Zernike polynomials

The first 21 Zernike polynomials $Z_{n}^{l}(\rho ,\varphi )$, ordered vertically by radial degree $n$ and horizontally by azimuthal degree $l$

In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike, laureate of the 1953 Nobel Prize in Physics and the inventor of phase-contrast microscopy, they play important roles in various optics branches such as beam optics and imaging where they are used to describe optical aberrations.