Quantitative error analysis for non-mechanical phase-controlled beam steering based on symmetrical radial sub-aperture coherence algorithm

Based on the fundamental of traditional Sub-aperture coherence (SAC) algorithm, Radial Sub-aperture coherence (RSAC) and Symmetrical Radial Sub-aperture coherence (SRSAC) have been designed to achieve non-mechanical beam steering with ultra-high precision and stability by utilising two-dimensional Liquid Crystal Optical Phased Array (LCOPA). Both of them inherit the original advantages, that is, to eliminate the local pointing accuracy defects and greatly improve the angular resolution of the beam steering system. Meanwhile, the steering angle error caused by the aperture variation and the alignment error can be also effectively restricted by SRSAC. In this paper, the essential mathematical framework of SRSAC and its affiliated local error elimination method was established to supplement the theoretical support of these phase generation algorithms. By dissecting the generation mechanism of each pointing error branch, the theoretical formulae with great universality are finally proposed, which provide visualised and necessary references for the specific application in other beam control situations.