Fluorescence calibration curve ($S=b+kc$)

A fluorescence calibration curve relates a measured fluorescence signal to known amounts or concentrations of a fluorescent substance under specified conditions. Standards measured with the same fluorometer settings and a matched sample background provide the comparison for an unknown. In a verified linear range, a useful model iswhere $S$ is the measured signal, $b$ the background intercept, $k$ the sensitivity and $c$ the concentration. The units of $k$ depend on the chosen signal and concentration units.

For a synthetic mass concentration example, standards at $0$, $1$ and $2\mathrm{mg}{\mathrm{L}}^{-1}$ give signals $10$, $60$ and $110$ in arbitrary instrument units. The line has $b=10$ and $k=50$ instrument units per $\mathrm{mg}{\mathrm{L}}^{-1}$. An unknown reading of $85$ then givesThese are stipulated numbers illustrating the inference, not reported measurements. Repeated standards and a linear regression allow scatter and departures from the straight-line model to be assessed; three perfectly chosen numbers do not establish a real instrument's linear range.

A fluorescence blank tests the background. If the true intercept rises from $10$ to $20$ while the old line is still used, the inferred concentration is too high by $10/50=0.2\mathrm{mg}{\mathrm{L}}^{-1}$. If only signal uncertainty contributes and $b$ and $k$ are treated as exact, a signal standard uncertainty of $2$ instrument units gives a concentration standard uncertainty of $2/50=0.04\mathrm{mg}{\mathrm{L}}^{-1}$. Actual propagation of uncertainty also includes the fitted slope and intercept, their covariance, and standard preparation.

A calibration applies to its tested conditions. Excitation and emission bands, detector gain, solvent, temperature and sample background can change the response. At larger concentrations, absorption of excitation or emitted light produces an inner filter effect; fluorescence quenching can also prevent proportionality. Bracketing an unknown with standards in the tested range gives a stronger basis for inference than extending a line far beyond the standards.

One physical application is dye-based flow measurement: the Bureau of Reclamation describes fluorometer readings for detecting downstream tracer concentrations. The optical calibration supplies a concentration; a separate mixing and conservation model is then required to infer flow. An accurate calibration cannot compensate for inadequate tracer mixing.^[ref]