The propagation of electromagnetic waves in stratified media has been discussed by Born and Wolf [19]. The field of optics of thin films has been reviewed by various authors, e. g. Heavens [20], Holland [21], Anders [22], Knittl [23], and Macleod [24]. Due to the multiple reflections between the different interfaces, the problem of the optical behaviour of a multilayered thin film stack is non-trivial. It can be treated, though, by the method of characteristic matrices, which defines one matrix Mr per individual layer. From this matrix product, transmission and reflectance spectra can be computed. Extended calculations are usually carried out by a computer.

The visible reflectance RVIS is a measure for the brightness of a surface as it appears to the human eye under certain illumination conditions. Its determination is based on the photopic luminous efficiency function V(A.) and depends on the choice of the illuminant

Iill(^):

where R(A.) is the simulated or measured hemispherical reflectance of the sample.

For the assessment of colored solar collectors it is useful to introduce a figure of merit. In a previous publication [17] we defined the ratio of the visible reflectance RVIS under daylight illumination D65 and the solar reflectance Rsoi (based on the solar spectrum AM1.5 global[25,26]) as figure of merit M:

M = (Rvis under daylight illumination D65) / (Rsol for AM1.5 global) (2)

Being large in the case of high visible reflectance or low solar energy losses Rsol, this number describes the energy efficiency of the visual perception ("brightness per energy cost”).

An alternative approach is to use for both the evaluation of the visual impression and the energetic reflection losses the same illuminant Isol.

M’ = (RVIS under solar illumination AM1.5 global) / (Rsol for AM1.5 global) (3)

In practice, the resulting values for M and M’ are always rather close to each other. It can be shown that the principal upper limit for M and M’ amounts to the value of approx. six (in the ideal case). Of course the energy-effectiveness of the colored reflection should not be the only criterion for the evaluation of a colored collector glazing. A sufficient solar transmission is certainly one of the most important requirements.