Karhunen-Loeve Basis Functions of Kolmogorov Turbulence in the Sphere

Abstract

The statistically independent Karhunen-Loeve modes of refractive indices with isotropic Kolmogorov spectrum of the covariance are calculated in a sphere of given radius, rendered as series of 3D Zernike functions. Many of the symmetry arguments of the associated 2D problem for the circular input pupil remain valid. The technique of efficient diagonalization of the eigenvalue problem in wavenumber space is founded on the Fourier representation of the 3D Zernike basis.