Validity of the empty-beam correction in near-field imaging

Abstract

Extended wavefronts are used for coherent full field imaging of objects based on solving the inverse Fresnel diffraction problem. To this end, the conventional data correction step is given by division of the recorded object image by the intensity pattern of the empty beam. This division of intensities in the detection plane is a rather crude approximation for the separation of the complex valued object and probing fields. Here we present a quantitative error estimate, along with its mathematical proof, and confirm the prediction with numerical simulations. Finally the problem is illustrated with experimental results. PACS number(s): 42.40.−i, 42.30.Wb, 87.59.−e u 0 (r ) := u(r ,0) = ι(r ,0)O(r ), r = (x,y) ∈ R 2 .

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.…”

“…In conventional NFH, when dealing with distorted probes the approximative hologram of O [54] is recovered by flat-field correction and then used as input for a phase reconstruction algorithm. In contrast to this standard approach we make use of the two available measurements in an iterative reconstruction scheme, cf.…”

“…In previous studies, we have shown that under these conditions the commonly used standard flat-field correction, i.e. the division of measured intensities with the specimen in the beam by measured intensities without specimen in the beam, induces artifacts [ 53,54], as illustrated in Fig. 5.…”

“…In order to process the raw images in propagation imaging, before phase retrieval is applied, idealizing assumptions are made on the beam, such as point-source emission or distortion-free wavefront. The validity of such assumptions has recently been investigated, showing that they lead to reduced resolution and image quality [53,54]. Aiming at more appropriate schemes to treat the data, recent work has introduced the concept of simultaneous reconstruction of probe and object to near-field (propagation) imaging [13,14].…”

Phase retrieval problems in x-ray physics

“…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.…”