In this paper we describe theoretically the relationship between the finite thickness of a phosphor screen and its spatial-frequency-dependent detective quantum efficiency DQE(f-). The finite thickness of the screen causes a variation in both the total number of light quanta emitted from the screen in a burst from a given x-ray interaction and in the spatial distribution of the quanta within the light burst [i.e., shape or point spread function (PSF) of the light burst]. The variation in magnitude of the burst gives rise to a spatial-frequency-independent reduction in DQE, characterized by the scintillation efficiency As. The variation in PSF causes a roll off in DQE with increasing spatial frequency which we have characterized by the function Rc(f). Both As and Rc(f) can be determined from the moments of the distribution of the spatial Fourier spectrum of light bursts emitted from the phosphor and thus they are related: As is a scaling factor for Rc(f). Our theory predicts that it is necessary for all light bursts which appear at the output to have the same magnitude to maximize As and the same shape to maximize Rc(f). These requirements can lead to the result that the fluorescent screen with the highest modulation transfer function will not necessarily have the highest DQE(f) even at high spatial frequencies.