WAVE-FRONT TEMPORAL SPECTRA IN HIGH-RESOLUTION IMAGING THROUGH TURBULENCE

A general formulation is given for the derivation of theoretical tempo ral power spectra of quantities related to turbulent wave-front phase. These temporal power spectra and their asymptotic power laws and cuto ff frequencies are presented for various quantities of interest in the field of interferometry (differential piston), wave-front sensing (Sh ack-Hartmann and curvature sensor), adaptive optics (Zernike polynomia ls), and seeing monitoring (differential angle of arrival). We show th at the differential piston spectrum has two cutoff frequencies and exh ibits a very steep decrease at high frequencies. The curvature sensor is shown to be much less sensitive than the Shack-Hartmann sensor to t he low temporal frequencies. A study of the Zernike temporal power spe ctra shows that their cutoff frequencies increase with the polynomial radial degree. Both single-layer and multilayer plane and spherical wa ves are considered. The effect of wind direction is also taken into ac count. We point out the influence of the cone effect on the temporal p ower spectra when Rayleigh or sodium laser guide stars are used for wa ve-front sensing. The cone effect results in a temporal decorrelation between natural and laser guide star wave fronts. Finally, we demonstr ate that in adaptive optics systems low-order modes require higher ser voloop bandwidths than do high-order modes in order for the residual v ariance to be balanced between the corrected modes. The same conclusio n applies to fringe tracking in large telescope interferometers equipp ed with adaptive optics systems.