Abstract

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.

© 1970 Optical Society of America

Time-Average Holographic Interferometry of a Circular Plate Vibrating Simultaneously in Two Rationally Related Modes*

Alan D. Wilson and Douglas H. Strope
J. Opt. Soc. Am. 60(9) 1162-1165 (1970)

Effects of Beam Modulation on Fringe Loci and Localization in Time-Average Hologram Interferometry

Karl A. Stetson
J. Opt. Soc. Am. 60(10) 1378-1388 (1970)

Characteristic Fringe Function for Time-Average Holography of Periodic Nonsinusoidal Vibrations

P. C. Gupta and K. Singh
Appl. Opt. 14(1) 129-133 (1975)

Computed Time-Average Holographic Interferometric Fringes of a Circular Plate Vibrating Simultaneously in Two Rationally or Irrationally Related Modes

Alan D. Wilson
J. Opt. Soc. Am. 61(7) 924-929 (1971)

Time-averaged digital holography

Pascal Picart, Julien Leval, Denis Mounier, and Samuel Gougeon
Opt. Lett. 28(20) 1900-1902 (2003)