We have analyzed the influence of stochastic amplifying and scattering mechanisms on the transfer of signal and noise through multistage imaging systems in terms of multivariate moment-generating functions. Stochastic amplification of photon noise by one stage of an imaging system is shown to constitute an effective signal to the next, while the underlying photon-noise component is unaffected by a subsequent scattering process. In the case of stationary, photon-limited inputs, these considerations then lead to useful expressions for the noise power spectrum and detective quantum efficiency for multistage image systems. The application of these results to the analysis of radiographic screen-film imaging systems is discussed.

Over recent decades a quiet revolution has taken place in the application of modern imaging theory to many fields of applied imaging. Nowhere has this movement been more dramatic than within the field of diagnostic medical x-ray imaging, to the extent that there is now a growing consensus around a universal imaging language for the description and inter-comparison of the increasingly diverse range of technologies. This common language owes much to the basic quantum-limited approach pioneered by Rose and his contemporaries. It embodies the fundamentally statistical nature of image signals, and enables scientists and engineers to develop new system designs optimized for the detection of small signals while constraining patient x-ray exposures to tolerable levels. In this paper we attempt to provide a summary of some of the more salient features of progress being made in the understanding of the signal-to-noise limitations of medical imaging systems, and to place this progress within historical context. Reflecting the experiences of both authors, emphasis will be given to medical diagnostics based on x-ray imaging techniques.

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