Planckian Regression Temperature for Least Spectral Error and Least CIELAB Error

Correlated colour temperature (CCT) provides a simple and useful descriptor for a given spectral power distribution as well as an approximation of the full spectrum of the measured illuminant. But typically the CCT is calculated on the basis of distance in the chromaticity plane. Here we suggest that, while familiar, this metric is not the most effective for actually generating a useful spectral approximation. Given the recent interest in whole-spectrum calculations, we consider what optimization would be most sensible for identifying the nearest Planckian in terms of wholespectrum RMS error; in that case we are calculating a variant of the Distribution Temperature (DT), another simple descriptor. This effectively means that instead of one value T we instead describe a spectrum in terms of both T and an intensity I . In general, we wish to balance the need for (i) a best mapping of the whole spectrum and (ii) smallest CIELAB error. As a first step we show how to calculate the spectrum analytically in the case when RMS spectral error minimization is the sole goal. Generalizing, we consider an optimization that tries to minimize a balance of RMS and CIELAB error, leading to a family of solutions. Finally we suggest a specific optimization that arguably forms a best tradeoff of these two objectives, which we denote the Planckian Regression Temperature (PRT). Results are shown for some standard test illuminants, and then for a further 102 measured spectra, with results separately reported for fluorescent and non-fluorescent illuminants. c © 2011 Optical Society of America