Previous implementations of the iterative phase shifting method, in which the phase of a test object is computed from measurements using a phase shifting interferometer with unknown positions of the reference, do not provide an accurate way of knowing when convergence has been attained. We present a new approach to this method that allows us to deterministically identify convergence. The method is tested with a home-built Fizeau interferometer that measures optical surfaces polished to lambda/100 using the Hydra tool. The intrinsic quality of the measurements is better than 0.5 nm. Other possible applications for this technique include fringe projection or any problem where phase shifting is involved.
"In order to overcome the shortcomings of the mentioned approach, other approaches have been developed by other researchers. Advanced iterative algorithms and their further development versions       are examples of the solutions in this regard which in turn are also faced with the problem of convergence . This paper presents a technique for increasing the stability of estimating aberration function related to the additive noise. "
[Show abstract][Hide abstract] ABSTRACT: Reduction of image quality under the effects of wavefront aberration of the optical system has a direct impact on the vision system's performance. This paper tries to estimate the amount of aberration with the use of wavelet transform profilometry. The basic idea is based on the principle that under aberration effects, the position of the fringes' image on the image plane will change, and this change correlates with the amount of aberration. So the distribution of aberration function can directly be extracted through measuring the amount of changes in the fringes' image on the image plane. Experimental results and the empirical validity of this idea are evaluated.
[Show abstract][Hide abstract] ABSTRACT: Extracting phase distribution from arbitrary phase-shifted fringe patterns, if possible, is very useful in phase-shifting interferometry. The advanced iterative algorithm (AIA) is introduced and the windowed Fourier ridges and least squares fitting (WFRLSF) is proposed. Both algorithms are sensitive to noise, which limits their applications to almost perfect fringe patterns. The windowed Fourier filtering (WFF) algorithm is proposed for both pre-filtering and post-filtering to suppress the noise. Simulation results show that with the effective noise suppression, the phase error is reduced to less than 0.1 rad. Experimental examples are also given for verification. The almost identical results produced by the AIA and the WFRLSF suggest that both algorithms can be used for phase extraction with cross-validation.
Optics and Lasers in Engineering 06/2010; 48(6-48):684-689. DOI:10.1016/j.optlaseng.2010.01.009 · 2.24 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Using standard optical shop equipment, it is possible to implement simple, low-cost, phase-shifting Newton interferometers sufficiently accurate for surface evaluation. The simplification of the phase-shifting mechanism is compensated with image-processing algorithms that can deal with vibrations and uneven, nonsequential steps. The results are cross-compared with a Fizeau phase-shifting interferometer to verify the effectiveness of the method.
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