Photometric calibration

NIST Measurement Services: Photometric Calibrations by Yuqin Zong and others describes a concrete experiment (§§3.2–3.3.2): a silicon photodiode, multilayer photometric matching filter, precision aperture, temperature sensor and current-to-voltage converter. A monochromator supplies a small beam; scanning wavelength yields spectral responsivity, and scanning position checks response across the aperture. Finite spectral bandwidth requires correction. The average aperture response converts uniform illumination to illuminance.

On the photometric bench (§§3.4.1, 3.5.3, 3.5.6), align lamp and aperture reference planes, set the lamp's electric current, stabilize, and compare a check lamp with standard photometers. The readout is a voltmeter signal. Subtract the shutter-closed reading (§3.4.4), divide by converter gain to infer electric current, and use calibrated illuminance responsivity $S_A$ to obtain $E_v=i/S_A$. For a distant source, luminous intensity follows from $I_v=E_v{d}^2$, with $d$ between reference planes.

Controls include repeat lamp operations, distance changes to test the inverse-square law, temperature corrections and gain linearity checks. Spectral mismatch correction is source dependent (§3.4.3). Unknown optical spectra, spatial nonuniformity and incorrect reference planes remain limitations.^[ref]

For collected spectral radiant flux $f(\lambda )$ and a linear photodiode with spectral responsivity $r(\lambda )$, the dark-subtracted electric current is $i=\int rfd\lambda$. A reference optical spectrum $f_A$ sets the conversion $C_A$ from electric current to collected luminous flux. Applying it to another optical spectrum $f_T$ givesAssume nonzero calibration and test signals. Then $F{\Phi }_{v,\mathrm{indicated}}$ is the corrected luminous flux. Multiplying either optical spectrum by an overall positive scale leaves $F$ unchanged. If $r$ is proportional to $V$, $F=1$ for every optical spectrum. Uniformly overfilled aperture measurements use wavelength-resolved irradiance instead, multiplying the electric current expression by aperture area; the same ratio cancellation gives the illuminance correction. This is the algebra behind source-dependent calibration, rather than a new measured correction curve. ^[ref]

Use the triangular $w$ in equal radiant power under visual weighting and stipulate the detector's spectral responsivityThis model has nonnegative response: $w$ is zero outside $405$–$705\mathrm{nm}$. For a $1\mathrm{mW}$ ideal calibration line at $555\mathrm{nm}$, $i_A=0.5\mathrm{mA}$ and ${\tilde{\Phi }}_{v,A}=0.683\mathrm{lm}$, so $C_A=1366\mathrm{lm}{\mathrm{A}}^{-1}$. An equal-radiant flux test line at $630\mathrm{nm}$ gives $w=1/2$, $r=0.375\mathrm{A}{\mathrm{W}}^{-1}$ and $i_T=0.375\mathrm{mA}$. The unchanged conversion indicates $0.51225\mathrm{lm}$, whereas the model's intended weighted result is $0.3415\mathrm{lm}$. The required spectral mismatch correction is $F=2/3$: the uncorrected result is 50% too large. All these numbers are declared model outputs, not instrument measurements or standard photometry data.