This work presents the x-ray extended range technique for measuring x-ray mass attenuation coefficients. This technique includes the use of multiple foil attenuators at each energy investigated, allowing independent tests of detector linearity and of the harmonic contributions to the monochromated synchrotron beam. Measurements over a wide energy range allow the uncertainty of local foil thickness to be minimized by the calibration of thin sample measurements to those of thick samples. The use of an extended criterion for sample thickness selection allows direct determination of dominant systematics, with an improvement of accuracies compared to previous measurements by up to factors of 20. Resulting accuracies for attenuation coefficients of copper (8.84 to 20 keV) are 0.27–0.5 %, with reproducibility of 0.02%. We also extract the imaginary component of the form factor from the data with the same accuracy. Results are compared to theoretical calculations near and away from the absorption edge. The accuracy challenges available theoretical calculations, and observed discrepancies of 10% between current theory and experiments can now be addressed.

• Received 27 June 2001

DOI:https://doi.org/10.1103/PhysRevA.64.062506