Monochromatic optical detection is often desired. One technique to accomplish this is to place the detector within an optical resonator. The authors consider the theoretical description of resonant optical detection using an intrinsic semiconductor detector layer placed within a monolithic vertical cavity. The effects of wavelength-dependent index and absorption are included in the analysis. It is found that, unlike passive Fabry-Perot filters, the resonant detector can have a single resonant peak and thus strong suppression of out-of-band light.