Models for the angle-dependent optical properties of coated glazing materials

Optical transmittance and reflectance of window materials can be measured accurately at normal incidence using standard equipment. Sunlight often strikes at angles for which the transmittance and reflectance are significantly different from their values at normal incidence. A reliable procedure for extrapolating from normal properties to oblique properties is thus needed for accurate annual energy performance calculations and product comparisons. The structural models for the materials are greatly constrained by the limited amount of data that is usually available. For monolithic materials such as uncoated glass or plastic substrates it is possible to solve directly for the optical indices and then apply Fresnel’s equation to obtain the oblique properties. For coated glass, the situation is more complex, but a numerical solution is often possible. First, detailed optical models were constructed and accurate angle-dependent data were generated for a wide selection of coated glazing materials. Then, a set of very simple thin-film models were chosen that would converge given a limited amount of data. At 60° incidence, the monolithic model was often accurate to within 2% but frequently deviated farther up to 8%. The single-layer thin-film model fared little better. Highly constrained multilayer models often deviated less than 1% although convergence became increasingly specific to similar coating types.