The bidirectional solar-optical properties of a fenestration system are necessary to accurately determine its luminous and thermal performance. Bidirectional transmittance and reflectance can be determined experimentally for fenestration systems of arbitrary complexity using a scanning radiometer, after which the total directional absorptance can be calculated. However, for the case of multilayer fenestration systems, this approach does not provide information about the net absorptance of each layer. Moreover, the same layers can be ordered in more than one way, resulting in fenestration systems with different solar-optical properties, the determination of which requires additional experimental procedures. This paper describes a mathematical model for the calculation of the bidirectional solar-optical properties of multi-layer fenestration systems, using the bidirectional solar-optical properties of each layer. The model is based on the representation of the bidirectional solar-optical properties using matrices. Matrix operations are then used to calculate the bidirectional solar-optical properties of any combination of layers, considering the interreflections between them. This approach offers two advantages: (1) the reduction of the experimental procedures to those required for the determination of the bidirectional transmittance and reflectance of fenestration layers, rather than complete fenestration systems, and (2) the determination of the net absorptance of each layer as part of the fenestration system, rather than the total absorptance of the complete fenestration system.

1 aPapamichael, Konstantinos, M.1 aWinkelmann, Frederick, C. uhttps://buildings.lbl.gov/publications/solar-optical-properties-multilayer