= Background-dependent photoresistor spectral response
A <background-dependent photoresistor spectral response> is the differential change of a <photoresistor>'s output with wavelength-specific illumination, evaluated at a stated background state. It can depend on illumination level, spectral composition, bias, temperature and prior adaptation. The primary CdS datasheet specifies light-adaptation preconditioning before electrical tests, demonstrating that a measurement condition includes more than the instantaneous lux value.<NSL-5162 CdS photoresistor datasheet by Advanced Photonix>[page 2, light-adaptation footnote and test-source conditions]{ref}
Let the steady <electrical conductance> be a functional $G=\mathcal F[E_\lambda]$ of incident <spectral irradiance>. About a background $E_{\lambda,0}$, define the local response by
$$
\delta G=\int s_G(\lambda;E_{\lambda,0})\,\delta E_\lambda(\lambda)\,d\lambda+o(\|\delta E_\lambda\|).
$$
This derivative concerns small changes after specifying the operating state. A finite change or rapid modulation needs further nonlinear or dynamic characterization. <Photoresistor spectral calibration> establishes the required optical and electrical conditions.
An original separable model makes a useful distinction. Suppose $g=\int a(\lambda)E_\lambda(\lambda)\,d\lambda$ and $G=G_d+\kappa g^\gamma$, with positive $g,\kappa,\gamma$. Then
$$
s_G(\lambda;g_0)=\kappa\gamma g_0^{\gamma-1}a(\lambda).
$$
The amplitude changes with background, but the normalized spectral shape remains $a(\lambda)$. With $\gamma=0.7$, quadrupling $g_0$ multiplies the absolute differential response by $4^{-0.3}\approx0.6598$. For a small one-percent generation increment, the leading fractional conductance change above the dark contribution is $0.7\%$; the exact model gives $(1.01)^{0.7}-1\approx0.69895\%$.
A change in spectral shape requires more than that single separable nonlinearity. For an illustrative two-band response in dimensionless input coordinates, let
$$
G(E_a,E_b)=\sqrt{E_a}+E_b.
$$
The derivatives are $\partial G/\partial E_a=1/(2\sqrt{E_a})$ and $\partial G/\partial E_b=1$. Changing the first-band background from $E_a=1$ to $4$ changes their ratio from $1/2$ to $1/4$. This toy model shows how relative spectral sensitivity can change; it is not measured behavior of a named component. <Separable and nonseparable photoresistor spectral-response models> should consequently be distinguished in a calibration analysis.
Resistance readout adds another operating-point factor: since $R=1/G$, $\delta R=-\delta G/G_0^2$. A resistance-divider output has yet another derivative. Comparing raw electrical slopes without converting to the same output variable can imitate a change in material response. Likewise, equal <illuminance> need not mean equal detector excitation, because the <photopic luminous efficiency function> supplies a different spectral weighting.<Realization of the candela>[Detector-based realization, illuminance responsivity and spectral integrals]{ref}
A proposed apparatus combines a stable background source with a weak wavelength-selectable probe beam, a monitored reference detector and a fixed illumination geometry. At each background, measure the output derivative while decreasing probe amplitude to test the small-signal regime, then repeat after the prescribed settling or adaptation period. Normalize spectra only after retaining their absolute scale. This separates a changing overall gain from a changing spectral shape and from readout loading; it does not assume that a curve measured at one background transfers to every illumination condition.
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