Recent advances in thin film transistor array technology have enabled the possibility of “back-irradiated” (BI) indirect active-matrix flat-panel imagers (AMFPIs), in which x-rays first expose the scintillator through the optical sensor, and “dual-screen” AMFPIs, in which two scintillating screens are sandwiched around a bidirectional active matrix. We developed a theoretical treatment of such detectors. The theory is used to investigate possible imaging performance improvements over conventional “front-irradiation” (FI) AMFPIs, where the active matrix is opposite the x-ray entrance surface. Simple expressions for the modulation transfer function, normalized noise power spectrum, Swank factor (A_s), Lubberts function L  (  f  )  , and spatial frequency-dependent detective quantum efficiency DQE  (  f  )   are derived and used to compute these quantities for a variety of FI, BI, and dual-screen detector configurations. DQE  (  f  )   is used as the figure of merit for optimizing and comparing the performance of the various configurations. Large performance improvements over FI single-screen systems are found possible with BI. Further improvements are found possible with dual-screen configurations. The ratio of the thicknesses of the two screens that optimizes DQE is generally asymmetric, with the thinner screen facing the incident flux. The optimum ratio depends on the x-ray attenuation length in the screen.