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Abstract
The color matching possibilities between (reference) phosphor-converted LEDs (pc-LEDs) and replacement metameric LEDs made by color mixing technology (cm-LEDs) were evaluated in the classical 20th century CIE 1976 color space developed for perpendicular viewing (based on a 2° colorimetric observer) and in the latest CIE 2015 cone fundamental color space developed for wide field of view observers (10° colorimetric observer). For each given pc-LED 10 different sets of cm-LEDs were designed and evaluated for color consistency in 2°and 10° color spaces. There were 10 different B-color LEDs considered along with constant RGA LEDs. There are thousands of possible distributions that are metameric in the CIE 1976 color space and thousands of possible distributions that are metameric in the CIE 2015 color space for each set of LEDs. From the population of SPDs, we selected 10 metameric SPDs characterized by maximum differences between chromaticities. The results provide evidence that evaluating LED color consistency based only on the CIE 1976 color space is not fully informative because it may provide inaccurate information about light color consistency when the observer has a wide field of view. There are cases showed in this paper where cm-LEDs are color consistent in the CIE 2015 color space but are not color consistent in the CIE 1976 color space and vice versa. Including color consistency in the new CIE 2015 color space should be treated as an additional evaluation tool proving the user additional information relevant to the intended use of the LED. The results illustrate differences in LED color consistency evaluated in different color spaces and provides incentive go beyond the 20th century color space in the evaluation of cm-LED color consistency.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
There is no doubt that we are in the midst of a revolution in lighting. Over the past 20 years, phosphor-converted LEDs (pc-LEDs) have replaced other light sources in lighting installations. In the U.S., the use of LEDs in commercial buildings increased more than fivefold between 2012 and 2018, when LEDs accounted for about 30% of all lamps used (Fig. 1). This is due to their high luminous efficacy (LES) (Fig. 2) and superb performance including photometric and colorimetric properties, lumen output and lifetime.
Fig. 2. Comparison of the luminous efficacy of pc-LED and cm-LED sources and their projected development [2,3].
It is estimated that by 2030, pc-LEDs will have no further improvements in their LES [2,3]. This is because those type of LEDs, regardless of correlated color temperature (CCT), emit radiation in spectral regions (shaded areas in Fig. 3) where the sensitivity of the human eye, given by the V(λ) function, is weak/negligible, three orders of magnitude less than for the maximum of V(λ) (at 555 nm).
Fig. 3. The spectral power distributions of (a) warm 3000 K and (b) cold 6500 K pc-LEDs (red wine lines) and cm-LEDs (blue lines); the dashed black line is the V(λ) function. The shaded regions illustrate the fact that pc-LEDs have a higher contribution of flux inefficiently converted into luminous flux radiation in their SPDs than cm-LEDs.
A new promising LED technology with high luminous efficacy and good color rendering ability is based on additive mixtures of color LEDs (cm-LED) [4–7]. Typically red (R), green (G), Blue (B) and Amber (A) LEDs are used to generate cm-LED spectral light output S(λ). In the case of cm-LEDs, their radiant flux is better matched to V(λ) than pc-LEDs (Fig. 3), and due to this fact, cm-LEDs can be considered as the successor to pc-LEDs in new lighting installations and also as a replacement for LEDs in lighting installations with multiple luminaires. As an example, consider the case where nine pc-LED lamps are used to illuminate a space. If one of them burns out, only that one will be replaced typically. Because of long lifetimes of LEDs, it is very likely that it will be difficult to purchase an exact replica of the pc-LED manufactured several years ago. In this work, we explore replacement of a pc-LED with a cm-LED.
To reduce the cost of replacing luminaires, the most rational approach is to replace individual luminaires, but you need to consider that the cm-LED luminaire should have the same lighting characteristics as the other luminaires. The new cm-LED luminaire should have a luminous flux, correlated color temperature (CCT) [8–10], and color rendering index (CRI) [11] similar to the remaining pc-LEDs. In addition, there should be no observable color variation between luminaires. This means that a new luminaire based on cm-LEDs must be color consistent with the existing fixtures. Color consistency in a lighting area occurs when there is no noticeable color difference between all the light sources used. This is highly desirable for both aesthetic and practical reasons, and is often required in architecture, museums, and various hospital and industrial settings.
In the days of fluorescent (FL) tube luminaires, color consistency metrics used the CCT and CRI. The CCT is a useful measure when describing differences in blue/yellow hue of light (Fig. 4(a)), and the CRI provides information about the color quality of the environment illuminated by a given lamp in relation to the quality of that space when illuminated by a reference light source.
Fig. 4. Representation at CIE1976 diagram: a) the arrows represent Duv (green/violet color variation) and the CCT (blue/yellow color variation), b) ANSI C78.377-2017 quadrangles requirements in the CIE 1976 diagram.
Neither the CCT nor the CRI adequately describe the green-violet color variation of the emitted light from LEDs. Consequently, the Duv parameter [12–15] has been developed to characterize the color quality of solid-state sources in the CIE 1976 color space (Fig. 4). Positive values of Duv reflect chromaticity coordinates that lie above the blackbody locus, while negative Duv values have chromaticity coordinates that lie below the curve. A negative Duv value indicates a magenta color variation, while a positive Duv value indicates a green color variation. The Duv parameter together with CCT and MacAdam ellipses [16–18] gives the basis for color consistency quantification (ANSI C78.377-2017 standard [19]) given by the standard deviation color mismatch (SDCM) step quadrangle tolerance method. Seven-step quandrangles, which were elaborated in ANSI C78.377 based on 7-step MacAdam ellipses are shown in Fig. 4(b). In practice, a series of constant MacAdam ellipses (also called as SDCM) can be drawn around any target chromaticity coordinates (Fig. 5), and the closer any given lamp chromaticity coordinates are to a target set of chromaticity coordinates, the less color deviation will be experienced when these lamps are placed side by side in an installation. For LEDs having the same CCTs but having different Duv values, there is no perceived color difference between those LEDs within an SDCM of 1 step. An SDCM of 2 or 3 means that there is a slight visible color difference between LEDs observable by some users, and an SDCM of 5 means that color differences are noticeable but acceptable by users.
Fig. 5. The chromaticity coordinates of a) a pc-LED-A (3000 K) and b) a pc-LED-B (6500 K) plotted in the CIE 1976 color space, where black ellipses are SDCMs and red circles are n-step CIE TN 001:2014 u’v’ circles.
Some LED light sources do not follow the traditional nominal CCTs and SDCMs. For them, the interpolation of the ellipses should be done for the LED’s CCT, but this is very inconvenient for practical use. To resolve this issue, the use of u’v’ circles (Fig. 5 red color) to replace SDCM in this white region near the Planckian locus in the CIE 1976 color space is recommended by CIE TN 001:2014 [20]. The “n-step u'v’ circle” corresponds to a n-step SDCM defined as a circle with a radius of “n” times 0.0011 from a center point of given CCT. According to this document recommendations the two sources are color consistent with each other if the maximum value of the “n” is 5 or less – meaning that two light sources chromaticity coordinates are inside the 5-step u'v’ circle [20]. In Fig. 5, the 1, 3 and 5-step u'v’ circles and SDCM are shown for a) a pc-LED-A (3000 K) and b) a pc-LED-B (6500 K). Because circles represent a smaller tolerance than SDCMs, they are more restrictive in terms of color consistency for both LEDs.
However, differences in perceived color for light sources with different SPDs and similar chromaticity were reported [21]. This effect may be due to the fact that the color matching functions (CMFs) of the CIE 1976 color space are derived for a standard 32 years-old 2° colorimetric observer [22,23], a situation in which light reaches the typical human eye almost perpendicularly [24–26]. There are very few situations where people view a source with a 2° spatial extent. More typically light reaches the eye from an extended field of view (FoV). The angular distribution of light entering the eye changes the illuminated area of the retinal surface where cones are distributed unevenly. The density of cones on the retina [27–29] is shown in Fig. 6. There are more blue color receptors outside the area of the central fovea of the retina [30–34]. When going from a 2° to a 10° FoV of the eye, the density of cones decreases by a factor of 15 or so. The responsivity spectra of human cone cells, S, M, and L types on the retina for the 2° [35] and 10° [36] FoV are shown in Fig. 7. Based on those data, the newest CMFs for 10° colorimetric observer (Fig. 7(b)) introduced at 2015 by CIE [36] accounts for these differences. The CIE 2015 10° CMFs differ from the CIE 1976 2° CMFs (Fig. 7(b)), with the greatest differences in the shortwave region, where the sensitivity differences in selected spectral regions exceed 20% between $\bar{z}(\mathrm{\lambda } )$ and ${\bar{z}_{F,10}}(\mathrm{\lambda } )$.
Fig. 6. Human eye illustrative drawing and retina cone density distribution changes as a function of the FoV. At the visualization of cones spread on the retina long wavelength cones (L) are marked as red dots, middle wavelength cones (M) are marked as green dots, and short wavelengths cones (S) are marked as blue dots.
Fig. 7. Relative values a) responsivity spectra of human cone cells, S, M, and L types on the retina for the 2° and 10° FoV, b) the CIE 1976 2° CMF used for CIE 1976 color space (solid line), the CIE 2015 10° CMFs (dash line).
The CIE 2015 (u’F,10, v’F,10) chromaticity diagram, abbreviated as CIE 2015, based on CIE 2015 10° CMFs is given by the solid blue lines in Fig. 8. The CIE 1976 chromaticity diagram (based on CIE 1976 2°CMFs) is given by the black lines in Fig. 8. The blackbody locus is magnified in Fig. 8(b), showing the two chromaticity diagrams where differences between the blackbody locus and the two color spaces are clearly visible.
Fig. 8. (a) The CIE 1976 and the CIE 2015 chromaticity diagrams; (b) zoomed view of the blackbody locus for those two color spaces.
The area of CIE 2015 chromaticity diagram has a restricted range compared with the CIE 1976 chromaticity diagram. A study [37] performed on 54 observers in bipartite 10° FoV circular matching shows that statistically (95% confidence interval) both ellipse orientation, area and shape extracted in the 10° FoV system are very close in CIE 1976 and CIE 2015 (Appendix A: Li et al. 2021 and graphically compared in CIE 1976 and CIE 2015 in Royer et al. 2022 [37,38]) for white light chromaticity near the blackbody locus (4613 K, Duv = 0.0056). Therefore, in the present work, analogous to the CIE TN 001:2014 recommendations for the CIE 1976 color space, it was decided to use the n-step circles u’F,10,v’F,10 in the CIE 2015 color space (in the both systems the n-step circle radius equals n $\cdot $ 0.0011) for color matching.
This work investigates the color consistency between reference pc-LEDs and cm-LED metameric replacements (Fig. 9) using the CIE 1976 and CIE 2015 color spaces. It is interesting to evaluate whether or not the selection of the replacement metameric light source which different SPDs but the same chromaticities in the CIE 1976 color space is sufficient to make it color consistent in the CIE 2015 color space. It is also interesting to evaluate the color consistency in the CIE 1976 color space of replacement metameric light sources that have different SPDs but the same chromaticities in the CIE 2015 color space. The cm-LEDs are based on red, green, blue and amber (RGBA) color LEDs. These studies were performed numerically by independently adjusting the SPDs of color LEDs (RGBA) to produce output radiation with exactly the same chromaticity coordinate as a given reference pc-LED in a given color space.
Fig. 9. The idea of cm-LEDs color consistency numerical evaluation light output adjusted to obtain the reference chromaticity coordinates in the given color space, for 2° and 10° given FoVs.
The CIE TN 001:2014 [20] document gives a 5-step circle tolerance for color consistency. In this work, we apply a more rigorous classification that assumes sources have been matched within a 3-step circle in both color spaces. We consider two light sources to be color consistent if the differences between the chromaticities (DBC) are within the 3-step circle in both color spaces (in the CIE 1976 and CIE 2015 the 3-step circle radius equals 0.0033), which increases the likelihood that the chromaticity difference would be difficult to detect in typical architectural lighting applications.
2. Materials and methods
The warm white (3000 K) and cold white (6500 K) pc-LEDs (Fig. 3 and Table 1) were used as reference LEDs. Based on their SPDs the target chromaticity coordinates were calculated in the CIE 1976 and CIE 2015 color spaces. The SPDs of metameric cm-LEDs were designed by using sets of RGBA color LEDs with chromaticity coordinates equal to reference pc-LEDs in a given color space - thus meeting the CCT and Duv ANSI requirements. For 3000 K LEDs, the CCT must be in the range between 2870 K to 3220 K and Duv between −0.0059 and 0.0061 for 6500 K LEDs, the CCT should be in the range between 6022 K and 7042 K and with Duv between −0.0029 to 0.0091) LEDs were selected with CRIs equal to or greater than 80.
Table 1. The reference pc-LEDs parameters.
Simulations were based on commercially available LEDs (Fig. 10). Their SPDs were measured between 190 nm and 800 nm by a spectroradiometer at Spectrally Tunable LED [39,40] using a 0.5 m integrating sphere against calibrated standard LEDs, with relative expanded uncertainty (k = 2) of ≈ 5%.
Fig. 10. The luminous flux of commercially available LEDs with different peak wavelengths. The solid line is the relative sensitivity of the human eye, V(λ) [39,40].
The information on luminous flux value versus peak wavelength for given commercially available color LEDs (Fig. 10) enabled the selection of RGBA color LEDs for use in cm-LEDs. One type “R”, one type “G” and one type “A” LED were selected for the simulations along with 10 different type “B” LEDs.
The “R” LEDs (Table 2) have the greatest luminous flux when their peak wavelength is around 640 nm. The SPD of a typical “R” LED peaked at 640 nm is shown in Fig. 11(a)). The cm-LEDs based on this type of red emitter will suffer from lack of radiation in the range between 680 nm and 780 nm. However in this range the sensitivity of the human eye, given by the V(λ) function, is very weak (Fig. 10) and its impact on luminous flux is negligible from a general lighting point of view. In addition, this deficiency is advantageous for the luminous efficiency (LES) of this type of light source because its luminous efficiency can reach higher values than when this spectral range is represented in the spectral composition. The choice of green LED is limited by a technology gap [41], and the only good quality LEDs are available with the peak wavelength at about 525 nm (Fig. 11(a)). A similar issue exists with technology limits for amber color LEDs [42,43], and the best choice is emitter with peak wavelength at 590 nm (Fig. 11(a)). There is a wide choice of short wavelength blue emitters. It is possible to find commercially available LEDs with peak wavelengths between 405 nm and 465 nm. Ten of them (Table 2, Fig. 11(b)) were selected to act as “Bn” LEDs, where “n” is from 1 to 10. Each “Bn” LED has a different peak wavelength and FWHM distribution. They were used to get SPDs of metameric replacement cm-LEDs. In Table 2, the chromaticity coordinates of LEDs are provided for CIE 1976 (Fig. 12(a)) and the CIE 2015 (Fig. 12(b)) color spaces. Based on those selected color LEDs, the ten different sets of RGBnA (RGB1A-RGB10A) LEDs were designed. Each of those sets has a different color gamut (Fig. 12).
Fig. 12. The chromaticity coordinates of color LEDs which served as the basis for reference metameric cm-LEDs.
Table 2. The parameters of RGBA LEDs used to obtain the metameric cm-LEDs.
In the case of RGBA cm-LEDs their SPDs, S(λ), are given by Eq. (1), where SR(λ), SG(λ), SB(λ), SA(λ) are SPDs of peak normalized RGBA color LEDs (Fig. 11).
The (u’, v’) and (x, y) chromaticity coordinates of S(λ) for given color space CMFs (Eq. (2)) can be calculated based on its X, Y, Z tristimulus values (Eq. (3)).
The coefficients CR, CG, CB, CA of the LED channels needed for getting metameric values of given cm-LEDs were calculated according to Eq. (4), where X, Y, Z are the tristimulus values the RGBA LED channels and (XR; YR; ZR) are the tristimulus values of reference pc-LED.
There are number of sets of coefficients that are solutions of Eq. (4). The Excel Solver, Nonlinear Generalize Reduced Gradient (NGRG) multi-start function was used to determine the value of the coefficients which ensures that the SPDs of cm-LEDs will be a metameric match to a pc-LED in one color space and the DBC in the other color space is maximized. The 10 solutions (SPDs) were selected for each RGBnA set. These solutions were checked for color consistency with the referenced pc-LED source. It was checked whether that the colorimetric system in which the calculations were performed affects the color consistency and whether among the selected LED sets there are any set that will always achieve color consistency for the selected reference pc-LEDs in both color spaces.
3. Results
The metameric replacements of the reference 3000 K pc-LED-A were designed using LED sets with ten different blue LEDs (RGB1A-RGB10A). For each RGBnA set the relative intensity of those four color LEDs were adjusted to obtain output SPDs (Fig. 13) which meet the selection criteria that: (1) the chromaticity coordinates of replacement LED’s must be exactly the same as the reference pc-LED-A in the CIE 1976 color space (2) with CCT and Duv which can be treated as 3000 K according to ANSI requirements and (3) have a CRI greater than 80. Of all the derived SPDs, the ten with the greatest difference between chromaticity coordinates calculated in the CIE 1976 and CIE 2015 were selected, which gives total of 100 of cm-LED SPDs (LED1-LED100) (Fig. 13(a)). Their lighting parameters are shown on polar type scatter graph which shown is given on Fig. 14 and their values (for given LEDs) are presented on Fig. 15. with CCTs in the range from 2991 K to 3000 K presented as circle line graph (Fig. 15(a)) where each RGBnA LEDs are located on given color line (each LED set is distinguished by different color). Those LEDs chromaticities are presented as blue dot symbols in Fig. 15(a) (which are the overlapped chromaticity coordinates for each of those 100 of the cm-LEDs). Their (LED1-LED100) Duv are shown at Fig. 15(b) and the CRI is in the range from 80 to 92 (Fig. 15(c)) which means that those cm-LEDs may have applications in general lighting.
Fig. 13. The relative SPDs of reference pc-LED-A (3000 K) and its replacement metameric cm-LEDs based on RGB1A-RGB10A color LED sets. Each RGBA set is designed to be metamers for the pc-LED-A at a) CIE 1976 color space, b) CIE 2015 color space.
Fig. 15. The a) CCT b) Duv c) and CRI of cm-LEDs which are metamers of pc-LED-A (3000 K) in the CIE 1976 color space); d) CCT e) Duv and f) CRI of cm-LEDs which are metamers of pc-LED-A in the CIE 2015 color space (black color for calculations in the CIE 1976 color space, blue color for calculations in the CIE 2015 color space.
When the chromaticities of these cm-LEDs (LED1-LED100) are calculated in the CIE 2015 color space, presented in Fig. 16(b) as blue squares, show a much greater variance in their differences from pc-LED-A. While many LED chromaticities fall within 3-step u’F,10,v’F,10 circle (64 LEDs), a significant fraction fall in between 3 and 5-step circles (18 LEDs) and outside 5-step circle (18 LEDs). When CCTs of LED1-LED100 are calculated in the CIE 2015 their values of CCTF,10 are different (in the range 2894 K−3010 K) than that for CIE 1976 (Fig. 15(a)). The DuvF,10 is in the range −0.0114 to 0.0007 and presented at Fig. 15(b).
Fig. 16. The chromaticity coordinates of reference pc-LED (LED-A with 3000 K) and its cm-LED replacements provided at (a) the CIE 1976 color space (the n-step u’v’ circles are red) and (b) the CIE 2015 color space (the n-step u’F,10v’F,10 circles are blue).
The other set of cm-LEDs were designed to meet the criteria that: (1) the chromaticity coordinates of replacement LED’s must be exactly the same as the reference pc-LED-A in the CIE 2015 color space (2) with CCTF,10 of 2911 K (3), DuvF,10 equal to −0.0031 and CRI greater than 80. Similarly, there were designed an additional 10 of cm-LED SPDs for each RGBnA set (LED101-LED200) that meet the criteria to be worst cases in view of difference between chromaticity coordinates calculated in the CIE 2015 and CIE 1976. Their SPDs are presented in Fig. 14(b) and their chromaticities are presented as black square in Fig. 16(b) (which are the overlapped chromaticity coordinates for each of those 100 of the cm-LEDs), the CCTF,10, DuvF,10 and CRI are presented at Fig. 15(d), (e), (f) (CCTF,10 is in the range from 2911 K to 2915 K; DuvF,10 is −0.0030 to −0.0028 and CRI is in the range between 80 and 92). When the chromaticities of these cm-LEDs (LED101-LED200) are calculated in the CIE 1976 color space, presented in Fig. 16(a) as black dot symbols, show a much greater variance in their differences from pc-LED-A. Number of LED chromaticities within within 3-step u’F,10v’F,10 circle are 62 LEDs, in between 3-step and 5-step circles are 26 LEDs and outside 5-step circle are 12 LEDs. When CCT of LED101-LED200 is calculated in the CIE 1976 its value CCT is different than CCTF,10 – it is in the range 2891 K−3035 K (Fig. 15(d)), the Duv is in the range from −0.0042 to 0.0056 (Fig. 15(e)).
The metameric replacements of the reference 6500 K pc-LED-B were designed using 6 of LED sets (RGB5A-RGB10A). There were no possibility to obtain SPDs with RGB1A-RGB4A sets which chromaticities and CRI meet the criteria that: (1) the chromaticity coordinates of replacement LED’s must be exactly the same as the reference pc-LED-B in the CIE 1976 color space (2) with CCT and Duv which can be treated as 6500 K according to ANSI requirements and (3) have a CRI greater than 80. Of all the obtained SPDs, the ten of them with the greatest difference between chromaticity coordinates calculated in the CIE 1976 and CIE 2015 were selected. Which gives total of 60 of cm-LED SPDs (LED201-LED260) (Fig. 17(a)) with CCT in the range from 6520 K to 6525 K (Fig. 18(a)). On Fig. 18 there are no marks at color line representing RGB1A-RGB4A sets. The chromaticities of designed 60 SPDs are presented as blue dot symbols in Fig. 19(a) (which are the overlapped chromaticity coordinates for each of those 60 of the cm-LEDs). Their (LED201-LED260) Duv are shown at Fig. 18(b) and the CRI is in the range from 80 to 94 (Fig. 18(c)) which means that those cm-LEDs may have applications in general lighting. When the chromaticities of these cm-LEDs (LED201-LED260) are calculated in the CIE 2015, presented in Fig. 19(b) as blue squares, show a much greater variance in their differences from pc-LED-B. While many LED chromaticities fall within 3-step u’F,10v’F,10 circle (40 LEDs), in between 3 and 5-step circles (4 LEDs) and outside 5-step circle (16 LEDs). When CCTs of LED201-LED260 are calculated in the CIE 2015 their values of CCTF,10 are different (in the range 6210 K−6469 K) than that for CIE 1976 (Fig. 18(a)). The DuvF,10 is in the range −0.0002 to 0.0081 and presented at Fig. 18(b).
Fig. 17. The relative SPDs of reference pc-LED-B (6500 K) and its replacement metameric cm-LEDs based on RGB5A-RGB10A color LED sets. Each RGBA set is designed to be metamers for the pc-LED-B at a) CIE 1976 color space, b) CIE 2015 color space.
Fig. 18. The a) CCT b) Duv c) and CRI of cm-LEDs which are metamers of pc-LED-B (6500 K) in the CIE 1976 color space); d) CCT e) Duv and f) CRI of cm-LEDs which are metamers of pc-LED-B in the CIE 2015 color space (black color for calculations in the CIE 1976 color space, blue color for calculations in the CIE 2015 color space.
Fig. 19. The chromaticity coordinates of reference pc-LED-B (6500 K) and its replacement cm-LEDs provided at (a) the CIE 1976 color space (the n-step u’v’ circles are red) and (b) the CIE 2015 color space (the n-step u’F,10v’F,10 circles are blue).
The other set of cm-LEDs were designed to meet the criteria that: (1) the chromaticity coordinates of replacement LED’s must be exactly the same as the reference pc-LED-B in the CIE 2015 (2) with CCTF,10 of 6346 K (3), DuvF,10 equal to 0.0016 and CRI greater than 80. There were no possibility to obtain SPDs with RGB1A-RGB4A sets which chromaticities and CRI meet the selection criteria. Similarly there were designed an additional 10 of cm-LED SPDs for each RGBnA set (LED261-LED320) that meet the criteria to be worst cases in view of difference between chromaticity coordinates calculated in the CIE 2015 and CIE 1976. Their SPDs are presented in Fig. 17(b) and their chromaticities are presented as black square in Fig. 19(b) (which are the overlapped chromaticity coordinates for each of those 60 of the cm-LEDs), the CCTF,10, DuvF,10 and CRI are presented at Fig. 18(d), (e), (f) (CCTF,10 is in the range from 6351 K to 6359 K; DuvF,10 is 0.0014 to 0.0015 and CRI is in the range between 80 and 92). When the chromaticities of these cm-LEDs (LED261-LED320) are calculated in the CIE 1976 color space, presented in Fig. 19(a) as black dot symbols, show a much greater variance in their differences from pc-LED-B. Number of LED chromaticities within 3-step u’F,10v’F,10 circle are 40 LEDs, in between 3-step and 5-step circles is 1 LED and outside 5-step circle are 19 LEDs. When CCT of LED261-LED320 is calculated in the CIE 1976 color space its value CCT is different than CCTF,10 – it is in the range 6425 K−6705 K (Fig. 18(d)), the Duv is in the range from −0.0018 to 0.0086 (Fig. 18(e)).
4. Discussion
Figure 20(a) compares the chromaticity coordinates of the cm-LEDs in the CIE 2015 color space (LED1-LED100) that are metamers of 3000 K pc-LED-A in the CIE 1976 color space. In this figure, for LED1-LED10 and LED13-LED20 (RGB1A and RGB2A sets), DBC exceeds 5-step u’F,10v’F,10 circles, their chromaticities differ mainly in the value of v’F,10 that have lower values than the reference pc-LED-A. This means they are slightly more magenta than the reference at 10° FoV. These are sets based on “B” LEDs which had the smallest values in their peak wavelength: 404.74 nm and 420.06 nm. From Fig. 21(a), we can clearly see that all SPDs obtained from RGB4A-RGB8A (439.92 nm to 446.12 nm) are color consistent with the 3000 K pc-LED-A reference. In addition, 9 out of 10 SPDs obtained from RGB3A (425.76 nm) and 5 out of 10 SPDs obtained from RGB9A (460.03 nm) are color consistent with the 3000 K pc-LED-A reference as well.
Fig. 20. The chromaticity coordinates in the CIE 2015 color space of pc-LED and metameric in the CIE 1976 color cm-LEDs for a) 3000 K and b) 6500 K.
Fig. 21. The chromaticities of pc-LED and its CIE 1976 color space cm-LEDs metameres being in the range of CIE 2015 color space color consistency circles. a) 3000 K LEDs b) 6500 K LEDs. In both graphs, the colored area corresponds to a for 3-step circle.
A similar graph (Fig. 20(b)) illustrates the chromaticity coordinates in the CIE 2015 color space of 60 cm-LEDs (LED201-LED260), which are metameric in the CIE 2015 color space. It was not possible to obtain SPDs with RGB1A-RGB4A sets whose chromaticity and CRI met the selection criteria. In this figure for LED241-LED246 and LED251-LED260 (RGB9A and RGB10A sets), DBC exceeds 5-step u’F,10v’F,10) circles. Their chromaticities differ mainly in the DuvF,10 and have a higher value which in 10° FoV lighting situation would be perceived as more greenish tint. These are sets based on “B” LEDs which had the largest values in the peak: 460.03 nm and 464.03 nm. From Fig. 21(b), we can clearly see that RGB5A-RGB8A (peak wavelengths from 442.81 nm to 446.12 nm) sets are color consistent with the 6500 K pc-LED-B reference.
Figure 22(a) compares the chromaticity coordinates of the cm-LEDs in the CIE 1976 color space (LED101-LED200), which are metameric with 3000 K pc-LED-A in the CIE 2015 color space. In this figure, for LED101-LED110 DBC exceeds 5-step u’v’ circles and their chromaticities differ mainly in Duv direction (positive value in relation to LED-A), which means that the color will be more greenish at 2° observer color space. Also, the LED191-LED192 (RGB10A sets) DBC exceeds 5-step u’v’ circles and their Duv value is lower than LED-A’s, so the color will be more pinkish. These are sets based on “B” LEDs with peak wavelengths of 404.74 nm and 464.03 nm. From Fig. 23(a), we can clearly see that RGB4A-RGB8A sets with peak wavelengths between 439.92 nm and 446.12 nm are color consistent with the 3000 K pc-LED-A. In addition, for RGB3A and RGB9A, 6 out of 10 SPDs obtained are color consistent the 3000 K pc-LED-A with as well
Fig. 22. The chromaticity coordinates located at the CIE 1976 color space of a) 3000 K pc-LED-A and cm-LEDs b) 6500 K pc-LED-B and cm-LEDs both are selected according to criterion where LEDs chromaticity coordinates are metameric in the CIE 2015 color space.
Fig. 23. The chromaticities of pc-LED and its CIE 2015 color space cm-LEDs metameres being in the range of CIE 1976 color space color consistency circles. a) 3000 K LEDs b) 6500 K LEDs. In both sides of this graph the color area is for 3-step circle.
A similar graph (Fig. 22(b)) illustrates the chromaticity coordinates in the CIE 1976 color space of 60 cm-LEDs (LED261-LED320), which are metameric with pc-LED-B in the CIE 2015 color space. It was not possible to obtain SPDs with RGB1A-RGB4A sets whose chromaticity and CRI met the selection criteria. In this figure for LED301-LED309 and LED311-LED320 DBC exceeds 5-step u’v’ circles and their chromaticities differ mainly in Duv direction (its Duv is smaller than for LED-B), which means that the color will be more magenta in the CIE 1976 color space. These are sets based on “B” LEDs which had the largest values in the peak: 460.03 nm and 464.03 nm. From Fig. 23(b) we can clearly see that RGB5A-RGB8A (442.81 nm to 446.12 nm) sets are color consistent for the 6500 K pc-LED-B reference.
The method used to find the least color consistent SPDs with the specified criteria for pc-LED-A and pc-LED-B showed that, regardless of the colorimetric system in which the calculations were performed, all solutions of SPDs from the RGB5A-RGB8A sets (Fig. 21 and Fig. 23) are color consistent. For the RGB3A and RGB9A sets, there is an ambiguous situation where only some of the obtained SPDs are color consistent for the reference 3000 K pc-LED-A. As can be seen in Fig. 20 and Fig. 22, DBC is variable, but mainly the largest changes occur in the direction described by the Duv parameter for the reference sources and RGBnA sets considered.
5. Conclusions
Using LEDs with consistent color is very important in general lighting applications. This work shows that when cm-LEDs are used to replace pc-LEDs, the definition of color consistency for narrow and wide FoVs should be considered. The data presented in this paper indicate that the use of the CCT and Duv measures as color consistency indicators are not sufficient for specifying color consistency because of the importance of the observer's FoV - the angles from which the light is seen by humans. Typically, colorimetry uses the standard 2° observer-based CIE 1976 color space to evaluate color quality. Radiation reaches the eye within such a narrow view angle only during precision work. In both work and home lighting conditions, most human activities take place when light enters the human eye at wider viewing angles. This means that the color space based on 10° colorimetry (CIE 2015) should be used to check the color consistency of light, as it more closely reflects the real conditions of LED use.
The above studies show that if metameric LEDs are rigorously selected using the CIE 1976 color space with a 2° observer, it can result in very significant differences in the perception of their colors when these lamps are used for general lighting applications where light is seen by humans with a wider FoV. In these cases, a 10° colorimetric observer should be used for their quality evaluation. This problem is not solved by selecting metameric LEDs in 10° color space (CIE 2015 color space), because this research shows that there are very significant DBC (in excess of 5-step circle) when these LEDs are used in lighting application where light reaches human eyes almost perpendicularly, i.e. CIE 1976 color space.
The blue LED peak is very important in the development of RGBA cm-LEDs designed to be a metameric light source of cold/warm white pc-LEDs. For the selected RGBA set, changing the peak of the B emitter in the range between 442.81 nm and 446.12 nm always allows the SPD to be adjusted to meet the colorimetric criteria to be a metameric replacement of selected cold/warm pc-LEDs. Consequently, they will always be color consistent with the pc-LEDs. If the B peak in the given RGBA set is outside this range (e.g. 425.76 nm or 460.03 nm), not all SPDs obtained for the reference pc-LED-A will be color consistent. Looking at the results where metameric LEDs are developed for the CIE 1976 color space and are subsequently evaluated in the CIE 2015 color space (and vice versa), it can be seen that many cm-LEDs lie within 3-step circle, so they should function fine for both narrow and broad illumination. At the same time, there are several cm-LEDs that do not meet color consistency when being evaluated in the 2 color spaces. So, either both 2° and 10° color spaces should be included with each cm-LED or LEDs should be preferentially selected that can be used in both narrow-field and broad-field applications.
Funding
Politechnika Bialostocka (POWR.03.05.00-00-ZR22/18, WZ/WE-IA/3/2023).
Acknowledgments
We would like to express our sincere gratitude to Dr. Steven W. Brown of the National Institute of Standards and Technology NIST, Gaithersburg, USA, for his invaluable guidance and support throughout this research. Thank you for the very fruitful discussions on modern colorimetry and LEDs.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request
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