Co-phasing Error Correction Of Segmented Primary Mirrors Based On Focal Plane Intensity

The co-phasing error sensing methods of segmented primary mirrors can be classified into two groups: One is the optical detection method, co-phasing error can be got through optical interference or diffraction between segmented primary mirrors, such as the Michelson interference method, the narrowband or broadband Shack-Hartman sensing, the dispersed fringe sensing, the phase retrieval or diversity, etc. These methods need to change the original optical path or insert the new optical elements, such as filters, dispersion prism and so on, which increases the complexity of optical system. Another kind is electrical method, Capacitance or inductance sensors which are installed in the back of segmented mirrors are used to measure the piston between adjacent sub mirrors. But the absolute zero position of each sub mirror should be calibrated firstly by optical method.In this paper, the image sharpness function is taken as metric function. The relationships between co-phasing errors of segmented mirror and the metric function are analyzed by simulation under monochromatic illumination or white-light illumination. Simulation results show that under monochromatic illumination, the dynamic range of piston error correction is less than 0.5?. Under white-light illumination, global optimization algorithm should be adopted because of the local maximums of metric function. When piston error is greater than 0.5?, stochastic parallel gradient descent(SPGD) algorithm is prone to falling into local maximum and genetic algorithm is capable of finding out the global optimum but with relatively slow iteration speed. A hybrid optimization algorithm based on SPGD algorithm and genetic algorithm is proposed for co-phasing error correction of segmented mirror in this paper. When piston error is from –? to ?, the correction accuracy of the hybrid optimization algorithm can be better than 10 nm.In order to further extend the sensing range of the piston error, a functional relationship between the modulation transfer function(MTF) under wide spectrum illumination and the piston error of the segmented mirror is established in this paper. Simulation results show that the sensing range and speed of piston error are different by?? under two-segmented mirrors model. When ?? =1nm, piston error is from –300? to 300?, the correction accuracy of this algorithm is less than 15?; When ?? =10nm, piston error is from –60? to 60?, the correction accuracy of this algorithm is less than 8?; When ?? =1nm, piston error is from –12? to 12?,the correction accuracy of this algorithm is less than 1?. So under the two-segmented mirrors model, this algorithm can be used to sense the piston error.According to the two-segmented mirrors model, the simulations show that the relationship between MTF and piston error also can be used under three-and four-segmented mirrors model. But piston error can't be calibrated and sensed separately in some model.