Exploring single-shot propagation and speckle based phase recovery techniques for object thickness estimation by using a polychromatic X-ray laboratory source.

Purpose: Propagation and speckle-based techniques allow reconstruction of the phase of an X-ray beam with a simple experimental setup. Furthermore, their implementation is feasible using low-coherence laboratory X-ray sources. We investigate different approaches to include X-ray polychromaticity for sample thickness recovery using such techniques.

Approach: Single-shot Paganin (PT) and Arhatari (AT) propagation-based and speckle-based (ST) techniques are considered. The radiation beam polychromaticity is addressed using three different averaging approaches. The emission-detection process is considered for modulating the X-ray beam spectrum. Reconstructed thickness of three nylon-6 fibers with diameters in the millimeter-range, placed at various object-detector distances are analyzed. In addition, the thickness of an in-house made breast phantom is recovered by using multi-material Paganin's technique (MPT) and compared with micro-CT data.

Results: The best quantitative result is obtained for the PT and ST combined with sample thickness averaging (TA) approach that involves individual thickness recovery for each X-ray spectral component and the smallest considered object-detector distance. The error in the recovered fiber diameters for both techniques is $<4\%$ , despite the higher noise level in ST images. All cases provide estimates of fiber diameter ratios with an error of 3% with respect to the nominal diameter ratios. The breast phantom thickness difference between MPT-TA and micro-CT is about 10%.

Conclusions: We demonstrate the single-shot PT-TA and ST-TA techniques feasibility for thickness recovery of millimeter-sized samples using polychromatic microfocus X-ray sources. The application of MPT-TA for thicker and multi-material samples is promising.