Extending the use of normal hemispherical transmittance (TNH) measurements by modeling 3D multiple scattering radiative transfer

Spectrophotometers or optical benches using integrating spheres to measure normal-hemispherical transmittance $T_{NH}$ are widespread laboratory equipments. Although it is known that they cannot be used for ”highly turbid” samples, because multiple scattering may lead transmitted radiation to miss the entrance of the integrating sphere, very little is generally known about their exact validity range. Here we present a method to characterize the validity range of any such spectrophotometer and observe that most of them fail to measure $T_{NH}$ for scattering optical thickness above 0.25 (i.e. for $T_{NH}<0.9$ in the case of non absorbing media with $g=0$). We also show how it is possible to continue using spectrophotometers even outside their $T_{NH}$ measurement validity range, without any calibration, thanks to a proper simulation of radiative transfer and geometrical optics. We make available the corresponding radiative transfer simulation tools as open access codes, that have been developed for a straightforward implementation on a wide range of experimental setups. The method is validated on three different spectrophotometers or optical benches using standardized latex microspheres, then its practical implementation is illustrated in the case of semi-conductor particles and photosynthetic microalgae. Errors in analysis arising from the misuse of such optical devices are discussed throughout the article.