Abstract
For iterative phase retrieval algorithms in near field x-ray propagation imaging experiments with a single distance measurement, it is indispensable to have a strong constraint based on a priori information about the specimen; for example, information about the specimen's support. Recently, Loock and Plonka proposed to use the a priori information that the exit wave is sparsely represented in a certain directional representation system, a so-called shearlet system. In this work, we extend this approach to complex-valued signals by applying the new shearlet constraint to amplitude and phase separately. Further, we demonstrate its applicability to experimental data.
Highlights
The first observation of propagation-based phase contrast in the x-ray regime some 20 years ago at the European Synchrotron Radiation Facility (ESRF, Grenoble) [1, 2] has started a considerable activity in developing this lens-less full field imaging approach to resolve micro- and nanostructures in the interior of specimens [3,4,5]
For iterative phase retrieval algorithms in near field x-ray propagation imaging experiments with a single distance measurement, it is indispensable to have a strong constraint based on a priori information about the specimen; for example, information about the specimen’s support
The a priori information that an object transmission function may be sparsely represented in a certain representation system can be advantageously used for near field phase retrieval
Summary
The first observation of propagation-based phase contrast in the x-ray regime some 20 years ago at the European Synchrotron Radiation Facility (ESRF, Grenoble) [1, 2] has started a considerable activity in developing this lens-less full field imaging approach to resolve micro- and nanostructures in the interior of specimens [3,4,5]. By allowing the transmitted wave field (the so-called exit wave field) to freely propagate between the specimen and the detector (at distance z), the induced phase variations are transformed into intensity variations in such a way that the detected intensity distribution is a function of both the amplitude and the phase of the exit wave field, see Fig. 1(a) for the experimental setup By this means, x-ray propagation imaging is able to extract and visualize information about both β and δ of the analyzed specimen. For phase retrieval in (far field) coherent diffractive imaging (CDI) iterative algorithms that make use of a priori information of the signal to be reconstructed represent an established strategy [14,15,16,17] Likewise, they have become a powerful tool in (near field) x-ray propagation imaging in the holographic regime [18,19,20,21].
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