  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.

Optics