What is ptychography, in a nutshell? I've heard of ptychography as an imaging technique a number of times in the past, and recently I found myself in need of a refresher on what it actually entails. Unfortunately, the Wikipedia page on the subject is extremely technical and laden with detail, but it does an extremely poor job at conveying the fundamentals of the technique, and naive web searches quickly go into paywalled research papers that won't be particularly readable for a general public.
So, in a nutshell: What is ptychography? That is:


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*What is the conceptual core of the method?

*What are the core physical requirements on the light source used for illumination?

*To what extent does the method rely on algorithmic and computational reconstruction? Is it fully constrained, or do the algorithms require models of the sample to work? That is, does the measured experimental data contain complete information to uniquely specify the image?

*What is the method for? I.e., what advantages does it have with respect to competing methods?


I'm primarily interested in imaging using XUV and soft x-rays (i.e. the sort of things that might come out of a high-order harmonic source), and to make this answer as broadly useful as possible (or at least, in a manner commensurate to the specialized nature of the technique), I'd like answers to be accessible to undergraduates with a solid course in optics under their belt.
 A: Ptychography is a high resolution imaging technique. In standard microscopy light goes through a sample where it is absorbed and refracted, followed by a lens to form an image. In diffractive imaging or ptychography you replace the lens with a detector which can be larger than the lens and therefore enable higher resolution. Propagation from the sample to the detector (scattering/diffraction) using a coherent monochromatic wavefront is basically a Fourier transform (Fraunhofer approx) therefore higher Numerical Aperture (acceptance angle) leads to higher spatial frequency, i.e. resolution. The caveat is that the detector records the intensity of the complex diffracted wavefront and you need the phase to propagate back to the sample and get an image.
The phase retrieval optimization problem is generally non-linear and non-convex and numerical solvers don't always work in general. This issue is fixed in Ptychography by moving the sample around and recording diffraction data from overlapping regions of the sample. The redundancy due to overlap helps convergence. The numerical solver needs to ensure that (1) each region is consistent with overlapping ones, and (2) diffraction from each region is consistent with the measured data. The simplest algorithm just enforces these constraints in an alternating fashion. Convergence guarantees are still outstanding but in practice cases where solvers fail are rare enough if the redundancy is sufficient.
Requirements are coherent, quasi-monochromatic light and thin sample approximation, although some partial coherence, limited spectral bandwidth, multiple wavelengths, and sample thickness can be handled with more complex solvers.
The big advantages are (1) enabling higher resolution since lenses for x-rays are hard to make below 10 nm resolution, along with providing (2) the complex refractive index, i.e.  phase and absorption contrast. Ptychography can also be used for (3) wavefront metrology/sensing at nm scales by solving for the illumination. Related techniques include Fourier ptychography, basically synthetic aperture imaging with phaseless measurements, and near field ptychography which replaces Fraunhofer approx with Fresnel and enables phase-contrast imaging but no magnification.
S. Marchesini, Ph. D.
