Robust fitting of Zernike polynomials to noisy point clouds defined over connected domains of arbitrary shape

A new method for fitting a series of Zernike polynomials to point clouds defined over connected domains of arbitrary shape defined within the unit circle is presented in this work. The method is based on the application of machine learning fitting techniques by constructing an extended training set in order to ensure the smooth variation of local curvature over the whole domain. Therefore this technique is best suited for fitting points corresponding to ophthalmic lenses surfaces, particularly progressive power ones, in non-regular domains. We have tested our method by fitting numerical and real surfaces reaching an accuracy of 1 micron in elevation and 0.1 D in local curvature in agreement with the customary tolerances in the ophthalmic manufacturing industry.

Application of principal component analysis in phase-shifting photoelasticity

Principal component analysis phase shifting (PCA) is a useful tool for fringe pattern demodulation in phase shifting interferometry. The PCA has no restrictions on background intensity or fringe modulation, and it is a self-calibrating phase sampling algorithm (PSA). Moreover, the technique is well suited for analyzing arbitrary sets of phase-shifted interferograms due to its low computational cost. In this work, we have adapted the standard phase shifting algorithm based on the PCA to the particular case of photoelastic fringe patterns. Compared with conventional PSAs used in photoelasticity, the PCA method does not need calibrated phase steps and, given that it can deal with an arbitrary number of images, it presents good noise rejection properties, even for complicated cases such as low order isochromatic photoelastic patterns. © 2016 Optical Society of America.

Nonclassical light revealed by the joint statistics of simultaneous measurements

Nonclassicality cannot be a single-observable property, since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior of light states from the joint statistics arising in the practical measurement of multiple observables. Beside embracing previous approaches, this protocol can disclose nonclassical features for standard examples of classical-like behavior, such as SU(2) and Glauber coherent states. When combined with other criteria, this would imply that every light state is nonclassical.