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.