IMPROVED COLOR MATCHING FUNCTIONS FOR BETTER VISUAL MATCHING OF LED
SOURCES
Csuti, P.1, Schanda, J.1, Petluri, R.2, McGroddy, K.2, Habers, G.2
1
University of Pannonia, Veszprém, Hungary and LightingMetrics Ltd. Budapest, Hungary,
2 Xicato, San Jose, USA
csutip@gmail.com
Abstract
It is common in lighting installations for colour differences to be observed between luminaires using
LED sources and those using traditional light sources such as Tungsten-Halogen. These differences
can, in most cases, be confirmed by measuring the chromaticity coordinates, but we found that they
can also be caused by failing of the CIE 1931 colour matching functions (CMFs), in particular with LED
sources with a relative high blue peak, which is the subject of this paper. For this purpose, visual
matching experiments were performed to evaluate the CIE 2° and 10° standard observer CMFs, the
tentative 2° and 10° CMFs under discussion in TC 1-361, and a modified set of 2° CMFs developed at
the University of Pannonia2.
Keywords: Photometry, Colour matching functions, LEDs.
1 Introduction
Errors in the CIE 1931 colour matching functions (CMFs) are well known. References on the failure of
CIE colorimetry in light source measurements can be found in the literature (see e.g. 3). DB Judd
proposed as early as in 1951 a revision of the V() function and calculated modified CMFs 4, but these
were not accepted by the CIE as the benefits were regarded as marginal. In 1978 Vos revised this
calculation and proposed updated CMFs5, these have been widely used in the vision research
community, but have not been accepted to form a new system of colorimetry, although we could show
that the CIE-Judd-Vos functions provide better description of metameric matches, where RGB-LED
light had to be matched with the light of traditional sources6.
CIE started coordinated research to derive to better CMFs and established its TC 1-36 technical
committee entitled “Fundamental Chromaticity Diagram with Physiologically Significant Axes”, with the
task to establish a chromaticity diagram of which the coordinates correspond to physiologically
significant axes. This TC published in 2006 its first report 7 that contained already cone fundamentals,
i.e. cornea level spectral sensitivity data for the Long-, Medium- and Short-wavelength sensitive
cones. A draft report also contains the proposal for a matrix by the help of which these cone
fundamentals can be transformed into CIE colorimetry like 𝑥̅ F(), 𝑦̅F(), 𝑧̅F() CMFs (the F index stands
for “fundamental”).
Since above early findings, experiments were conducted at the University of Pannonia (referred to in
the following as UP and previously called University of Veszprém) to understand where CIE
colorimetry breaks down for LED measurements. First results of a parallel investigation conducted
together with the University of Ilmenau were reported at the CIE Visual Appearance symposium in
Paris8, where it was shown that if RGB-ÉED lights were visually matched with either incandescent
lamp light or the light of a high pressure discharge lamp, an instrumental mismatch was observed.
Follow up investigations 9 have shown that the difference between visual and instrumental matches is
produced by the error of the short wavelength colour matching functions. Using the 𝑥̅ F(), 𝑦̅F(), 𝑧̅F()
CMFs provides better results as using the CIE 1931 CMFs, but the difference between instrumental
and visual mismatch could only be halved. In a further consolidating experiment10 one could show that
by shifting the S-cone fundamental spectral responsivity function by -6 nm, much improved colour
matches could be obtained.
Using the -6 nm displayed S-fundamental the following (l(),m(),s())  𝑥̅ MF(), 𝑦̅MF(), 𝑧̅MF()
transformation equation was developed:
 xMF (   1,9260000 -1,3763289 0,3904850  l (  
 y (     0,6597958 0,4111496 0,0000000  m(  
 MF
 



 zMF (    0,0000822 0,0000000 1,9750000  s( ) 
1. )
A comparison between the CIE 1931 and 1964, the CIE TC 1-36 tentatively suggested CMFs for the
2° and 10° observers and the UP suggested 2° Observer are shown in Figure 1.
x2(l)
CMFs
y2(l)
2.5000
z2(l)
2.0000
X10(l)
rel. value
1.5000
Y10(l)
1.0000
Z10(l)
0.5000
xF(l)
0.0000
-0.5000
350
400
450
500
550
600
650
700
wavelength, nm
yF(l)
zF(l)
Figure 1. CMFs for the CIE 1931 and 1964 standard observers, comparing them with the CIE TC 1-36
tentative CMFs and the UP 2°modified observer.
Visual colour matches were performed between a filtered incandescent lamp and RGB-LEDs, at nine
chromaticities, as shown on Figure 2. Spectral power distributions (SPD) reaching the eye from both
the broad band (filtered incandescent) and the RGB-LED illuminated 2° visual field were determined
and chromaticity coordinates were found using the CIE 1931 CMFs, CIE TC 1-36 tentatively
recommended CMFs and the UP developed CMFs (according to the transformation shown in
 xMF (   1,9260000 -1,3763289 0,3904850  l (  
 y (     0,6597958 0,4111496 0,0000000  m(   1. ).
 MF
 



 zMF (    0,0000822 0,0000000 1,9750000  s( ) 
Instrumental chromaticities
calculated using the CIE 1931 2° CMFs
0.6
#5
#6
#9
#4
0.5
#8
#7
v'
#3
#1
0.4
RGB LED
Visual average
Broad-band reference
#2
0.3
0.0
0.1
0.2
0.3
0.4
0.5
u'
Figure 2. Chromaticities of instrumental colour matches for nine chromaticities: Δ shows the
chromaticity of filtered incandescent lamp,  shows chromaticities measured for visual colour match
with above filtered incandescent of RGB-LEDs,  is the average of the visual matches.
Chromaticity differences between the corresponding filtered incandescent and the RGB-LED colours
were calculated and are displayed in Figure 3. As can be seen the CIE TC 1-36 fundamental based
CMFs provide improved results, but real progress could be obtained by using the UP CMFs.
Chromaticity differences using different CMFs (CIE 1976 u'v')
0,050
0,045
CIE 1931 2° CMFs
Fundamental CMFs
Modified Fundamental CMFs
0,040
0,035
0,030
0,025
0,020
0,015
0,010
0,005
0,000
Sample
#1
Sample
#2
Sample
#3
Sample
#4
Sample
#5
Sample
#6
Sample
#7
Sample
#8
Sample
#9
Figure 3. Chromaticity differences calculated using the CIE 1931 CMFs, the CIE TC 1-36 tentative
CMFs and the UP modified fundamental based CMFs.
2 Applying the UP CMFs to independent data sets
Results shown in Figure 3 might be due to the fact that the optimization of the shift in the s() function
was performed based on the investigations depicted in the figure. Thus further experiments were
conducted to prove the applicability of the method. In the following three experiments will be described
that have been performed on different white LEDs built using blue LEDs and yellow-red phosphors.
2.1 Chromaticity match between low and high colour rendering factor LEDs
The LED sources used in these experiments are remote phosphor modules, using phosphor plates
placed over a cavity containing blue LEDs. The compositions of the plates were altered to obtain
different spectral power distributions (SPDs). In a first series of experiments, modules were made
producing SPDs closely matching 4000K, 3000K and 2700K black body radiators, having a relatively
high colour rendering index (CRI) of ~95. Then modules with relative low CRI were produced
(75<CRI<80), which were a visually close match to the high CRI versions of the module. Spectra of
the modules are shown in Figure 4.
Xicato LED spectra
1.0000
X01
0.9000
0.8000
X02
0.7000
rel. intensity
0.6000
X03
0.5000
X04
0.4000
0.3000
X05
0.2000
0.1000
X06
0.0000
350
400
450
500
550 600 650
wavelength, nm
700
750
800
Figure 4. Spectra of the visually matching low and high Ra module pairs.
The chromaticity coordinates of these matched modules were calculated with the different CMFs, and
we found that the modified CMFs developed at the UP gave the smallest chromaticity difference for
two of the three CCT , for the 3000 K module pair the CIE TC 1-36 CMFs gave the best instrumental
match for the visually matching modules, but the residual mis-match between the low and high CRI
pair was largest for this module pair, see Table 1.
On one side it was interesting to find that even relatively small differences in spectra, as shown
between pairs of low and nigh CRI modules could produce visible mismatch for instrumentally
matching modules, but we thought - on the other side – that the observed discrepancy for the 3000 K
modules needs further investigation.
Table 1. Colorimetric data for the low and high CRI modules of three Tcc-s
LED Nr.
Tcc, K
Ra
X06
2723
76
X03
2745
96
X04
3072
76.6
X05
3058
95.5
X02
4113
84
X01
4173
94
u':
v':
u':
v':
Δ(u'v'):
CIE 2° Obs. TC1-36 2°Obs.
0.2626
0.2652
0.5272
0.5278
0.2633
0.2654
0.5240
0.5261
0.0032
0.0017
UP 2°Obs.
0.2646
0.5300
0.2648
0.5302
0.0003
u':
v':
u':
v':
Δ(u'v'):
0.2488
0.5203
0.2510
0.5177
0.0034
0.2511
0.5212
0.2528
0.5204
0.0019
0.2508
0.5239
0.2525
0.5255
0.0024
u':
v':
u':
v':
Δ(u'v'):
0.2238
0.4979
0.2244
0.4951
0.0029
0.2248
0.5009
0.2251
0.4989
0.0020
0.2248
0.5066
0.2249
0.5059
0.0008
2.2 Follow up on the 3000 K modules
To try to understand the relatively poor performance on the 3000 K modules, further experiments with
such modules were performed. A high CRI module, termed X05 with Ra= 95 and Tcc= 3000 K was
used as reference, and six modules of similar CCT but Ra  80 were used as test samples. Spectra of
the seven modules are seen in Figure 5. As can be seen there is a slight difference between the
maximum of the blue LED peak between the modules.
0.025
1: X05
rel. intensity
0.02
2:X16
0.015
3:X15
0.01
4:X14
0.005
5:X13
6:X12
0
400
450
500
550
600
wavelength, nm
650
700
750
7:X11
Figure 5. Spectra of the reference high CRI module (X05) and the six modules with only slight
chromaticity difference to the reference, but low CRI of about 80.
The samples were mounted on a translucent board in a honey comb arrangement with the reference
module in the middle. The view for visual observation panel is seen in Figure 6.
Figure 6. View of the visual experimental set-up.
We would like to emphasize that the big chromaticity difference in the here reproduced figure is an
artefact of the camera, it is due to the poor colorimetric match of the camera CMFs to the CIE CMFs.
Visually slight differences could be observed and had to be evaluated.
First the luminance of the modules was set to equal value, then the observers had to rank order the
chromaticity difference between the module seen in the middle (the high CRI module) and the other
six modules. For all modules the spectra were measured and the chromaticity difference and CIELAB
colour difference to the value of X05 determined. Both the visual data and the Δ(u’,v’) as well as ΔEab*
values are shown in Table 2.
Table 2. Visual and instrumental differences of the six modules to the reference high CRI module
Vis dif to X05
7:X11
3:X15
5:X13
2:X16
6:X12
4:X14
28.7
29.3
52.8
61.8
65.5
76.8
Δ(u',v')
ΔEab*
Standard deviation
Lum, cd/m2
CIE 1931
CIE TC 1-36
UP.
CIE 1931
CIE TC 1-36
UP.
1.3
1.3
1.1
1.0
0.8
1.4
1134
1152
1162
1140
1127
1147
0.004
0.0021
0.0021
7.66
4.35
1.28
0.0028
0.0023
0.0032
6.52
3.56
2.02
0.0025
0.0016
0.0025
5.68
2.79
2.24
0.0033
0.0015
0.0026
5.09
1.7
4.15
0.0022
0.0027
0.0038
6.65
3.58
2.52
0.0035
0.0022
0.0035
4.62
3.23
6.61
As can be seen – at least for the three modules of smallest visual colour difference, the visual rank
order and the according to the UP. calculated colour differences agree. The differences calculated
using the CIE 1931 CMFs fail considerably, while the CIE TC 1-36 CMF based calculations are also
worse than the UP CMF based rank order.
As small differences in the blue band of the modules could be observed, and the UP modified
fundamental based CMFs are most sensitive for the blue part of the spectrum we decided to
investigate this further.
2.3 Testing for differences in the blue band of white p-LEDs
In practice, module manufacturers get the blue LEDs binned for luminous flux and dominant
wavelength. The final question we wanted to answer whether the differences in the blue band
spectrum have an influence on the visual appearance f the objective chromaticities have been set
according to one or the other CMFs. Five modules have been constructed with different blue LEDs,
but reasonable similar colorimetric data, see Figure 7. and Table 3.
0.045
rel. Intensity, arb. Units
0.04
0.035
0.03
X31
0.025
X32
0.02
X33
0.015
X34
0.01
X35
0.005
0
350
400
450
500
550
600
650
700
750
800
wavelength, nm
Figure 7. Spectra of five p-LED modules with different blue LED chips.
Table 3. Colorimetric data of the five p-LED modules with different blue chips
Rel. Intensity
x (CIE 1931)
y (CIE 1931)
CCT [K]
CRI
X31
100.0
0.4438
0.4186
3002.1
76.7
X32
85.7
0.4359
0.4092
3059.3
81.0
X33
93.8
0.4324
0.4008
3050.3
84.7
X34
84.3
0.4275
0.3939
3081.2
86.7
X35
51.8
0.4108
0.3778
3268.2
79.5
As the modules were visually different, we decided not to scale the visual difference to one reference,
as was done for the LEDs described in the previous section, but to set up a visual colour matching
experiment, where the modules were visually matched to a reference RGB-LED system. Results of
this colour matching experiment are reproduced in Table 4.
Table 4. u’,v’ chromaticity differences for visual colour match of the X31-X35 white p-LED modules
compared to an RGB-LED system
CIE1931
X31
X32
X33
X34
X35
0.0075
0.0066
0.0041
0.0055
0.0049
CIE TC 1-36
UP
0.0055
0.0057
0.0038
0.0051
0.0037
0.0045
0.0052
0.0037
0.005
0.0048
For four of the five modules the UP. CMFs provided the best (smallest) chromaticity difference for
visual colour match. For one p-LED (X35, with a 470 nm blue peak LED) the CIE TC 1-36 CMFs
turned out to be better, although for an other two modules the (X33 and X34) the differences are not
significant.
3 Summary and conclusion
Summing up we could show – using an independent data-set – that the CMFs developed by the UP
group describe colour matches between broad-band sources and LED based light sources
considerably better than the traditional CIE 1931 CMFs. In this report the 2°CMFs developed by the
CIE TC 1-36 and at the UP have been compared to the CIE 1931 standard observer CMFs. Both the
CIE TC 1-36 and the UP-CMFs predict visual match much better than the CIE 1931 2°Observer. The
UP-CMFs provide for almost all cases better agreement with visual matches than the CIE TC 1-36
suggested ones. The only problem is that physiological knowledge does not support the -6 nm
displacement of the S cone fundamental spectral sensitivity. At present we still do not have any firm
explanation for this discrepancy.
Experiments are going on to test visual matches done with larger fields of view, where the 10°
observer, both CIE 1964 and TC 1-36 can be applied. This might become important for the practical
applications, as LED modules are often used to illuminate larger surfaces, and due to their inherent
properties, to illuminate large surfaces (as in case of wall washer applications) several units have to
be used side-by-side. The observer sees the illuminated wall with the light patches produced by the
single units side-by-side, and certainly with larger than the 4°visual angle (maximum angle of view for
the 2° standard observer). Thus these modules have to be visual matches to be acceptable, and. For
the proper description we need the CMFs to be able to calculate the chromaticity that correspond to
the visual observation. We have these now for the 2° observer, and hope to be able to give some
guidance for the 10° observer within short.
References
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