Johannes Hagemann

Reconstruction of wave front and object for inline holography from a set of detection planes

We illustrate the errors inherent in the conventional empty beam correction of full field X-ray propagation imaging, i.e. the division of intensities in the detection plane measured with an object in the beam by the intensity pattern measured without the object, i.e. the empty beam intensity pattern. The error of this conventional approximation is controlled by the ratio of the source size to the smallest feature in the object, as is shown by numerical simulation. In a second step, we investigate how to overcome the flawed empty beam division by simultaneous reconstruction of the probing wavefront (probe) and of the object, based on measurements in several detection planes (multi-projection approach). The algorithmic scheme is demonstrated numerically and experimentally, using the defocus wavefront of the hard X-ray nanoprobe setup at the European Synchrotron Radiation Facility (ESRF).

Probe reconstruction for holographic X-ray imaging.

A comparison of different schemes for probe characterization of an X-ray nano-probe in a near-field imaging setting is presented.

The fluence–resolution relationship in holographic and coherent diffractive imaging

In this work the fluence efficiency of two coherent X-ray imaging techniques is studied by numerical experiments. The techniques surveyed are near-field holography and far-field diffraction imaging.

SciPAL: Expression Templates and Composition Closure Objects for High Performance Computational Physics with CUDA and OpenMP

We present SciPAL (scientific parallel algorithms library), a C++-based, hardware-independent open-source library. Its core is a domain-specific embedded language for numerical linear algebra. The main fields of application are finite element simulations, coherent optics and the solution of inverse problems. Using SciPAL algorithms can be stated in a mathematically intuitive way in terms of matrix and vector operations. Existing algorithms can easily be adapted to GPU-based computing by proper template specialization. Our library is compatible with the finite element library deal.II and provides a port of deal.IIs most frequently used linear algebra classes to CUDA (NVidias extension of the programming languages C and C++ for programming their GPUs). SciPALs operator-based API for BLAS operations particularly aims at simplifying the usage of NVidias CUBLAS. For non-BLAS array arithmetic SciPALs expression templates are able to generate CUDA kernels at compile time. We demonstrate the benefits of SciPAL using the iterative principal component analysis as example which is the core algorithm for the spike-sorting problem in neuroscience.

Reconstructing mode mixtures in the optical near-field.

We propose a reconstruction scheme for hard x-ray inline holography, a variant of propagation imaging, which is compatible with imaging conditions of partial (spatial) coherence. This is a relevant extension of current full-field phase contrast imaging, which requires full coherence. By the ability to reconstruct the coherent modes of the illumination (probe), as demonstrated here, the requirements of coherence filtering could be relaxed in many experimentally relevant settings. The proposed scheme is built on the mixed-state approach introduced in [Nature494, 68 (2013)], combined with multi-plane detection of extended wavefields [Opt. Commun.199, 65 (2001), Opt. Express22, 16571 (2014)]. Notably, the diversity necessary for the reconstruction is generated by acquiring measurements at different defocus positions of the detector. We show that we can recover the coherent mode structure and occupancy numbers of the partial coherent probe. Practically relevant quantities as the transversal coherence length can be computed from the reconstruction in a straightforward way.

Coherence-resolution relationship in holographic and coherent diffractive imaging

We study by numerical simulation how spatial coherence affects the reconstruction quality of images in coherent diffractive x-ray imaging. Using a conceptually simple, but computationally demanding approach, we have simulated diffraction data recorded under partial coherence, and then use the data for iterative reconstruction algorithms using a support constraint. By comparison of experimental regimes and parameters, we observe a significantly higher robustness against partially coherent illumination in the near-field compared to the far-field setting.

Phase retrieval for near-field X-ray imaging beyond linearisation or compact support

X-ray phase contrast imaging based on free space propagation relies on phase retrieval to obtain sharp images of micro- and nanoscale objects, with widespread applications in material science and biomedical research. For high resolution synchrotron experiments, phase retrieval is largely based on the single step reconstruction using the contrast transfer function approach (CTF), as introduced almost twenty years ago [Cloetens et al., Appl. Phys. Lett. 75, 2912 (1999)]. Notwithstanding its tremendous merits, this scheme makes stringent assumptions on the optical properties of the object, requiring, in particular, a weakly varying phase. In this work, we show how significant the loss in image quality becomes if these assumption are violated, and how phase retrieval can be easily improved by a simple scheme of alternating projections. Importantly, the approach demonstrated here uses the same input data and constraint sets as the conventional CTF-based phase retrieval, and is particularly well suited for the holographic regime.X-ray phase contrast imaging based on free space propagation relies on phase retrieval to obtain sharp images of micro- and nanoscale objects, with widespread applications in material science and biomedical research. For high resolution synchrotron experiments, phase retrieval is largely based on the single step reconstruction using the contrast transfer function approach (CTF), as introduced almost twenty years ago [Cloetens et al., Appl. Phys. Lett. 75, 2912 (1999)]. Notwithstanding its tremendous merits, this scheme makes stringent assumptions on the optical properties of the object, requiring, in particular, a weakly varying phase. In this work, we show how significant the loss in image quality becomes if these assumption are violated, and how phase retrieval can be easily improved by a simple scheme of alternating projections. Importantly, the approach demonstrated here uses the same input data and constraint sets as the conventional CTF-based phase retrieval, and is particularly well suited for the ...

Divide and update: towards single-shot object and probe retrieval for near-field holography.

We present a phase reconstruction scheme for X-ray near-field holographic imaging based on a separability constraint for probe and object. In order to achieve this, we have devised an algorithm which requires only two measurements - with and without an object in the beam. This scheme is advantageous if the standard flat-field correction fails and a full ptychographic dataset can not be acquired, since either object or probe are dynamic. The scheme is validated by numerical simulations and by a proof-of-concept experiment using highly focused undulator radiation of the beamline ID16a of the European Synchrotron Radiation Facility (ESRF).

Parallel statistical multiresolution estimation for image reconstruction.

We show that a careful parallelization of statistical multiresolution estimation (SMRE) improves the phase reconstruction in X-ray near-field holography. The central step in, and the computationally most expensive part of, SMRE methods is Dykstras algorithm. It projects a given vector onto the intersection of convex sets. We discuss its implementation on NVIDIAs compute unified device architecture (CUDA). Compared to a CPU implementation parallelized with OpenMP, our CUDA implementation is up to one order of magnitude faster. Our results show that a careful parallelization of Dykstras algorithm enables its use in large-scale statistical multiresolution analyses.