Title: Optical transfer function for incomplete circular pupil 

Author(s): Zhang, YF (Zhang, Yongfeng); Xian, H (Xian, Hao) 

Source: OPTIK  Volume: 198  Article Number: 162957  DOI: 10.1016/j.ijleo.2019.162957  Published: DEC 2019   

Abstract: Highly segmented primary mirror is always utilized to construct the next-generation large astronomical telescope for the sake of obtaining unprecedented high imaging resolution. One of the factors, which would impact the final image quality, is the piston error resulting from the rigid random movement of each single segment along the optical axis. The broadband/narrowband algorithm is proposed to sense this special error with addition modified Shack-Hartmann sensor. In essential, for each lenslet, the sensing aperture is an incomplete circular pupil. We derive the optical transfer function for this pupil analytically, and discuss its properties, including supported set region, side-lobe peak's variation as a function of gap. The results presented here give a deeper insight into Keck's co-phasing approach, and are of great help for developing new co-phasing algorithm based on existing hardware. 

ISSN: 0030-4026 

eISSN: 1618-1336