= Detector linearity
\b[Detector linearity] describes how consistently a detector's corrected output remains proportional to input over a stated range and under specified conditions. For <optical power> $P$ and output $y$, an affine measurement model is $y=y_0+SP$, where $y_0$ is background and $S$ is constant. After background subtraction, doubling power should double output. A change in <detector responsivity> with input level is evidence of departure from that proportional relation.
For an original two-level test, suppose independently established powers are $P_1=0.1\,\mathrm{mW}$ and $P_2=0.2\,\mathrm{mW}$. A background reading is $y_0=0.020\,\mathrm V$, while illuminated readings are $y_1=0.220\,\mathrm V$ and $y_2=0.412\,\mathrm V$. Define the response ratio
$$
Q=\frac{y_2-y_0}{2(y_1-y_0)}
=\frac{0.392}{0.400}=0.98.
$$
The second corrected output is $2\%$ below the doubling expected from the first. Ignoring the background would instead give $0.412/(2\cdot0.220)\simeq0.936$, confusing offset with nonlinearity. These are stipulated teaching readings, not measured performance of a named detector.
A primary apparatus example is NIST's characterization of a <photodiode> at $633\,\mathrm{nm}$. It reports responsivity relative to the low-power value, using a <beam splitter> to illuminate two photodiodes at about a $10:1$ intensity ratio, with the detector aperture uniformly filled. The report explicitly notes that the observed linearity depends on irradiation geometry.<Spectroradiometric Detector Measurements: Ultraviolet, Visible, and Near-Infrared Detectors for Spectral Power by Thomas C. Larason and others>[2008edition, §9.1, printed pp85–86, linearity method and Figure9.2]{ref}
A useful test therefore controls wavelength, beam position and size, bias, temperature, readout gain and source stability while changing input level. Reference-detector nonlinearity or a changing beam ratio can imitate nonlinearity of the test detector. Quantify the uncertainty in the comparison before interpreting a small response-ratio departure.
<Detector saturation> is a strong limiting case, but detectable nonlinearity can arise before the output becomes flat. A satisfactory response ratio at two levels also does not establish <detector linearity> over every intermediate level or different operating conditions. Record the tested range and the reference relation with the <measurement result>.
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