The sparse subaperture stitching, the accuracy of which is closely related to the arrangement, number and size of subapertures, is one of the main methods of quality testing for large aperture optical systems. A ma-thematical model was established to deduce the relation curve between the subaperture number k and fill factor M when the value of k ranges from one to infinity. As a result, the optimal arrangement layout, consisting of seven sparse subapertures, was obtained for the detection systems below 1.5 m. Autocollimation interference detection of Φ200 mm validated the rationality of the arrangement.%稀疏子孔径拼接检测是大口径、超大口径光学系统像质检测的主要方法之一,其拼接检测的精度与子孔径排列方式、数目以及大小密切相关.本文通过建立数学模型,推导出子孔径个数k在1到无穷区间取值,子孔径个数k与填充因子M的关系曲线,从而得出在1.5 m以下系统检测的最优的七个稀疏子孔径排列布局图,并通过Φ200 mm自准干涉检验,验证了这种排列布局的合理性.
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