizing proper optics, the scale change effects of matched filtering are shown to give a quantitative measure of deformation of the strained object. Dependence of sensitivity upon signal characteristics is discussed.

© 1972 Optical Society of America

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References

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  1. R. Menzel, F. M. Shofner, Appl. Opt. 9, 2073 (1970).
    [CrossRef] [PubMed]
  2. F. M. Shofner, R. O. Webb, R. L. Fradenburg, Laser J. 2, 13 (March/April 1970).
  3. R. A. Binns, A. Dickinson, B. M. Wastrasiewicz, Appl. Opt. 7, 1045 (1968).
    [CrossRef]
  4. T. H. Gee, W. Linton, Instrum. Aerospace Ind. 16, 126 (1970).
  5. E. Marom. Appl. Opt. 9, 1387 (1970).
    [CrossRef]

1970 (4)

R. Menzel, F. M. Shofner, Appl. Opt. 9, 2073 (1970).
[CrossRef] [PubMed]

F. M. Shofner, R. O. Webb, R. L. Fradenburg, Laser J. 2, 13 (March/April 1970).

T. H. Gee, W. Linton, Instrum. Aerospace Ind. 16, 126 (1970).

E. Marom. Appl. Opt. 9, 1387 (1970).
[CrossRef]

1968 (1)

R. A. Binns, A. Dickinson, B. M. Wastrasiewicz, Appl. Opt. 7, 1045 (1968).
[CrossRef]

Binns, R. A.

R. A. Binns, A. Dickinson, B. M. Wastrasiewicz, Appl. Opt. 7, 1045 (1968).
[CrossRef]

Dickinson, A.

R. A. Binns, A. Dickinson, B. M. Wastrasiewicz, Appl. Opt. 7, 1045 (1968).
[CrossRef]

Fradenburg, R. L.

F. M. Shofner, R. O. Webb, R. L. Fradenburg, Laser J. 2, 13 (March/April 1970).

Gee, T. H.

T. H. Gee, W. Linton, Instrum. Aerospace Ind. 16, 126 (1970).

Linton, W.

T. H. Gee, W. Linton, Instrum. Aerospace Ind. 16, 126 (1970).

Marom, E.

E. Marom. Appl. Opt. 9, 1387 (1970).
[CrossRef]

Menzel, R.

Shofner, F. M.

R. Menzel, F. M. Shofner, Appl. Opt. 9, 2073 (1970).
[CrossRef] [PubMed]

F. M. Shofner, R. O. Webb, R. L. Fradenburg, Laser J. 2, 13 (March/April 1970).

Wastrasiewicz, B. M.

R. A. Binns, A. Dickinson, B. M. Wastrasiewicz, Appl. Opt. 7, 1045 (1968).
[CrossRef]

Webb, R. O.

F. M. Shofner, R. O. Webb, R. L. Fradenburg, Laser J. 2, 13 (March/April 1970).

Appl. Opt. (3)

R. Menzel, F. M. Shofner, Appl. Opt. 9, 2073 (1970).
[CrossRef] [PubMed]

R. A. Binns, A. Dickinson, B. M. Wastrasiewicz, Appl. Opt. 7, 1045 (1968).
[CrossRef]

E. Marom. Appl. Opt. 9, 1387 (1970).
[CrossRef]

Instrum. Aerospace Ind. (1)

T. H. Gee, W. Linton, Instrum. Aerospace Ind. 16, 126 (1970).

Laser J. (1)

F. M. Shofner, R. O. Webb, R. L. Fradenburg, Laser J. 2, 13 (March/April 1970).

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Figures (9)

Fig. 1
Fig. 1

Holographic velocimeter: recording phase.

Fig. 2
Fig. 2

Cross correlation with nonlinearly recorded signals and nonlinear matched filters.

Fig. 3
Fig. 3

Signal modes.

Fig. 4
Fig. 4

Linear filter selectivity curve for rectangular t(r) model.

Fig. 5
Fig. 5

Plot of normalized maximum intensity of correlation spot for signal recorded on different films.

Fig. 6
Fig. 6

Selectivity curves for expanded coordinates.

Fig. 7
Fig. 7

Correlation of signal under uniform expansion (transmissive signal).

Fig. 8
Fig. 8

Correlation of signal under uniform coordinate expansion (reflecting signal).

Fig. 9
Fig. 9

Unidimensional illumination of object.

Equations (11)

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I ( r ) A 2 Z 2 [ 1 + Z 2 z 0 a 2 z 0 J 1 ( kar z 1 ) - 2 Z z 0 a r J 1 ( kar z 1 ) sin ( k r 2 2 z 1 z 0 Z ) ] .
C ( x 3 , y 3 ) = s * s 0 = s ( ξ , η ) s 0 * ( ξ - x 3 , η - y 3 ) d ξ d η ,
r 0 = [ ( λ z 1 / 2 ) ( Z / z 0 ) ] 1 2 .
r = α r 0 , R = α r 00 , r = β r 0 , R = β r 00 .
C ( 0 ) = 2 π 0 ρ t ( ρ ) t 0 ( ρ ) d ρ = { π ( R 2 - r 2 ) z 1 z 10 , π ( r 2 - R 2 ) z 1 z 10 .
C ( 0 ) = π λ 2 ρ 2 Z z z 10 ( 1 - α 2 β 2 z 1 z z 0 z 10 ) , z 1 > z 10 .
K λ f 1 S * ( x 2 λ f 1 , y 2 λ f 1 ) exp ( - j 2 π β y 2 ) ,
U ( x 3 , y 3 ) 1 λ z - s ( ξ , η ) s * ( ξ + x 3 f 1 z η + y 3 f 1 z + β λ f 1 ) d ξ d η ,
1 / z = ( 1 / f 3 ) - ( 1 / f 1 ) and d = f 1 ,
A exp [ k j 2 d ( x 2 2 + y 2 2 ) ] λ d f 2 d G ( x 2 λ d α , y 2 λ d α ) .
1 / z = ( 1 / f 3 ) - ( α / f 1 ) .

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