Fig. 3.

Images and profiles of paper wedge phantom with (a)+(e) attenuation contrast, (b)+(f) dark-field contrast, (c)+(g) single-shot hybrid contrast using Eq. (14) with $\gamma =551{\mathrm{m}\mathrm{r}\mathrm{a}\mathrm{d}}^{-2}$ , and (d)+(h) the absolute value of the refraction signal, $|\mathrm{\Delta }{\overline{x}}_{\mathrm{r}\mathrm{e}\mathrm{f}}|$ . Profiles are taken by averaging all rows within the green ROI, with error bars taken as the standard deviation in the y-axis of the image, and plot horizontal axes correspond to the x-coordinates of the image. The sub-resolution features of the paper fibers are resolved in (i) using a light microscope. Additionally in (j) we show the signal retrieved using Eq. (7) with $t=1$ alongside the conventional dark-field signal, where a large discrepancy is found and the signal is overestimated due to the non-negligible contribution from attenuation that is not accounted for. We show the same in $(k)$ for the linearized single-shot hybrid contrast, where a linear signal that is much closer to the conventional dark-field signal is retrieved.