Study On The Phase Diversity Of Off-axis Field View For The Sparse Aperture System

Sparse aperture optical system is a large aperture imaging system which is composed of space distribution and mutual interference multiple small apertures. It has the characteristics of small volume, light weight, easy processing, low cost and its resolution which is similar to single-caliber system. However, because of each sub-mirror independent, high degree of freedom, which leads to produce large errors in the alignment of the sparse aperture telescope system. Sub-mirror alignment error would reduce the resolving power of the system, affecting the final image quality greatly, so how to solve one of its alignment errors become a key issue. People put forward to use the phase diversity to detect and recover the image. The error of a sub mirror is represented by the first three terms in the Zernike polynomial. The error of the sub mirror is obtained through the optimization of the objective function which is constructed under the Gauss noise model. But the traditional Zernike polynomial is only in a single field view to reconstruct the wavefront error, because of the lack of field parameters the corresponding Zernike term is not a real wave aberration function.There is a different incident field, which leads to the detection of the wavefront distortion inaccuracy and affects the final sub mirror image restoration for the actual imaging optical system.In this paper we discuss the impact of two-mirror optical system with three sub-mirrors sparse aperture by field view and sub-mirror error derived double Zernike polynomials contains field view factors based on the phase diversity and determine the change caused by field view in the coefficient of Zernike polynomials. We analyze the influence of different fields of view on Zernike first three coefficients, and construct the correlation matrix which contains the sub mirror error, field view and Zernike coefficients. We also calculate and verify the parameters of the matrix, and put forward the relative ambiguity function and the peak signal to noise ratio to evaluate the optical image quality with different assemble errors. We obtain images from the focus and defocus surface from the optical system with assemble errors respectively. After analyzing two images by the phase diversity method and use of genetic algorithm optimization, we can calculate out the assemble errors and wavefront distortion caused by field view, and restore the original target image successfully.