Numerical analysis of sinusoidally-amplitude-modulated holographic interferograms by algorithm like fringe-shifting technique

This paper presents the algorithm for determining the vibration amplitude of an object from the Bessel functions of various orders whose arguments contain the vibration amplitude (the Bessel functions can be separated from sinusoidally-amplitude-modulated holographic interferograms). This algorithm is similar to the one in fringe-shifting technique developed by Stetson, which can analyze sinusoidally-phase-modulated holographic interferograms. The algorithm here assumes that the Bessel functions of the even and odd orders are cosine and sine functions, respectively. Then, their argument, i.e., the vibration amplitude can be calculated by are tangent of their ratio. The calculated value can be corrected to the true one by the relationship between them. The pair of the Bessel functions of the 0th and Ist orders is best in accuracy. The pairs of those of higher orders have a wider region where unwrapping does not required. In comparison with previous algorithms, our one requires only two Bessel functions, unwrapping and determination of the signs of the Bessel functions, but does not require determination of their coefficients.