Table of lowest order Zernike polynomials Postcard

The elegance of orthogonal polynomials unleashed! We all studied orthogonal polynomials and many of us work with them. Now, the visual beauty of these forms is evident using Zernike's set orthogonal over the unit disk. The coloration is created to highlight the small variations about the zero mean. The effect is captivating. We see the polynomials arranged in a table; the order increases moving down; the angular frequency increases to the right. The top row represents the real polynomials, the rotationally invariant set (m = 0). The bottom row shows the analytic set (n = m). The middle row represents the complex set, which is everything else (m > 0, n != m). The Nobel Prize in Physics was awarded to Zernike in 1953 for his discovery of phase contrast microscopy