 Collection geometry in nail-transmission measurements

Collection geometry in nail-transmission measurements specifies which light emerging from a nail plate reaches the detector. A narrow forward detector and an integrating sphere can report different signals from the same specimen because light scattering redistributes directions. The reported transmittance must identify its collection conditions.

The primary 1983 nail study measured total transmitted radiation at fifteen wavelengths from 300 to 600 nm through thirteen autopsy toenails, using a monochromator, integrating sphere and photodiode.^[ref] The angular collection is part of the measurement, alongside the wavelength and the separate correction for fluorescence.

An original angular model separates on-axis direct transmission $T_d$ from a diffuse transmitted fraction $T_s$. Suppose the diffuse component has constant radiance over the outgoing hemisphere. A detector accepting all azimuths up to angle ${\theta }_m$ from the surface normal collects the fractionThe cosine accounts for projected emitting area. Assuming the direct beam is entirely collected, $T_{\mathrm{measured}}=T_d+\eta T_s$. This is a constructed angular distribution, not a measured scattering law for nails.

At stipulated $T_d=0.04$, $T_s=0.08$ and ${\theta }_m=30$ degrees, $\eta =0.25$ and the detected fraction is 0.06 although total transmission is 0.12. Aperture-dependent diffuse transmission in nail measurements also depends on distance. For a small emitting region facing a circular aperture of radius $a$ at distance $r$, $\eta =a^2/(a^2+r^2)$ in this model. With $a=5$ mm, distances 10 and 20 mm give approximately 0.0560 and 0.0447 for measured transmission, respectively, without a specimen change.

An integrating sphere collects a much broader angular distribution, but its ports, coating and detector coupling still require characterization. A useful comparison holds the specimen, incidence and spectral band fixed while changing collection aperture or recording angular response. Correcting fluorescence does not recover scattered light that was never collected, and a calibration made in one geometry does not automatically apply in another.