= Detector linearity test
A \b[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 is
$$
y(P)=b+RP,
$$
where $P$ 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.<Spectroradiometric Detector Measurements: Ultraviolet, Visible, and Near-Infrared Detectors for Spectral Power by Thomas C. Larason and others>[§9.1, printed pp. 85–86 and Figure 9.2]{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 $1.940\,\mathrm{\mu A}$ at input powers $1$, $2$ and $4\,\mathrm{\mu W}$. Normalizing the apparent <spectral responsivity> to the first point gives
$$
\frac{I/P}{0.500\,\mathrm{A/W}}=1.000,\quad0.990,\quad0.970.
$$
The last point has three percent less response per unit power than the first. A straight line through the origin with slope $0.500\,\mathrm{A/W}$ would predict $2.000\,\mathrm{\mu A}$ there instead of $1.940\,\mathrm{\mu A}$.
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.
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