A simple phase estimation employing cubic and average interpolations to solve the oversampling problem in smooth modulated phase images is described. In the context of a general phase-shifting process, without phase-unwrapping, the modulated phase images are employed to recover wavefront shapes with high fringe density. The problem of the phase reconstruction by line integration of its gradient requires a form appropriate to the calculation of partial derivatives, especially when the phase to recover has higher-order aberration values. This is achieved by oversampling the modulated phase images, and many interpolations can be implemented. Here an oversampling procedure based on the analysis of a quadratic cost functional for phase recovery, in a particular case, is proposed.
© 2012 Optical Society of America
Instrumentation, Measurement, and Metrology
Original Manuscript: September 14, 2011
Revised Manuscript: October 31, 2011
Manuscript Accepted: October 31, 2011
Published: March 15, 2012
Alejandro Téllez-Quiñones and Daniel Malacara-Doblado, "Phase recovering without phase unwrapping in phase-shifting interferometry by cubic and average interpolation," Appl. Opt. 51, 1257-1265 (2012)