Modifications of the Robertson Method for Calculating Correlated Color Temperature to Improve Accuracy and Speed

ABSTRACT

Correlated color temperature (CCT) is one of the principal metrics used in the engineering and specification of lighting. One of the most common methods used for calculating CCT was first proposed by Robertson in 1968. It utilizes a 31-row lookup table (LUT) based on isotemperature lines and a formula to interpolate CCT values between the lines. The original Robertson method is known to have modest errors in determining CCT, so many alternative methods demonstrating improved accuracy have been subsequently proposed. Rather than an entirely new method, this analysis proposes three changes to the original Robertson method: recalculation of the LUT with an increase in the resolution to an increment of 1%, a correction to address CCT errors in the region between isotherms with slopes of opposite sign, and the application of a Fibonacci or binary search algorithm to efficiently search the expanded LUT. These changes result in a CCT calculation method, denoted Robertson2022, that produces CCT errors less than 0.1 K throughout the range of 1,500 K to 40,000 K with Duv between −0.05 and 0.05.

KEYWORDS:

• Correlated color temperature
• Fibonacci
• lookup table
• Robertson

Acknowledgments

The authors gratefully acknowledge the input from members of the IES Color Committee regarding the improvement and standardization of methods for calculating CCT.

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/15502724.2023.2166060

Additional information

Funding

This work was supported by the U.S. Department of Energy’s Lighting R&D Program, part of the Building Technologies Office within the Office of Energy Efficiency and Renewable Energy (EERE).