The signal noise ratio of a quantum detector is considered under conditions where background illumination is the dominant noise component. It is shown that this is a function of the optical (pre-detector) and post-detector bandwidths. To obtain as general a case as possible, the modulation (information) signal is assumed to be white-noise of a defined bandwidth.Two separate methods of analysis are used. The first method assumes that the received light may be described in terms of its electromagnetic field while the other assumes that simple quantum theory is more appropriate. The first approach is valid for high levels of background radiation, the second for low levels. Theoverlap is shown to be in the region where the average quantum rate is just sufficient to define the pre-detector bandwidth—a result which is in agreement with sampling theory.The results are shown to be applicable to superhetrodyne and homodyne (synchronous detection) detectors by suitable parameter adjustment.