Fresnel diffraction in the case of an inclined image plane

An extension of the theoretical formalism of Fresnel diffraction to the case of an inclined image plane is proposed. The resulting numerical algorithm speeds up computation times by typically three orders of magnitude, thus opening the possibility of utilizing previously inapplicable image analysis algorithms for this special type of a non shift-invariant imaging system. This is exemplified by adapting an iterative phase retrieval algorithm developed for electron microscopy to the case of hard x-ray imaging with asymmetric Bragg reflection (the so-called “Bragg Magnifier”). Numerical simulations demonstrate the convergence and feasibility of the iterative phase retrieval algorithm for the case of x-ray imaging with the Bragg Magnifier.