S. Marchesini, D. Shapiro, H. Krishnan (LBL) F. Maia (Uppsala) and H-T. Wu (Stanford)
The Super Resolution Revolution in X-ray Imaging: Phase Retrieval in High Dimensional Space
Ever since Wilhelm Röntgen shocked the world with a ghostly photograph of his wife’s hand in 1896, the imaging power of X-rays has been exploited to help see the unseen. Their penetrating power allows us to view the internal structure of many objects, perhaps the most everyday application of X-rays, while their short wavelength allows scientists to look at nanometre-scale objects. Through the development of X-ray crystallography in the early twentieth century, the arrangement of atoms within crystals has been revealed. Imaging with X-rays is also attractive for other reasons, offering the abilitiy to examine aspects of a
sample, including chemical, orbital, electronic or magnetic properties at atomic resolution, by exploiting mechanisms such as resonance and polarization. This allows one to gain far more knowledge than is available with visible microscopy. This is not so straightforward, but recent advances in X-ray sources and detectors have made it possible to image what could not be seen before, namely, macroscopic specimens in 3D at near wavelength resolution with chemical state specificity.
Ptychography enables one to build up very large images at wavelength resolution (i.e. potentially atomic) by combining the large field of view of a high precision scanning microscope system with the resolution enabled by diffraction measurements. Each recorded diffraction pattern contains short-spatial Fourier frequency information about features that are smaller than the x-ray beam-size, enabling higher resolution. At short wavelengths, however, it is only possible to measure the intensity of the diffracted light. To reconstruct an image of the object, one needs to retrieve the phase, made even more challenging in the presence of noise, experimental uncertainties, and perturbations of the experimental geometry.
The phase retrieval problem is made tractable by recording multiple diffraction patterns from the same region of the object. Ptychography uses a small step size—relative to the size of the illuminating beam—when scanning the sample. Diffraction measurements from neighboring regions are related to each other by this illumination geometry. This motivates us to consider augmented projections and synchronization strategies aiming to organize local information in a global way to handle the big imaging data in the coming new light source era.
The imaging revolution unleashed by high-throughput, high-resolution ptychography will have profound effects on our understanding of nature. In catalysis for example, nanoscale internal structures hold the key to achieving very high reactivity, in photovoltaics, charge separation happens through nm scale interfaces. In CO2 sequestration by porous rock, the finest pore, often at nm scale, is often rate-limiting. In general high resolution macroscale imaging will help scientists from around the world understand ever more complex nano-materials, self-assembled devices, or to study different length-scales involved in life, from macro-molecular machines to bones, and whenever observing the whole picture is as important as recovering local atomic arrangement of the components.