Fourier telescopy based on spatial non-uniform Fourier transform

In order to reconstruct the image using sparse emitter array, a process based on spatial non-uniform Fourier transform (NDFT) method was proposed. According to the relationship between the extracted spatial frequency of target and the position of Fourier telescope emitters and considering the MATLAB program characteristics, we completed the inverse Fourier transform of non-uniform airspace and reconstructed the image of target. Sparse emitter array configuration is as follows: 11 launch telescopes are placed on the T-array single arm, eight low-frequency components are continuously extracted and then followed by three high-frequency components. We selected four satellites with different shape and gray distribution as the imaging target. Comparing our reconstructed images with those by fast Fourier transform with zero-padding, we found that in the presence of noise (100 dB signal-to-noise ratio), the Strehl ratios of the images reconstructed with NDFT method are improved and the highest one is enhanced by 0.159 8.