Abstract

The number of holograms that can be linearly superimposed on one photographic plate has two fundamental limits; one is the finite extent of the characteristic amplitude transmittance vs energy-of-exposure (TaE) film curve, and the other is holographic reciprocity law failure [ K. M. Johnson, L. Hesselink, and J. W. Goodman, Appl. Opt. 23, 218 ( 1984)], the chronological decrease in brightness of reconstructed images in a multiple-exposure hologram. In this paper a multistep hologram, called the multiple multiple-exposure hologram, is presented which increases the number of holograms that can be linearly superimposed on one photographic plate and reconstructs images of equal brightness. The brightness of the reconstructed images in the final display hologram is a function of the reference-to-object beam ratio K in the intermediate and final steps of the multiple multiple-exposure hologram. By choosing different values for K in each step of this technique, a cross section can be displayed with the same diffraction efficiency in the initial multiple-exposure holograms and the final multiple multiple-exposure hologram. The trade-off between the maximum number of holograms that can be linearly superimposed on one photographic plate and the signal-to-noise ratio in the final display hologram is also discussed.

© 1985 Optical Society of America

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References

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  1. K. M. Johnson, L. Hesselink, J. W. Goodman, “Holographic Reciprocity Law Failure,” Appl. Opt. 23, 218 (1984).
    [CrossRef] [PubMed]
  2. H. Akahori, K. Sakurai, “Information Search Using Superimposed Holograms,” Appl. Opt. 10, 665 (1971).
    [CrossRef] [PubMed]
  3. R. L. Powell, K. A. Stetson, “Interferometric Vibration Analysis by Wavefront Reconstruction,” J. Opt. Soc. Am. 55, 1593 (1965).
    [CrossRef]
  4. T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).
  5. K. M. Johnson, L. Hesselink, J. W. Goodman, “Multiexposure Holographic Display of CT Medical Data,” Proc. Soc. Photo-Opt. Instrum. Eng. 367, 149 (1982).
  6. G. B. Brandt, “Image Plane Holography,” Appl. Opt. 8, 1421 (1969).
    [CrossRef] [PubMed]
  7. R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 171–173, 204.
  8. W. E. Kock, L. Rosen, “Focused Image Holography—the Third Dimension in the Recording of Conventionally Focused Photographs,” Proc. IEEE 55, 80 (1967).
    [CrossRef]
  9. Y. N. Denisyuk, “Photographic Reconstruction of the Optical Properties of an Object in its Own Scattered Radiation Field,” Sov. Phys. Dokl. 7, 543 (1962); N. Nishida, M. Sakaguchi, “Improvement of Nonuniformity of the Reconstructed Beam Intensity from a Multiple-Exposure Hologram,” Appl. 10, 439 (1971).
    [CrossRef]
  10. H. M. Smith, Principles of Holography (Wiley, New York, 1969), pp. 257–260, 136.
  11. Y. I. Ostravsky, Holography and Its Applications (Mir, Moscow, 1973), pp. 123–127.
  12. W. Spierings, “Pyrochrome Processing Yields Color Controlled Results with Silver Halide Materials,” Holosphere 10, 1 (1981).
  13. O. V. Andreeva, V. I. Sukhandu, “Production of Unbleached Volume Holograms with High Diffraction Efficiency,” Opt. Spektrosk. 30, 786 (1971).
  14. M. Lehmann, J. P. Lauer, J. W. Goodman, “High Efficiencies, Low Noise, and Suppression of Photochromic Effects in Bleached Silver Halide Holography,” Appl. Opt. 9, 1948 (1970).
    [PubMed]

1984 (1)

1982 (1)

K. M. Johnson, L. Hesselink, J. W. Goodman, “Multiexposure Holographic Display of CT Medical Data,” Proc. Soc. Photo-Opt. Instrum. Eng. 367, 149 (1982).

1981 (1)

W. Spierings, “Pyrochrome Processing Yields Color Controlled Results with Silver Halide Materials,” Holosphere 10, 1 (1981).

1971 (2)

O. V. Andreeva, V. I. Sukhandu, “Production of Unbleached Volume Holograms with High Diffraction Efficiency,” Opt. Spektrosk. 30, 786 (1971).

H. Akahori, K. Sakurai, “Information Search Using Superimposed Holograms,” Appl. Opt. 10, 665 (1971).
[CrossRef] [PubMed]

1970 (1)

1969 (1)

1967 (1)

W. E. Kock, L. Rosen, “Focused Image Holography—the Third Dimension in the Recording of Conventionally Focused Photographs,” Proc. IEEE 55, 80 (1967).
[CrossRef]

1965 (1)

1962 (1)

Y. N. Denisyuk, “Photographic Reconstruction of the Optical Properties of an Object in its Own Scattered Radiation Field,” Sov. Phys. Dokl. 7, 543 (1962); N. Nishida, M. Sakaguchi, “Improvement of Nonuniformity of the Reconstructed Beam Intensity from a Multiple-Exposure Hologram,” Appl. 10, 439 (1971).
[CrossRef]

Akahori, H.

Andreeva, O. V.

O. V. Andreeva, V. I. Sukhandu, “Production of Unbleached Volume Holograms with High Diffraction Efficiency,” Opt. Spektrosk. 30, 786 (1971).

Brandt, G. B.

Burkhardt, C. B.

R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 171–173, 204.

Collier, R. J.

R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 171–173, 204.

Denisyuk, Y. N.

Y. N. Denisyuk, “Photographic Reconstruction of the Optical Properties of an Object in its Own Scattered Radiation Field,” Sov. Phys. Dokl. 7, 543 (1962); N. Nishida, M. Sakaguchi, “Improvement of Nonuniformity of the Reconstructed Beam Intensity from a Multiple-Exposure Hologram,” Appl. 10, 439 (1971).
[CrossRef]

Goodman, J. W.

Hesselink, L.

K. M. Johnson, L. Hesselink, J. W. Goodman, “Holographic Reciprocity Law Failure,” Appl. Opt. 23, 218 (1984).
[CrossRef] [PubMed]

K. M. Johnson, L. Hesselink, J. W. Goodman, “Multiexposure Holographic Display of CT Medical Data,” Proc. Soc. Photo-Opt. Instrum. Eng. 367, 149 (1982).

Johnson, K. M.

K. M. Johnson, L. Hesselink, J. W. Goodman, “Holographic Reciprocity Law Failure,” Appl. Opt. 23, 218 (1984).
[CrossRef] [PubMed]

K. M. Johnson, L. Hesselink, J. W. Goodman, “Multiexposure Holographic Display of CT Medical Data,” Proc. Soc. Photo-Opt. Instrum. Eng. 367, 149 (1982).

Kock, W. E.

W. E. Kock, L. Rosen, “Focused Image Holography—the Third Dimension in the Recording of Conventionally Focused Photographs,” Proc. IEEE 55, 80 (1967).
[CrossRef]

Lauer, J. P.

Lehmann, M.

Lin, L. H.

R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 171–173, 204.

Okoshi, T.

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).

Ostravsky, Y. I.

Y. I. Ostravsky, Holography and Its Applications (Mir, Moscow, 1973), pp. 123–127.

Powell, R. L.

Rosen, L.

W. E. Kock, L. Rosen, “Focused Image Holography—the Third Dimension in the Recording of Conventionally Focused Photographs,” Proc. IEEE 55, 80 (1967).
[CrossRef]

Sakurai, K.

Smith, H. M.

H. M. Smith, Principles of Holography (Wiley, New York, 1969), pp. 257–260, 136.

Spierings, W.

W. Spierings, “Pyrochrome Processing Yields Color Controlled Results with Silver Halide Materials,” Holosphere 10, 1 (1981).

Stetson, K. A.

Sukhandu, V. I.

O. V. Andreeva, V. I. Sukhandu, “Production of Unbleached Volume Holograms with High Diffraction Efficiency,” Opt. Spektrosk. 30, 786 (1971).

Appl. Opt. (4)

Holosphere (1)

W. Spierings, “Pyrochrome Processing Yields Color Controlled Results with Silver Halide Materials,” Holosphere 10, 1 (1981).

J. Opt. Soc. Am. (1)

Opt. Spektrosk. (1)

O. V. Andreeva, V. I. Sukhandu, “Production of Unbleached Volume Holograms with High Diffraction Efficiency,” Opt. Spektrosk. 30, 786 (1971).

Proc. IEEE (1)

W. E. Kock, L. Rosen, “Focused Image Holography—the Third Dimension in the Recording of Conventionally Focused Photographs,” Proc. IEEE 55, 80 (1967).
[CrossRef]

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

K. M. Johnson, L. Hesselink, J. W. Goodman, “Multiexposure Holographic Display of CT Medical Data,” Proc. Soc. Photo-Opt. Instrum. Eng. 367, 149 (1982).

Sov. Phys. Dokl. (1)

Y. N. Denisyuk, “Photographic Reconstruction of the Optical Properties of an Object in its Own Scattered Radiation Field,” Sov. Phys. Dokl. 7, 543 (1962); N. Nishida, M. Sakaguchi, “Improvement of Nonuniformity of the Reconstructed Beam Intensity from a Multiple-Exposure Hologram,” Appl. 10, 439 (1971).
[CrossRef]

Other (4)

H. M. Smith, Principles of Holography (Wiley, New York, 1969), pp. 257–260, 136.

Y. I. Ostravsky, Holography and Its Applications (Mir, Moscow, 1973), pp. 123–127.

R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 171–173, 204.

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).

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Figures (6)

Fig. 1
Fig. 1

First step of the multiple multiple-exposure hologram: recording the master hologram.

Fig. 2
Fig. 2

Second step of the multiple multiple-exposure hologram: recording the copy hologram from the real images of the master holograms.

Fig. 3
Fig. 3

Experimental apparatus for recording master holograms.

Fig. 4
Fig. 4

Experimental apparatus for recording the copy hologram.

Fig. 5
Fig. 5

Image plane hologram of a point source.

Fig. 6
Fig. 6

Experimental apparatus for generating an image plane hologram of CT data.

Tables (2)

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Table I Relative Exposure Energies and Image Diffraction Efficiencies of a Four-Exposure Hologram of CT Data

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Table II Procedure for Pyrogallol Development

Equations (16)

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η n ( Δ t ) = | β ( Δ t ) · E b · MTF ( α n ) · m i | 2 4 ,
I m ( x , y ) = n = 1 N | O n ( x , y ) exp [ i ϕ n ( x , y ) ] + R 1 exp ( k · r ) | 2 ,
I m ( x , y ) = N ( O 1 2 + R 1 2 ) + 2 R 1 O 1 n = 1 N cos [ ϕ n ( x , y ) k · r ] .
m m = 2 R 1 O 1 N ( R 1 2 + O 1 2 ) ,
= 2 K N ( K + 1 ) ,
O m ( x , y ) = c = 1 N O c , m ( x , y ) exp [ i ϕ c , m ( x , y ) ] .
I c ( x , y ) m = 1 M | O m ( x , y ) + R c exp ( i k · r ) | 2 = m = 1 M | c = 1 N O c , m ( x , y ) exp [ i ϕ c , m ( x , y ) ] + R c exp ( i k · r ) | 2 .
I c ( x , y ) = m = 1 M { N O c 2 + R c 2 + 2 O c , m R c c = 1 N cos [ ϕ c , m ( x , y ) k · r ] + 2 O c 2 c = 1 N j = 1 N cos [ ϕ c , m ( x , y ) ϕ j , m ( x , y ) ] } ,
= M ( N O c 2 + R c 2 ) + 2 O c , m ( x , y ) R c m = 1 M c = 1 N × cos [ ϕ c m , ( x , y ) k · r ] + 2 O c 2 m = 1 M c = 1 N j = 1 N cos [ ϕ c , m ( x , y ) ϕ j , m ( x , y ) ] .
s ( x , y ) = 2 O c 2 m = 1 M c = 1 N j = 1 N cos [ ϕ c , m ( x , y ) ϕ j , m ( x , y ) ] .
m copy = 2 O c R c M ( N O c 2 + R c 2 ) .
K c = R c 2 N O c 2 ,
m copy = 2 K c / N M ( 1 + K c ) .
K N ( 1 + K ) = K c / N M ( 1 + K c ) .
K 2 ( N K c ) + K ( 2 K c N M 2 2 K c M 2 K c 2 M 2 ) + K c N = 0 .
K 2 16 K + 1 = 0 , K = 16 ,

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