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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 60, Iss. 8 — Aug. 1, 1970
  • pp: 1068–1071

Characteristic Functions for Time-Average Holography

ALAN D. WILSON  »View Author Affiliations

JOSA, Vol. 60, Issue 8, pp. 1068-1071 (1970)

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This paper presents an analysis of the fringes obtained by time-average holographic interferometry of a generalized time-dependent optical phase function. The generalized optical phase function considered is the sum of a series of sinusoidal functions of time having arbitrary amplitudes, frequencies, and relative phases. Characteristic functions are determined for various optical phase functions of interest in time-average holography. In general, the characteristic functions are sums of products of Bessel functions (zero order and higher orders) and exponential phase factors. Rationally and irrationally related frequencies are included in this analysis. An example of vibrating string is considered, to illustrate the application of the results of this paper to objects vibrating at a multitude of frequencies.

ALAN D. WILSON, "Characteristic Functions for Time-Average Holography," J. Opt. Soc. Am. 60, 1068-1071 (1970)

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  1. M. L. Horman, Appl. Opt. 4, 333 (1965).
  2. J. M. Burch, Prod. Eng. 44, 431 (1965).
  3. R. J. Collier, E. T. Doherty, and K. S. Pennington, Appl. Phys. Letters 7, 223 (1965).
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  8. At the time of the drafting of this paper, Refs. 4 and 7 of the Molin and Stetson (1969) paper were not available to the author. Consequently, there may be some unavoidable overlap of the present paper with the following "in press" articles: R. L. Powell, in 1968 Symposium on the Engineering Uses of Holography, Glasgow (Cambridge University Press, Cambridge, 1970); K. A. Stetson, in same collection.
  9. See Refs. 5–7.
  10. A. Kozma, ICO Symposium on Applications of Coherent Light (Florence, 1968).
  11. G. Goertzel and N. Tralli, Some Mathematical Methods of Physics (McGraw-Hill, New York, 1960).
  12. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University Press, Cambridge, 1966).

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