A non-iterative reconstruction method for direct and unambiguous coherent diffractive imaging

We develop a deterministic algorithm for coherent diffractive imaging (CDI) that employs a modified Fourier transform of a Fraunhofer diffraction pattern to quantitatively reconstruct the complex scalar wavefield at the exit surface of a sample of interest. The sample is placed in a uniformly-illuminated rectangular hole with dimensions at least two times larger than the sample. For this particular scenario, and in the far-field diffraction case, our non-iterative reconstruction algorithm is rapid, exact and gives a unique analytical solution to the inverse problem. The efficacy and stability of the algorithm, which may achieve resolutions in the nanoscale range, is demonstrated using simulated X-ray data.