Abstract

The theory of one-step rainbow holography of the diffused 3-D objects with no slit is explored. The synthetic exit slit is composed by the time exposure of a slow linear translating object. The position of the slit is determined by the direction of the translation. Experimental results are also included.

© 1983 Optical Society of America

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References

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  1. C. P. Grover, H. M. van Driel, J. Opt. Soc. Am. 70, 335 (1980).
    [CrossRef]
  2. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  3. H. Chen, Q. Shan, M. Chen, Appl. Opt. 20, 3557 (1981).
    [CrossRef] [PubMed]
  4. H. Chen, F. T. S. Yu, Opt. Lett. 2, 85 (1978).
    [CrossRef] [PubMed]
  5. H. Chen, Appl. Opt. 17, 3290 (1979).
    [CrossRef]
  6. S. A. Benton, H. S. Mingace, W. R. Walter, Proc. Soc. Photo-Opt. Instrum. Eng. 215, 156 (1980).

1981 (1)

1980 (2)

C. P. Grover, H. M. van Driel, J. Opt. Soc. Am. 70, 335 (1980).
[CrossRef]

S. A. Benton, H. S. Mingace, W. R. Walter, Proc. Soc. Photo-Opt. Instrum. Eng. 215, 156 (1980).

1979 (1)

1978 (1)

Benton, S. A.

S. A. Benton, H. S. Mingace, W. R. Walter, Proc. Soc. Photo-Opt. Instrum. Eng. 215, 156 (1980).

Chen, H.

Chen, M.

Grover, C. P.

Mingace, H. S.

S. A. Benton, H. S. Mingace, W. R. Walter, Proc. Soc. Photo-Opt. Instrum. Eng. 215, 156 (1980).

Shan, Q.

van Driel, H. M.

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

Walter, W. R.

S. A. Benton, H. S. Mingace, W. R. Walter, Proc. Soc. Photo-Opt. Instrum. Eng. 215, 156 (1980).

Yu, F. T. S.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

S. A. Benton, H. S. Mingace, W. R. Walter, Proc. Soc. Photo-Opt. Instrum. Eng. 215, 156 (1980).

Other (1)

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

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Figures (5)

Fig. 1
Fig. 1

Basic recording configuration.

Fig. 2
Fig. 2

Coherent reconstructed sinc function with recording parameters 0 = 0.023 mm, θt = 22°.

Fig. 3
Fig. 3

Coherent reconstructed sinc function with recording parameters 0 = 0.023 mm, θt = 24°.

Fig. 4
Fig. 4

Coherent reconstructed sinc function with recording parameters 0 = 0.009 mm, θt = 22°.

Fig. 5
Fig. 5

White-light reconstructed holographic image.

Equations (11)

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U ( x 0 , y 0 , z 0 ) = A ( x 0 , y 0 , z 0 ) exp [ j 2 π ( β y 0 + γ z 0 ) ] ,
U ( x 0 , y 0 , z 0 ; , η ) = A ( x 0 , y 0 , z 0 η ) exp [ j 2 π ( β y 0 + γ z 0 ) ] = U ( x 0 , y 0 , z 0 η ) exp [ j 2 π ( β + γ η ) ] .
U f 1 ( x 1 , y 1 ; , η ) = 1 j λ f exp { j 2 π [ ( β y 1 λ f ) + η γ ] } d z 0 exp ( j 2 π z 0 λ ) exp [ j π λ f ( 1 z 0 f ) ( x 1 2 + y 1 2 ) ] { F x 0 , y 0 [ U ( x 0 , y 0 , z 0 η ) ] } f x 0 = x 1 / λ f , f y 0 = y 1 / λ f = U f ( x 1 , y 1 ) exp { j 2 π [ β + η ( 1 λ + γ ) ] } exp { j 2 π [ y 1 λ f + η 2 λ f 2 ( x 1 2 + y 1 2 ) ] } .
U f ( x 1 , y 1 ) 1 j λ f d z 0 exp ( j 2 π λ z 0 ] exp [ j π λ f ( 1 z 0 f ) ( x 1 2 + y 1 2 ) ] { F x 0 , y 0 [ U ( x 0 , y 0 , z 0 ) ] } f x 0 = x 1 / λ f , f y 0 = y 1 / λ f .
U p 1 ( x 1 , y 1 ; , η ) = C d x 1 d y 1 ( U f 1 ( x 1 , y 1 ; , η ) exp { j π λ z f p [ ( x 1 x 2 ) 2 + ( y 1 y 2 ) 2 ] } ) .
I ( x 2 , y 2 ; , η ) = | U p 1 ( x 2 , y 2 ; , η ) + U r ( x 2 , y 2 ) | 2 = | U p 1 | 2 + | U r | 2 + U p 1 ( x 2 , y 2 ; , η ) U r * ( x 2 , y 2 ) + U p 1 * ( x 2 , y 2 ; , η ) U r ( x 2 , y 2 ) .
I ( x 2 , y 2 ) = 0 / 2 0 / 2 U p 1 ( x 2 , y 2 ; , b ) U r * ( x 2 , y 2 ) d = C U r * ( x 2 , y 2 ) U f ( x 1 , y 1 ) exp { j π λ z f p [ ( x 1 x 2 ) 2 + ( y 1 y 2 ) 2 ] } 0 sinc [ 0 β + 0 b ( 1 λ + γ ) 0 y 1 λ f b 0 2 λ f 2 ( x 1 2 + y 1 2 ) ] d x 1 d y 1 .
( y 1 ) s = f [ λ β + b ( 1 + λ γ ) ] .
tan θ t = b = λ β λ γ + 1 .
W = ( 2 λ f ) / 0 .
z i p = 1 z c p + λ λ ( 1 z o p 1 z υ p ) ,

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