Patent Number: 
Section: claims

1. An X-ray computed tomography (=CT) apparatus, the apparatus comprising:an X-ray source emitting an X-ray beam or a divergent X-ray beam, along a beam axis;a stage for an object to be investigated with an attenuated X-ray beam;a filter element disposed between said X-ray source and said stage and attenuating said X-ray beam, said filter element having a spatially varying X-ray absorption capability along a cross direction which is perpendicular to both said beam axis and to a rotation axis, said spatially varying X-ray absorption capability exhibiting a maximum absorption along said cross direction at a zero position, wherein X-rays passing through said filter element at said zero position intersect said rotation axis;a 2D X-ray detector disposed downstream of said stage, said 2D X-ray detector having a detection area; anda gantry system structured to simultaneously rotate an entirety of said X-ray source, said filter element and said 2D X-ray detector about said rotation axis or structured to rotate said stage for the object about said rotation axis, wherein said rotation axis is perpendicular to said beam axis. 2. The CT apparatus of claim 1, wherein said filter element is made of a material exhibiting a higher absorption for low energy X-rays than for high energy X-rays. 3. The CT apparatus of claim 2, wherein said material exhibits an absorption coefficient for 5 keV X-rays which is at least 10 times larger or at least 50 times larger than an absorption coefficient for 40 keV X-rays. 4. The CT apparatus of claim 1, wherein said filter element is made of aluminum or of a material containing aluminum. 5. The CT apparatus of claim 1, wherein said filter elementhas a spatially varying thickness along said cross direction, with a maximum thickness at said zero position. 6. The CT apparatus of claim 5, wherein said filter element exhibits a thickness variation along said cross direction by a factor of 2 or more or by a factor of 5 or more, in an area of said filter element which shadows said detection area of said 2D X-ray detector. 7. The CT apparatus of claim 1, wherein said spatially varying X-ray absorption capability exhibits an absorption variation along said cross direction by a factor of 5 or more, a factor of 20 or more or a factor of 50 or more, in an area of said filter element which shadows said detection area of said 2D X-ray detector. 8. The CT apparatus of claim 1, wherein said X-ray absorption capability exhibits a monotonic decreasing absorption or a strict monotonic decreasing absorption, on both sides away from said zero position along said cross direction, in an area of said filter element which shadows said detection area of said 2D X-ray detector. 9. The CT apparatus of claim 1, wherein said spatially varying X-ray absorption capability exhibits at least approximately a Gaussian type distribution of absorption with respect to said cross direction, centered around said zero position, in an area of said filter element which shadows said detection area of said 2D X-ray detector. 10. The CT apparatus of claim 1, wherein said the X-ray source is a microfocus X-ray tube. 11. The CT apparatus of claim 10, wherein said the X-ray source has a tungsten anode. 12. The CT apparatus of claim 1, wherein the object to be investigated is located on said stage. 13. The CT apparatus of claim 12, wherein a longitudinal object orientation is along said rotation axis. 14. The CT apparatus of claim 1, wherein said stage is moveable along a longitudinal axis which is parallel to said rotation axis. 15. A method for using the CT apparatus of claim 1, wherein an object to be investigated is located on the stage and a plurality of projection images of the object are recorded with the 2D X-ray detector at different rotation positions of the gantry system and a dataset of cross-sections is generated by a back projection reconstruction algorithm from a dataset of projection images. 16. The method of claim 15, wherein a plurality of projection images of the object are also recorded at different movement positions of said stage along a longitudinal axis which is parallel to said rotation axis. 17. The method of claim 15, wherein object is a living animal of up to a size of a rat or a non-living object of up to that size.