Estimating Spectral Information of Complex Fenestration Systems in a Video-Goniophotometer

The effective use of complex fenestration systems in buildings requires knowledge of their optical spectral and directional properties. While the directional properties are commonly assessed by the measurement of bidirectional transmission or reflection distribution functions, the addition of spectral information would significantly aid in the design and analysis of such systems. This paper describes the development of a spectral estimation method that reconstructs reflectance and transmittance spectra of unknown complex fenestration samples in the Heliodome, an innovative video-goniophotometer. The estimation method relies on the digital output of a tri-chromatic Charge-Coupled Device camera in eight filterbands to reconstruct a sample's spectrum using the truncated generalized singular value decomposition. This method is validated by comparing estimated spectra with documented reflectance and transmittance spectra of reference samples. In most spectrally selective materials, the method achieved average improvements of 50% over the Heliodome's previous quasi-spectral assessment method. 3 Nomenclature BSDF Bidirectional Scattering Distribution Function (sr-1) CS λ (θ i ,φ i ,θ r ,φ r) discrete conglomerate spectrum for designated incident and emerging angles (μW/m 2-sr) d digital response vector (components in units NDL/s) E λ (θ i ,φ i ,θ r ,φ r) discrete spectral bidirectional irradiance of initial polychromatic beam for the wavelength interval between 380nm and 945nm f 1 ' CIE (1987) measure of agreement between two spectra (percentage) j (subscript) filter combination number k (as index) truncation parameter (constant) L λ (θ i ,φ i ,θ r ,φ r) spectral bidirectional radiance in a polychromatic beam for the wavelength interval between 380nm and 945nm in discrete wavelength increments (μW/m 2-sr) L λ spectral radiance viewed by the camera in discrete wavelength increments (μW/m 2-sr) L λ,j spectral radiance viewed by the camera through filter j in discrete wavelength increments (μW/m 2-sr) M HMI, λ spectral excitance of the HMI dedolight in discrete wavelength increments (μW/m 2) n (index) index identifying element in discretized vector 4 N spectral modifier matrix (components in units NDL/s) NDL RGB normalized digital level (digital level divided by 2 8) in the red, green, or blue channel Q f flatness quotient defined in Eq. 16, where flatness is defined as having a Q f <0.1 Q s smoothness quotient defined in Eq. 15, where smoothness is defined as having a Q s <0.1 r RGB absolute spectral responsivity of CCD camera in the red, green, and blue channel (NDL/(μJ/m 2-sr)) S second difference smoothing matrix t …