The elegant paper by Maiden, Humphry, Zhang and Rodenburg makes a significant contribution to the theory and practice of superresolution, via a convincing demonstration based on ptychographic principles.
Ptychography, initiated by Walter Hoppe in the late 1960s, is a technique for solving the phase problem and has been taken to a new level in the current paper. In essence, ptychography involves collection of a series of coherent diffraction patterns obtained using a number of overlapping probe positions; it then utilizes the redundancy in the resulting diffraction datasets to assist with the problem of reconstructing the sample from such data.
Building on earlier work termed the extended ptychographical iterative engine (ePIE), the authors develop a superresolved (SR) algorithm termed SR-PIE. In two separate experiments, one of which studies a resolution grid and the other of which considers a pollen sample, resolution improvements by a factor of 3 are observed. The SR-PIE procedure is a stable and robust superresolution algorithm that effects a more efficient use of hitherto-unexploited present in ptychographic datasets.
This exciting work is being pursued further by the authors, who report that preliminary extensions of their just-published paper suggest that superresolution improvements by a factor of 5 or more will be possible using SR-PIE. I eagerly anticipate the publication of these still more impressive results and warmly recommend the current paper to your attention.
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