Fast Fresnel propagation through a set of inclined reflecting planes applicable for X-ray imaging.

We present a fast and accurate method for wave propagation through a set of inclined reflecting planes. It is based on the coordinate transformation in reciprocal space leading to a diffraction integral, which can be calculated only by using two 2D Fast Fourier Transforms and one 2D interpolation. The method is numerically tested, and comparisons with standard methods show its superiority in both computational speed and accuracy. The direct application of this method is found in the X-ray phase contrast imaging using the Bragg magnifier-an optics consisting of crystals asymmetrically diffracting in Bragg geometry.

Phase retrieval for arbitrary Fresnel-like linear shift-invariant imaging systems suitable for tomography.

We present a generalization of the non-iterative phase retrieval in X-ray phase contrast imaging applicable for an arbitrary linear shift-invariant (LSI) imaging system with a non-negligible amount of free space propagation (termed as Fresnel-like). Our novel approach poses no restrictions on the propagation distance between optical elements of the system. In turn, the requirements are only demanded for the transfer function of the optical elements, which should be approximable by second-order Taylor polynomials. Furthermore, we show that the method can be conveniently used as an initial guess for iterative phase retrieval, resulting in faster convergence. The proposed approach is tested on synthetic and experimentally measured holograms obtained using a Bragg magnifier microscope - a representative of Fresnel-like LSI imaging systems. Finally, the algorithm is applied to a whole micro-tomographic scan of a biological specimen of a tardigrade, revealing morphological details at the spatial resolution of 300 nm - limiting resolution of the actual imaging system.

Estimation of PKCδ autophosphorylation in U87 MG glioma cells: combination of experimental, conceptual and numerical approaches.

Golgi apparatus (GA) is a center for lipid metabolism and the final target of ceramide pathway, which may result in apoptosis. In this work localization of highly hydrophobic hypericin is followed by time-resolved imaging of NBDC6 (fluorescent ceramide) in U87 MG glioma cells. Decrease of NBDC6 fluorescence lifetimes in cells indicates that hypericin can also follow this pathway. It is known that both, ceramide and hypericin can significantly influence protein kinase C (PKC) activity. Western blotting analysis shows increase of PKCδ autophosphorylation at Ser645 (p(S645)PKCδ) in glioma cells incubated with 500 nM hypericin and confocal-fluorescence microscopy distinguishes p(S645)PKCδ localization between GA related compartments and nucleus. Experimental and numerical methods are combined to study p(S645)PKCδ in U87 MG cell line. Image processing based on conceptual qualitative description is combined with numerical treatment via simple exponential saturation model which describes redistribution of p(S645)PKCδ between nucleus and GA related compartments after hypericin administration. These results suggest, that numerical methods can significantly improve quantification of biomacromolecules (p(S645)PKCδ) directly from the fluorescence images and such obtained outputs are complementary if not equal to typical used methods in biology.

Single-distance phase retrieval algorithm for Bragg Magnifier microscope.

We present an improved, single-distance phase retrieval algorithm applicable for holographic X-ray imaging of biological objects for an in-line germanium Bragg Magnifier Microscope (BMM). The proposed algorithm takes advantage of a modified shrink-wrap algorithm for phase objects, robust unwrapping algorithm as well as other reasonable constraints applied to the wavefield at the object and the detector plane. The performance of the algorithm is analyzed on phantom objects and the results are shown and discussed. We demonstrated the suitability of the algorithm for the phase retrieval on a more complex biological specimen Tardigrade, where we achieved successful phase retrieval from only a single hologram. The spatial resolution obtained by Fourier spectral power method for biological objects is ∼ 300 nm, the same value as obtained from the reconstructed test pattern. Our results achieved using the new algorithm confirmed the potential of BMM for in-vivo, dose-efficient single-shot imaging of biological objects.