  Dark-field x-ray microscopy utilizes Bragg diffraction to collect full-field
x-ray images of "mesoscale" structure of ordered materials. Information
regarding the structural heterogeneities and their physical implications is
gleaned through the quantitative analyses of these images. Namely, one must be
able to extract diffraction features that arise from lattice modulations or
inhomogeneities, quantify said features, and identify and track patterns in the
relevant quantitative properties in subsequent images. Due to the necessity to
track features with a wide array of shapes and length scales while maintaining
spatial resolution, wavelet transforms were chosen as a potent signal analysis
tool. In addition to addressing multiple length scales, this method can be used
in conjunction with other signal processing methods such as image binarization
for increased functionality. In this article, we demonstrate three effective
use of wavelet analyses pertaining to DFXM. We show how to extract and track
smooth linear features-which are diffraction manifestations of twin
boundaries-as the sample orientation changes as it is rotated about momentum
transfer. Secondly, we show that even the simplest wavelet transform, the Haar
transform, can be used to capture the primary features in DFXM images, over a
range of length scales in different regions of interest within a single image
enabling localized reconstruction. As a final application, we extend these
techniques to determine when a DFXM image is in focus.
