Fengzhao Dai,1
Xiangzhao Wang,1,*
and Osami Sasaki2
1Laboratory of Information Optics and Opto-Electronic Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
2Faculty of Engineering, Niigata University, Niigata-shi 950-2181, Japan
By nonrecursive matrix method using the Zernike circle polynomials as the basis functions, we derived a set of polynomials up to fourth order which is approximately orthonormal for optical systems with an annular pupil having a cross-shaped obstruction. The performance of the polynomials is compared with the strictly orthonormal polynomials with some numerical examples.
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