Spectral invariance under daylight illumination changes.

We develop a method for calculating invariant spectra of light reflected from surfaces under changing daylight illumination conditions. A necessary part of the method is representing the illuminant in a suitable form. We represent daylight by a function E(lambda, T) = h(lambda)exp[u(lambda)f(T)], where lambda is the wavelength, T is the color temperature, h(lambda) and u(lambda) are any functions of lambda but not T, and f(T) is any function of T but not lambda. We use an eigenvalue decomposition on the logarithm of the CIE daylight standard at various color temperatures to obtain the necessary functions and show that this gives an extremely good fit to CIE daylight over our experimental range. We obtain experimental data over the range 350-830 nm from a range of standard colored surfaces for 50 daylight conditions covering a wide range of illumination spectra. Despite a considerable variation in the spectra of the reflected light, we show only small variations when the transformation is used. We investigate the possible causes of the residual variation and conclude that using the above approximation to daylight is unlikely to be a major cause. Some variation is caused by local daylight conditions being different from the CIE standard and the rest by measurement and modeling errors.