A fast calculation algorithm for three-dimensional atomic image reconstruction from X-ray fluorescence holography (Barton's method) is described. This method employs HEALPix, an algorithm that is used to subdivide a spherical surface in which each pixel covers an identical surface area. Using this algorithm, the computing time for atomic image reconstruction is reduced by a factor of 14.5. The time can be reduced further by parallel processing and an optimization of the resolution parameter of HEALPix.
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