Linear-Systems Modeling of Parallel Cascaded Stochastic Processes: The NPS of Radiographic Screens with Reabsorption of Characteristic X Radiation

Linear-systems theory can be used to characterize the performance of many imaging systems in terms of signal-transfer and noise-transfer relationships. Using this approach, complex systems are described as serial cascades of simple processes. In a series of articles by Shaw, Rabbani, Van Metter, Barrett, Wagner and others, key processes have been identified and relationships developed which describe the transfer of the auto-covariance function and noise-power spectrum (NPS). However, to date only serial cascades have been described. In this article, this approach is extended to also include parallel cascades under certain conditions. Parallel cascades are used to describe systems in which the output signal is the sum of two or more serial cascades. The output NPS is therefore the sum of the NPS from each serial cascade plus cross-spectral density terms which are required to account for statistical correlations between the serial cascades. An expression for the cross-spectral density term is developed for the special case of a serial cascade branching into two parallel cascades at a point where image quanta are uncorrelated. This work was inspired by an article published by Metz and Vyborny who showed the effect of reabsorption of characteristic x rays on the NPS of radiographic screens using a complex statistical analysis. The linear-systems approach is used here to derive the same result making use of a “flow diagram” which represents the sequence of events giving rise to light emission in a radiographic screen as three serial cascades of stochastic point processes. For many, the flow diagram approach is more readily understood than a statistical analysis, and may offer more physical insight into an understanding of the results.