 Detector linearity test

A detector linearity test checks whether changes in a detector's output remain proportional to changes in its incident signal over a stated operating range. For a photodetector with a fixed wavelength, geometry and readout gain, a linear response model iswhere $P$ is radiant power, $b$ is the baseline and $R$ is the appropriate response coefficient. A detector baseline subtraction removes the offset before comparing $y-b$ with $P$. Linearity concerns the shape of that relation; an incorrectly calibrated constant $R$ can still give a linear detector.

A documented apparatus uses a beam splitter to illuminate two photodiodes at approximately a ten-to-one intensity ratio. NIST's measurement at $633\mathrm{nm}$ compared responsivity with its low-power value, with the aperture filled and uniformly irradiated. The report explicitly notes dependence on irradiation geometry.^[ref] A detector's response to a small concentrated spot need not reproduce its response to the same total power spread over the aperture.

For an original numerical example, stipulate baseline-corrected electric currents of $0.500$, $0.990$ and $1.940\mu \mathrm{A}$ at input powers $1$, $2$ and $4\mu \mathrm{W}$. Normalizing the apparent spectral responsivity to the first point givesThe last point has three percent less response per unit power than the first. A straight line through the origin with slope $0.500A/W$ would predict $2.000\mu \mathrm{A}$ there instead of $1.940\mu \mathrm{A}$.

A useful test varies incident power while monitoring source stability and holding the beam position, illuminated area and electronic settings fixed. Record blocked-beam readings as well as illuminated readings. A residual that exceeds the combined measurement uncertainty identifies a departure from the tested model; it does not by itself locate the cause in the photodiode rather than an amplifier or other readout stage.

For pulses, average power alone may hide a nonlinear response to high peak power. A continuous-illumination test therefore does not automatically validate pulse energy measurement with a photodiode at a different pulse duration or spot size. Test the illumination and electrical range actually used, and distinguish a change in slope from a change in baseline.