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.^[ref]

The distinction is between irradiance and illuminance. With spectral irradiance $E_{\lambda }(\lambda )$, illuminance is approximatelywhere $V$ 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.^[ref]

For a locally linear small-signal model about a fixed operating state, writeHere $s_G$ 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 $R_b/R_a=4^{-0.7}\approx 0.379$. 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.^[ref] The result is a calibration valid for stated conditions, not a universal conversion from resistance to optical power.

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.^[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 byThis 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 $g,\kappa ,\gamma$. ThenThe 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 $4^{-0.3}\approx 0.6598$. For a small one-percent generation increment, the leading fractional conductance change above the dark contribution is $0.7\%$; the exact model gives $(1.01{)}^{0.7}-1\approx 0.69895\%$.

A change in spectral shape requires more than that single separable nonlinearity. For an illustrative two-band response in dimensionless input coordinates, letThe 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.^[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.