Signal and noise transfer properties of photoelectric interactions in diagnostic x-ray imaging detectors

Image quality in diagnostic x-ray imaging is ultimately limited by the statistical properties governing how, and where, x-ray energy is deposited in a detector. This in turn depends on the physics of the underlying x-ray interactions. In the diagnostic energy range (10-100 keV), most of the energy deposited in a detector is through photoelectric interactions. We present a theoretical model of the photoelectric effect that specifically addresses the statistical nature of energy absorption by photoelectrons, K and L characteristic x rays, and Auger electrons. A cascaded-systems approach is used that employs a complex structure of parallel cascades to describe signal and noise transfer through the photoelectric effect in terms of the modulation transfer function, Wiener noise power spectrum, and detective quantum efficiency (DQE). The model was evaluated by comparing results with Monte Carlo calculations for x-ray converters based on amorphous selenium (a-Se) and lead (Pb), representing both low and high-Z materials. When electron transport considerations can be neglected, excellent agreement (within 3%) is obtained for each metric over the entire diagnostic energy range in both a-Se and Pb detectors up to 30 cycles/mm, the highest frequency tested. The cascaded model overstates the DQE when the electron range cannot be ignored. This occurs at approximately two cycles/mm in a-Se at an incident photon energy of 80 keV, whereas in Pb, excellent agreement is obtained for the DQE over the entire diagnostic energy range. However, within the context of mammography (20 keV) and micro-computed tomography (40 keV), the effects of electron transport on the DQE are negligible compared to fluorescence reabsorption, which can lead to decreases of up to 30% and 20% in a-Se and Pb, respectively, at 20 keV; and 10% and 5%, respectively, at 40 keV. It is shown that when Swank noise is identified in a Fourier model, the Swank factor must be frequency dependent. This factor decreases quickly with frequency, and in the case of a-Se and Pb, decreases by up to a factor of 3 at five cycles/mm immediately above the K edge. The frequency-dependent Swank factor is also equivalent to what we call the "photoelectric DQE," which describes signal and noise transfer through photoelectric interactions.