Abstract

Thermal blooming is the critical phase-distortion degrading factor preventing a ground-based high-energy laser system from achieving a diffraction-limited irradiance profile at a distant target. Adaptive optical systems have been used to correct thermal-blooming-induced phase variation by applying the proper amount of each correcting mode (tilt, defocus, astigmatism, and coma) to the entire aperture. I have developed the analytical expression for these correcting modes,¹ which are represented by Zernike polynomials for a uniform beam, and I have also explored the Zernike decomposition of phase variation for the Gaussian beam. In this paper, I present the analytic expression for the phase-variation decomposition for the Gaussian beam in the infinite and truncated cases. As a result, the expressions are reduced to error functions in terms of beam diameter, beam waist, and wind velocity. I compare these results with those of the uniform-beam case and obtain the steady-state limit, i.e., when the elapsed time is longer than the wind-clearing time.

© 1990 Optical Society of America