SUMMARY The sounding problem of 1‐D layered media has been solved with wave energy transfer equations. Forward and backward wave propagation at any trajectory point are calculated. Analytical solutions for simple trajectories are derived. In the general case the solutions can be determined numerically. For certain active seismic sounding problem having good data coverage, this algorithm can be used to invert for characteristics of the layered media.

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The prospects for image recovery of space objects, observed in the visible range through the turbulent atmosphere by using large aperture telescope, were discussed and evaluated. A "dual" adaptation was introduced: at first -hardware adaptation, using reflected solar radiation from the space object or laser star, then algorithmic. We considered two scenarios for observation.The criterion of image quality was chosen to be potentially full compensation of phase distortion. The characteristics of photoreadout statistics for the various scenarios were analyzed.

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