= Collection geometry in nail-transmission measurements
\b[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>.<The transmission of optical radiation through human nails by S. G. Parker and B. L. Diffey>[Abstract, specimen set and apparatus]{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 fraction
$$
\eta=\frac{\int_0^{\theta_m}\cos\theta\sin\theta\,d\theta}{\int_0^{\pi/2}\cos\theta\sin\theta\,d\theta}=\sin^2\theta_m.
$$
The cosine accounts for projected emitting area. Assuming the direct beam is entirely collected, $T_{\rm measured}=T_d+\eta T_s$. 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.
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