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 lambda which scatters at a small angle theta with respect to its initial direction of travel has a change in momentum characterized by the photon momentum transfer argument x = lambda(-1) sin(theta/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/square root(K(air)c) = 12.8 +/- 0.2 (mJ/kg)(-1/2) when using the photons between x = 0.5 and 0.7 nm(-1). Here K(air)c is 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/square root(K(air)c) = 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(-1) then, despite the detection of more scattered photons, experimentally SNR/square root(K(air)c) decreases 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 theta = 3 degrees 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.