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 mathematical 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.