Phase Retrieval and Tomographic Reconstruction in X-ray Near-field Diffractive Imaging: Inverse Problems at Work - An Experimentalist’s View

Tim Salditt
Georg-August-Universität zu Göttingen

Tim Salditt, Institut für Röntgenphysik, Universität Göttingen, and Collaborative Research Center “Mathematics of Inverse Problems” of the German Science Foundation

X-rays can provide information about the structure of matter, on multiple length scales from bulk materials to nanoscale devices, from organs to organelle, from the organism to macromolecule. Due to the widespread lack of suitable lenses, the majority of investigations are rather indirect – apart from classical shadow radiography perhaps. While diffraction problems have been solved since long, the modern era has brought about lensless coherent imaging with X-rays, down to the nanoscale. How much more room for improvement is offered by full exploitation of indirect measurements, sophisticated analysis and high performance algorithms, and how far can this go? In this talk we discuss image formation and reconstruction in the optical far- and near-field, the limits imposed by partial coherence, optical constants, and object constraints, the role of imperfect lenses and photon correlations. We show how solutions and algorithms of mathematics of inverse problems [1-3] help us to meet the challenges of phase retrieval, tomographic reconstruction, and more generally image processing of bulky data. All to the benefit of ambitious imaging projects such as mapping the human brain [4,6] of fighting infectious diseases [6].


[1] T. Salditt, A. Egner and R. D. Luke (Eds.)
Nanoscale Photonic Imaging
Springer Nature (2020), TAP, 134, Open Access Book

[2] L. M. Lohse, A.-L. Robisch, M. Töpperwien, S. Maretzke, M. Krenkel, J. Hagemann and T. Salditt
A phase-retrieval toolbox for X-ray holography and tomography
Journal of Synchrotron Radiation (2020), 27, 3

[3] S. Huhn, L.M. Lohse, J. Lucht, T. Salditt
Fast algorithms for nonlinear and constrained phase retrieval in near-field X-ray holography based on Tikhonov regularization - arXiv preprint arXiv:2205.01099 (2022)

[4] M. Eckermann, B. Schmitzer, F. van der Meer, J. Franz, O. Hansen, C. Stadelmann and T. Salditt
Three-dimensional virtual histology of the human hippocampus based on phase-contrast computed tomography
Proc. Natl. Acad. Sci. (2021), 118, 48, e2113835118

[5] M. Eckermann, J. Frohn, M. Reichardt, M. Osterhoff, M. Sprung, F. Westermeier, A.Tzankov, C. Werlein, M. Kuehnel, D. Jonigk and T. Salditt
3d Virtual Patho-Histology of Lung Tissue from Covid-19 Patients based on Phase Contrast X-ray Tomography
eLife (2020), 9:e60408

[6] M. Reichardt, P.M. Jensen, V.A. Dahl, A.B. Dahl, M. Ackermann, H. Shah, F. Länger, C. Werlein, M.P. Kuehnel, D. Jonigk and T. Salditt
3D virtual histopathology of cardiac tissue from Covid-19 patients based on phase-contrast X-ray tomography
eLife (2021), 10:e71359

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