Abstract
We present an asynchronous phase-shifting demodulation approach based on the principal component analysis demodulation method that is robust to typical problems as turbulence, vibrations, and temporal instabilities of the optical setup. The method brings together a two-step and a phase-shifting asynchronous demodulation method to share their benefits while reducing their intrinsic limitations. Thus, the proposed approach is based on a two-fold process. First, the modulating phase is estimated from a two-step demodulation approach. Second, this information is used to compute weights to each phase-shifted pattern of the interferogram sequence, which are used in a novel weighted principal component demodulation approach. The proposed technique has been tested with simulated and real interferograms affected by turbulence and vibrations providing very satisfactory results in challenging cases.
Highlights
Phase-shifting interferometry (PSI) is an accurate optical metrology technique for measuring the modulating phase of interferograms
We compared the results obtained from a two-step demodulation approach (Kreis demodulation approach [12]), the PCA demodulation method [6] and the proposed weighted demodulation approach
We introduce a method to improve the demodulation of phase-shifting interferograms affected by uncontrolled mechanical vibrations, air turbulence, temperature changes or temporal instabilities of the optical setup
Summary
Phase-shifting interferometry (PSI) is an accurate optical metrology technique for measuring the modulating phase of interferograms. The PCA demodulation method is a popular algorithm that provides a direct solution for both the modulating phase and the phase-shifts through the first two estimated principal components of the phase-shifted interferogram sequence This approach is very fast and does not require any optimization process, initial guess of the phase-shifts, or additional constrains such as the background and modulation terms to be constant along the field of view. We proposed the UV factorization approach [10] This method is based on an iterative factorization approach and non-linear boosting that expresses the interferogram sequence as the multiplication of two matrices, one depending on the phase-shifts and the other on the modulating phase. The method is based on providing weights to all different interferograms according to their similarity to a first estimated modulating phase obtained by a two-step demodulation approach This phase map is assumed to be not affected by thermal and mechanical instabilities of the optical setup. The weights and the phase-shifted interferograms are processed by a robust weighted principal component demodulation approach to compute an improved and robust to noise modulating phase
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