Hybrid algorithm for phasing a segmented mirror based on moment analysis and a convolutional neural network

The paper considers the problem of controlling the phase state of a segmented mirror in an optoelectronic telescopic system using the intensity distribution in the focal plane. Misalignment of mirror segments leads to phase errors, which cause degradation of the focal image, a decrease in energy concentration in the central maximum, and the appearance of additional diffraction structures. To solve this problem, it is important to develop methods that make it possible to estimate phasing error parameters from intensity images without explicit wavefront reconstruction.

Purpose – the objective of this work is to develop the architecture of a hybrid algorithm for phasing a segmented mirror based on the joint application of moment analysis of the focal image and a convolutional neural network for regression estimation of mirror tilt parameters.

A two-branch architecture of a hybrid algorithm for phasing a segmented mirror is proposed. The first branch is intended for processing the focal image using a convolutional neural network that extracts spatial features of the intensity distribution. The second branch processes moment features that characterize the position of the energy centroid, width, asymmetry, and energy concentration of the focal image. After merging the feature representations, a regression block is used to estimate the phasing parameters for each mirror segment. A scheme for forming a synthetic training dataset based on a diffraction model of a segmented aperture is described. Quality assessment criteria for the algorithm are also defined: mean absolute error, root mean square error, maximum error, and the proportion of states within a specified tolerance.

The practical significance of the work lies in the possibility of using the proposed architecture as a basis for developing methods for monitoring and diagnosing the phase state of segmented optical systems. The hybrid approach combines physically interpretable features of the focal image with trainable analysis of its spatial structure, which can potentially improve the robustness and diagnostic transparency of the algorithm. The proposed method can be used in the development of phasing systems for segmented mirrors in optoelectronic telescopic systems, including under conditions where the composition of measuring equipment is limited.