Measurement of Small-Slope Free-Form Optical Surfaces with the Modified Phase Retrieval

In this paper, we demonstrate the use of the modified phase retrieval as a method for application in the measurement of small-slope free-form optical surfaces. This technique is a solution for the measurement of small-slope free-form optical surfaces, based on the modified phase retrieval algorithm, whose essence is that only two defocused images are needed to estimate the wave front with an accuracy similar to that of the traditional phase retrieval but with less image capturing and computation time. An experimental arrangement used to measure the small-slope free-form optical surfaces using the modified phase retrieval is described. The results of these experiments demonstrate that the modified phase retrieval method can achieve measurements comparable to those of the standard interferometer.

Phase-shifting digital holography with an unknown reference beam

In digital holography, errors of the reference field degrade the quality of the reconstructed object field. In this paper, we propose an effective method in phase-shifting digital holography in which the reference field does not need to be known and perfect. The unknown complex amplitudes of both reference and object fields are derived simultaneously. The method employs only five digital holograms and a single execution of a phase retrieval algorithm. So, the required measurements and algorithm executions in this method are fewer than those in other methods; it suggests a simpler and faster method. The effectiveness of the suggested method is indicated by simulation, under noise-free and noisy conditions. Moreover, the capability of the method to extract full information about the phase singularities in both fields is demonstrated.

Complex Wavefront Shaping through a Multi-Core Fiber

Wavefront shaping through a multi-core fiber (MCF) is turning into an attractive method for endoscopic imaging and optical cell-manipulation on a chip. However, the discrete distribution and the low number of cores induce pixelated phase modulation, becoming an obstacle for delivering complex light field distributions through MCFs. We demonstrate a novel phase retrieval algorithm named Core–Gerchberg–Saxton (Core-GS) employing the captured core distribution map to retrieve tailored modulation hologram for the targeted intensity distribution at the distal far-field. Complex light fields are reconstructed through MCFs with high fidelity up to 96.2%. Closed-loop control with experimental feedback denotes the capability of the Core-GS algorithm for precise intensity manipulation of the reconstructed light field. Core-GS provides a robust way for wavefront shaping through MCFs; it facilitates the MCF becoming a vital waveguide in endoscopic and lab-on-a-chip applications.