= Excitation-band selectivity in nail fluorescence corrections
{title2=$i=aP_t+bP_f$}
\b[<Excitation-band selectivity in nail fluorescence corrections>] describes how well the detection system distinguishes transmitted illumination from light emitted by the <nail plate>. Selecting the illumination with a <monochromator> does not force every detected photon to remain in that spectral band: <fluorescence> can contribute at other wavelengths.
For an original linear detection model, write the transmitted and emitted spectral powers as $P_t h(\lambda)$ and $P_f f(\lambda)$, where both spectral shapes integrate to one. If an <optical filter> has transmission $\tau(\lambda)$ and a detector has <spectral responsivity> $R(\lambda)$, its current after subtraction of <dark current> is
$$
i=\int R(\lambda)\tau(\lambda)\bigl[P_t h(\lambda)+P_f f(\lambda)\bigr]\,d\lambda
=aP_t+bP_f.
$$
The coefficients $a,b$ are spectrum-weighted responsivities, with units of amperes per watt. A selective filter can reduce $b$ while also reducing $a$, so an uncorrected smaller current does not establish lower specimen <transmittance>.
For stipulated $a=0.30\,\mathrm{A/W}$, $b=0.020\,\mathrm{A/W}$, $P_t=80\,\mu\mathrm W$ and $P_f=20\,\mu\mathrm W$, current is $24.4\,\mu\mathrm A$. Assigning all of it to transmitted illumination gives $i/a=81.33\,\mu\mathrm W$, a 1.67% relative overestimate. These chosen coefficients illustrate leakage; they are not measured filter characteristics for nails.
<Emission-spectrum mismatch in nail fluorescence subtraction> matters when the assumed $f(\lambda)$ differs from the specimen's emission. If analysis subtracts $b_0P_f$ while the true coefficient is $b$, then
$$
\widehat P_t-P_t=\frac{(b-b_0)P_f}{a}.
$$
At the same powers and $a$, using $b_0=0.010\,\mathrm{A/W}$ instead of 0.020 leaves a $0.667\,\mu\mathrm W$ positive bias. A precisely known total emitted power would not eliminate this spectral mismatch.
The historical nail-transmission experiment explicitly corrected for <fluorescence>.<The transmission of optical radiation through human nails by S. G. Parker and B. L. Diffey>[Abstract, fluorescence correction]{ref} The integral above is an explanatory extension, not a reconstruction of its unpublished correction coefficients. An experimental test would characterize detector/filter response and compare detection bands while keeping illumination and <collection geometry in nail-transmission measurements> fixed. Spectral rejection and angular collection constrain different parts of the measurement.
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