Research

Algorithms for ptychography

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One main objective of our group is the development of various data analysis tools and reconstruction algorithms for advanced X-ray imaging methods. An important example is the phase retrieval problem inherent to ptychography, which we solve using iterative techniques. One successful approach is the difference map[bibcite key=Thibault2009], a meta-algorithm that can solve a wide variety of constraint-based problems. Another method, most often used as a refinement step, is based on maximum likelihood principles[bibcite key=Thibault2012]. Both methods have been implemented in our open-source python package ptypy[bibcite key=Enders2016a].

Top: Schematic of the setup used for the first demonstration of mixed-state reconstruction. By opening the entrance slits wider than the transverse coherence length, we have demonstrated the success of the mixed-state approach (lower left) compared to the usual reconstruction method (lower right)

Top: Schematic of the setup used for the first demonstration of mixed-state reconstruction. By opening the entrance slits wider than the transverse coherence length, we have demonstrated the success of the mixed-state approach (lower left) compared to the usual reconstruction method (lower right)

In the last years it became clear that the degree of coherence to carry out a ptychography experiment could be much lower than initially assumed. Drawing from a formalism developed in the field of quantum tomography, we have demonstrated that the incoming X-ray photons can be accurately represented as a state mixture, which is then reconstructed along with the image of the sample[bibcite key=Thibault2013]. This approach has proven beneficial for multiple sources of data degradation, such as detector point spread[bibcite key=Enders2014] or blurring caused by sample motion[bibcite key=Pelz2014].

We have also demonstrated with simulations that the mixed state formalism can be applied to decoherence effects caused by the sample itself. This feature opens the door to a wealth of new investigation directions, for instance to image fluctuations that have typical time scales orders of magnitude faster than the shortest exposure times accessible at synchrotron facilities.

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Ptychographic nano-CT

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The result of the first ptychographic nano-CT demonstration, done at the cSAXS beamline (Swiss Light Source). The sample is a small piece of mouse femure 30 μm in diameter.

The result of the first ptychographic nano-CT demonstration, done at the cSAXS beamline (Swiss Light Source). The sample is a small piece of mouse femure 30 μm in diameter.

Ptychography is a lensless imaging technique that produce quantitative maps of a sample’s transmission function from multiple far-field diffraction measurements. First developed in the 70s to improve the resolution of transmission electron microscopy, it has got tremendous success within the last decade as a synchrotron-based X-ray microscopy technique.

The 3D extension of the technique appeared soon after its demonstration in 2D. This step is conceptually simple but technically rather tricky, since it requires stable and reproducible translation stage down to the nanometre scale, a fast photon detector, and various adaptations to the reconstruction algorithms. We like to call the result “ptychography nano-CT” or simpy “tomo-ptychography”. This technique is applied or planned at many dedicated instruments in most synchrotron facilities.

Our group was part of the pioneering team for ptychographic nano-CT[bibcite key=Dierolf2010a], and is still active in the development and improvement of the technique[bibcite key=Zanette2015].

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Near-field ptychography

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Results from the first near-field ptychography demonstration. Top right: a standard Fresnel diffraction pattern. Top left: the diffraction pattern after scrambling the incident X-ray wavefront using a static diffuser. Bottom: the NF ptychographic reconstructions, showing the beneficial effects of the diffuser for phase retrieval.

Results from the first near-field ptychography demonstration. Top right: a standard Fresnel diffraction pattern. Top left: the diffraction pattern after scrambling the incident X-ray wavefront using a static diffuser. Bottom: the NF ptychographic reconstructions, showing the beneficial effects of the diffuser for phase retrieval.

Near-field ptychography is a recent and exciting development in X-ray phase-contrast imaging. The method applies the reconstruction principles of far-field ptychography to near-field Fresnel diffraction patterns, as those typically collected at inline holography setups. Compared to its far-field brother, NF ptychography can cover larger field of views in fewer measurements, and uses better the limited dynamic range of typical detectors. Thanks to the strong mixing produced by a diffuser placed in the beam, the phase retrieval step is more robust and reliable than other approaches used in digital inline holography.

The picture above was the first test, from measurements carried out at the ID22 beamline of ESRF, in a collaboration with Peter Cloetens and the Pfeiffer group at TUM[bibcite key=Stockmar2013].

Further demontration of the technique have highlighted the strength of the technique for strongly absorbing and phase-shifting samples [bibcite key=Stockmar2015] and for quantitative tomography [bibcite key=Stockmar2015b].

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