where K is a constant, p and Z are the density and the atomic number of the investigated material gia © 
and E is the energy of the incident photons. located In 
This attenuation law explains the contrast observed in the x-ray radiograph of a bulky material Synchrotl0 
because each point of a detector placed behind the sample is situated in front of a different path. If eles 
the material is heterogeneous, the integral value of u(x,y,z) varies also with y and z. the elects” 
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X-ray Tomography features (2 
o Very 
The drawback of radiography is that a high amount of information is projected on one single plane, py: 
and the resulting image can be difficult to interpret if the number of microstructural features along depend 
the thickness of the sample is important. Tomography overcomes this drawback by combining the SA OB 
information of a high number of such radiographs, each being taken with a different orientation of fra 
the sample in front of the detector. If the angular step between each radiograph is small enough, it is wii 
possible from the complete set of radiographs, to recalculate the local value of u(x,y,z) in each point fo 
of the sample. This reconstruction is performed thanks to an appropriate software based on the | N 
filtered back-projection algorithm described for instance in (1). ER . 
Different setups can be used. They all contain a source, a rotation stage on which the object is fixed, The D - 
and a x-ray detector. The easiest way of getting digitized images is to use directly a two- (Des 
dimensional radioscopic detector composed of a screen transforming the x-rays into visible light shel 2 
which are then transferred by appropriate optic lenses to a cooled CCD camera (lines and rows of rsd 
sensitive elements). The common geometric constraint of the different setups is that the axis of ~~ 5% 
rotation of the sample must be parallel to the plane of the detector and its image must be aligned 
with one of the colums of the CCD (preferably the central column). The crucial point in applying 
tomography to materials science is the achievable spatial resolution. Its limit value is mainly 
governed by the available photon flux at the level of the sample and by the setup as it will be 
described in the two next sections. For medicine tomography (medical scanner) this limit resolution 
if of the order of 300 pm. Materials scientists whishing to see and distinguish features with a size of 
the order of 1 um had to develop appropriate tools. 
Medium resolution microtomography 
For a limit resolution of the order of 8 um (medium resolution), a cone beam system can be used 
with a classical microfocus x-ray tube as the source. Such a device has been for instance assembled 
in the CNDRI laboratory at INSA de Lyon. With this diverging geometry (see figure 1), the 
magnification can be easily varied by changing the position of the sample in the space between the 
source and the detector. The limit resolution is there due to the size of the micro-focus which 
introduces blur in the projected image. This size has a minimum value because if the source size . 
gets too small, the flux at the level of the sample becomes so low that the acquisition time required ! qi 
to record a single radiograph is too long for a realistic analysis. In such a laboratory setup a © * 
polychromatic source is used in order to keep the acquisition time acceptable. This may introduce (De 
artefacts due to beam-hardening and does not allow to reconstruct quantitatively the absorption 
coefficient u. Phase co 
High resolution microtomography LES 
Ia 
We emphasized in the previous section that the setups using x-ray tubes are limited because of the Mere 
flux delivered by this kind of source. The best quality images in terms of signal to noise ratio and Between 
20