Spectral Power Distribution of Fluorescent Lamp as a Function of Correlated Color Temperature and the General Color-Rendering Index

This paper describes a formulation by which one can obtain spectral power distributions of fluorescent lamps with any correlated color temperature Tc, and with any general color-rendering index Ra, provided that their chromaticity points lie on the daylight locus or the plankian locus.The spectral power distribution J (λ) is constructed by a linear combination of the averaged spectral power distribution J0 (λ) and three characteristic functions T1 (λ), T2 (λ) and T3 (λ) as follows:J(λ) =J0(λ) +h1T1(λ)+h2T2 (λ) +pT3 (λ)In the equation, T1 (λ) and T2 (λ) are derived so that the first and the second coefficients h1, h2 are determined by correlated color temperature Tc, irrespective of Ra. The third coefficient p is related to both Tc and Ra. An approximated formula is derived which relates p with Ra including Tc as parameter.The formulation is applied to derive the spectral power distributions of fluorescent lamps with Tc ranging from 3000 K to 7000 K and with Ra of 50 to 94. The computations reconstitute well the spectral power distributions of fiuorescent lamps having the pre-specified values of Tc and Ra. The mean error in Ra is 0.14.