This section is intended to provide a background or context to the invention recited in the claims. The description herein may include concepts that could be pursued, but are not necessarily ones that have been previously conceived or pursued. Therefore, unless otherwise indicated herein, what is described in this section is not prior art to the description and claims in this application and is not admitted to be prior art by inclusion in this section.
Understanding nanoscale processes is key to improving the performance of advanced technologies, such as batteries, catalysts, and fuel cells. However, many processes occur inside devices at short length and time scales in reactive environments and represent a significant imaging challenge. One way to study such structures is by using coherent diffraction imaging (CDI). CDI is a lensless technique for reconstructing a 3D image of an object based on a diffraction pattern. In CDI, a coherent beam of x-rays or electrons is incident on an object, the beam scattered by the object produces a diffraction pattern that is measured by an area detector, and an image is reconstructed from the diffraction pattern. When the diffraction pattern is measured by the area detector, the data is based on a number of counts of photons or electrons. This gives rise to the “phase problem” or loss of phase information when a diffraction pattern is collected. In order to recover the phase information, Fourier-based iterative phase retrieval algorithms are utilized.
Another example of CDI is Bragg coherent diffractive imaging (BCDI). In BCDI, the object is rotated around a tilt axis and a sequence of 2D diffraction patterns are measured at different sample orientations. BCDI is a powerful technique for investigating dynamic nanoscale processes in nanoparticles immersed in reactive, realistic environments. With current BCDI methods, 3D image reconstructions of nanoscale crystals have been used to identify and track dislocations image cathode lattice strain during battery operation, indicate the presence of surface adsorbates, and reveal twin domains. The temporal resolution of current BCDI experiments, however, is limited by the oversampling requirements for current phase retrieval algorithms.
Conventional phase retrieval algorithms present a problem in improving the time resolution of an imaging technique (e.g., CDI, BCDI, etc.). The imaging technique requires a computer algorithm to convert the experimental data into a real space image of the object (e.g., nanocrystals) in reactive environments. Oversampling refers to the number of measurements that are required to faithfully reproduce the image. The autocorrelation of the image must be sampled at the Nyquist frequency, which is twice the highest frequency in the system. Because each measurement takes time, the oversampling requirement results in a lengthy process that may include prolonged radiation dose. Moreover, if the oversampling requirement is too high, it may not be possible to image a dynamic process such as crystal growth, catalysis or strain in battery cathode nanoparticles that occur too rapidly (i.e., faster than the amount of time it takes to satisfy the oversampling requirements).
A need exists for improved technology, including a method for phase retrieval that allows for the time resolution to be improved, for example, by reducing the oversampling requirement at each time step.