Abstract

A special type of hologram with cylindrical symmetry, which may be treated as an intermediate structure between volume and plane holograms, is described. Its properties and applications in optical processing and storage of information are discussed.

© 1982 Optical Society of America

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  1. See, for example, R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).
  2. T. Jannson, "Information capacity of Bragg holograms in planar optics," J. Opt. Soc. Am. 71, 342–347 (1981).
  3. See, for example, D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972), Chap. I.
  4. It should be noted that Eq. (3) is satisfied just approximately when N0(x, y) is slowly varying compared to the wavelength.3 The analysis of the validity of this approximation is similar to that in Ref. 2.
  5. The efficiencies of the Bragg-diffracted beams may be, however, different for TE and TM polarizations (see, e.g., Chap. 9 of Ref. 1).
  6. Such a situation is somewhat similar to that in planar Bragg holography (see Sec. 2.B of Ref. 2), where in the multimode case the recording and reconstruction processes may be realized by two different modes in two formally different planar media.
  7. P. J. van Heerden, "Theory of optical information storage in solids," Appl. Opt. 2, 393–400 (1962).
  8. V. V. Aristov and V. Sh. Shektman, "Properties of three-dimensional holograms," Sov. Phys. Usp. 14, 263–277 (1971).
  9. T. Jannson, "Structural information in volume holography," Opt. Appl. 9, 169–177 (1979).
  10. T. Jannson, "Shannon number of an image and structural information capacity in volume holography," Opt. Acta 27, 1335–1344 (1980).
  11. Formula (7) is derived on the basis of the first Born approximation. A similar formula for the rectangular cross section is given in Ref. 2, and its validity in the case of high diffraction efficiencies is discussed in detail in Ref. 10.
  12. J. W. Goodman, "An introduction to the principles and applications of holography," Proc. IEEE 59, 1292–1304 (1971).
  13. The Ewald construction was used in volume holography, e.g., by V. I. Sukhanov and Yu. N. Denisyuk, "On the relationship between spatial frequency spectra of a three-dimensional object and its three-dimensional hologram," Opt. Spectrosc. 28,63–66 (1970); M. R. B. Forshaw, "Explanation of the venetian blind effect in holography, using the Ewald sphere concept," Opt. Commun. 8, 201–206 (1973); S. I. Ragnarsson, "Scattering phenomena in volume holograms with strong coupling," Appl. Opt. 17, 116–127 (1978); S. Kusch and R. Guther, "Theoretical considerations on the bit capacity of volume holograms," Exp. Tech. Phys. 22,37–51 (1974); Refs. 8–10.
  14. Of course, the resolving power of 1D image spectrum obtained after the filtering operation depends on the transverse dimensions of the hologram. The problem is then strictly analogous to that in conventional Bragg holography (see, e.g., Ref. 1).
  15. See, for example, J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, Sec. 1.

1981 (1)

1980 (1)

T. Jannson, "Shannon number of an image and structural information capacity in volume holography," Opt. Acta 27, 1335–1344 (1980).

1979 (1)

T. Jannson, "Structural information in volume holography," Opt. Appl. 9, 169–177 (1979).

1971 (1)

V. V. Aristov and V. Sh. Shektman, "Properties of three-dimensional holograms," Sov. Phys. Usp. 14, 263–277 (1971).

1970 (1)

The Ewald construction was used in volume holography, e.g., by V. I. Sukhanov and Yu. N. Denisyuk, "On the relationship between spatial frequency spectra of a three-dimensional object and its three-dimensional hologram," Opt. Spectrosc. 28,63–66 (1970); M. R. B. Forshaw, "Explanation of the venetian blind effect in holography, using the Ewald sphere concept," Opt. Commun. 8, 201–206 (1973); S. I. Ragnarsson, "Scattering phenomena in volume holograms with strong coupling," Appl. Opt. 17, 116–127 (1978); S. Kusch and R. Guther, "Theoretical considerations on the bit capacity of volume holograms," Exp. Tech. Phys. 22,37–51 (1974); Refs. 8–10.

1962 (1)

Aristov, V. V.

V. V. Aristov and V. Sh. Shektman, "Properties of three-dimensional holograms," Sov. Phys. Usp. 14, 263–277 (1971).

Burckhardt, C. B.

See, for example, R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).

Collier, R. J.

See, for example, R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).

Denisyuk, Yu. N.

The Ewald construction was used in volume holography, e.g., by V. I. Sukhanov and Yu. N. Denisyuk, "On the relationship between spatial frequency spectra of a three-dimensional object and its three-dimensional hologram," Opt. Spectrosc. 28,63–66 (1970); M. R. B. Forshaw, "Explanation of the venetian blind effect in holography, using the Ewald sphere concept," Opt. Commun. 8, 201–206 (1973); S. I. Ragnarsson, "Scattering phenomena in volume holograms with strong coupling," Appl. Opt. 17, 116–127 (1978); S. Kusch and R. Guther, "Theoretical considerations on the bit capacity of volume holograms," Exp. Tech. Phys. 22,37–51 (1974); Refs. 8–10.

Goodman, J. W.

See, for example, J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, Sec. 1.

J. W. Goodman, "An introduction to the principles and applications of holography," Proc. IEEE 59, 1292–1304 (1971).

Jannson, T.

T. Jannson, "Information capacity of Bragg holograms in planar optics," J. Opt. Soc. Am. 71, 342–347 (1981).

T. Jannson, "Shannon number of an image and structural information capacity in volume holography," Opt. Acta 27, 1335–1344 (1980).

T. Jannson, "Structural information in volume holography," Opt. Appl. 9, 169–177 (1979).

Lin, L. H.

See, for example, R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).

Marcuse, D.

See, for example, D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972), Chap. I.

Shektman, V. Sh.

V. V. Aristov and V. Sh. Shektman, "Properties of three-dimensional holograms," Sov. Phys. Usp. 14, 263–277 (1971).

Sukhanov, V. I.

The Ewald construction was used in volume holography, e.g., by V. I. Sukhanov and Yu. N. Denisyuk, "On the relationship between spatial frequency spectra of a three-dimensional object and its three-dimensional hologram," Opt. Spectrosc. 28,63–66 (1970); M. R. B. Forshaw, "Explanation of the venetian blind effect in holography, using the Ewald sphere concept," Opt. Commun. 8, 201–206 (1973); S. I. Ragnarsson, "Scattering phenomena in volume holograms with strong coupling," Appl. Opt. 17, 116–127 (1978); S. Kusch and R. Guther, "Theoretical considerations on the bit capacity of volume holograms," Exp. Tech. Phys. 22,37–51 (1974); Refs. 8–10.

van Heerden, P. J.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Opt. Acta (1)

T. Jannson, "Shannon number of an image and structural information capacity in volume holography," Opt. Acta 27, 1335–1344 (1980).

Opt. Appl. (1)

T. Jannson, "Structural information in volume holography," Opt. Appl. 9, 169–177 (1979).

Opt. Spectrosc. (1)

The Ewald construction was used in volume holography, e.g., by V. I. Sukhanov and Yu. N. Denisyuk, "On the relationship between spatial frequency spectra of a three-dimensional object and its three-dimensional hologram," Opt. Spectrosc. 28,63–66 (1970); M. R. B. Forshaw, "Explanation of the venetian blind effect in holography, using the Ewald sphere concept," Opt. Commun. 8, 201–206 (1973); S. I. Ragnarsson, "Scattering phenomena in volume holograms with strong coupling," Appl. Opt. 17, 116–127 (1978); S. Kusch and R. Guther, "Theoretical considerations on the bit capacity of volume holograms," Exp. Tech. Phys. 22,37–51 (1974); Refs. 8–10.

Sov. Phys. Usp. (1)

V. V. Aristov and V. Sh. Shektman, "Properties of three-dimensional holograms," Sov. Phys. Usp. 14, 263–277 (1971).

Other (9)

See, for example, R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).

See, for example, D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972), Chap. I.

It should be noted that Eq. (3) is satisfied just approximately when N0(x, y) is slowly varying compared to the wavelength.3 The analysis of the validity of this approximation is similar to that in Ref. 2.

The efficiencies of the Bragg-diffracted beams may be, however, different for TE and TM polarizations (see, e.g., Chap. 9 of Ref. 1).

Such a situation is somewhat similar to that in planar Bragg holography (see Sec. 2.B of Ref. 2), where in the multimode case the recording and reconstruction processes may be realized by two different modes in two formally different planar media.

Of course, the resolving power of 1D image spectrum obtained after the filtering operation depends on the transverse dimensions of the hologram. The problem is then strictly analogous to that in conventional Bragg holography (see, e.g., Ref. 1).

See, for example, J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, Sec. 1.

Formula (7) is derived on the basis of the first Born approximation. A similar formula for the rectangular cross section is given in Ref. 2, and its validity in the case of high diffraction efficiencies is discussed in detail in Ref. 10.

J. W. Goodman, "An introduction to the principles and applications of holography," Proc. IEEE 59, 1292–1304 (1971).

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