Analysis of comprehensive effects of piston error and sub-aperture aberrations on the image quality of sparse-optical-synthetic-aperture system

To improve the image quality of sparse-optical-synthetic-aperture system, the effects of sub-aperture self aberrations and piston errors among different sub-apertures should be considered comprehensively. Based on the pupil of sparse-optical-synthetic-aperture system, the system Strehl Ratio (SR) is deduced using the principle of Fourier optics, which leads to the theoretical result of the systems SR metric with the form of separated sub-aperture aberration and piston error. As for the bi-aperture system, the variances of the system SR metric are calculated and analyzed with different sub-apertures aberrations for conditions of corrected piston error and un-corrected piston error. Therefore, the comprehensive effects of sub-aperture aberrations and the piston errors among different sub-apertures on the system image quality are analyzed theoretically. From these analyses, the physical mechanism for the comprehensive effect of sub-aperture aberration and the piston error on the sparse-optical-synthetic-aperture system image quality is revealed, and it could be seen that the compensation of piston error is meaningful only if the sub-aperture self aberration is corrected to be in a certain limit.