Measuring the absorption coefficient of optical materials with arbitrary shape or distribution within an integrating sphere

The absorption coefficient of a material is classically determined by measuring the transmittance of a homogeneous sample contained within flat optical faces and under collimated illumination. For arbitrary shapes this method is impracticable. The characterization of inhomogeneous or randomly distributed samples such as granules, powders or fibers suffers the same problem. Alternatively, an integrating cavity permits us to illuminate a sample under a homogenous and isotropic light field where the analysis simplifies. We revisit this strategy and present a new formal basis based on simple radiometric laws and principles. We introduce a new concept to describe the absorption: the optical form factor. We tackle a rigorous treatment of several regular forms, including full absorption range and the reflection at its surfaces. We also model and improve an integrating sphere setup to perform reliable measurements. Altogether, it permits achieving simple but general conclusions for samples with arbitrary shape or spatial distribution, from weak to highly absorbing, expanding the applicability of quantitative absorption spectroscopy. Finally, we validate it by measuring different sample formats made of PMMA: a cube, groups of granules and injection molding loose parts. The absorption coefficient of PMMA varies near three orders of magnitude in the explored range (380-1650 nm).