Over the past 15 years, ptychography applications and methods have advanced significantly. Ptychography is a computational microscopy technique for acquiring images with resolutions beyond the limits imposed by beam diameter, optical aberration, and numerical aperture—NA, a measure of the range of incident angles an optical system can accept. Nowadays it encompasses various experimental techniques with visible light, UV light, x rays, and electrons. Emerging applications include, for example, accurate wavefront-aberration measurement for space telescopes.

Ptychography was introduced in 1969 in a three-part paper1 by Walter Hoppe, an influential figure in the field of electron microscopy. (For more about the technique’s name, see box 1.) But it gained little traction during his lifetime: In 1982 Hoppe described ptychography as one of his “nearly forgotten old ideas.”2 Only once computers gained sufficient memory and computing power, and after a few other technical difficulties were addressed, did ptychography gradually reemerge....

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