A generalised algorithm for spectral reconstruction in Compton spectroscopy with corrections for coherent scattering.

Reconstruction of primary-photon energy spectra from pulse-height distributions obtained in a Compton spectrometer has earlier been performed under the assumption that coherent scattering in the scatterer is negligible. This holds for most clinical x-ray units operated in the range 40-150 kV. In mammography, and to some extent in dental radiography, the relatively high frequency of low-energy photons (less than 30 keV) in the primary beam makes it necessary to extend the algorithms to allow for significant contribution of coherent scattering. This extension is performed as a perturbation calculation to the algorithms developed earlier in which a modified Klein-Nishina scattering cross section was taken as the total scattering cross section. Comparison with energy spectra measured in the primary beam indicates that the Compton spectrometer with the extended algorithm is an excellent instrument for measuring energy spectra with energies down to a few keV.

Compton spectroscopy in the diagnostic x-ray energy range. II. Effects of scattering material and energy resolution.

The overall performance of a Compton spectrometer and, in particular, its energy resolution are investigated both experimentally and theoretically for different scattering materials. Using low-Z (less than or equal to 8) scatterers of moderate sizes (scatterer diameter d less than or equal to 5 mm), there are negligible disturbances due to coherent and/or multiple scattering at 90 degrees scattering angle and photon energies above 20 keV. Two factors contribute to decreasing the energy resolution compared with that in direct measurements: (i) the velocity distribution of the electrons in the scatterer and (ii) the scattering geometry. Of these, (i) is dominant for photon energies less than or equal to 100 keV. The optimal scattering material is a metal of as low Z as possible, i.e. beryllium. However, polyethylene and lucite are normally sufficiently good scatterers. The scattering geometry may become the dominating factor decreasing energy resolution at high photon energies hv greater than or equal to 150 keV.

A Compton scattering spectrometer for determining X-ray photon energy spectra.

With the use of more sophisticated diagnostic technologies it is becoming increasingly important to know the energy spectra of the primary photons from clinical x-ray tubes. At the high fluence rates used under working conditions, it is necessary to greatly reduce the number of photons to the detector per unit time in order to avoid pulse pile-up. The Compton scattering method is very suitable for this reduction and hence it has been further developed in this work in the primary-photon energy range 20-200 keV. The movement of the electrons in the scattering target causes an energy broadening of the Compton scattered photons. This broadening results in a decreased energy resolution, which is particularly seen as a smearing out of the characteristic x-ray peaks of the anode material. Comparison between the spectrum obtained using a Compton spectrometer and unfolded with our reconstruction and the spectrum measured directly in the primary beam shows very good agreement even though relatively simple reconstruction algorithms have been used.

Calculation of scattering cross sections for increased accuracy in diagnostic radiology. I. Energy broadening of Compton-scattered photons.

In this work, scattering cross sections differential with respect to both the scattering angle and the energy of the scattered photon are derived in the relativistic impulse approximation for the light elements H, Be, and Al, and photon energies between 30 and 200 keV. The energy broadening of the scattered photons reflects the momentum distribution of the target electrons. It increases with both increasing atomic number of the scatterer and with scattering angle. Even in light elements, the energy broadening is comparable with the intrinsic energy resolution of modern Ge spectrometers. In reconstructing primary photon energy spectra by means of a Ge spectrometer and Compton scattering techniques, i.e., by measuring the photons incoherently scattered at a given angle, the energy resolution is markedly impaired compared to direct measurements in the primary beam. This is usually explained as an effect of the nonzero acceptance angle of the detector. It is shown, however, that the fundamental energy broadening of the scattered photons is alone sufficient as an explanation. The Compton scattering technique is valuable in determining energy spectra in clinical situations. Aspects of its optimal performance are discussed. The commonly used scattering angle of 90 degrees seems adequate. At small scattering angles, the incoherent-scattering cross section is badly known due to electron-electron interactions and, for photon energies less than 100 keV, coherent scattering contributes appreciably to the total scattering even in media of low atomic number. In cases where coherent scattering dominates and where the energy degradation of the incoherently scattered photons is small compared to the energy resolution of the spectrometer, the reconstruction is simplified. The double-differential cross sections derived can be used to simplify calculations of the Compton component of the mass-energy absorption coefficient.