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

Abstract

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.

Model-based phase shifting interferometry

“…The resulting coupled, nonlinear model equations cannot be solved directly, so the approach is to linearize the model and apply iterative least-squares (LS) techniques. Though this approach has been considered before [7][8][9][10][11][12], the large number of unknowns has made efficient solutions difficult, producing unreliable or slow convergence or requiring restricted physical models that do not account for many important effects. No previous work has been general enough to account for all of the influences mentioned above and their cross couplings.…”

Modified three-step iterative algorithm for phase-shifting interferometry in the presence of vibration

“…Considering the fact that the wavefront is invariable during the measuring period, researchers have developed many algorithms to extract wavefront phase from interferograms subjected to vibration. These algorithms include detecting phase shifts from spatial-carrier interferograms [6][7][8], calculating wavefront phase by iteration [9][10][11][12][13] and some other methods [14,15]. These algorithms compensate the relative tilt between the test and reference wavefronts and have better performance than those algorithms that only consider the piston phase shifting.…”

“…The algorithm is a modification of our previous algorithm: a three-step iterative algorithm (TIA) [12]. TIA could calculate wavefront phase from tilt-shift interferograms by solving linear least-squares equations but could not handle interferograms with contrast fluctuation.…”

Ultrasonic Lamb waves detection using an unstabilized optical interferometer with uncalibrated phase shifts

“…Many different techniques for quantitative phase retrieval from interference patterns have been developed in the last decades [11][12][13][14]. To recover the phase from the interference signal, phase shifts are usually introduced during the measurement, which need to be precisely calibrated.…”