Optimum momentum transfer arguments for x‐ray forward scatter imaging

In our research program we have shown through modeling, related numerical calculations, and experimental measurements that there exists a potential use of scattered radiation for medical x‐ray imaging. Each incident photon of wavelength λ which scatters at a small angle θ with respect to its initial direction of travel has a change in momentum characterized by the photon momentum transfer argumentx = λ− 1  sin ( θ / 2 ) . In this work, we show that in order to maximize the signal‐to‐noise ratio (SNR) obtained with scattered x rays, one must detect photons with specific x values. Using a photon counting detector to distinguish 2‐cm‐thick polymethyl methacrylate and nylon targets situated within a 15‐cm‐diam spherical water phantom with an 80 kV beam yields experimentally SNR /K c air= 12.8 ± 0.2   ( mJ / kg ) − 1 / 2when using the photons between x ̄ = 0.5 and 0 . 7   nm − 1. Here K c airis the air collision kerma and the average momentum transfer argument, x ̄ , is calculated by weighting x by the incident photon fluence distribution. The model predicts a value of SNR /K c air= 12.9   ( mJ / kg ) − 1 / 2 . If we choose to form the signal with the range in x ̄ extended to be from 0.5 to 1 . 0   nm − 1then, despite the detection of more scattered photons, experimentally SNR /K c airdecreases by 38% to 7.9 ± 0.3   (mJ / kg )− 1 / 2. The model predicts a value of 9.46   (mJ / kg )− 1 / 2. Results for energy integrating detectors are in general similar to those for photon counters, but there exist cases where a significant decrease in SNR can occur. For example, for measurements in air with the two plastics at θ = 3 ° the SNR for an energy integrator was found to be 52% that of a photon counter. Numerical calculations predict that the effects of spectral blur can be significant when a narrow angular range is used for detection. Preliminary numerical predictions for breast tissues suggest a potential use of x‐ray scatter in the field of mammography.