Quiroga Mellado, Juan AntonioVilla Hernández, José de JesúsServín Guirado, Manuel2023-06-202023-06-202000-02-010003-693510.1364/AO.39.000502https://hdl.handle.net/20.500.14352/58791© 2000 Optical Society of America. We acknowledge the support of a postdoctoral grant from the Universidad Complutense de Madrid, the “Becas Internacionales Flores-Valles” program, Spain, and the Consejo Nacional de Ciencia y Tecnología (CONACyT), México.We propose a robust procedure based on the regularized phase-tracking (RPT) technique to demodulate squared-grating deflectograms. The use of squared gratings, already reported, lets us multiplex the information of the deflections in two orthogonal directions in a single image, thus avoiding the necessity of rotating the gratings. The good noise-rejection characteristics of the RPT technique are improved by use of a quasi-Newton optimization algorithm and a quality-map-based algorithm for the crystal-growing process.engjournal articlehttp://dx.doi.org/10.1364/AO.39.000502http://www.opticsinfobase.org/open access535Moire DeflectometryFourier-TransformFringe-PatternInterferometerDemodulationDiffractionImageÓptica (Física)2209.19 Óptica Física