Full-foil x-ray mapping of integrated column density applied to the absolute determination of mass attenuation coefficients

Recent measurements of mass attenuation coefficients have identified the determination of the thickness of the absorbing specimen as the major limitation to the accuracy of the measurement. We present a technique for determining the mass attenuation coefficient with high accuracy. The technique uses the integral of the density along a column extending through the thickness of the absorber, which we term the integrated column density. Attenuation measurements mapped across the entire absorber are used to determine a relative map of the integrated column density. These relative measurements are then placed on an absolute scale by comparison with the average integrated column density and are used to determine the mass attenuation coefficient. This approach correctly treats variations in the integrated column density across the foil. We illustrate the technique with an absolute measurement of the x-ray mass attenuation coefficient of molybdenum using a synchrotron beam of energy 41.568 keV ± 0.005 keV. We obtain [ μ ρ ] = 11.6514 cm2 g−1 ± 0.0032 cm2 g−1, accurate to 0.028%—over one order of magnitude more accurate than any previous work. The full-foil technique used to determine the mass attenuation coefficient is used to determine an integrated column density profile of a sample to a precision of around 0.05% of the thickness of the absorber. We demonstrate the sensitivity of the technique by observing a periodic thickness variation of order 0.1 μm occurring over a 5 mm length scale on a nominally 50 μm thick molybdenum foil.