Abstract
.X-ray cone-beam holotomography of unstained tissue from the human central nervous system reveals details down to subcellular length scales. This visualization of variations in the electron density of the sample is based on phase-contrast techniques using intensities formed by self-interference of the beam between object and detector. Phase retrieval inverts diffraction and overcomes the phase problem by constraints such as several measurements at different Fresnel numbers for a single projection. Therefore, the object-to-detector distance (defocus) can be varied. However, for cone-beam geometry, changing defocus changes magnification, which can be problematic in view of image processing and resolution. Alternatively, the photon energy can be altered (multi-E). Far from absorption edges, multi-E data yield the wavelength-independent electron density. We present the multi-E holotomography at the Göttingen Instrument for Nano-Imaging with X-Rays (GINIX) setup of the P10 beamline at Deutsches Elektronen-Synchrotron. The instrument is based on a combined optics of elliptical mirrors and an x-ray waveguide positioned in the focal plane for further coherence, spatial filtering, and high numerical aperture. Previous results showed the suitability of this instrument for nanoscale tomography of unstained brain tissue. We demonstrate that upon energy variation, the focal spot is stable enough for imaging. To this end, a double-crystal monochromator and automated alignment routines are required. Three tomograms of human brain tissue were recorded and jointly analyzed using phase retrieval based on the contrast transfer function formalism generalized to multiple photon energies. Variations of the electron density of the sample are successfully reconstructed.
Highlights
In the hard x-ray regime with multi-keV photon energy E, variations in the index of refraction n 1⁄4 1 − δ þ iβ are dominated by δ, and the imaginary contribution β accounting for absorption becomes extremely weak
The main interaction of light exploitable for imaging is related to the local phase shifts of the incoming radiation in proportion to the amount and electron density of the material traversed by the beam
For the holographic regime and based on the contrast transfer function (CTF), a phase retrieval algorithm taking different energies into account was proposed by Kashyap et al.[20]
Summary
In the hard x-ray regime with multi-keV photon energy E, variations in the index of refraction n 1⁄4 1 − δ þ iβ are dominated by δ, and the imaginary contribution β accounting for absorption becomes extremely weak. For the direct contrast or edge enhancement regime, this has been explored by Gureyev et al.[21] For the holographic regime and based on the CTF, a phase retrieval algorithm taking different energies into account was proposed by Kashyap et al.[20] there exist iterative techniques for the multi-E setting.[22,23] Since geometrical magnification remains constant, image registration and interpolation steps are not necessary.[20,21] On top, by varying the wavelength, one probes the response of the sample material with respect to different photon energies.
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