A one-dimensional stochastic model is proposed to analyze the characteristics of quantum noise in flat-panel detectors (FPD) for medical imaging applications. The number of x-ray photons is modeled as a Poisson process, and explicit expressions for the autocorrelation function and noise power spectrum density (NPSD) are obtained in terms of the exposure dose, blur shape in the capture element, and pixel size. The results from the proposed model are validated with numerical simulations, and it is shown that this model can be used for the analysis of the noise properties of the FPD. The influence of these three parameters on the NPSD is then investigated.