Abstract

Based on optical correlation in a defocused system with two masks, strong phase variations can be contour mapped. Typical systems are analyzed mathematically by virtue of the backward impulse response suggested here. Three general parameters are defined to characterize performances. The condition of invariant correlation is discussed, and the process of contour mapping is investigated in detail. It is found that the configurations are the same as for quasi-interferometers with coded correlation filtering but treated from different viewpoints. Combining the analyses in the space domain with the explanations in the spatial frequency domain, a simple way is provided to synthesize any new type of quasi-interferometer. In addition, the necessary requirements for construction are introduced, and further examples are given.

© 1983 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), p. 163.
  2. J. Knopp, M. F. Becker, Appl. Opt. 17, 984 (1978).
    [CrossRef] [PubMed]
  3. L. Liu, Appl. Opt. 21, 2817 (1982).
    [CrossRef] [PubMed]
  4. L. Liu, Appl. Opt. 21, 3839 (1982).
    [CrossRef] [PubMed]
  5. L. Liu, Opt. Commun. 44, 301 (1983).
    [CrossRef]
  6. L. Liu, Opt. Commun. 45, 215 (1983).
    [CrossRef]

1983

L. Liu, Opt. Commun. 44, 301 (1983).
[CrossRef]

L. Liu, Opt. Commun. 45, 215 (1983).
[CrossRef]

1982

1978

Becker, M. F.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), p. 163.

Knopp, J.

Liu, L.

Appl. Opt.

Opt. Commun.

L. Liu, Opt. Commun. 44, 301 (1983).
[CrossRef]

L. Liu, Opt. Commun. 45, 215 (1983).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), p. 163.

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Figures (5)

Fig. 1
Fig. 1

First typical configuration (heavy lines for determining C between solid lines for K and dotted lines for R).

Fig. 2
Fig. 2

Second typical configuration (heavy lines for C between solid lines for K and dotted lines for R).

Fig. 3
Fig. 3

Equivalent configuration of quasi-interferometer with coded correlation Fourier filtering.

Fig. 4
Fig. 4

Fresnel transform quasi-interferometer.

Fig. 5
Fig. 5

Negative lens Fourier transform quasi-interferometer.

Equations (54)

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1 l 26 + 1 l 67 = 1 f 2 .
1 l 13 + 1 l 35 = 1 f 1 .
1 l 32 = 1 l 32 1 f 1 .
K = l 32 l 25 ( l 32 + l 13 + Δ 1 ) l 32 ,
K = 1 l 13 l 35 + Δ 1 l 25 ( 1 l 32 f 1 ) .
x = Δ 1 l 35 l 26 l 25 l 13 l 67 x d , y = Δ 1 l 35 l 26 l 25 l 13 l 67 y d .
C = Δ 1 l 35 l 25 l 13 N .
x = tan β x ( x d N , y d N ) l 32 ( l 13 + l 32 + Δ 1 ) l 32 , y = tan β y ( x d N , y d N ) l 32 ( l 13 + l 32 + Δ 1 ) l 32 .
l 32 ( l 13 + l 32 + Δ 1 ) l 32 = l 13 l 25 l 35 + Δ 1 ( 1 l 32 f 1 ) .
R = l 13 l 25 l 35 + Δ 1 ( 1 l 32 f 1 ) .
S 2 { K [ x C x d R tan β x ( x d N , y d N ) ] , K [ y C y d R tan β y ( x d N , y d N ) ] } ,
I ( x d , y d ) = S 1 ( x , y ) S 2 { K [ x C x d R × tan β x ( x d N , y d N ) ] , K [ y C y d R tan β y ( x d N , y d N ) ] } dxdy .
K = l 35 l 13 Δ 2 l 12 ( 1 l 23 f 1 ) ,
C = 1 N [ 1 + l 12 l 23 f 1 ( l 35 Δ 2 ) l 35 Δ 2 f 1 ] ,
R = l 12 .
S ( x , y ) = S 1 ( x , y ) * S 2 ( x , y ) ,
S 1 ( x , y ) * S 2 ( mx , my ) 1 .
I ( x d , y d ) = S 1 ( x , y ) S 2 [ PK ( x C x d R tan β x , y C y d R × tan β y ) ] dxdy .
I ( x d , y d ) = S [ C x d + R tan β x ( x d N , y d N ) , C y d + R tan β y ( x d N , y d N ) ] .
S ( x , y ) = k δ ( x ± kD ) .
S ( x , y ) = k δ ( r kD ) ,
I ( x d , y d ) = S [ R tan β x ( x d N , y d N ) , R tan β y ( x d N , y d N ) ] .
I ( x d , y d ) = k δ [ R tan β x ( x d N , y d N ) ± kD ] .
tan β x ( x d N , y d N ) = kD R .
I ( x d , y d ) = k δ [ R tan β ( x d N , y d N ) kD ] .
tan β ( x d N , y d N ) = kD R .
I ( x d , y d ) = k δ ( C 2 x d 2 + C 2 x d 2 kD ) ,
I ( x d , y d ) = k δ [ R tan β x ( x d N , y d N ) + C x d ± kD ] .
tan β x ( x d N , y d N ) = C x d kD R .
I ( x d , y d ) = k δ [ ( R tan β x + C x d ) 2 + ( R tan β y + C y d ) 2 kD ] ,
( R tan β x + C x d ) 2 + ( R tan β y + C y d ) 2 = kD .
grad ϕ ( x , y ) = 2 π λ sin β ( x , y ) .
C R = Δ 1 l 35 2 l 25 2 l 13 2 N ,
C R = Δ 2 f 1 2 N .
K = f q / l q ,
R = l q ,
C = [ l q / ( N f 0 ) ] .
f q = KR ,
l q = R ,
f 0 = [ R / ( NC ) ] .
K = l 25 / l 12 ,
R = l 12 ,
C = [ l 15 / ( l 25 N ) ] ,
f q = l 25 ,
l q = l 12 ,
f 0 = ( l 12 l 25 ) / l 15 .
K = l 25 l 31 l 23 ( l 13 + l 31 ) ,
1 l 31 = 1 l 32 1 f 1 ,
K = f 1 l 25 f 1 l 12 l 13 l 32 ;
C = 1 N l 25 ( l 32 l 13 f 1 l 15 ) ,
R = l 12 l 13 l 32 f 1 ,
f q = l 25 ,
l q = l 12 l 13 l 32 f 1 ,
1 f 0 = 1 l 25 f 1 l 13 l 32 l 12 f 1 .

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