We examine the difference between the newly developed IES TM-30 color indices and some of the most common previously established color indices for LED systems which are used for lighting purposes, focusing on the influence of realistic spectral variations among different system designs and manufacturing runs. We find a significantly stronger influence of the employed blue InGaN wavelength on TM-30 Rf and Rg than on CRI Ra and FCI. In addition, for the established combination of green converted InGaN chips with red InGaAlP chips, we observe large differences in the effect of the wavelength of the red emission of InGaAlP chips on Rf and Ra.
© 2017 Optical Society of America
Currently, the application requirements regarding color quality for general lighting refer to CIE Ra in most countries in the world. Since the definition of Ra, continuing research in the field of color perception has led to improved metrics for most steps involved in the calculation of Ra . In addition, researchers started to agree that a single number is not sufficient to describe the color quality of a light source sufficiently [2–4]. These developments have been used in the IES TM-30-15 color metric  consisting of the color rendering or fidelity index Rf, the gamut index Rg, and a standardized plot visualizing color deviations.
1.1 Color rendering index comparison
Rf has been compared to Ra for a large set of light sources, showing a good correlation with significant scatter. Sources with narrow emission peaks have been identified to show the tendency of a lower Rf compared to Ra . A recent study shows good agreement of perceived color differences with Rf , but employed only LED light sources with Ra below 70, which, according to existing regulations, do not qualify for most general lighting systems. In addition, differences in the correlation with different color indices could hardly be worked out in this study as the employed LED light sources show a good correlation between Rf and Ra.
Until now, we only know of one perception study indicating an improvement of the correlation of Rf to human perception of color rendering compared to Ra. In this study , a very poor correlation of the perceived normalness with Ra with an r2 value of 0.06 was obtained, while the correlation with Rf was also not fully convincing with r2 = 0.35. A better correlation with r2 = 0.83 was obtained for a linear combination of Rf with Rcs,h1, which is the chroma shift in the nominally red hue angle bin 1. The study has been conducted using 26 combinations of LED spectra including two types of blue LEDs with about 450 and 475 nm dominant wavelength, covering a wide range of Rf and Rg values, while the full spectra of the 26 combinations have not been disclosed.
Further studies on the comparison of Ra and Rf would be helpful for quantifying the benefit of Rf compared to Ra regarding the correlation with human perception of color rendering. Such a study would benefit from the use of light sources with a poor correlation between Rf and Ra in order to distinguish differences in correlation with human perception. One purpose of this work is to identify spectral features available in common LED light sources which cause large deviations between Rf and Ra, making them ideal candidates for related perception studies.
1.2 Color gamut index comparison
Gamut indices quantify the average chroma change of objects illuminated with the test light source relative to a reference light source, which correlates to the vividness of the appearance of colored objects. Prior to the definition of Rg, GAI has often been used for this purpose . A similar aspect is quantified by FCI , which has been demonstrated to correlate well with the human perception of vividness [9,10]. A typical spectral feature for light sources which increase vividness compared to incandescent lamps is a spectral gap in the yellow region close to 580 nm , which can be realized in LED spectra in multiple ways.
The comparison of color rendering and gamut indices is typically done for color coordinates on the blackbody locus. Several studies suggest an apparent preference for light sources below the blackbody locus, both regarding whiteness  and preference , while other studies done with a different setup indicate that the effect of chromaticities off the blackbody locus on vividness and preference is very weak . This work compares the dependence of gamut indices on the chromaticity relative to the blackbody locus and on typical features of LED spectra in order to work out the differences among the analyzed indices.
2. Investigated LED spectra
Most commercial LED systems are based on phosphor converted LEDs, where a mixture of red and green phosphors is applied on a blue emitting InGaN chip. The phosphors convert a part of the blue light into green, yellow and red. Together with the remaining blue chip emission, this results in white light. The phosphor emission is usually optimized for maximum efficacy at a given target Ra, and the phosphor amount is adjusted such that the target chromaticity is obtained. For low Ra target values, the spectrum is adjusted such that the amount of long wavelength red is minimized, maximizing luminous efficacy. Higher Ra targets require a larger red content, leading to lower luminous efficacy. In all cases, a blue peak wavelength in the range between 430 and 460 nm, corresponding to ~435 to ~465 nm dominant wavelength, is usually chosen because of maximum efficacy. However, the blue wavelength is usually not specified in datasheets of commercially available LEDs, enabling the manufacturers to use a wide production range of blue InGaN chips for white LED products, increasing the overall yield as the wavelength spread even across a single production wafer can reach more than 10 nm. In this work, we investigate three representative blue dominant wavelengths, 442 nm, 450 nm, and 458 nm, with phosphor combinations designed to achieve a typical CRI of 70, 80, and 90.
Higher luminous efficacies can be obtained when a narrow banded red emission is employed, such as the emission of InGaAlP chips. This implies a multichip solution with blue and green emission from a green converted InGaN chip combined with a red InGaAlP chip. We call this combination “Brilliant Mix”. In this combination, a yellow gap in the overall spectrum can be adjusted by the wavelength of the red chip, with a longer red wavelength leading to increased vividness, which can be quantified by FCI . However, a yellow gap can also be achieved using an adequately designed phosphor mixture. This is often preferred, as Brilliant Mix solutions require a temperature dependent adjustment of the InGaAlP chip due to the strong temperature dependence of its efficacy, which implies a high effort in the driver electronics.
The spectra of both types of LEDs have been simulated using a calibrated raytracing algorithm including experimentally calibrated properties of the LED phosphors. The simulation of the spectra enables the precise adjustment of identical chromaticity for different LED types, which is not available in experiment for all investigated chromaticities, chip wavelenghts and phosphor combinations. A selection of the LED spectra investigated in this study is shown in Fig. 1.
It should be noted that the phosphor absorption can effectively shift the blue peak transmitted through the phosphor. This is mainly the case for the CRI 70 phosphor mixture and for all Brilliant Mix LED combinations, where the green phosphor exhibits an absorption maximum close to 460 nm, resulting in a shift of the transmitted blue peak towards shorter wavelengths, and effectively broadening the 458 nm blue peak. Hence, identical blue chips will result in different peaks in the blue spectral range when different phosphors are applied. In this study, the blue wavelength always refers to the dominant wavelength of the chip, regardless of a peak deformation due to phosphor absorption.
3. Comparison of rendering indices
Figure 2 shows the comparison of Rf and Ra for the investigated LED spectra at 3000K on blackbody locus. Qualitatively similar results have been obtained at higher color temperatures. As long as a chip wavelength of 450 nm is employed for phosphor mixtures, Rf and Ra give very similar values. Apart from the CRI 70 mixture, where the blue peak is shifted towards a shorter wavelength due to phosphor absorption, both longer and shorter chip wavelengths result in a significant penalty in Rf, while Ra shows only a small change. This results in the situation that, for example, a CRI-80-phosphor with 450 nm reaches almost the same Rf as a CRI-90-phosphor with 458 nm, while Ra shows a difference of 13 points.
This strongly enhanced influence of the blue wavelength on Rf compared to Ra is even more pronounced in Brilliant Mix spectra. Here, an 8 nm change of the blue dominant wavelength from 450 to 442 nm results in a reduction of Rf by about 13 points, while Ra only decreases by 4 to 5 points, regardless of the employed red InGaAlP wavelength. The main reason for this strong dependence of Rf on the blue wavelength is the use of the CAM02UCS color space in TM-30 instead of u*v*w* in CIE Ra , because CAM02UCS is reported to yield a better correlation with perceived color differences . However, the wavelength influence of a blue peak in the range between 430 and 460 nm, as it is typical for LED light sources, has not been investigated in that study.
The opposite dependence is observed for the red InGaAlP wavelength in Brilliant Mix LEDs. Here, Ra shows a continuous decrease by at least 10 points for a dominant wavelength shift from 612 to 625 nm, while Rf exhibits only a very weak decrease. Both differences lead to extreme deviations between Rf and Ra for certain Brilliant Mix variants. The combination of short wavelength blue and red exhibits an Ra of 86 and an Rf of only 70, while the use of long wavelength blue and red leads to an Rf of 86 and an Ra of only 78. These discrepancies are larger than reported earlier [1,16] for all types of spectra including fluorescent and different types of LEDs.
4. Comparison of gamut indices
The gamut indices FCI, Rg, and GAI at 3000K of the investigated LED spectra are compared in Fig. 3. Similar to Rf, Rg exhibits a strong dependence on the blue wavelength. Taking into account the blue wavelength shift to shorter wavelengths due to phosphor absorption for the CRI 70 phosphor mixture (lowest FCI) and for the Brilliant Mix LEDs, all LED spectra follow the same trend, showing an excellent correlation of Rg and FCI for identical blue peaks. Even the systematically different Brilliant Mix spectra with varying red wavelength follow this trend, with longer red wavelengths achieving the larger gamut indices, corresponding to increased vividness .
While FCI is almost independent of the blue wavelength, Rg decreases significantly towards longer wavelengths and increases towards shorter wavelengths. This dependence is so pronounced that Rg of a CRI 90 phosphor converted LED pumped with 442 nm blue light, exhibiting a balanced spectrum in the green to red range, is smaller than Rg of a CRI 70 LED with 450 nm, where the phosphor emission consists of a broad yellow peak. In other words, Rg does not predominantly quantify the effect of diminished yellow emission and the corresponding enhanced saturation of red objects on color gamut. Instead, the spectral gap in the blue-green region is dominating the Rg value, with short wavelength blue leading to enhanced saturation of yellow and green test colors in the TM-30 metric, as shown in Fig. 4. It has been shown [7,17] that the saturation in the green to yellow region has a much smaller effect on color preference than the saturation in the red region. Hence, it can be expected that the change of Rg when varying the blue wavelength will only exhibit a weak correlation to color preference. The difference in the blue wavelength dependence among FCI and Rg hence stresses the difference in the purpose of the two indices, with FCI being designed as a preference index, while Rg is designed as a gamut index.
GAI exhibits a similar behavior as Rg, but shows a weaker relative dependence on the blue wavelength, as the dependence on the phosphor emission spectrum is slightly stronger than the blue wavelength dependence.
5. Chromaticity dependence
The above described trends are very similarly observed at all color temperatures between 6000K and 2700K, with a weak dependence of the absolute values of Rf and Ra on the correlated color temperature (CCT) mainly caused by the different weight of the deep red and blue-green spectral regions at different color temperatures. The gamut indices exhibit clear trends inherent to their definition with FCI systematically decreasing and GAI systematically increasing with increasing CCT, while Rg is almost CCT independent for identical phosphor solutions as intended by its definition.
If the chromaticity is varied at constant CCT along a Judd line, the rendering indices Ra and Rf both exhibit only small variations for chromaticities closer than ~12 MacAdams steps from the blackbody locus, as reported earlier for Rf . In contrast, as shown in Fig. 5, gamut indices exhibit a very strong dependence on the distance from the blackbody locus, however to a strongly different extent.
All gamut indices show a systematic increase with increasing distance for chromaticities below the blackbody locus. This almost linear increase is very similar for all types of LED spectra and shows no systematic dependence on the chip wavelengths or the phosphor solution. If the color coordinate is shifted above the blackbody locus, the trend continues and the gamut indices decrease. However, the ratio between the slope of this chromaticity dependence and the difference between different spectral shapes varies strongly among the investigated gamut indices.
Relative to the difference between different phosphor solutions, the chromaticity dependence is strongest for GAI. Only 8 MacAdams steps below Planck, GAI of a CRI 80 phosphor solution with a distinct yellow emission peak equals GAI of a high gamut phosphor solution with a yellow gap in its emission spectrum on Planck. In other words, GAI is more sensitive on the chromaticity than on the general shape of the emission spectrum. In contrast, FCI exhibits the weakest relative dependence on chromaticity. Rg, which shows an intermediate dependence, suggests a CRI 80 phosphor mixture reaches the gamut of a CRI 90 phosphor mixture when its chromaticity is shifted about 15 MacAdams steps below the blackbody locus.
These differences reflect the differences in the chromatic adaptation calculations. While GAI includes no chromatic adaptation at all, Rg uses CAT02, which is believed to be the best currently available adaptation formula. Hence, it is plausible that the predictions of Rg are closer to human perception. However, this is very difficult to verify as the chromatic adaptation influence depends strongly on the experimental setup used in perception studies, so a large scatter of experimental data on this aspect can be expected.
We have found significant differences in the dependence of color indices on LED chip wavelengths. Rf, Rg and GAI exhibit a much stronger dependence on the blue chip wavelength than Ra and FCI. As the InGaN chip wavelength additionally exhibits a systematic temperature drift by ~5 nm within an 80°C temperature range as it is typical for LED applications, this implies also an unavoidable and significant temperature dependence of Rf, Rg and GAI for most blue LED wavelengths. This is particularly relevant when the same LED product is used in different applications with different thermal properties, or when lighting systems have a high thermal capacity and hence only reach their nominal temperature after more than half an hour of operation. Hence, the use of Rf in application requirements can increase the cost of solid state lighting, as it would negatively impact the chip usage, the production yield and consequently the LED cost, in particular if these requirements have to be fulfilled within a wide temperature range. Alternatively, the general level of Rf could be increased in order to fulfil the requirement for a wider range of chip wavelengths. However, this would lead to a reduced energy efficiency of solid-state lighting.
The improvements in the calculation of Rf compared to Ra, like the use of the CAM02UCS color space, the larger set of color samples, or the improved chromatic adaption calculations, strongly suggest a significant improvement in its correlation with human perception of color rendering. The degree of this improvement for commercially relevant light sources is not yet fully quantified. Hence, further perception studies on these differences are suggested. These studies require spectra with strong differences between both indices. Such spectra with high application relevance are presented in this paper. Due to the increasing importance of gamut indices and chromaticities below blackbody, and due to the strong differences among various gamut indices as also shown in this work, perception studies investigating these aspects would also be highly beneficial for the ability to reliably evaluate and optimize the attractiveness and efficiency of lighting.
German Federal Ministry of Education and Research (BMBF) (FKZ 16ES0267K)
The authors acknowledge John Selverian for programming the calculation of several color indices, and Elmar Baur and Alexander Wilm for valuable discussions.
References and links
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