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Recently, an approach to tomography with extended anisotropic radiation sources has been introduced, which helps to overcome the challenges resulting from the low brilliance typical for x-ray laboratory sources. The method is based on the three-dimensional Radon transform (3DRT) which uses planar integrals instead of line integrals. By extending the source spot in one direction, more photons can contribute to image formation while the impact on the resolution is minor with the 3DRT approach. In this work we present a more comprehensive description of the method, derive quantitative error estimates for the extraction of these planar integrals measured with a finite source size, and validate the 3DRT scheme by analytical theory. We also demonstrate a simple and efficient reconstruction algorithm for 3D Radon data. Finally, we further substantiate the method with experimental results obtained at a microfocus x-ray source with an extremely anisotropic source spot.

Tomography with extended sources: Theory, error estimates, and a reconstruction algorithm