High-accuracy piston error measurement with a large capture range based on coherent diffraction

Segmented and deployable primary mirror telescope is adopted to realize a higher resolution observation. Meanwhile the cophasing error is introduced. The piston error between the segments should be smaller than λ/20 RMS to achieve a diffraction-limited imaging. However the initial piston error is about 200 μm. A high-accurate piston error measurement with a large capture range is needed. We propose a method to simultaneously detect the multi-piston errors between segments with a high accuracy in a large capture range. A mask with a sparse sub-aperture configuration is set in the exit-pupil plane of the telescope to sample the wave from the segments. The relation between the piston error of any two segments and the amplitude of the modulation transfer function (MTF) sidelobes (MTF_nph) is derived according to the Fourier optics principle. The piston error can be retrieved by this relation after measuring the MTF_nph. Simulation and experiments have been carried out to validate the feasibility of the method. The results state that this method's capture range is the operating light's coherence length, the accuracy is 0.026λ RMS (λ = 633 nm). The MTF model of a mask with sparse multi-subaperture configuration is established. The arrangement rules, to avoid the sidelobes overlapping, are obtained. The mask with a sparse 18 subaperture configuration is designed, which makes the MTF sidelobes distribution non-redundant. Consequently, just a mask with a sparse multi-subaperture configuration is needed, simultaneous detection of the multi-piston errors can be realized in term of this method.