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).
Highlights
X-ray propagation full field imaging and tomography have become powerful imaging techniques, based on successful development of phase retrieval algorithms [1,2,3,4,5]
The exit wavefront and the complex-valued sample transmission function of the object O can be reconstructed from the intensity distribution in the detection plane at some distance z behind the object plane, based, for example, on the transport-of-intensity equation (TIE) or various iterative algorithms [1, 6, 7]
While this development has been driven by the brilliance and coherence of synchrotron radiation, to some extent the method can be translated to compact laboratory-scale μ-CT instruments, preserving fully quantitative reconstruction [13]
Summary
X-ray propagation full field imaging and tomography have become powerful imaging techniques, based on successful development of phase retrieval algorithms [1,2,3,4,5]. A wide spectrum of applications ranging from material science [8], paleontology [9], histology [10], small arthropod biology [11] has emerged, taking advantage of the unprecedented 3D imaging capability, including fast tomography applications of dynamic processes [12] While this development has been driven by the brilliance and coherence of synchrotron radiation, to some extent the method can be translated to compact laboratory-scale μ-CT instruments, preserving fully quantitative reconstruction [13]. In order to achieve higher spatial resolution, propagation imaging and tomography can be extended from the parallel beam case to quasi-spherical beams, allowing for adjustable geometric magnification [14,15,16] With this approach, projection micrographs and tomograms of biological cells [16, 17], tissues and small organisms [18] can be recorded with quantitative density contrast and pixel size below 50 nm
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