Hofmann R., Schober A., Hahn S., Moosmann J., Kashef J., Hertel M., Weinhardt V., Hanschke D., Helfen L., Salazar I.A.S., Guigay J.-P., Xiao X., Baumbach T.
in Optics Express, 24 (2016) 4331-4348. DOI:10.1364/OE.24.004331
© 2016 Optical Society of America.The interactions of a beam of hard and spatio-temporally coherent X-rays with a soft-matter sample primarily induce a transverse distribution of exit phase variations δφ (retardations or advancements in pieces of the wave front exiting the object compared to the incoming wave front) whose free-space propagation over a distance z gives rise to intensity contrast gz. For single-distance image detection and |δφ|<1 all-order-in-z phase-intensity contrast transfer is linear in df. Here we show that ideal coherence implies a decay of the (shot-)noise-to-signal ratio in gz and of the associated phase noise as z-1-2 and z-1, respectively. Limits on X-ray dose thus favor large values of z. We discuss how a phase-scaling symmetry, exact in the limit δφ → 0 and dynamically unbroken up to |δφ| 1, suggests a filtering of gz in Fourier space, preserving non-iterative quasi-linear phase retrieval for phase variations up to order unity if induced by multi-scale objects inducing phase variations δφ of a broad spatial frequency spectrum. Such an approach continues to be applicable under an assumed phase-attenuation duality. Using synchrotron radiation, ex and in vivo microtomography on frog embryos exemplifies improved resolution compared to a conventional single-distance phase-retrieval algorithm.