Formation of images in strong turbulence (spherical-wave log-amplitude variance greater than 0.25) is a well-known challenge. Such imaging with coherent active illumination poses special difficulties due to the presence of laser speckle in the image, which is similar to atmospheric speckle and so it is difficult to separate the two forms of speckle. However, imaging with laser illumination has the potential benefit of enhanced signal and added information in the laser speckle. In this paper, several image processing approaches are investigated with simulation that show promise for good image quality in such conditions. These approaches include pupil-plane techniques that filter phase based on an assumed atmospheric spatial phase structure function, branch-cut filtering and intensity-weighted branch cut minimization. Also included in the analyses are focal-plane techniques. Significant improvements can be found for Rytov variances up to and beyond 0.4 and up to 10 atmospheric coherence lengths (r0) across the aperture, in uniform turbulence scenarios over a 30 km range with objects of limited extent. The approaches are optimized for fast execution and minimal number of image frames required to form an acceptable image. The results are compared using several image metrics and also compared with a corresponding idealized adaptive-optics approach using an incoherent beacon.
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