Impact of random segment pose errors for deployable telescope and its tolerance allocation

Segmented primary mirror is very sensitive to co-phasing errors, especially the random segment pose errors produced by positioning deviations. This paper proposes the linear sensitivity matrix of the pose-error-caused wavefront deformation, derives the corrected-prediction formula of the deformation, and presents a method of weighted tolerance allocation in order to control the pose-phasing platform cost. Results indicate that random pose errors will generate uncertain wavefront deformation, which can be predicted by the formula with prediction errors of the expectation less than ±1% and variance less than ±5%. And the technical difficulty of the platform construction can be minimized using the allocation method.