In optics, Zernike polynomials are widely used in testing, wavefront sensing, and aberration theory. This unique set of radial polynomials is orthogonal over the unit circle and finite on its boundary. This Letter presents a recursive formula to compute Zernike radial polynomials using a relationship between radial polynomials and Chebyshev polynomials of the second kind. Unlike the previous algorithms, the derived recurrence relation depends neither on the degree nor on the azimuthal order of the radial polynomials. This leads to a reduction in the computational complexity.
© 2013 Optical Society of America
Original Manuscript: May 7, 2013
Revised Manuscript: June 15, 2013
Manuscript Accepted: June 16, 2013
Published: July 9, 2013
Vol. 8, Iss. 8 Virtual Journal for Biomedical Optics
Barmak Honarvar Shakibaei and Raveendran Paramesran, "Recursive formula to compute Zernike radial polynomials," Opt. Lett. 38, 2487-2489 (2013)