### Abstract

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 |

### Fingerprint

### Keywords

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

### Cite this

*Metrologia*,

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

}

*Metrologia*, vol. 54, no. 4, pp. 524-534. https://doi.org/10.1088/1681-7575/aa7b39

**Method for estimating effects of unknown correlations in spectral irradiance data on uncertainties of spectrally integrated colorimetric quantities.** / Kärhä, Petri; Vaskuri, Anna; Mäntynen, Henrik; Mikkonen, Nikke; Ikonen, Erkki.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Method for estimating effects of unknown correlations in spectral irradiance data on uncertainties of spectrally integrated colorimetric quantities

AU - Kärhä, Petri

AU - Vaskuri, Anna

AU - Mäntynen, Henrik

AU - Mikkonen, Nikke

AU - Ikonen, Erkki

PY - 2017/7/18

Y1 - 2017/7/18

N2 - 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.

AB - 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.

KW - color coordinates

KW - color temperature

KW - Monte Carlo

KW - spectral irradiance

KW - uncertainty

UR - http://www.scopus.com/inward/record.url?scp=85026417680&partnerID=8YFLogxK

U2 - 10.1088/1681-7575/aa7b39

DO - 10.1088/1681-7575/aa7b39

M3 - Article

VL - 54

SP - 524

EP - 534

JO - Metrologia

JF - Metrologia

SN - 0026-1394

IS - 4

ER -