### Abstract

Spectral irradiance data are often used to calculate
colorimetric properties, such as color coordinates and
color temperatures of light sources by integration. The
spectral data may contain unknown correlations that
should be accounted for in the uncertainty estimation. We
propose a new method for estimating uncertainties in such
cases. The method goes through all possible scenarios of
deviations using Monte Carlo analysis. Varying spectral
error functions are produced by combining spectral base
functions, and the distorted spectra are used to
calculate the colorimetric quantities. Standard
deviations of the colorimetric quantities at different
scenarios give uncertainties assuming no correlations,
uncertainties assuming full correlation, and
uncertainties for an unfavorable case of unknown
correlations, which turn out to be a significant source
of uncertainty. With 1% standard uncertainty in spectral
irradiance, the expanded uncertainty of the correlated
color temperature of a source corresponding to the CIE
Standard Illuminant A may reach as high as 37.2 K in
unfavorable conditions, when calculations assuming full
correlation give zero uncertainty, and calculations
assuming no correlations yield the expanded uncertainties
of 5.6 K and 12.1 K, with wavelength steps of 1 nm and 5
nm used in spectral integrations, respectively. We also
show that there is an absolute limit of 60.2 K in the
error of the correlated color temperature for Standard
Illuminant A when assuming 1% standard uncertainty in the
spectral irradiance. A comparison of our uncorrelated
uncertainties with those obtained using analytical
methods by other research groups shows good agreement. We
re-estimated the uncertainties for the colorimetric
properties of our 1 kW photometric standard lamps using
the new method. The revised uncertainty of color
temperature is a factor of 2.5 higher than the
uncertainty assuming no correlations.

Original language | English |
---|---|

Pages (from-to) | 524-534 |

Number of pages | 11 |

Journal | Metrologia |

Volume | 54 |

Issue number | 4 |

DOIs | |

Publication status | Published - 18 Jul 2017 |

MoE publication type | A1 Journal article-refereed |

### Keywords

- color coordinates
- color temperature
- Monte Carlo
- spectral irradiance
- uncertainty

## Fingerprint Dive into the research topics of 'Method for estimating effects of unknown correlations in spectral irradiance data on uncertainties of spectrally integrated colorimetric quantities'. Together they form a unique fingerprint.

## Cite this

Kärhä, P., Vaskuri, A., Mäntynen, H., Mikkonen, N., & Ikonen, E. (2017). Method for estimating effects of unknown correlations in spectral irradiance data on uncertainties of spectrally integrated colorimetric quantities.

*Metrologia*,*54*(4), 524-534. https://doi.org/10.1088/1681-7575/aa7b39