Error Estimation For The Methods Of Correlated colour Temperature Calculation

Abstract

To date, a lot of methods have been developed for calculating correlated colour temperature (CCT). There are both numerical solutions (Robertson’s method, Yoshi Ohno method, binary search algorithm) and analytical (Javier Hernandez-Andres’s method, McCamy’s method). At the same time, the information about their accuracy is of a segmental fragmentary nature, therefore, it is very difficult to develop recommendations for the application of methods for certain radiators. In this connection, it seems extremely interesting to compare the error of the most well-known CCT calculating methods, using a single universal approach. The paper proposes an algorithm for researching the error of the methods for calculating correlated colour temperature, based on the method for plotting lines of constant CCT of a given length. Temperatures corresponding to these lines are taken as true, and the chromaticity lying on them are used as input data for the researched method. The paper proposes an approach when first the distribution of the error in the entire range of determination of CCT is determined, followed by bilinear interpolation for the required chromaticity. Using this approach, the absolute errors of the following methods for calculating CCT: McCamy, Javier Hernandez, Robertson, and Yoshi Ohno were estimated. The error was estimated in the range occupied by quadrangles of possible values from ANSI C78.377 chromaticity standard, developed by American National Standards Institute for LED lamps for indoor lightning. The tabular and graphical distribution of the absolute error for each investigated method was presented in the range of (2000–7000) K. In addition, to clarify the applicability of the methods for calculating CCT of the sky, the calculation of the distribution of the relative error up to 100000 K was performed. The results of the study can be useful for developers of standards and measurement procedures and for software developers of measuring equipment.