Single-shot phase retrieval for aspheric surface testing based on the transport of intensity equation and a prism-mirror module

摘要

Transport of intensity equation (TIE) relates the longitudinal intensity derivative of propagating light wave to the transverse phase gradient. The phase is retrieved by measuring the intensity of propagating light wave at two or more longitudinally displaced planes by moving the detector and then solving the TIE. We present a single-shot transport of intensity equation-based phase retrieval using a prism-mirror based module to capture the two defocused intensity images simultaneously. The results obtained by single-shot transport of intensity equation-based phase retrieval have been compared with interferometry and profilometer-based measurements. We highlight an important aspect of the TIE-based approach that this formulation decouples the intensity and the unwrapped phase of the unknown field. Intensity and phase are individually low-bandwidth functions when compared to the complex field associated with the unknown wavefront. When compared to interferometry, the TIE-based approach therefore inherently has many reduced sampling requirements. For a given array sensor, TIE can therefore measure large phase deviations for which an interferometer would produce very high density fringes that are impossible to sample as per the Nyquist criterion. The prism-mirror module shown in this work is easy to fabricate, align, and can be easily integrated with an experimental setup. The applications of the proposed method for the wavefront measurement of spherical and aspheric lenses are demonstrated. (c) 2022 Society of Photo-Optical Instrumentation Engineers (SPIE)