The detectivity D of a photodetector is a figure of merit, defined as the inverse of the noise-equivalent power (NEP). The larger the detectivity of a photodetector, the more it is suitable for detecting week signals which compete with the detector noise.
The specific detectivity D* is the detectivity normalized to a unit detector area and detection bandwidth; one can calculate it by multiplying the detectivity with the square root of the product of detector area (in square centimeters) and the detector bandwidth (in Hz). That term is useful for comparing the performance of different detector technologies. If the detector bandwidth scales inversely with the active area, e.g. because of the limiting impact of the electrical capacitance, the specific detectivity will be independent of the active area.
For a given detector, one may decrease the noise level, thus reducing the noise-equivalent power and increasing the detectivity, by restricting its detection bandwidth (e.g. by adding a low-pass filter). Assuming white noise, one will then obtain the same specific detectivity as before.