Transparent wood (TW) is an emerging optical material combining high optical transmittance and haze for structural applications. Unlike nonscattering absorbing media, the thickness dependence of light transmittance for TW is complicated because optical losses are also related to increased photon path length from multiple scattering. In the present study, starting from photon diffusion equation, it is found that the angle-integrated total light transmittance of TW has an exponentially decaying dependence on sample thickness. The expression reveals an attenuation coefficient which depends not only on the absorption coefficient but also on the diffusion coefficient. The total transmittance and thickness were measured for a range of TW samples, from both acetylated and nonacetylated balsa wood templates, and were fitted according to the derived relationship. The fitting gives a lower attenuation coefficient for the acetylated TW compared to the nonacetylated one. The lower attenuation coefficient for the acetylated TW is attributed to its lower scattering coefficient or correspondingly lower haze. The attenuation constant resulted from our model hence can serve as a singular material parameter that facilitates cross-comparison of different sample types, at even different thicknesses, when total optical transmittance is concerned. The model was verified with two other TWs (ash and birch) and is in general applicable to other scattering media.
Keywords: anisotropic scattering; attenuation coefficient; photon diffusion equation; transmittance; transparent wood.