A spatial-frequency dependent quantum accounting diagram and detective quantum efficiency model of signal and noise propagation in cascaded imaging systems

The detective quantum efficiency (DQE) is a system parameter that can be used to accurately describe image noise transfer characteristics through many imaging systems. A simpler approach used by some investigators, particularly when evaluating new ideas and system designs, is to describe the system as a series of cascaded stages. Each stage may correspond to either an increase in the number of quanta (e.g., conversion from x-ray to optical quanta in a radiographic screen), or a loss (a detection or coupling probability). The number of secondary quanta at each stage per incident primary quantum is given by the product of all preceding gains, and can be displayed graphically for convenient interpretation. The stage with the fewest quanta is called the "quantum sink," limiting the pixel signal-to-noise ratio to less than the square root of the number of quanta per pixel. This conventional zero-spatial-frequency "quantum accounting diagram" (QAD), however, neglects the spatial spreading of secondary quanta and can seriously underestimate image noise. It is shown that this problem is avoided with the introduction of a spatial-frequency dependent QAD, expressed as the product of the gains and squared modulation-transfer functions (MTF) of each stage. A generalized expression is developed for the DQE of a cascaded imaging system that is dependent only on the gain, gain Poisson excess (related to the variance), and MTF, of each stage. A direct relationship is then shown to exist between the DQE and values in the QAD. The QAD of a hypothetical system consisting of a charge-coupled device camera and a scintillating screen is evaluated as an illustrative example. The conventional zero-frequency analysis suggests two quantum sinks occur with approximately equal importance: one in the number of x rays, and one in the number of optical quanta. The spatial-frequency dependent analysis, however, shows the optical quantum sink becomes severe and dominates at nonzero frequencies. The necessary increase in gain or optical numerical aperture required to prevent the optical quantum sink for spatial frequencies of interest is determined from the QAD analysis. The visual impact of this nonzero spatial-frequency quantum sink is shown in images generated using a Monte Carlo simulation of the cascading process.