This calculator plots orthonormal polynomials for circular, annular, rectangular, hexagonal, and elliptical apertures. FRINGE Zernikes are used for the circular apertures. The annular apertures uses the polynomials derived by V. N. Mahajan, "Zernike annular polynomials for imaging systems with annular pupils," J. Opt. Soc. Am., Vol. 71, No. 1, pg 75-85 (1981). All other polynomials are from the paper V. N. Mahajan and G. M. Dai, "Orthonormal polynomials in wavefront analysis: analytical solution," Vol. 24, No. 9, pg 2994-3016 (Sept. 2007). Any errors in functions in the program are my own.
To plot a function, choose a tab from the top of the GUI, input some coefficient values in the GUI table, choose a plot mode, and click 'Update Display.'