Design of adaptive digital filters for phase extraction in complex fringe patterns obtained using the Ronchi test

A powerful technique is presented for processing complex fringe patterns with high noise levels and arbitrary distributions of spatial frequencies, which can successfully extract the phase information. Artifacts that arise from phase extraction in local filtering approaches are avoided by using a simple design and implementation strategy for the adaptive filter, based on the theory of digital filter design used in electronics, and applied to pixel rows (or columns) in the fringe-pattern. The filter designed in this manner is then applied to phase extraction in an experimental fringe pattern measured in a digital Ronchi test setup using a Carre phase-shifting procedure. The filtering strategy has a very low computational cost and allows phase extraction in noisy ronchigrams regardless their spatial frequency distribution, provided the fringes are still visible.