Zernike polynomials

Summary

The Zernike polynomials are an orthogonal family of polynomials on the closed unit disk. In polar coordinates each one is a radial polynomial times $\cos(m\varphi)$ or $\sin(m\varphi)$. They are the standard basis in optics for describing the aberrations of a wavefront through a circular lens or mirror. Their radial parts are Jacobi polynomials in disguise.