 Excitation-band selectivity in nail fluorescence corrections

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 isThe 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 $a=0.30A/W$, $b=0.020A/W$, $P_t=80\mu \mathrm{W}$ 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 $b_0{P}_f$ while the true coefficient is $b$, thenAt the same powers and $a$, using $b_0=0.010A/W$ 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corrected for fluorescence.^[ref] The integral above is an explanatory extension, not a reconstruction of its unpublished correction coefficients.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.