Figures of merit for detectors in digital radiography. I. Flat background and deterministic blurring

Digital radiography systems can be thought of as continuous linear shift-invariant systems followed by sampling. This view, along with the large number of pixels used for flat-panel systems, has motivated much of the work which attempts to extend figures of merit developed for analog systems, in particular noise equivalent quanta (NEQ) and detective quantum efficiency (DQE). A more general approach looks at the system as a continuous-to-discrete mapping and evaluates the signal-to-noise ratio (SNR) completely from the discrete data. In this paper, we study the effect of presampling blur on these figures of merit for a simple model that assumes that the background fluence is constant and that the blurring of the signal is deterministic. We find that for small signals, even in this idealized model, commonly used DQE/NEQ formulations do not accurately track the behavior of the fully digital SNR. Using these NEQ-based figures of merit would lead to different design decisions than using the ideal SNR. This study is meant to bring attention to the assumptions implicitly made when using Fourier methods.