Phase Retrieval of One-Dimensional Objects by the Multiple-Plane Gerchberg–Saxton Algorithm Implemented into a Digital Signal Processor

Abstract

In the current study, we address the phase retrieval of one-dimensional phase objects from near-field diffraction patterns using the multiple-plane Gerchberg–Saxton algorithm, which is still widely used for phase retrieval. The algorithm was implemented in a low-cost digital signal processor capable of fast Fourier transform using Q15 arithmetic, which is used by the previously mentioned algorithm. We demonstrate similarity between one-dimensional phase objects, i.e., vectors cut out of a phase map of the tertiary spherical aberration retrieved by the multiple-plane Gerchberg–Saxton algorithm, and these vectors are measured with a non-contact profiler. The tertiary spherical aberration was induced by a phase plate fabricated using grayscale lithography. After subtracting the vectors retrieved by the algorithm from those measured with the profiler, the root mean square error decreased, while a corresponding increase in the Strehl ratio was observed. A single vector of size 64 pixels was retrieved in about 2 min. The results suggest that digital signal processors that are capable of one-dimensional FFT and fixed-point arithmetic in Q15 format can successfully retrieve the phase of one-dimensional objects, and they can be used for applications that do not require real-time operation, i.e., analyzing the quality of cylindrical micro-optics.