Detector responsivity

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 iswhere $I_0$ is the background current and $P_{\lambda }$ is incident optical power. Its units are $\mathrm{A}{\mathrm{W}}^{-1}$. NIST's detector-calibration publication develops spectral radiant-power responsivity as the quantity transferred from optical standards to photodetectors.^[ref]

For an original example, $20\mu \mathrm{W}$ incident power produces $10\mu \mathrm{A}$ net photocurrent, giving $R_{\lambda }=0.5\mathrm{A}{\mathrm{W}}^{-1}$. If readout electronics convert that current to $1\mathrm{V}$, the complete system's voltage responsivity is $50,000\mathrm{V}{\mathrm{W}}^{-1}$. 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 $I=\eta e\Phi$. ThereforeAt $800\mathrm{nm}$, the original $0.5\mathrm{A}{\mathrm{W}}^{-1}$ example corresponds to $\eta \simeq 0.775$. 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.