= Photoresistor spectral calibration
<Photoresistor spectral calibration> determines how a <photoresistor>'s electrical reading depends on the illumination spectrum under specified geometry, background, <temperature>, bias and adaptation history. A resistance-versus-lux curve measured with one lamp is not automatically valid for another spectrum. The manufacturer's primary CdS datasheet specifies a $2854\,\mathrm K$ source for its light-resistance tests and preconditions cells with light before electrical measurements.<NSL-5162 CdS photoresistor datasheet by Advanced Photonix>[page 2, light-resistance test conditions and adaptation footnote]{ref}
The distinction is between <irradiance> and <illuminance>. With <spectral irradiance> $E_\lambda(\lambda)$, <illuminance> is approximately
$$
E_v=683\,\mathrm{lm/W}\int V(\lambda)E_\lambda(\lambda)\,d\lambda,
$$
where $V$ is the <photopic luminous efficiency function>. The detector weights wavelengths according to its own physical response, which need not be proportional to $V$. NIST's detector-based photometric realization measures that spectral response, rather than assuming an arbitrary detector reproduces the photometric weighting.<Realization of the candela>[Detector-based realization, illuminance responsivity and spectral integrals]{ref}
For a locally linear small-signal model about a fixed operating state, write
$$
\delta G=\int s_G(\lambda)\,\delta E_\lambda(\lambda)\,d\lambda.
$$
Here $s_G$ is the differential <spectral responsivity> of <electrical conductance>, including the stated illumination geometry. It is not automatically a global, illumination-independent material constant. A <background-dependent photoresistor spectral response> requires rechecking this <derivative> when the operating point changes.
An original two-band example makes the mismatch quantitative. Stipulate relative photometric weights $V_a=0.8$, $V_b=0.2$ and equal detector generation weights $s_a=s_b$ for two narrow bands. Equal <illuminance> requires four times as much <irradiance> in band $b$, so its detector-weighted generation is four times greater. If, over this illustrative range, $R\propto g^{-0.7}$, the resistance ratio is $R_b/R_a=4^{-0.7}\approx0.379$. These weights and exponent are stipulated, not measured specifications or tabulated values for named wavelengths. Equal lux can produce substantially unequal resistance.
A proposed spectral characterization uses narrow-band sources or a <monochromator>, a reference detector to measure incident <irradiance>, fixed beam geometry and controlled detector <temperature>. Record resistance or conductance after a defined settling time at several background levels. A separate calibrated photometer can establish <illuminance>; it cannot by itself establish the <photoresistor>'s spectral weighting. Keep electrical loading and self-heating fixed while changing the source.
For a broadband transfer, characterize the reference and test spectra and test whether the measured spectral-response model predicts their relative readings. Existing <spectral mismatch correction> methods address the analogous transfer problem for photometers, but a nonlinear <photoresistor> first needs a justified operating-point model.<NIST Measurement Services: Photometric Calibrations by Yuqin Zong and others>[§3.4.3, equation 22, and §3.6.2, spectral mismatch for sources different from the calibration lamp]{ref} The result is a calibration valid for stated conditions, not a universal conversion from resistance to <optical power>.
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