Effects of wind and finite bandwidth on adaptive phase compensation of atmospheric turbulence

The power spectrum is formulated for time-dependent expansion coefficients of Zernike polynomials of a wavefront distorted by atmospheric turbulence. This expression is shown to be more general than that derived by Hogge and Butts. The low frequency asymptotic results are examined along with the effects of the outer scale of turbulence and propagation distance. The integrated power spectra are plotted against bandwidth for several low-order correcting modes. These graphs are then used to study the combined effect of transverse wind and finite bandwidth on the Strehl ratio, based on residual phase error over the aperture.