Simultaneous multi-piston measurement method in segmented telescopes.

We propose a method to simultaneously detect the multi-piston between segments. The relation between the piston of any two segments and amplitude of the modulation transfer function (MTF) sidelobes (MTFnph) is derived. The piston can be retrieved by this relation after measuring the MTFnph. This method's capture range is the operating light's coherence length, the accuracy is 0.026λ (λ = 633 nm) RMS. 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 sub-aperture configuration is designed, which makes the MTF sidelobes distribution non-redundant.