Hologram Interferometry of Nonsinusoidal Vibrations Analyzed by Density Functions

Abstract

The characteristic fringes of hologram interferometry can be analyzed by the use of density functions, i.e., functions that specify what fraction of the exposure time an object point spends in any one place. In many cases, this method of analysis avoids cumbersome series solutions for fringe functions; in this paper the method is applied to nonlinear vibrations and to combinations of sinusoidal oscillations whose frequencies are related by rational numbers. For nonlinear vibrations, results are obtained that allow direct calculation of nonlinear spring functions, without presumption of a solution to the nonlinear differential equation of motion.