In this paper we present the theoretical background required for evaluating phase compensation as a technique for reducing the effects of thermal blooming. By using a time-dependent approach for thermal blooming, we can define and evaluate the instantaneous Green’s function for the heated atmosphere. The phase at the mirror is determined by propagating a point source from the focal point to the laser. The effectiveness of this technique is determined by propagating point sources within a diffraction-limited spot to the laser and comparing the resulting phase to the phase of a point source at the focal point. The phase difference will be small and the increase in irradiance large if the heating occurs where geometric optics is valid. The phase difference is large and the increase in irradiance small if atmospheric heating occurs where significant diffractive spreading is also occurring. The resulting gradients lie in the geometric shadow of the aperture and are not accessible to correction by contouring the mirror. Numerical results illustrating the analysis are presented for both cw and pulsed lasers.
© 1977 Optical Society of America
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