Abstract

This paper presents an analysis of the number of diffraction-limited resolvable elements and the spatial extent of object space when a hologram of a specific number of independent elements is used. The analysis includes a study of both plane and spherical reference waves, and both plane and solid objects. A generalized spatial offset of the reference wave is used to separate the desired hologram terms. The spatial extent and number of elements that can be defined in the object are reduced by spatial offset. A system is mentioned in which separation is accomplished without spatial offset, by temporal offset of the frequency of the reference beam. Without spatial offset, in the optimum configuration, the number of resolvable elements of a plane object, using the Rayleigh criterion, is equal to the number of independent elements in the hologram. For solid objects, a hologram with <i>n</i>×<i>n</i> independent samples can resolve <i>n</i><sup>3</sup>/3 elements in object space, if the optimum configuration is used.

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  1. D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).
  2. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).
  3. A. Macovski, Ph.D. dissertation, 1968, Stanford University; University Microfilms, Ann Arbor, Mich., Order No. 69–258.
  4. A. Macovski, Appi. Phys. Letters 14, 166 (1969).
  5. L. H. Enloe, W. C. Jakes, Jr., and C. B. Rubinstein, Bell System Tech. J. 47, 1875 (1968).
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Co., New York, 1968).
  7. Principles of Optics, M. Born and E. Wolf, Eds. (Pergamon Press, Ltd., London, 1965), 3rd ed.

Enloe, L. H.

L. H. Enloe, W. C. Jakes, Jr., and C. B. Rubinstein, Bell System Tech. J. 47, 1875 (1968).

Gabor, D.

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Co., New York, 1968).

Jakes, Jr., W. C.

L. H. Enloe, W. C. Jakes, Jr., and C. B. Rubinstein, Bell System Tech. J. 47, 1875 (1968).

Leith, E. N.

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

Macovski, A.

A. Macovski, Ph.D. dissertation, 1968, Stanford University; University Microfilms, Ann Arbor, Mich., Order No. 69–258.

A. Macovski, Appi. Phys. Letters 14, 166 (1969).

Rubinstein, C. B.

L. H. Enloe, W. C. Jakes, Jr., and C. B. Rubinstein, Bell System Tech. J. 47, 1875 (1968).

Upatnieks, J.

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

Other

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

A. Macovski, Ph.D. dissertation, 1968, Stanford University; University Microfilms, Ann Arbor, Mich., Order No. 69–258.

A. Macovski, Appi. Phys. Letters 14, 166 (1969).

L. H. Enloe, W. C. Jakes, Jr., and C. B. Rubinstein, Bell System Tech. J. 47, 1875 (1968).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Co., New York, 1968).

Principles of Optics, M. Born and E. Wolf, Eds. (Pergamon Press, Ltd., London, 1965), 3rd ed.

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