Extending Capture Range for Piston Error in Segmented Primary Mirror Telescopes Based on Wavelet Support Vector Machine With Improved Particle Swarm Optimization

Haifeng Cao,Ye Wang,Jingxu Zhang,Qichang An,Fei Yang

doi:10.1109/access.2020.3002901

Abstract

In the co-phasing techniques applied to the segmented telescope, a Shack-Hartmann wavefront sensor cannot accurately detect the piston error of the segment. Although the phase diversity (PD) algorithm can detect the piston error of each segment, it fails to reconstruct the wavefront quickly, and its dynamic range is small. Other technologies, such as prisms or micro-lens arrays, will significantly increase the complexity and construction cost of the optical system. Moreover, they may also introduce non-common path errors. In this study, we propose an approach to address this challenging problem via curvature sensing. This method uses multi-wavelength to eliminate the influence of $2\pi $ ambiguity and improve the capture range of co-phasing detection. However, curvature sensing is easily influenced by atmospheric seeing. We propose a wavelet support vector machine optimized via particle swarm optimization (PSO-WSVM) method to deal with this problem, and to improve the application scope of curvature sensing. We reshape SVM with a wavelet kernel function, and improve the PSO algorithm. We train the SVM to build a prediction model to distinguish the piston error range of each pair of adjacent segments and surpass $2\pi $ ambiguity. First, we obtain defocused images by means of the convolution technique. Second, we propose a prediction model based on SVM. We select the correlation coefficient between the sampling signal and the template signal at different wavelengths as the input vector, and we choose a wavelet basis function as the kernel function of SVM. Third, we improve the PSO algorithm with the exponential decreasing inertia weight (EDIW) to tune the parameters of SVM. Finally, we perform a simulation experiment on a real optical system model based on the Keck telescope. The results indicate that the performance of this method is better than that of other state-of-the-art SVM-based classifiers, and it works rapidly during the observation.

Highlights

We aim to control the 2π ambiguity in the wavefront sensing, something may be learned from the idea of redundant measurements, and it is applied to improve the robustness of the algorithm
We proposed a exponential decreasing inertia weight (EDIW)-PSOWSVM algorithm to solve the challenging problems posed by 2π ambiguity and the effects of atmospheric exposure
We proposed a EDIW-PSO-WAVELET SUPPORT VECTOR MACHINE (WSVM) algorithm combining four different wavelengths of the light source

Summary

Introduction

Astronomers need larger and larger telescopes to observe more distant and weaker celestial phenomena across vast distances and enormous spans of time. Segmentation is a necessity to build telescopes larger than the 8 m class due to. The associate editor coordinating the review of this manuscript and approving it for publication was Shuihua Wang. Limitations in processing, manufacturing, transportation, and cost. A larger segmented mirror means a stronger ability to collect light, and a higher spatial resolution, but the discontinuous primary mirror has difficulty co-phasing due to gravity, wind, thermal drift, movement during slewing and other factors. In order to achieve the same optical performance as a monolithic mirror, the piston errors between the segments should be controlled to an accuracy of several nanometers.

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Conclusion