Analysis and performance of non-circular polygonal polynomials in the wavefront modeling

摘要

Imaging system design is not limited to circular aperture shapes. However, non-circular apertures require a different set of polynomials, because broadly used Zernike polynomials are not orthogonal over non-circular shapes. Applying the Gram-Schmidt orthogonalization process provide the adopted set of orthogonal polynomials over selected non-circular aperture shape. However, when the aperture shape is complicated, non-symmetrical, the resulting set of polynomials can be very complex. In the case of odd-sided polygons is the analytical form of the polynomials inappropriate due to their complexity and these polynomials have to be expressed in their numerical form. Concerning the laborious complexity of some non-circular polynomials, we analyze the desired accuracy of such polynomials and their performance of the wavefront modeling according to classical circular Zernike polynomials.