Abstract

In this paper, a Fourier-optics approach to scatterplate interferometry is introduced. In particular, it is used to explain how energy is conserved for both “phase”- and “density”-type scatterplates.

© 1979 Optical Society of America

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References

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  1. J. M. Burch, “Scatter Fringe Interferometry,” J. Opt. Soc. Am. 52, 600 (1962).
  2. R. M. Scott, “Scatter Plate Interferometry,” Appl. Opt. 8, 531–537 (1969).
  3. J. B. Houston, “How to Make and Use a Scatterplate In Interferometer,” Opt. Spectra 4, 32 (1970).
  4. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley-Interscience, New York, 1978) p. 216.

1970 (1)

J. B. Houston, “How to Make and Use a Scatterplate In Interferometer,” Opt. Spectra 4, 32 (1970).

1969 (1)

R. M. Scott, “Scatter Plate Interferometry,” Appl. Opt. 8, 531–537 (1969).

1962 (1)

J. M. Burch, “Scatter Fringe Interferometry,” J. Opt. Soc. Am. 52, 600 (1962).

Burch, J. M.

J. M. Burch, “Scatter Fringe Interferometry,” J. Opt. Soc. Am. 52, 600 (1962).

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley-Interscience, New York, 1978) p. 216.

Houston, J. B.

J. B. Houston, “How to Make and Use a Scatterplate In Interferometer,” Opt. Spectra 4, 32 (1970).

Scott, R. M.

R. M. Scott, “Scatter Plate Interferometry,” Appl. Opt. 8, 531–537 (1969).

Appl. Opt. (1)

R. M. Scott, “Scatter Plate Interferometry,” Appl. Opt. 8, 531–537 (1969).

J. Opt. Soc. Am. (1)

J. M. Burch, “Scatter Fringe Interferometry,” J. Opt. Soc. Am. 52, 600 (1962).

Opt. Spectra (1)

J. B. Houston, “How to Make and Use a Scatterplate In Interferometer,” Opt. Spectra 4, 32 (1970).

Other (1)

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley-Interscience, New York, 1978) p. 216.

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Figures (5)

FIG. 1
FIG. 1

Schematic of scatterplate interferometer.

FIG. 2
FIG. 2

Scatterplate interferogram obtained testing parabolic mirror.

FIG. 3
FIG. 3

Unfolded schematic of a scatterplate interferometer.

FIG. 4
FIG. 4

Schematic of a scatterplate interferometer used in noncommon path mode.

FIG. 5
FIG. 5

Simplified view of how the density scatterplate absorbs light.

Equations (21)

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I f = I 0 | e i k w [ S + ] * * [ S ] | 2 = I 0 | [ ( [ e i k w ] * * S + ) S ] | 2
S + = S = S .
S p = A exp [ i k ( n 1 ) h ] ,
S p A [ 1 + i k ( n 1 ) h ] .
[ S p ] = [ A ] * * { δ + i k ( n 1 ) [ h ] } ,
S D = A [ t 0 + t 1 ]
[ S D ] = [ A ] * * ( t 0 δ + [ t 1 ] ) ,
S p + = A [ e i ϕ + i k ( n 1 ) h ] ,
S D + = A [ e i ϕ t 0 + t 1 ] ,
I f = | A 2 ] e i ( ϕ ) + i k ( n 1 ) × ( e i k w [ A h ] ) * * [ A ] + i [ A 2 ] h e i ϕ k ( n 1 ) k 2 ( n 1 ) 2 ( e i k w [ A h ] ) * * [ A h ] | 2 ,
I f = [ A ] { [ A ] + 2 k ( n 1 ) [ A h ] sin ( ϕ k w ) 2 k 2 ( n 1 ) 2 Re { e i ϕ B * } + 2 k 2 ( n 1 ) 2 [ 1 + cos ( k w ϕ ) ] ( [ A h ] ) 2 + k 4 ( n 1 ) 4 | B | 2 2 k 3 ( n 1 ) 3 [ A h ] Re { i e i ϕ B * } 2 k 3 ( n 1 ) 3 [ A h ] Re { i e i k w B * } ,
I f = [ A ] ( [ A ] + 2 k ( n 1 ) [ A h ] sin ϕ 2 [ A h 2 ] k 2 ( n 1 ) 2 cos ϕ ) } I D D + 2 k 2 ( n 1 ) 2 ( 1 + cos ϕ ) ( [ A h ] ) 2 } I S + k 4 ( n 1 ) 4 ( [ A h 2 ] ) 2 + 2 k 3 ( n 1 ) 3 × [ A h ] [ A h 2 ] sin ϕ } I S S ,
I f d A I = A S 2 k 2 ( n 1 ) 2 A S h 2 cos ϕ } hotspot + 2 k 2 ( n 1 ) 2 A S h 2 ( 1 + cos ϕ ) } signal + k 4 ( n 1 ) 4 A S h 4 } background ,
= A S + 2 k 2 ( n 1 ) 2 A S h 2 + k 4 ( n 1 ) 4 A S h 4 , independent of ϕ ,
[ A ] [ A h 2 ] d A 1 = A A h 2 d A S = A S h 2 .
I f = [ A ] ( t 0 4 [ A ] + 2 t 0 3 [ A t 1 ] ( 1 + cos ϕ ) + 2 t 0 2 [ A t 1 2 ] cos ϕ ) } I D D + 2 t 0 2 ( [ A t 1 ] ) 2 ( 1 + cos ϕ ) } I S + ( [ A t 1 2 ] ) 2 + 2 t 0 [ A t 1 ] [ A t 1 2 ] ( 1 + cos ϕ ) } I S S .
I f d A I = t 0 4 A S + 2 t 0 2 A S t 1 2 cos ϕ } hotspot + 2 t 0 2 A S t 1 2 ( 1 + cos ϕ ) } signal + t 1 4 } background .
I 2 + = | A ( e i ϕ t 0 + t 1 ) | 2 = A 2 ( t 0 2 + 2 t 1 t 0 cos ϕ + t 1 2 ) .
T 2 = A 2 ( t 0 2 + 2 t 1 t 0 + t 1 2 ) ,
E S = A S ( 1 I 2 + T 2 ) d A = A S ( A S t 0 4 + t 1 4 + 2 t 0 2 t 1 2 + 4 t 0 2 t 1 2 cos ϕ )
E S + A S I f d A = A S