Abstract

A ground-based high energy laser system is prevented from achieving diffraction-limited irradiance profiles at a distant target due to the degrading effect of thermal blooming-induced phase distortions. This difficulty can often be corrected by use of an adaptive optical system which corrects classical aberrations such as tilt, defocus, astigmatism, and coma by applying the proper amount of each correcting mode to the entire aperture. These correcting modes are represented by Zernike polynomials. Assuming a uniform subsonic wind across the aperture, in the isobaric approximation with near field heating, we present an analytic solution of the linearized hydrodynamic equation for the density variation and resulting phase profiles. In this approximation, the time-dependent phase variation is the sum of the phase generated at the current time, plus a wind-transported contribution from the previous phase. For the case of a uniform circular irradiance profile, we obtain a closed form expression, which we expand in Zernike polynomials. The results agree with the previously evaluated steady state limit in the long time limit, i.e., when the time is larger than the wind-clearing time.

© 1989 Optical Society of America