In the last decades a new type of detector which is based on photostimulable image plates was developed. The quantum efficiency of this detector type depends on several parameters which account for the primary X-ray absorption, the spreading of light in the detection medium during the readout, and parameters of the readout system, as the light intensity of the readout laser and the detection efficiency of the photostimulated luminescence. A theoretical model is presented which allows the calculation of the quantum efficiency from these parameters. The model is exemplary applied to the case of radiographic imaging with a commercial image plate and the quantum efficiency is calculated for various X-ray energies, readout intensities and detection efficiencies of the readout system. It is shown that quantum efficiencies near 100% can be reached for X-ray energies below 20 keV using the image plate.