Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry

Abstract

A direct phase shift extraction and wavefront reconstruction method in two-step generalized phase-shifting interferometry (GPSI) with arbitrary unknown phase shift is proposed. In this method the unknown phase shift α can be extracted by a determinate formula directly without iteration or additional judgment of its correct value from two or more phase shift solutions as necessary before. By an appropriate formula of GPSI the complex object field in the recording plane can be calculated and then the object wavefront in the original object plane obtained. This method is applicable for GPSI of any frame number K≥2 and for both the amplitude and phase objects. Computer simulations have shown that the phase shift extraction errors are below 0.01 rad in a wide range of 0.4 rad<α<2.6 rad and the computation time is greatly reduced by a factor of about 20 compared with the previous method. The effectiveness and accuracy of this method are also verified by optical experiments.

Phase stitching and error correction in aperture synthesis for generalized phase-shifting interferometry

“…The experimental setup is shown in Fig. 2, which is similar to that given in [25], but with a moveable CCD device, and the resolution target is replaced by a slightly divergent spherical wave on original object plane. The wavelength of the HeNe laser used is 632.8 nm.…”

“…Cai et al [21] developed a generalized phase-shifting interferometry (GPSI) technique for more convenience and high precision in phaseshifting interferometry. Several two-step GPSI methods [22][23][24][25][26] were recently introduced to achieve a higher precision of the extracted phase shift and a higher quality of the reconstructed image.…”

Fast Method of Recovering Reference-Wave Intensity in Two-Step-Only Quadrature Phase-Shifting Holography

“…Xu et al [11] have proposed an algorithm called two-step generalized phase-shifting interferometry, which still needs two intensity images. Meng et al [12] have researched an algorithm using only two holograms and one intensity image, but the original complex object wave also needs to be recorded.…”

Phase shifts extraction algorithm based on Gram–Schmidt orthonormalization of two vectors

“…For instance, the advanced iterative algorithm (AIA) can simultaneously obtain the phase shifts and measured phase with high precision Han 2004, 2007), however, it is very time-consuming due to the iterative process. By searching for the intensity maximum and the intensity minimum of each pixel of interferograms, the background and the modulation amplitude of interferogram can be determined, Xu et al (2010) proposed the arccosine algorithm (ACA) to retrieve phase shifts and phase by an arccosine function. However, the background and the modulation amplitude of interferogram are calculated by pixel by pixel, this ACA algorithm is also time-consuming.…”