Interference fringe analysis based on recurrence computational algorithms

The approach to interference fringe analysis using description of fringe intensity variations as a nonlinear transform of supposed dynamic system evolution in a state space is considered. In recurrence algorithms, fringe signal is predicted to a following discretization step utilizing full information available before this step, and fringe signal prediction error is used for step-by-step dynamic update of fringe parameters. Peculiarities of Markov optimal nonlinear filtering, extended Kalman filtering and unscented Kalman filtering with application to fringe processing are considered and discussed. Examples of practical application of recurrence algorithms to noise-immune dynamic fringe processing, solving fringe phase unwrapping problem including accurate 3-D wavefront recovery and fringe envelope evaluation in Optical Coherence Tomography are presented. ► Recurrence algorithms allow processing fringe signals dynamically with fringe phase unwrapping. ► Markov nonlinear filtering, extended and unscented Kalman filtering are investigated and compared. ► Experimental results of applying recurrence algorithms to evaluate fringe parameters are given.