Reconstruction of Daylight Spectral Power Distribution Based on Correlated Color Temperature: A Comparative Study between the CIE Approach and Localized Procedures in Assessing Non-image Forming Effects

ABSTRACT

Spectrally and spatially resolved information on daylight is critically important when planning for non-image forming (NIF) responses. Nevertheless, the availability of such data is scarce given the high initial costs and complex on-site maintenance of high-end spectral measurement devices. The CIE (Commission Internationale de l’Éclairage) reconstruction procedure allows for the derivation of the daylight spectral power distribution (SPD) from the chromaticity coordinates or the correlated color temperature ($T_{cp}$). However, several studies have suggested that both the daylight locus and the reconstruction procedure are erroneous, and specifically SPDs with a higher $T_{cp}$ cannot be reproduced accurately.

This paper studies the reconstruction accuracy of the SPD of daylight, and contextualizes the findings in relation to NIF effects. The analysis comprises a comparative study to determine the accuracy of the CIE procedure compared to two localized reconstruction procedures, and a sensitivity study to examine the impact of accuracy on the assessment of NIF responses, as represented by all five retinal photoreceptors and expressed in the α-opic efficacy of luminous radiation. The results indicated that a localized procedure, adjusting both the daylight locus and the PCA components of daylight, outperformed the CIE reconstruction method. However, improvement in the reconstruction accuracy had no effect on NIF assessment. The RSMPE for α-opic quantities did not exceed 4% for any procedure. In practical terms, this implies that cost-effective sensors and the representation of spectral properties in sky models with a single value – the correlated color temperature – can be used for NIF purposes. These findings bridge theory and practice by opening up new insights into the understanding of simplified methods used to determine NIF effects of daylight.

HIGHLIGHTS

• Using a localized procedure to define spectral power distribution (SPD) based on correlated color temperature ($T_{cp}$) outperforms the CIE method.

• Accuracy depends on the computation procedure rather than the daylight locus location.

• Higher accuracy does not affect the α-opic responses used in defining non-image forming (NIF) effects.

• Findings confirm the applicability of simplified measuring and representation methods for daylight SPDs.

• $T_{cp}$ can be used to represent daylight SPD in planning software to assess NIF effects.

KEYWORDS:

• Daylight
• reconstruction procedure
• spectral power distribution
• daylight locus
• non-image forming effects

Nomenclature

BLN1	=	Locally adjusted reconstruction method using Berlin daylight locus
BLN2	=	Locally adjusted reconstruction method using Berlin daylight locus and Berlin components
CIE	=	Commission Internationale de l’Éclairage
$\mathrm{G}\mathrm{F}\mathrm{C}$	=	Goodness-of-Fit Coefficient
$K_{\alpha ,v,Re}$	=	α-opic efficacy of luminous radiation (α-opic ELR)
${\mathrm{M}}_1,$ ${\mathrm{M}}_2$	=	Weighting factors
$\mathrm{M}\mathrm{A}\mathrm{P}{\mathrm{E}}_{\alpha }$	=	Mean absolute percentage error for α-opic quantities
$\mathrm{M}\mathrm{P}{\mathrm{E}}_{\alpha }$	=	Mean percentage error for α-opic quantities
NIF	=	Non-image forming
$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{P}{\mathrm{E}}_{\alpha }$	=	Root mean square percentage error for α-opic quantities
PCA	=	Principal component analysis
$S_i\left(\lambda \right)$	=	PCA components
$S_{Me}\left(\lambda \right)$	=	Measured spectral power distribution
$S_{Re}\left(\lambda \right)$	=	Reconstructed spectral power distribution
SPD	=	Spectral power distribution
$T_{cp}$	=	Correlated color temperature
x$,y$	=	Chromaticity coordinates
$x_D,y_D$	=	Daylight chromaticities, daylight locus

Acknowledgments

The authors would like to thank Eric Rockstädt, Lukas Liegener, Dimitri Belostotski, and Frederic Rudawski for their valuable support in programming.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed on the publisher’s website.

Additional information

Funding

The authors have disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Aicha Diakite-Kortlever received a fellowship by the Velux Foundation (grant number 1087: “Development and Application of Spectral Sky Models in Urban Planning”).