Review and experimental comparison of speckle-tracking algorithms for X-ray phase contrast imaging.

X-ray speckles have been used in a wide range of experiments, including imaging (and tomography), wavefront sensing, spatial coherence measurements, X-ray photon correlation spectroscopy and ptychography. In this review and experimental comparison, we focus on using X-ray near-field speckle grains as wavefront markers and numerical methods for retrieving the phase information they contain. We present the most common tracking methods, introducing the existing algorithms with their specifications and comparing their performances under various experimental conditions. This comparison includes applications to different types of samples: phantoms for quantitative analysis and complex samples for assessing image quality. Our goal is to unify concepts from several speckle tracking methods using consistent terminology and equation formalism, while keeping the discussion didactic and accessible to a broad audience.