Optimization of transverse translation diverse phase retrieval for optical elements with mid-spatial frequency errors

Abstract

During the fabricating procedure of optical elements, computer-controlled tools will introduce some periodic structured errors, named mid-spatial frequency errors, which may scatter the laser beams, create filamentous spots or even damage the optical components in Inertial Confinement Fusion (ICF) high power laser system. Transverse translation diverse phase retrieval (TTDPR) is an ingenious phase retrieval method for measuring aspheric and freeform surfaces. In this paper, we explore the measurement of optical elements with mid-spatial frequency errors by using TTDPR. First, we briefly introduce the features of mid-spatial frequency errors and establish the relation between mid-spatial frequency errors and diffraction pattern. Second, with the knowledge of the mid-spatial frequency error, we analyze the feasibility of optical elements with mid-spatial frequency error measurement by using TTDPR. In order to improve the convergence and measurement accuracy of phase retrieval algorithm, initial inputs are optimized for the following iterative phase retrieval algorithm. Results indicate that a 50% higher reconstruction accuracy can be achieved, when the initial input is the ideal lens to recover the phase of lens with mid-spatial frequency errors. For TTDPR, sub-aperture illuminated with overlapping part among adjacent sub-apertures will improve accuracy of iterative phase algorithm than never overlapped sub-aperture, while it encumbers the efficiency of iterative phase retrieval algorithm. Based on the characteristics of the particular optical surfaces, the influence of major parameter of sub-aperture including the size of sub-aperture and the overlapped proportion among adjacent sub-aperture to accuracy and efficiency of TTDPR are also discussed.