Petherbridge(1) developed a technique for calculating the directional solar transmittance of non-clear, heat-absorbing solar control glasses based upon the Fresnel monochromatic radiation equations. Sharples(2) modified this technique to allow the directional daylight transmittance of such glasses to be estimated.

*Input*- Specular monochromatic reflectance,
*rx* - Angle of incidence,
*i* - Normal incidence KL value for daylight,
*KL* - Refractive index of the glass,
*n* *Equation*

- The
*x*subscript signifies that each component must be evaluated separately for radiation polarised with its planes of vibration parallel (rpl) and perpendicular (rpd) to the plane of the glass, where

- The angle of refraction, ,
is found from Snell's law : sin
*i*=*n*sin - For non-polarised radiation the value of
*ti*is based on the average of the parallel and perpendicular reflectances.

- The parameter
*g*represents the fraction of the incident energy remaining after transmission through the glass, and is found from

- If the normal incidence KL value for daylight is not known it can be
derived from the normal incidence daylight transmittance
*to*via the equation*KL*= loge*X*where

- For completeness, the directional absorptance
*aix*and the directional reflectance*rix*are given here:

*Source*- Sharples(2)
**References**- 1. Petherbridge P
*Transmission characteristics of window glasses and sun controls*Sunlight and buildings: CIE Conference Bouwcentrum, Rotterdam 1967. - 2. Sharples S, Page J K and Souster C G Incorporating body-tinted glazing
into daylight computer models
*Lighting Res & Tech***16**(3) 143-145 (1984) .

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