How to measure the volume fraction of granular assemblies using x-ray radiography

When investigating dynamical processes in granular systems, it is frequently necessary to measure the time-resolved local material density. Recently, x-ray radiography facilities became available in many laboratories and can be used to measure the volume fraction via the attenuation of x-ray radiation along the beam direction. Naïve application of the Beer-Lambert law yields, however, unacceptably large systematic errors due to beam hardening. We present a calibration protocol which allows to reliably measure the local volume fraction based exclusively on reference measurement of known packing fraction.