Chemical detectors (“sensors”) usually consist of a two-dimensional array of receptors exposed to the solution to be tested, from whose output the bulk solution concentration of the analyte of interest can be determined. Both input and output—the number of analyte particles striking the array in a given interval of time, and the number captured—are countable events. The gain is the quotient of these two numbers, and the detectivity the quotient of their fluctuations. The gain and detectivity provide a universal framework for comparing different types of sensors, and in which the desirable properties of sensors, e.g. their ability to detect very weak signals (“sensitivity”), and to detect the analyte in the presence of a large excess of other molecules (“selectivity”), can be related to various physico-chemical parameters such as the packing density and size of receptors, and their affinity for the analyte. Analyte multivalence, although formally a source of inefficiency, is very useful for making the sensor more resistant to spurious chemical noise. An important result is that chemical fog engendered by a huge excess of nonspecifically binding particles has no effect on the detectivity, provided that the nonspecific interaction is reversible
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