Colour prediction in multilayer polymer systems under polarized light for packaging applications

Abstract

Conventional colour measurement methods do not fully account for the optical properties of multilayer polymer systems in transmitted polarized light. This work presents a Mueller-calculus-based model that predicts the spectral radiance and perceived colour of multilayer anisotropic polymer film stacks viewed in polarized light, targeting design needs in packaging. The model accepts the light source spectrum, polarizer and analyser angles, film optical-axis orientations, polymer film birefringence, and the spectral transmittance of added colour filters. The model was implemented in Python using SymPy and Colour libraries. Validation experiments employed stacks 1–3 layers at a 45-degree angle of 25±5 µm thickness BOPP films between parallel and crossed polarizers with a measured LED light source and X‑Rite i1Pro spectrophotometer, including stacks combined with three gel colour filters and three flexographically printed patches on BOPP; BOPP birefringence was retrieved as Δn 0.015 via spectral analysis and it is consistent with the literature. The model reproduced key spectral features and colour coordinates, yielding absolute spectral RMSEs of 0.34-1.01 mW/(m2·sr·nm) for stacks without colour filters and a mean RMSE of 0.27 mW/(m2·sr·nm) with colour filters. The mean colour difference ∆E76 across configurations with colour filters was 10.8. The model can be used for preview prototyping of polarized-light effects and security features in multilayer packaging and may provide a basis for an intelligent colour-management system.

Article history: Received (September 25, 2025); Revised (January 11, 2026); Accepted (January 21, 2026)