Typical current tomographic reconstruction algorithms either ignores diffraction entirely or treats only a single wavelength and does not have a principled theory of partial coherence. These can lead to unphysical reconstructions of high and low densities near material boundaries.
The invention is a method for creating improved tomographic reconstructions in the presence of diffraction. The new feature is the recognition that it is possible to make an iterative method which has the same scaling in computation time as projective tomography.
The method is applicable to lower Fresnel number than current methods, but does not require the far field limit used in ptychography. The method gives superior resolution of abrupt edges between materials of different density. Such differences are extremely common in both engineered and natural systems.