Is there any paper or description available about measuring the thickness of a metal foil (or something similar) of several micrometers thickness, by using only one photo (i.e. a 2D scan) with an X-ray (CT) scanner?
The thickness of the foil should be directly related to the X-ray absorption by using the Lambert-Beer law, i.e. I = I0 exp (– Ax), in which x is the thickness, I0 is the incoming intensity, I is the resulting intensity at a certain thickness, and A is a calibration constant.
Dear Tijmen,
the calibration constant 'A' in the Lambert-Beer law is only a constant when monochromatic radiation is used.
The radiation emerging from an x-ray tube however is far from being monochromatic. When increasing the thickness of a sample the radiation gets harder and harder; i.e. the low energy photons of the x-ray beam are more efficiently attenuated compared to the high energy ones.
In your case 'A' is also dependent on 'x' (thickness of the sample).
A way out of this dilemma is a calibration using a series of samples of different thicknesses.
An elegant way to do this is to use a wedge calibration sample of same material composition compared to your sample and known wedge geometry. This has to be placed close to your sample at the same distance to the source
When comparing the gray value of your sample to the gray values of your wedge, you can see which part of the wedge has got the same gray value. The geometry of the wedge now tells you the thickness of your sample.
You can do this is a 2D set up (fluoroscpy set up).
When using a CT you have to use the projection(s) taken perpendicular to the sample and wedge arrangement. CT data reconstruction makes no sense here, because the result will be a 2D/3D distribution of mean µ values *). Thicknesses do not show up.
*) Often 'normalized' into HU (Hounsfield units)
Dear Gerhard Martens ,
Many thanks for your reply. I already feared that this would be the case, and I was actually also thinking of using some sort of a wedge to check the quality of the measurement.
Do you have any experience with these kinds of calibrations and/or measurements?
Thanks!
I have no experience which this kind of calibrations.
I have done thickness measurements (or mass coverages) in the x-ray regime by using a classical attenuation set up acoording the Lambert Beer law.
Source is an x-ray tube and detector is a energy resolving detector (e.g. HPGe or Si(Li)). The constant 'A' can be taken from published x-ray attenuation data ( e.g. NIST XCOM).
A very elegant way here is to use the relative step height of the attenuation edge of the material. Using this way you can omit the measurement of the primary beam, which often is a critical one due to high photon flux and related dead time and pile up effects of the detector.
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