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Title: Contribution to the assessment and improvement of Colour Rendering

Metrics for artificial light sources

Author(s): Renoux, D.; Nonne, J.; Sabol, D.

Journal: Proceedings of CIE 2012 'Lighting Quality and Energy Efficiency'

Year: 2012,

Event name: CIE 2012: 'Lighting Quality and Energy Efficiency, place: Hangzhou, China, date: 19

- 21 September 2012

Funding programme: EMRP A169: Call 2009 Energy

Project title: ENG05: Lighting: Metrology for Solid State Lighting

Copyright note: This is an author-created, un-copyedited version of an article accepted for

publication in the Proceedings of CIE 2012: 'Lighting Quality and Energy Efficiency.

EURAMET Secretariat Bundesallee 100 38116 Braunschweig, Germany Phone: Fax: [email protected] www.euramet.org +49 531 592-1960 +49 531 592-1969

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Contribution to the assessment and improvement of Colour Rendering

Metrics for artificial light sources

RENOUX D.1, NONNE J.2, SABOL D. 3 1 & 2

Laboratoire National de Métrologie et d’Essais, Trappes, France, 3 Slovenský Metrologický Ústav, Bratislava, Slovakia

[email protected]

Abstract

The current Colour Rendering Index (CRI) of the CIE (International Commission on Illumination) fails to predict the subjective ranking of the newly introduced lighting sources based on LED (light emitting diode). The aim of this study is to draw a proposal to completing or supplementing the actual and internationally recognised but failing CIE CRI. To acquire a deeper understanding, which would result in more accurate psycho-physical representation of the colour rendition, an extensive review and assessment of the new proposals and the CIE current indices for colour rendering are performed. The assessment is based on an extensive computation of the relevant metrics and colorimetric calculations and on a visual experiment. The subjective experiment uses a real size furnished living room featured with a special diffusing window in the ceiling to change only the spectra of lighting. Preliminary results of this on-going study are given.

Keywords: Colour Rendering, LED lighting, colour quality index, colour metric, colorimetry

1 Introduction

The term colour rendering can be associated with many definitions. CIE defines colour rendering of an illuminant as:”the effect of the illuminant on the colour appearance of objects by conscious or subconscious comparison with their colour appearance under a reference illuminant”[1]. This definition has been implemented in a numerical general index well-know under the acronym CRI Ra, approved by the CIE members and revised the last time in 1974. This well established and recognised index, used in many standards and regulations, on behalf several published studies, e.g. [2, 3] fails to predict the subjective ranking of recently introduced solid-state lighting (SSL) which are today LED or OLED (organic LED) based lighting. The CIE recommends to develop new indices for complementing or supplementing the CRI Ra. The issue with CRI is not the only one encountered with quality metrics applied to SSL due to many factors like their specific Spectral Power Distribution (SPD), their point-like source emission, their emission directivity, their junction temperature dependence, and the driving electronics.

To tackle theses issues the EMRP (European Metrology Research Program) funds an on-going Joint Research Project, the ENG05 LIGHTING: Metrology for Solid State Lighting, involving about fifteen European National Metrology Institutes (NMIs). The ENG05 aims to the development of more reliable and robust metrology for SSL to accelerate the uptake by the consumers of this new lighting, providing them with clear and unambiguous specifications. The underlying goal is to exploit the energy saving potential of this very efficient lighting. In the framework of this project several NMIs work on quality metrics related to the subjective perception of lighting, namely the colour rendition and the visual comfort. The presented study focuses on colour rendering metrics.

The first part summarizes the large review of colour rendering metrics which has been conducted, their analysis and implementation. These metrics have been applied on a collection of SPDs and the results analysed based upon the technology of lighting. The second part describes the large subjective experiment which has been conducted in real life condition. The preliminary results are presented computed for some metrics deemed worthy of consideration by CIE. This paper is just a summary of the preliminary results of the work performed for the ENG05 project.

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2

Review of Colour Quality Indices or metrics

A bibliographical survey of proposals for new metric for colour rendition had been completed. The literature search covered all types of publications: academic or technical papers, presentations, conferences proceedings, qualifying or quantifying colour rendition of light sources. The first targeted key feature for the search was any scientific or technical communication dealing with the colour rendering. After realizing that the underlying colorimetric support plays a primary role in the colour rendition metric/index, a deeper survey focused on uniform colorimetric spaces, and related colour shifts computation, has been conducted. Today, the collection of relevant papers comprises at least 48 journal publications, 14 conference proceedings, 2 diploma theses and 4 recommendations from CIE. The relevant indices identified by the CIE are included. Contacts have been undertaken to get updated methods and implementation details. Different classification and analysis have been performed. Family of indices and metrics and their colorimetric components have been identified and analysed. The studied methods for the colour rendition can be organised into the following categories:

Generic reference source based methods: the principle of these methods is based on comparing the colour coordinates of the rendered colour of a set of test colour samples (TCS) illuminated by: (i) the test light source, and (ii) the corresponding reference light source. The reference light source is either Plankian radiator or daylight depending on Correlated Colour Temperature (CCT) of the tested light source. A chromatic adaptation transform (CAT) is usually performed on the test source to match the reference source. Most of the methods are reference-based exploiting different aspects of colour rendering property (e.g. fidelity, gamut, categorisation, harmony), using different set of TCSs with different colorimetric computation and are briefly described hereafter.

Fidelity based methods: the average colorimetric distance between the tested and reference stands for the colour rendition fidelity. The only internationally accepted method quantifying colour rendering properties of light sources is the Colour Rendering Index (CRI), general index Ra, established by CIE in 1965 [1]. It is archetype of the reference source based method and many other methods have been derived as modifications of CRI, updating the colorimetric computation [4]. For instance the first version of CRI-CAMUCS [5] is exactly the same method but with the latest update of colorimetric calculations. The CIE updated the CRI index proposing Ra96 in 1999 but has not been adopted.

Non fidelity based methods: they are in fact the fidelity based methods which however includes subjective aspects of colour perception like flattery or colour preference (Flattery index [6], Colour Quality Scale (CQS) [7]). The flattery index adjusts chromaticity with preferred colour shifts while the CQS general index Qg in the colorimetric difference computation does not penalise the contribution of increased colour saturation.

Gamut based methods: the principle characteristic for these methods is absolute or relative measure of the area bounded by chromaticity coordinates of TCSs. Larger surface suggests ability to render more saturated or a broader range of colours by the light source (GAI/GAS) [7][8]. One method uses also the brightness as a third dimension to derive a feeling of contrast index (FCI [9]). Other methods develop a volume of reproducible colours [10][11]. These methods are generally intended to be supplementing the fidelity index to establish a two-dimensional metric [8].

Statistical methods: these methods use a broad set of TCS and rather than computing an average property they count whether the rendered colour shift to the reference fall within a tolerance volume, Colour Fidelity Index CFI [12], or if the rendered colours fall within the same colour category than the reference. Reference [13] presents an index based on area intersection of the colour categories (CCRI) under the reference and the test light source. Colour harmony method: harmony is computed from predictive harmony formulae applying to a set of pairs and triads of colours. Then the harmony rendering index (HRI) [14] is derived from the absolute difference between the harmony coefficients of the test and the reference source respectively.

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Other methods: the ranking colour rendering index (RCRI) [15] is based on the CRI-CAMUCS method but rather than take a continuous scale the method use an ordinal scale.

Memory colour methods: the memory rendering colour index (MCRI) [16] is not a reference-based method, the method does not use any reference light source, instead the method uses similarity functions in a uniform colour space that describe the degree of similarity of memory colour objects or tones that have been a priori determined by performing visual rating experiments.

3 Computation of selected CQI metrics

In this sections the results of computation for the selected reviewed indices/metrics examined by a collection of 122 SPDs including classical lighting and LED-based lighting sources, are presented. The metrics have been implemented in a modular C++ program exactly as the authors recommended to do it with the original data (test colour samples/TCS and parameters) or referenced data (Munsell Atlas, Macbeth ColourChecker ® SG). Some of them have been compared to their original implementation – mainly Excel ® spreadsheets – whenever they are provided by the CIE or directly by the authors. It must be stressed out that our computed HRI Dataset of spectral power densities (SPD) do not match exactly the author’s results, nonetheless both results show sufficient correlation for a preliminary assessment.

3.1 Dataset of spectral power densities (SPD)

The SPD collection has been established from the SPDs of author’s Excel ® spreadsheets, CIE publications for standard illuminants, and LNE’s measurements. The collection can be broken down in the following main subsets:

• 7 SPDs of incandescent, halogen lamps and Planckian radiator with or without filter, • 49 SPDs of fluorescent tubes and compact lamps, with CIE standards (Fn, F3.n) • SPDs of miscellaneous lamps (HMI, Mercury arc, Xenon arc)

• 9 SPDs of HPS lamps, including some CIE standards (HPn)

• 52 SPDs of 3 subsets of LED lamp types including: phosphors converted (PC), phosphors converted with NUV excitation (NUV), and LED clusters.

The SPDs have been sorted to easily see the result per type. Similar SPDs in each main subset have been removed and a more accurate selection using correlation analysis will be performed later. Spectra of LED based lighting sources are shown in Figure 1.

LED clusters & phosphor converted spectra (43)

0,00000 0,20000 0,40000 0,60000 0,80000 1,00000 1,20000 380 430 480 530 580 630 680 730 780 Wavelenght (nm) S p e c tr a l d e n s it y

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3.2

Correlation between metrics

The following Tables 1 and 2 for the fluorescent and LED-based sources respectively expose the Pearson correlation coefficient of original or modified indices and combined indices obtained for the collection of 122 SPDs. All the acronyms of indices of the table can be found in the Section 2. W e explore some combined metrics using the weighted or un-weighted average of indices (N*index1+ M*index2). The statistical index CFI (CFI xy) has been updated, as recommended by the authors, using the colour appearance model CAM02 (CFI CAM). One interesting result arising from the Table 1 and 2 is that good correlation between the metrics is achieved for the fluorescent light sources but much lower correlation for the LED light sources. Other performed correlations are not exposed here and further analyses are in progress.

Table 1 –Correlation values between the metrics for the fluorescent sources.

Metric/Metric CIE CIE CQS CRI RCRI MCRI CFI CCRI HRI CFI GAI GAS FCI 2*HRI

(Fluorescent) Ra Ra96 Qg CAM xy CAM +Ra +Qg +Ra +Ra

CIE Ra 13.3 0,99 0,99 0,99 0,95 0,97 0,91 0,96 0,82 0,91 0,90 0,99 0,93 0,98 CIE Ra96 1,00 0,99 0,96 0,95 0,92 0,97 0,79 0,94 0,90 0,98 0,90 0,96 CQS Qa 0,99 0,96 0,94 0,92 0,98 0,78 0,95 0,91 0,98 0,89 0,96 CRI-CAMUCS 0,96 0,95 0,90 0,98 0,77 0,94 0,91 0,97 0,88 0,96 RCRI 0,90 0,91 0,94 0,77 0,94 0,85 0,94 0,87 0,93 MCRI 0,81 0,93 0,81 0,82 0,87 0,96 0,93 0,96 CFI - xy 0,87 0,79 0,96 0,77 0,91 0,86 0,90 CCRI 0,74 0,92 0,94 0,95 0,83 0,93 HDI - 2D |r-k| 0,73 0,69 0,88 0,93 0,92 CFI-CAM-UCS 0,83 0,90 0,80 0,89 GAI+CRI Ra 0,89 0,74 0,87 GAS + CQS Qg 0,96 0,99 FCI+CRI Ra 0,97 2*HDI+CRI Ra Average 0,95 0,94 0,94 0,94 0,91 0,91 0,88 0,92 0,80 0,89 0,85 0,87 0,88 0,94

Table 2 – Correlation values between the metrics for the LED sources.

Metric/Metric CIE CIE CQS CRI RCRI MCRI CFI CCRI HRI CFI GAI GAS FCI 2*HRI

LED clusters Ra Ra96 Qg CAM xy CAM +Ra +Qg +Ra +Ra

CIE Ra 13.3 0,98 0,88 0,99 0,85 0,31 0,85 0,94 0,95 0,83 0,44 0,06 0,07 0,99 CIE Ra96 0,91 0,97 0,84 0,30 0,83 0,93 0,93 0,82 0,39 0,09 0,08 0,96 CQS Qa 0,92 0,80 0,58 0,79 0,80 0,72 0,78 0,61 0,48 0,40 0,81 CRI-CAMUCS 0,89 0,40 0,84 0,93 0,91 0,84 0,49 0,17 0,15 0,96 RCRI 0,51 0,73 0,85 0,77 0,73 0,50 0,22 0,12 0,82 MCRI 0,19 0,18 0,04 0,22 0,79 0,81 0,70 0,17 CFI - xy 0,90 0,80 0,99 0,50 0,10 -0,01 0,83 CCRI 0,95 0,89 0,42 -0,06 -0,16 0,96 HDI - 2D |r-k| 0,77 0,22 -0,21 -0,19 0,99 CFI-CAM-UCS 0,54 0,13 -0,02 0,81 GAI+CRI Ra 0,64 0,41 0,33 GAS + CQS Qg 0,87 -0,08 FCI+CRI Ra -0,06 2*HDI+CRI Ra Average 0,70 0,70 0,73 0,73 0,66 0,40 0,64 0,66 0,59 0,64 0,48 0,22 0,18 0,65

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4 The subjective experiment

4.1 Description of subjective room.

The aim of the subjective test room (see Figure 2) is to record the observer’s perception of the colour rendition in a familiar environment having only the spectrum of the light source being changed. The change of the spectrum only avoids the contribution of other parameters not related to the colour rendition that could alter the subjective scoring such as light distribution. The living room is one of the most familiar places and one of the most versatile places for the colour rendition experiment for interior lighting. Therefore we built a real living room (4,5 m x 4 m) with a special design of the lighting system.

The best location in order to uniformly illuminate the room and the objects inside is the ceiling. A removable transparent, diffusing window (1,2 m x 1,2 m) was integrated into the ceiling and a mechanical system was built above the room to place 12 clusters of lamps above the diffusing window. The mechanical system supporting the lamps comprises 3 frames: one fixed frame located just above the diffuser, and two sliding frames that can be quickly brought above the diffuser and removed. Each cluster is a set of identical lamps. The light level of each cluster inside the room can be adjusted by the number of lamps and in addition by a dimming system whenever it is available. Black panel covers are placed in such a way that the light from the 2 sliding frames cannot enter the central diffusing window when the frames are moved away from the centre to the sides. This enables to warm up the lamps on the sliding panels while the fixed frame illuminates the room. An external switching board and a potentiometer board control the power on/off and the dimming levels of the lamps. As a result less than 10 seconds are needed to switch the lighting source.

Figure 2 – Views of the Subjective Room.

The room’s decor was selected to provide a casual European home ambiance. Thus the individuals, after introduction to the room and some preliminary training, are placed in the best condition to judge the lighting as if they were at home or at a friend’s place. The decor was chosen in a view to have the largest choice of familiar colours with different usual materials, namely: wood, rock, textile, wool, plastic, metal, glass, ceramic, candle wax, paper and painted surfaces. We added some natural objects as several plants in a corner, 12 kinds of fruit and vegetables in a basket (see Figure 3), and the Macbeth digital colour chart.

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Figure 3 – appearance of fruits/vegetables

(top, left to right: HAL, LED WW, CFL, LED WR, RGBY; down, left to right: FL, LED NUV, LED CW, LED RGB)

4.2 Specifications of lighting sources

The choice of the lighting sources was governed by two constraints. The constrains are: 1. It is necessary to use all lighting technologies currently available, including LED, in order to develop a new colour rendering index, which must be established for any type of lighting; and 2. Two different colour temperatures are needed, warm and cold, to enable us to study the metrics on the whole set of lamps or separately on the lamps having the same colour temperature to quantify the effect of the colour temperature that could contribute to preference in a living room based experiment.

We selected nine different light sources divided into two groups of colour temperature: around 5000 K and 2700 K. There are: one halogen source (warm); two fluorescent sources (one warm, one cold); and six LED sources: one RGB cluster (cold), one RGBY cluster (warm), two blue excitation with yellow phosphor (both warm and cold), one blue peak excitation with yellow phosphors and a red LED peak (warm), one purple (NUV) excitation with RGB-phosphors (cold). The LED-based spectra are represented on Figure 4.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 380 480 580 680 780 Wavelenght (nm) S p e c tr a l d e n s it y LED WW 2700K LED WR 2700K LED RGBY 2700K LED RGB 5000K LED NUV 5000K LED CW 5000K

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Each solution was populated with lamps to produce the same illuminance level inside the room: 345 lux (± 9%) at one metre height at the centre of the room. The nine light sources were characterized in terms of CCT, CRI Ra, CQS, MCRI, CRICAM UCS, RCRI. These measurements were performed with two different set-ups: the first working with a white reflectance diffuser (Spectralon) and a spectro-radiometer and the second working with a cosine corrected head connected to another spectro-radiometer. The results of the characterisation are given in the Table 3, showing significant differences convenient for a discriminating experiment.

Table 3 – characterization of the light sources inside the test room ( K ) C I E R a C Q S M C R I U C S R C R I F L 5 0 0 0 K 4 7 4 5 9 3 . 7 9 6 . 5 9 2 . 3 9 4 . 3 1 0 0 . 0 L E D N U V 5 0 0 0 K 5 0 2 4 9 8 . 1 9 9 . 1 9 0 . 7 9 8 . 5 1 0 0 . 0 L E D C W 5 0 0 0 K 5 4 8 1 7 0 . 7 7 1 . 3 7 5 . 7 7 1 . 0 5 6 . 1 L E D R G B 5 0 0 0 K 5 2 9 3 3 5 . 6 6 2 . 9 9 4 . 5 4 9 . 7 5 6 . 1 L E D W R 2 7 0 0 K 2 9 0 6 8 8 . 6 9 0 . 5 9 1 . 2 8 6 . 8 9 8 . 0 C F L 2 7 0 0 K 2 7 0 8 8 2 . 0 7 5 . 8 7 7 . 9 7 6 . 0 7 4 . 4 R G B Y 2 7 0 0 K 2 7 8 1 7 6 . 2 7 9 . 1 9 0 . 0 8 0 . 3 8 0 . 9 H A L 2 7 0 0 K 2 7 3 9 9 9 . 7 9 6 . 9 8 9 . 4 9 9 . 0 1 0 0 . 0 L E D W W 2 7 0 0 K 2 6 2 4 8 2 . 8 7 9 . 4 8 5 . 2 7 8 . 8 7 4 . 4

4.3 The subjective experiment

43 observers volunteered for the experiment, 14 females and 29 males aged from 20 to 62 years. They all successfully passed the 15 Farnsworth Munsell desaturated vision test under a daylight source.

At the beginning of the experiment, observers were instructed about the purpose of the test and of the different phases of the test. Then they were given an explanation of the questionnaire and were trained with four lighting sources allowing them to get familiar with the variations in the perceived colour. The selected training sources were the following: FL 5000K, HAL 3000K, LED WW 3000K, LED RGB 5000 K.

Finally the observers were asked to rate the colour rendition of each lighting source, i.e. colour appearance of objects under the light from each lighting source. The test room was illuminated in succession by all lighting sources in such a way that moments of darkness were prevented by swapping (changing) the lighting sources. The swapping was executed in line with nine pre-defined orders. The observer experienced two different sequences out of nine available and ranked the colour quality perception in each.

The used scale is a 5-point quality scale; from 5 (excellent) to 1 (very bad), 3 being the neutral point of the scale. Eight rendering attributes have to be rated. The rendering attributes are listed hereafter, followed by some proposed definitions or means that were explained to the observers to guide their judgement:

1. overall preference - according to the observer’s own criteria,

2. fidelity of colours - how much colour of objects match their usual colour, 3. quality of vividness - how much the observer likes the vividness,

4. overall naturalness - global perception of naturalness in the room, 5. naturalness of plants - how much the foliage of the plans appear natural, 6. naturalness of fruit/vegetables - how much the fruit/vegetables appear natural, 7. naturalness of complexion - how much the observer’s complexion appear natural

with the help of mirrors for his face

8. rendering quality of the colour chart - assessment of observed colour balance, saturation, discrimination.

Note: a selected example was given to illustrate the difference between “naturalness” and “fidelity”; our own complexion could appear more coloured or tanned, so presenting a low degree of fidelity while keeping a good degree of naturalness.

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Figure 5 is a plot of the averaged results, over the all observers, of each rated attribute for the nine light sources; we only plot the global naturalness in order to maintain the graph’s clarity. Cold and warm lighting sources are within the same range except the RGB 5000 K.

The correlation and statistical analysis of the subjective results are still on going. The main goals of these analyses are to compute intra- and inter-observer variability, the correlation between attributes, and an attempt to model the preference against the other rendering attributes. W aiting for the results of the analysis, we can just comment on the curves and observe that there are some strong correlations between the different rendering attributes except for the quality of vividness. One result, that will be more thorough understood later, is that the lack of saturation always implies a lower perceived quality, but also an excessive saturation can implies lower perceived quality as well.

0.5 1 1.5 2 2.5 3 3.5 4 4.5 FL 5000K LED NUV 5000K LED CW 5000K LED RGB 5000K LED WR 2700K CFL 2700K LED RGBY 2700K HAL 2700K LED WW 2700K Global preference Fidelity Quality of vividness Naturalness Chart quality

Figure 5 – mean values of each attribute

5 Comparison of CQI metrics and subjective scores

Figure 6 plots the “preference” rating, averaged over all observers, and the results of five metric/index proposals for each light source. Table 4 shows the Pearson correlation of the metrics/indices with the “preference” rating of the subjective experiment considering different subsets of the tested lighting sources.

Table 4 – Pearson coefficient of correlation with general indices

CRI Ra CQS MCRI CRI CAMUCS RCRI

all light sources (9) 91,3% 76,0% -6,6% 86,5% 78,8%

cold sources (4) 99,7% 96,4% -1,3% 99,7% 89,6%

warm sources (5) 59,7% 56,9% 10,5% 65,6% 61,3%

all LED sources (6) 92,3% 84,0% -0,1% 92,3% 84,2%

all cold LED (3) 99,8% 95,2% -20,2% 99,6% 86,0%

all warm LED (3) -3,7% 47,7% 98,3% 64,1% 71,3%

These results are preliminary results; deeper analyses and supplementing subjective experiments might be required in order to draw the final statements. The number of lighting sources by category is too low to get robust assessment. Nevertheless some interesting trends arise from the Table 4. Predictions for the cold sources are better than predictions for the warm sources. For the cold sources the CRI Ra and CRICAM UCS show a very good prediction. CRI Ra completely fails for the warm LED sources, while the remaining index proposals give good or average predictions. On the other hand MCRI fails for the majority of

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the sources, however gives a very good, in fact the best, prediction for the warm LED. The other reviewed and implemented metrics will be compared in the same way.

20 30 40 50 60 70 80 90 100 110 120 FL 5000K LED NUV 5000K LED CW 5000K LED RGB 5000K LED WR 2700K CFL 2700K RGBY 2700K HAL 2700K LED WW 2700K CIE Ra CQS MCRI CRICAM-UCS RCRI Global preference

Figure 6 –mean values of global preference and metric’s predictions

6 Conclusion and perspective

The presented study, within the framework of the running project ENG05, is still in progress, and this paper presents some preliminary results of this study, for the colour rendition and observer’s preference.

To learn about the current or proposing colour rendering metrics, a large review of colour rendering metrics has been conducted. The metrics have been sorted and detailed for a complete analysis. The relevant metrics, including those judged worthy of consideration by the CIE, have been successfully implemented, except the HRI. The metrics have been applied on a collection of 122 SPDs and the results compared against the type of lighting sources. To learn about the perceived quality of lighting a large subjective experiment has been conducted in real life condition. The experiment provides us with important data of subjective ranking for a complete set of lightings representing all currently available technologies.

Considering the detailed review, showing the differences in approaches, the differences of computed predictions and considering the preliminary results of the subjective experiment one can deduce that we are apparently far to find a consensus for a colour rendering metric to better rank the new light sources.

So the continuation of this study will address these issues. Using the developed modular C++ program, which allows the implementation to be easily modified, new metrics, refining and supplementing the proposals, will be tested against the obtained subjective scores. The detailed subjective scores, with the help of relevant statistical analyses, will be further exploited to model observer’s preference. Additional subjective experiments might be also carried out to consolidate the outcome of this study.

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Acknowledgment

The research leading to these results has received funding from the European Union on the basis of Decision No 912/2009/EC.

We wish to thank to all authors who shared their metric implemented, in particular to OHNO Y. and SMET K. for their willingness to share their metric implementation Excel ® spreadsheet (CQS and, MCRI respectively) and we also thank Dr FUMIO O. from Mitsubishi Chemical who donated us incoming NUV peak and three phosphors converted LED which were used in the experiment.

We kindly appreciate effort and valuable contribution of all observes participating in the study.

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References

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