Calculation of light transmittance in a film: considerations of the coating geometry, the agent distribution, and its probability density distribution

Abstract: Transmittance is an important parameter for various films such as sunscreen films and creams, biofilms, coating materials, etc. Even if amounts of a sunscreen agent are the same, the transmittance greatly changes depending on the coating geometry (CG) and the agent distribution (AD) in the film. In this study, we calculate the transmittance considering CG and AD. In addition, we associate the transmittance with probability density distribution of the thickness of the film. We found analytical and numerical solutions of the transmittance in several model cases. It can be used for prediction of performance of the sunscreen film and for a fair comparative evaluation. Mathematical techniques in calculation of the transmittance are also explained in detail.