MTF non-redundant distribution for multi-piston errors detection of segmented telescopes

We propose a MTF non-redundant distribution method, with which the multi-piston errors of segmented telescope can be detected simultaneously. A mask with a sparse multi-subaperture configuration is set in the exit pupil of the segmented telescope. One subaperture matches to one segment and samples the wave-front reflected by this segment. Coherent diffraction patterns, produced by each pair of the wave-fronts, are recorded as point spread function (PSF). A Fourier transform is performed for the PSF to obtain the optical transfer function (OTF). Then, relationship between the piston error and the amplitudes of the MTF sidelobes is derived. The piston error can be retrieved accurately by this relationship, and the capture range is the coherent length of the operating light. The key to realize a multi-piston errors simultaneous detection using this relationship is to avoid overlap of the MTF sidelobes which formed by each pair of subwaves. We research and derive the MTF model of a mask with a sparse multi-subaperture configuration. According to Fourier optics principle, the MTF distribution of this model is analyzed, and rules for the MTF sidelobes non-redundant distribution are obtained. Simulations have been done to validate the rules. Taking an 18-segment mirror as an example, a mask with a sparse 18 sub-apertures configuration is designed to realize the MTF sidelobes non-redundant distribution. Thus, just need to set a mask with a sparse multi-subaperture configuration in the conjugate plane of the segmented mirror, the piston errors of the full aperture can be retrieved simultaneously.