Criticality in single-distance phase retrieval.

We investigate why in free-space propagation single-distance phase retrieval based on a modified contrast-transfer function of linearized Fresnel theory yields good results for moderately strong pure-phase objects. Upscaling phase-variations in the exit plane, the growth of maxima of the modulus of the Fourier transformed intensity contrast dominates the minima. Cutting out small regions around the latter thus keeps information loss due to nonlocal, nonlinear effects negligible. This quasiparticle approach breaks down at a critical upscaling where the positions of the minima start to move rapidly. We apply our results to X-ray data of an early-stage Xenopus (frog) embryo.