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Multivariate Statistical Analysis of Series of Diffraction Patterns

Commercial-based x-ray hyperspectral imaging (full X-ray spectrum at each pixel in an array versus simple mapping of pre-chosen elements) systems have been available since the mid-1990’s [1]. Similar to the evolution of X-ray mapping to hyperspectral imaging, position-resolved electron diffraction is evolving from just orientation information from pre-chosen phases [2] to acquisition of full diffraction patterns at each point in an array. In the case of hyperspectral data, advanced statistical analysis methods have proven efficient and effective at reducing the dimensionality of the data to just a handful of chemically relevant components [3]. An analogous method has been applied to electron backscattered diffraction (EBSD) data [4]. This yielded a dimensional reduction and discrimination of similar space groups (Fd3m versus Fm3m). This was achieved by looking at all the detail in the patterns (not just angles between planes) as well as being robust to mixed patterns from two grains illuminated in one pattern. In the TEM, much progress has been made in orientation imaging by collecting series of diffraction patterns, analyzing data via template matching [5] and also using precession to minimize dynamical effects [6]. In this paper we describe the application of multivariate statistical analysis (MSA) methods to a parallel-beam nano-diffraction image-resolved data set, modifying and building upon the methods developed in [4]. In addition we will also discuss the use of similar methods to analyze data from a direct electron detector in scanning TEM (STEM) mode.