A three-step least-squares iterative method for tilt phase-shift interferometry.

An iterative method based on least-squares fittings is proposed to retrieve wavefront phase from tilt phase-shift interferograms. In each iteration cycle, proposed method calculates wavefront phase and tilt phase shifts in x- and y-directions in three individual least-squares fitting steps. In tilt phase shifts extracting steps, phase shifts of interferograms columns or rows are calculated with least-squares method, and then tilt phase shifts of interferograms in x- or y-direction are determined by linear regressions. At least three interferograms of three by three pixels are required with proposed method. The performance of proposed method is demonstrated by simulations and experiments. Tilt gradients and translational phase shifts could be extracted with high accuracy and large wavefront tilts could be well handled with proposed method. The method could be applied to temporal phase-shift interferometers with uncalibrated transducers or that in vibrating environment.