The use of the Principal Components Analysis (PCA) for recovering the modulating phase, given a sequence of Phase-Shifted Interferograms (PSI), is a very important contribution to the field. However, its verbatim translation from statistics to PSI has limited the view to consider only constant background illuminations. Here, we show that the Singular Value Decomposition (SVD), used in PCA, actually separates the background illumination (constant or not) and the phase modulation terms. We show that the modulating phase can be correctly recovered if the phase-shifts sample full periods uniformly, independently of the spatial distribution of the number of fringes.
We model a set of Phase-Shifting Interferogram (PSI) images in a new and versatile way that allows exploring
interesting numerical approaches for the analysis of PSI. We show how this representation can be used to recover
the modulating phase if the phase steps are known, and we also show how it can be used as the baseline for an
iterative algorithm. For the case in which the phase steps are known we compare against the four step algorithm.
For the case of unknown phase steps, we compare against the Principal Component Analysis (PCA) and the
Advanced Iterative Algorithm (AIA).
In optical interferometry, noise and distortions in the recovered wrapped phase are very common, and their nature is inherent to the quality and visibility of the fringe patterns that modulate the phase. Filtering these phase imperfections from the wrapped phase is not straightforward since we cannot directly apply filters without damaging their information, that is, its modulus 2π phase jumps. However, having a way to filter noise and distortions from the wrapped phase is desirable and very important because, at the end, the filtered phase is closer to the expected, errors are reduced, and the unwrapping task can be less complex. We propose a modulus 2π filtering method to remove noise and distortions directly from the wrapped phase without damaging its information. The presented method is a global filtering process, but we use the local frequencies from the wrapped phase in such a way that each pixel is tuned to its instant frequency.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.