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iterations of the HIO process. To ensure reproducibility the process is typically repeated with new sets of random phases with each run having typically hundreds to thousands of cycles. The constraints imposed in real and reciprocal space typically depend on the experimental setup and the sample to be imaged. The real space constraint is to restrict the imaged object to a confined region called the "support". For example, the object to be imaged can be initially assumed to reside in a region no larger than roughly the beam size. In some cases

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