X-Ray tomography with anisotropic sources

For classical computed tomography (CT), especially for analytical CT, point-like radiation sources are necessary. The invention presented here, however, allows tomographic measurements using anisotropic radiation sources. Image reconstruction can be performed by means of an inverse 3D radon transform. One advantage of the new device is that significantly cheaper laboratory radiation sources can be used. Furthermore, the fluence of the source can be used completely.


The achievable resolution for classical CT measurements is limited by the size of the radiation source. To obtain a high resolution, collimated and focused synchrotron radiation can be used. Unfortunately, this is expensive and neither flexible in terms of time nor location. The typical alternative is to use cheaper laboratory sources and to limit the size of the emitted radiation beams through collimating grids. However, this restriction of the beam reduces the usable source fluence. Consequently, the necessary measurement time increases and the singal-to-noise ratio deteriorates.

Our Solution

Gerbil cochlea. Left: Acquired X-ray projection, middle: re-projection of the reconstructed sample volume, right: Slice through the reconstructed sample volume. (Source: Malte Vassholz)

The newly developed device for tomographic measurements comprises a sample holder that is designed to rotate the sample around two axis instead of only one axis as usual. Alternatively, one or both sample rotations can be replaced by a joined rotation of radiation source and detector. Hence, the dimensions of the radiation source can now be significantly larger in one direction lateral to the propagation direction than in the second lateral direction, without having a negative impact on the resolution. This anisotropy of the source is compensated by the rotation around two axes which enables different image reconstruction methods. For example the inverse 3D radon transform can be used instead of the 2D radon transform.
For this method, only the size of the source along one of the two lateral dimensions is relevant for the resolution. It is thus possible to use cheaper laboratory sources like for example X-ray tubes. Since with this new procedure it is no longer necessary to restrict the beam, the entire source fluence is available for the measurement. As a result, less measurement time per rotation step is required. Additional rotation steps are introduced by movement around the second rotation axis. However, the overall measurement time remains the same because each single position can be acquired in a shorter amount of time.
Additional advantages of this new procedure can be expected for the sector of local tomography where only few regions of interest are to be acquired with high resolution. Here the inverse 3D radon transform shows less artifacts than the conventional 2D radon transform.


  • Cheaper and smaller radiation sources usable
  • Higher portion of the source fluence usable
  • Independent from synchroton radiation
  • Local tomography possible
  • High spatial coherence possible for phase-contrast measurement


The most promising field of application is the analytical tomography where this new method shows all its advantages. Furthermore, medical applications are possible.

This method can be applied with different types of radiation, X-ray as well as electron or neutron beams can be used. Alongside the absorption and phase contrast measurements other observables, like for example fluorescence, can be used.

Development Status

The method has been successfully implemented and the according device and sample holder have been constructed.

Patent Status

German patent application: DE102015215323A1
US patent application: US2018164232A1

Applicant: Georg-August-Universität Göttingen Stiftung Öffentlichen Rechts


Tomography with extended sources: Theory, error estimates, and a reconstruction algorithm
L. M. Lohse, M. Vassholz, T. Salditt
Phys. Rev. A (2017), 96, 063804

New X-Ray Tomography Method Based on the 3D Radon Transform Compatible with Anisotropic Sources
M. Vassholz, B. Koberstein-Schwarz, A. Ruhlandt, M. Krenkel, T. Salditt
Phys. Rev. Lett. (2016), 116, 088101


Dr. Markus Muchow
Patent Manager Physics & Technology
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Reference: MM-1788-SUG

Tags: Laser physics and optics


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