# Responsivity

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Responsivity measures the input–output gain of a detector system. For a system that responds linearly to its input, there is a unique responsivity. For nonlinear systems, the responsivity is the local slope (derivative).[1]

In the specific case of a photodetector, responsivity measures the electrical output per optical input. Many common photodetectors respond linearly as a function of the incident power.

Responsivity of a photodetector is usually expressed in amperes per watt, or volts per watt, of incident radiant power. Responsivity is a function of the wavelength of the incident radiation and of the sensor properties, such as the bandgap of the material of which the photodetector is made. One simple expression for Responsivity (Rλ) commonly used with photodetectors is listed below, where η is the quantum efficiency (conversion efficiency of photons to electrons) of the detector for a given wavelength.

$R_\lambda=\frac{q}{h \nu}\times\eta\approx\frac{\lambda_{(\mu m)}}{1.23985}\times\eta$

The term responsivity is also used to summarize input–output relationship in non-electrical systems. For example, a neuroscientist may measure how neurons in the visual pathway respond to light. In this case, responsivity summarizes the change in the neural response per unit signal strength.

The responsivity in these applications can have a variety of units. The signal strength typically is controlled by varying either intensity (intensity-response function) or contrast (contrast-response function). The neural response measure depends on the part of the nervous system under study. For example, at the level of the retinal cones, the response might be in photocurrent. In the central nervous system the response is usually spikes per second. In functional neuroimaging, the response measure is usually BOLD contrast. The responsivity units reflect the relevant stimulus and physiological units.

When describing a specific part in which the mechanisms are well understood, such as an amplifier, the more common term is gain.

Deprecated synonym sensitivity. A system's sensitivity is the inverse of the stimulus level required to produce a threshold response, with the threshold typically chosen just above the noise level.