An energy-dispersive technique to measure x-ray coherent scattering form factors of amorphous materials

The material-dependent x-ray scattering properties of amorphous substances such as tissues and phantom materials used in imaging are determined by their scattering form factors, measured as a function of the momentum transfer argument, x. Incoherent scattering form factors, F(inc), are calculable for all values of x while coherent scattering form factors, F(coh), cannot be calculated except at large x because of their dependence on long-range order. As a result, measuring F(coh) is very important to the developing field of x-ray scatter imaging. Previous measurements of F(coh), based on crystallographic techniques, have shown significant variability, as these techniques are not optimal for amorphous materials. We have developed an energy-dispersive technique that uses a polychromatic x-ray beam and an energy-sensitive detector. We show that F(coh) can be measured directly, with no scaling parameters, by computing the ratio of two spectra: the first, measured at a given scattering angle and the second, the direct transmission spectrum with no scattering. Experiments have been constructed on this principle and used to measure F(coh) for water and polyethylene to explore the reliability of the technique. A 121 kVp x-ray spectrum and seven different scattering angles between 1.67 and 15.09 degrees were used, resulting in a measurable range of x between 0.5 and 9.5 nm(-1). These are the first measurements of F(coh) made without the need for a scaling factor. Resolution in x varies between 10% for small scattering angles and 2% for large scattering angles. Accuracy in F(coh) is shown to be strongly dependent on the precision of the experimental geometry and varies between 5% and 15%. Comparison with previous published measurements for water shows values of the average absolute relative difference between 8% and 14%.