= Detector responsivity
= Responsivity
{synonym}
\b[Detector responsivity] relates a detector's output to the incident radiant input under stated conditions. For a <photodiode> illuminated at a specified <wavelength>, current <spectral responsivity> is
$$
R_\lambda=\frac{I-I_0}{P_\lambda},
$$
where $I_0$ is the background current and $P_\lambda$ is incident <optical power>. Its units are $\mathrm{A\,W^{-1}}$. NIST's detector-calibration publication develops spectral radiant-power responsivity as the quantity transferred from optical standards to photodetectors.<Spectroradiometric Detector Measurements: Ultraviolet, Visible, and Near-Infrared Detectors for Spectral Power by Thomas C. Larason and others>[2008edition, Abstract and Figures6.2–6.3, spectral responsivity and quantum efficiency]{ref}
For an original example, $20\,\mathrm{\mu W}$ incident power produces $10\,\mathrm{\mu A}$ net photocurrent, giving $R_\lambda=0.5\,\mathrm{A\,W^{-1}}$. If readout electronics convert that current to $1\,\mathrm V$, the complete system's voltage responsivity is $50{,}000\,\mathrm{V\,W^{-1}}$. A value without its output quantity and units can therefore be misleading.
For a photodiode with no internal multiplication, let <quantum efficiency> $\eta$ be collected electrons per incident photon. A <photon> has energy $hc/\lambda$, with <Planck constant> $h$, <speed of light> $c$ and <elementary charge> $e$. Thus a photon arrival rate $\Phi$ gives $P=\Phi hc/\lambda$ and net current $I=\eta e\Phi$. Therefore
$$
R_\lambda=\eta\frac{e\lambda}{hc},\qquad
\eta=R_\lambda\frac{hc}{e\lambda}.
$$
At $800\,\mathrm{nm}$, the original $0.5\,\mathrm{A\,W^{-1}}$ example corresponds to $\eta\simeq0.775$. This relation assumes the stated charge-collection model; internal gain changes the interpretation.
Responsivity can depend on wavelength, irradiation geometry, bias and temperature. <Detector linearity> tests whether a response ratio stays constant as input level changes; <detector saturation> can make it strongly level-dependent. In a nonlinear response, the ratio of corrected output to input and the local <transducer sensitivity> are different quantities. Retain the wavelength, beam conditions, readout convention and <measurement uncertainty> when reporting a responsivity measurement.
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