= Absorbed-photon normalization in quantum-yield comparisons
{title2=$\Phi=N_{\mathrm{em}}/N_{\mathrm{abs}}$}
\b[<Absorbed-photon normalization in quantum-yield comparisons>] compares emitted events with the photons actually absorbed by the sample. The <quantum yield> uses absorbed photons as its denominator; equal incident <optical power> does not generally establish equal absorbed photon rates.<IUPAC Compendium of Chemical Terminology, fifth edition (Gold Book)>[quantum yield, Q04991]{ref}
For monochromatic incident power $P$, excitation wavelength $\lambda$ and <absorbance> $A$, the idealized <absorbed photon flux> is
$$
\dot N_{\mathrm{abs}}=\frac{P\lambda}{hc}\left(1-10^{-A}\right).
$$
This model assumes that the measured attenuation is attributed appropriately to absorption rather than unaccounted scattering or other optical losses. If background-corrected detected count rate is $D=\eta\Phi\dot N_{\mathrm{abs}}$, where $\eta$ includes the specified collection and detection efficiency, then
$$
\frac{\Phi_2}{\Phi_1}=
\frac{D_2}{D_1}\frac{\eta_1}{\eta_2}
\frac{P_1\lambda_1(1-10^{-A_1})}{P_2\lambda_2(1-10^{-A_2})}.
$$
Different emission spectra or collection conditions can change $\eta$; treating it as equal requires justification.
An original example uses equal incident powers at 400 and 600 nm, with absorbed fractions $1/2$ and $3/4$. The absorbed photon rates have ratio
$$
\frac{600(3/4)}{400(1/2)}=2.25.
$$
If count rates are 10,000 and 22,500 per second at equal detection efficiency, the inferred yield ratio is one. A raw brightness increase by 2.25 is entirely consistent with unchanged <fluorescence quantum yield>.
The weak-absorption approximation $1-10^{-A}\simeq(\log 10)A$ needs its stated range. At $A=\log_{10}2$, the exact absorbed fraction is 0.5 while the approximation gives $\log2\approx0.693$. Using it here would overestimate absorbed photons by about 39 percent and underestimate the inferred yield.
NIST's primary fluorescence-calibration guide separately treats emission response, excitation-beam intensity and relative quantum-yield measurement, including refractive-index corrections in its comparison model.<Standard Guide to Fluorescence - Instrument Calibration and Validation by Paul C. DeRose>[NISTIR 7458, §§5–6 and §11.2, Eq. (2)]{ref} Its framework motivates independently checking excitation and detection corrections. <Inner filter effects>, <photobleaching> and chemical changes can also defeat a naive comparison. Normalization corrects a specified measurement model; it should not force the <Kasha-Vavilov rule> to hold when corrected yields genuinely differ.
Back to article page
