= Fluorescence calibration curve
{title2=$S=b+kc$}
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 is
$$
S=b+kc,\qquad c=\frac{S-b}{k},
$$
where $S$ 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 $2\,\mathrm{mg\,L^{-1}}$ give signals $10$, $60$ and $110$ in arbitrary instrument units. The line has $b=10$ and $k=50$ instrument units per $\mathrm{mg\,L^{-1}}$. An unknown reading of $85$ then gives
$$
c=\frac{85-10}{50}=1.5\,\mathrm{mg\,L^{-1}}.
$$
These 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 $10/50=0.2\,\mathrm{mg\,L^{-1}}$. 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 $2/50=0.04\,\mathrm{mg\,L^{-1}}$. 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.<Water Measurement Manual by U.S. Bureau of Reclamation>[Chapter 12, §7, Tracer-Dilution Methods: concentration measurement, fluorometers and downstream mixing]{ref}
Back to article page
