Iterative improvement of shadowgraphic phase maps

This work demonstrates an iterative shadowgraphic method (ISM), which can eliminate diffraction blurring from shadowgraphically retrieved phase maps. The algorithm calculates iteratively wavefront corrections by solving the Poisson equation with a source term obtained from a reference shadowgram and an artificial shadowgram calculated from the approximated phase map obtained at the previous iteration. The convergence of ISM has been proved and several numerical tests have been performed to assess its performance.