Non-redundant MTF distribution method for sensing multi-piston simultaneously in segmented telescopes

Piston errors can be extracted from the modulation transfer function (MTF) side-lobe by setting a mask with a sparse multi-sub-pupil configuration on the segments’ conjugate plane. Non-redundant MTF distribution is the key for sensing multi-piston simultaneously. We put forward a sparse sub-pupils arrangement algorithm (SPAA) to design the sparse multi-sub-pupil configuration which makes the MTF distribution non-redundant. According to MTF distribution model of the multi-sub-pupils mask, restriction and constraint conditions of SPAA used to determine the multi-sub-pupil configuration of the mask are analyzed and obtained. The restriction condition act as the limitation condition of SPAA to randomly generate scheme of the multi-sub-pupils configuration. The constraint conditions work as the criteria to judge whether the MTF distribution of the scheme is non-redundant. Simulations and experiment have been done to validate the method. Taking 6-segmented and 18-segmented systems as examples, the corresponding sparse sub-pupils configurations are designed respectively by using SPAA. After 10 iterations for the 6-segmented system and 40 iterations for the 18-segmented system, the configurations which make the MTF distributions non-redundant can be obtained. Furthermore, an experiment setup is built up to verify the 18 sparse sub-pupils configuration.