The research of laser communication system primary mirror deformation caused by back surface shape variation was done in this paper. The usual mirror back surface shapes were sphere, double arch, flat and biconcave shape and so on. Based on the four shape mirror, with the center hole rim support pattern, the four shape mirror temperature distribution equation was inferred by thermal elastic theory, deformation are compared in 1-5℃ radius direction temperature difference, in the case of minor weight gap and equal maximum thickness. As a result, the deformation of sphere back surface shape mirror is minimal. So sphere back surface shape is fit for the primary mirror.
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