In this research, Zernike polynomials for a unit annular elliptical aperture (ellipse inscribed by a unit circle of unit radius obscured by elliptical obscuration) have been studied in Cartesian coordinates and in polar coordinates. These polynomials have been shown to form a complete basis orthogonal on a unit annular ellipse aperture, and they represent balanced classical aberrations just as Zernike circular polynomials in a unit circle.
© 2012 Optical Society of America
Diffraction and Gratings
Original Manuscript: August 13, 2012
Revised Manuscript: October 9, 2012
Manuscript Accepted: November 1, 2012
Published: December 10, 2012
Sundus Y. Hasan and Ali S. Shaker, "Study of Zernike polynomials of an elliptical aperture obscured with an elliptical obscuration," Appl. Opt. 51, 8490-8497 (2012)