Elementary signals in ptychography.

Ptychographic imaging has gained popularity for its high resolving power and sensitivity as well as for its ability to map simultaneously the sample's complex-valued refractive index and the illumination. Yet, despite significant progress that allows for reliable practical implementation, some of the technique's fundamentals remain poorly understood, and oftentimes successful data acquisition is either overly conservative or relies more on experimenters experience than on rational data acquisition strategies. Here, we propose a theoretical framework of ptychography, which is based on Gabor's notion of decomposition into elementary signals and the concept of frames. We demonstrate how this framework can straightforwardly be used to derive sampling requirements or to provide arguments on how to optimize the ptychographic scan. More generally, our theoretical framework can serve as a bridge between the experimental technique and the rich and well established mathematical disciplines of wavelets decomposition and spectrogram analysis.