An optical imaging system forms an object image by recollecting light scattered by the object. However, intact optical information of the object delivered through the imaging system is deteriorated by imperfect optical elements and unwanted defects. Image deconvolution, also known as inverse filtering, has been widely exploited as a recovery technique because of its practical feasibility, and operates by assuming the linear shift-invariant property of the imaging system. However, shift invariance is not rigorously hold in all imaging situations and it is not a necessary condition for solving the inverse problem of light propagation. Here, we present a method to solve the linear inverse problem of coherent light propagation without assuming shift invariance. Full characterization of imaging capability of the system is achieved by successively recording optical responses, using various laser illumination angles which are systematically controlled by a digital micro-mirror device. Experimental results show that image distortions caused by optical defocus can be restored by conventional deconvolution, but severe aberrations produced by a tilted lens or an inserted disordered layer can be corrected only by the proposed generalized image deconvolution. This work generalizes the theory of optical imaging and deconvolution, and enables distortion-free imaging under any general imaging condition.
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