Zernike Polynomials

Wavefront aberrations on the unit disk — the language of optics and adaptive optics

Zernike polynomials form an orthonormal basis on the unit disk, indexed by radial order n and azimuthal frequency m. They describe optical wavefront aberrations: piston, tilt, defocus, astigmatism, coma, trefoil, spherical aberration, etc. Adaptive optics systems measure and correct these modes in real-time.