By expressing the solution to the nonlinear wage equation in operator form, we derive two methods for calculating a corrective phase to compensate for thermal blooming. The first method employs a form of glint return in which the uncorrected beam is first propagated through free space to the target. The resulting field is then propagated backward through the heated atmosphere to the aperture. The final phase of the beam represents the conjugate phase correction. The second method is based on the assumption that the atmospheric lens can be represented by a thin lens at the aperture. In this method one simply propagates the thermally bloomed beam through free space to the aperture. Again the final phase represents the conjugate phase correction. The second scheme performs as well as other predictive schemes and has the combined virtues of simplicity and versatility.
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