Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence

The wavefronts of a point source of radiation that is immersed in a turbulent atmosphere become distorted and deformed as they propagate outward. The phase surfaces incident on an unobscured collecting aperture therefore will not be perfectly spherical, but instead will be aberrated in some way. We have expanded this phase profile in a set of orthonormal functions closely related to the Zernike polynomials and then determined the respective power spectra of the time dependent expansion coefficients. The results show, for all spectra, a sharp cutoff of for frequencies , where is the wind velocity transverse to the point source and the receiver, and is the aperture radius. In particular, for the tilt component expansion coefficients, this result differs from the usual phase difference power spectra previously used by many workers.