Numerical analysis of sinusoidally-amplitude-modulated holographic interferograms (1st report) - Separation of vibration phase and the bessel functions

This paper presents the algorithm to separate the vibration phase and the Bessel functions of various orders for the numerical analysis of sinusoidally-amplitude-modulated holographic interferograms of a vibrating object. By common phase shifting and vibration-phase shifting, the vibration phase and the Bessel functions whose arguments contain only the vibration amplitude can be easily separated (in the case of phase-modulated holographic interferograms, separation is very difficult), We first present the equations expressing the irradiances of the interferograms when one modulated the beam illuminating the object and/or the hologram in the optical system of real-time holographic interferometry. Secondly, we show the algorithms where the Bessel functions of the 0th, Ist and 2nd orders can be separated. Thirdly, we present the algorithms for determining the signs and the coefficients of the Bessel functions.