Generalized Beer-Lambert Law for Evaluating the Absorption of Heterogeneous Sunscreen Films

In this study, we first examined the morphology of a sunscreen product deposited on PMMA plates with an increasing developed interfacial area ratio (Sdr) to better understand the origin and impact of film heterogeneities on in vitro sun protection factor (SPF) measurements. This was achieved using a simple yet innovative UV photography setup combined with wetting measurements. By revisiting the fundamentals of absorption spectroscopy, we generalized and extended Beer-Lambert's law to nonuniform samples, modeling thickness distributions with a Gamma law. This enabled us to develop an analytical relationship between absorbance, thickness, and homogeneity of spread sunscreen films using the concept of linear attenuation coefficients. This model, which differentiates between spreading quality and absorption potential, was experimentally validated on three different sunscreens coated on smooth PMMA plates. It also helps explain the low correlation often observed between in vivo and in vitro tests, especially for high SPF values. We believe this approach will pave the way for more reproducible and consistent in vitro SPF measurements, leading to the development of more effective sunscreen products.