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

Abstract

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).

Phase retrieval problems in x-ray physics

“…the approximated source size. In this context, promising algorithms for the simultaneous reconstruction of the empty beam ι 0 and the object function by taking intensity measurements at several distances have been proposed recently [36,64]. Figures 2.7 and 2.8 also illustrate that in order to predict the reconstruction's quality the error value δ max has to be considered in relation to the hologram's contrast.…”

“…The following sections build up on the work that has been published by us in [36,48]. We study the validity of the product approximation in the detector plane in case of extended source sizes by providing a rigorous error estimate which also identifies the relevant experimental parameters.…”

Coherent X-ray diffractive imaging on the single-cell-level of microbial samples

“…Using equation (3.132), the holographic data of the object is obtained by dividing the raw data I( ρ , z 02 ) by the empty beam intensity I e [12 14, 94, 95, 115, 166] I h ≈ I( ρ , z 02 )/I e . As shown in [115], the accuracy of the empty beam division crucially depends on the smoothness of the illuminating beam. Here, it should be noted that the far-eld of the waveguides is indeed very smooth (cf.…”

X-Ray Near-Field Holography: Beyond Idealized Assumptions of the Probe

“…The division is carried out in intensities, which obviously can not be correct, since it neglects the complex-valued nature of the wave field. The error of this division has been previously illustrated [53] and mathematically analyzed [54]. In the case of a point source the division is correct, but not for extended sources.…”