Ptychographic Image Reconstruction Using Automatic Differentiation: First and Second Order Methods

Saugat Kandel, Argonne National Laboratory
Collection of ptychography imaging dataset

Collection of a ptychographic imaging data set in the simplest single-aperture configuration. (a) Coherent illumination incident from the left is locally confined onto an area of the specimen. A detector downstream of the specimen records an interference pattern. (b) The specimen is shifted (in this case, upwards) and a second pattern is recorded. Note that regions of illumination must overlap with one another to facilitate ptychographic shift-invariance constraint. (c) A whole ptychographic data set uses many overlapping regions of illumination. (d) The entire data set is four-dimensional: for each 2D illumination position (x , y), there is a 2D diffraction pattern (kx, ky).

Credit: 22sm22, Wikipedia

Ptychography is an increasingly popular imaging technique that has found application in a wide variety of experimental contexts, for imaging with X-rays, visible light, or electrons, in different experimental geometries---far-field or near-field, transmission or Bragg---and even with overlapping angles instead of positions. As the experimental model increases in complexity, the number and type of variables we could optimize for increases in scope, and it is more difficult and tedious to formulate an inversion procedure. 

We address this challenge by using modern automatic differentiation (AD) methods to design inversion procedures that do not require explicit calculations of closed-form gradient expressions. We show that we can use first-order as well as second-order AD methods to enable fast, memory-efficient, and robust solutions to ptychographic inversion problems. Remarkably, our second-order optimization approach incurs a computational cost that is often lower than that required by state-of-the-art first order ptychography algorithms. The algorithms we develop are general in scope and easy to apply for a variety of optimization problems beyond just the ptychography setting.


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