Diffractive imaging analysis of large-aperture segmented telescope based on partial fourier transform

Large-aperture segmented primary mirror will be widely used in next-generation space-based and ground-based telescopes. The effects of intersegment gaps, obstructions, position and figure errors of segments, which are all involved in the pupil plane, on the image quality metric should be analyzed using diffractive imaging theory. Traditional Fast Fourier Transform (FFT) method is very time-consuming and costs a lot of memory especially in dealing with large pupil-sampling matrix. A Partial Fourier Transform (PFT) method is first proposed to substantially speed up the computation and reduce memory usage for diffractive imaging analysis. Diffraction effects of a 6-meter segmented mirror including 18 hexagonal segments are simulated and analyzed using PFT method. The influence of intersegment gaps and position errors of segments on Strehl ratio is quantitatively analyzed by computing the Point Spread Function (PSF). By comparing simulation results with theoretical results, the correctness and feasibility of PFT method is confirmed.