Microtopography-driven variability in the optical response of sunscreen films on sandblasted PMMA substrates

The optical response of a deposited thin film depends not only on the material but on the morphology the film adopts as it forms, which can depend sensitively on the microtopography of the substrate beneath it. Engineered surfaces are routinely specified by standardised roughness parameters, yet whether those parameters determine optical performance (i.e. transmittance) is untested. We investigate this question using sunscreen films deposited on sandblasted polymethyl methacrylate (PMMA) plates, the substrate of the recently standardised ISO in vitro sun protection factor (SPF) method (ISO23675). We generate 10,000 synthetic surfaces that satisfy every prescribed roughness characterisation parameter, apply the same quantity of product to each, and model film formation from an optical path length distribution calibrated to reference sunscreen P2. For a test using the minimum of three plate pairs we obtain a 95% confidence interval of 8.5% of the calculated 18.1 mean SPF, half the tolerance permitted for a test conforming to ISO requirements, falling to 2.7% at ten pairs. A quite different assumption about how the film forms gives variability of the same magnitude. We also find that substrates certified as equivalent differ by up to 30% in optical response; while substrates with markedly different parameter values have almost identical SPF, indicating that characterising plates with additional parameters could reduce variability.