Residual errors in the wavefront from an active wavefront compensation device cause image degradation, especially for extended objects. Even if these errors are as small as one-sixth wave rms, the image degradation can be significant enough that post-processing of the resulting imagery is justified. To analyze the degradation present in this imagery, the characteristics of the image of a point source are found in terms of the statistics of the residual wavefront errors. The image of an extended object can be described in terms of the characteristics of the point image. In recording the imagery with a view to post-processing, certain requirements must be met by the recording device in order for the processing to be successful. The signal-to-noise ratio of the detection device, its resolution, and the integration time necessary to achieve these requirements are discussed. It is shown how criteria for these requirements can be treated in terms of the statistics of the residual wavefront errors, the size of the optics, and the source radiance. A method of post-processing of the imagery is suggested that is based on the recording of images at two different focal planes simultaneously.