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Algorithm for phase retrieval

The hybrid input-output (HIO) algorithm for phase retrieval is a modification of the error reduction algorithm for retrieving the phases in coherent diffraction imaging. Determining the phases of a diffraction pattern is crucial since the diffraction pattern of an object is its Fourier transform and in order to properly invert transform the diffraction pattern the phases must be known. Only the amplitude however, can be measured from the intensity of the diffraction pattern and can thus be known experimentally. This fact together with some kind of support constraint can be used in order to iteratively calculate the phases. The HIO algorithm uses negative feedback in Fourier space in order to progressively force the solution to conform to the Fourier domain constraints (support). Unlike the error reduction algorithm which alternately applies Fourier and object constraints the HIO "skips" the object domain step and replaces it with negative feedback acting upon the previous solution. Wikipedia →

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  1. Read the overview: Hybrid input-output algorithmA 5-minute orientation
  2. Skim a recent paper: Scatter imaging with super-memory effect based on adaptive β -parameter hybrid input-output algorithm-assisted estimation of point spread functionInfluential work since 2022
  3. Pick up a classic book: Modern Operating SystemsThe most-reprinted book on the subject
  4. Read the landmark paper: Estimation of interregional input–output table using hybrid algorithm of the RAS method and real-coded genetic algorithmCited 36 times
  5. Go sideways: Coherent diffraction imagingA closely related topic
  6. Go sideways: Phase retrievalA closely related topic

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