Phase-shifting interferometry based on the lateral displacement of the light source

Abstract

A simple and inexpensive optical setup to phase-shifting interferometry is proposed. This optical setup is based on the Twyman-Green Interferometer where the phase shift is induced by the lateral displacement of the point laser source. A theoretical explanation of the induced phase by this alternative method is given. The experimental results are consistent with the theoretical expectations. Both, the phase shift and the wrapped phase are recovered by a generalized phase-shifting algorithm from two or more interferograms with arbitrary and unknown phase shift. The experimental and theoretical results show the feasibility of this unused phase-shifting technique.

Phase Shifting Approaches and Multi-Channel Interferograms Position Registration for Simultaneous Phase-Shifting Interferometry: A Review

“…(4) Most SPSI systems adopt polarization phase-shifting interference schemes, and the stress deviation of optical components in the system and the measured phase object will affect the measuring results [45]. The simultaneous phase-shifting approach based on inclination angle deflection into the oblique incidence interferometry is also developed [46,47], but this approach has the limitation in measuring range. New phase-shifting schemes need to be further developed in the future to expand the application field and flexibility of SPSI.…”

How do phase-shifting algorithms work?

“…However, there are experiments where this condition is not met. For example, in the Michelson interferometer, the phase shift varies quadratically when the illumination source is translated laterally [30]. An efficient algorithm to estimate the functions ( ) ( )…”

“…The actual phase shift can be difficult to determine with precision in some experimental situations. For example, when the shifter is uncalibrated [21] or when the phase shift is induced manually [30]. Under these conditions, the phase shift is also an unknown to be determined [22].…”

Theory and algorithms of an efficient fringe analysis technology for automatic measurement applications

“…Some algorithms can work with fringe patterns where the visibility is not the same for all frames. These algorithms reduce the Due to the development of advanced technologies (e.g., liquid crystal spatial light modulators), the features of alternative experimental designs [48,49], and operating conditions [50], the requirements of phase-shifting algorithms have increased [51][52][53][54][55]. Particularly, it is necessary to process phaseshifted fringe patterns with unknown inhomogeneous phase shifts (i.e., the phase shift varies on both space p and time k) [56][57][58].…”

“…A Twyman-Green interferometer was employed to sense a wavefront distorted by a transparent material in the test arm. A phase shift was induced by a lateral displacement of the point laser source [49]. Figures 9(a) and 9(b) show two acquired phase-shifted fringe patterns.…”