IEC TS 61966-13:2023

IEC TS 61966-13 ®
Edition 1.0 2023-11
TECHNICAL
SPECIFICATION
colour
inside
Multimedia systems and equipment – Colour measurement and management –
Part 13: Measurement method of display colour properties depending on
observers
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IEC TS 61966-13 ®
Edition 1.0 2023-11
TECHNICAL
SPECIFICATION
colour
inside
Multimedia systems and equipment – Colour measurement and management –

Part 13: Measurement method of display colour properties depending on

observers
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 33.160.60  ISBN 978-2-8322-7450-7

– 2 – IEC TS 61966-13:2023 © IEC 2023
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
3.1 Terms and definitions . 7
3.2 Abbreviations . 8
4 Measuring equipment . 8
4.1 Light-measuring devices . 8
4.2 Viewing direction coordinate system . 9
5 Measuring conditions . 10
5.1 Standard measuring environmental conditions . 10
5.2 Power supply . 10
5.3 Warm-up time . 10
5.4 Standard measuring dark-room conditions . 10
5.5 Standard set-up conditions . 10
6 Measuring methods . 11
6.1 Individual colour-matching functions . 11
6.2 Reference colours . 11
6.3 Observer metamerism index . 12
6.3.1 Purpose . 12
6.3.2 Measuring conditions . 12
6.3.3 Measurement method . 12
7 Reporting form . 20
Annex A (informative) Generating a set of individual CMFs . 21
A.1 Age distribution data . 21
A.2 Example of individual CMFs dataset . 21
Annex B (informative) XYZ values of reference colour . 31
Annex C (informative) Measurement method of observer metamerism between
different displays . 32
C.1 General . 32
C.2 Reference colours and measurement method . 32
Annex D (informative) Colour-matching process for multi-ORU DUTs . 33
Annex E (informative) Working example of observer metamerism index . 35
E.1 Purpose . 35
E.2 DUT . 35
E.3 Process . 35
E.3.1 General . 35
E.3.2 Colour-matching . 36
E.3.3 Calculating the SPD of the DUT . 36
E.3.4 XYZ computation . 36
E.3.5 Colour difference computation . 37
E.3.6 Reporting . 37
Bibliography . 49

Figure 1 – Representation of the viewing direction (equivalent to the direction of
measurement) by the angle of inclination, θ and the angle of rotation (azimuth angle),
φ in a polar coordinate system . 9
Figure 2 – DUT Installation conditions. 11
Figure 3 – Flowchart of the overall evaluation method . 12
Figure 4 – 4 % area centre box patterns of primary colours . 13
Figure 5 – Reporting example of a graph of colour-matched metameric pair of
reference colour and DUT . 20
Figure E.1 – RGB primary spectrum of the DUT . 35
Figure E.2 – Example of graphs of colour-matched metameric pair of reference colour
(Macbeth white) and test colour of the DUT . 38

Table 1 – Reporting form of observer metamerism index . 20
Table A.1 – Example of age distribution data . 21
Table A.2 – Total number of individual CMFs example . 22
Table A.3 – Spectral sensitivity data of the individual CMFs (age group: 22, 27 and 32) . 22
Table A.4 – Spectral sensitivity data of the individual CMFs (Age group: 37, 42 and 47) . 24
Table A.5 – Spectral sensitivity data of the individual CMFs (Age group: 52, 57 and 62) . 26
Table A.6 – Spectral sensitivity data of the individual CMFs (Age group: 67, 72 and 77) . 28
Table B.1 – Reference XYZ values using CIE 1931 standard colorimetric observer . 31
Table E.1 – Optical properties of the DUT . 35
Table E.2 – Reference colour XYZ values of age group 22 individual CMFs . 36
Table E.3 – R, G and B weighting factors of the matched colours (age group 22). 36
Table E.4 – OMI calculation result of all 7 colours and age groups . 37
Table E.5 – Reporting of OMI results . 37
Table E.6 – R, G, B, W spectra of the DUT . 38
Table E.7 – R, G and B weighting factors of the matched colours . 47

– 4 – IEC TS 61966-13:2023 © IEC 2023
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
MULTIMEDIA SYSTEMS AND EQUIPMENT –
COLOUR MEASUREMENT AND MANAGEMENT –

Part 13: Measurement method of display colour
properties depending on observers

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
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IEC TS 61966-13 has been prepared by technical area 2: Colour measurement and
management, of IEC technical committee 100: Audio, video and multimedia systems and
equipment. It is a Technical Specification.
The text of this Technical Specification is based on the following documents:
Draft Report on voting
100/3928/DTS 100/4023/RVDTS
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this Technical Specification is English.
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available
at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are
described in greater detail at www.iec.ch/publications.
A list of all parts in the IEC 61966 series, published under the general title Multimedia systems
and equipment – Colour measurement and management, can be found on the IEC website.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under webstore.iec.ch in the data related to the
specific document. At this date, the document will be
• reconfirmed,
• withdrawn, or
• revised.
IMPORTANT – The "colour inside" logo on the cover page of this document indicates
that it contains colours which are considered to be useful for the correct understanding
of its contents. Users should therefore print this document using a colour printer.

– 6 – IEC TS 61966-13:2023 © IEC 2023
INTRODUCTION
In colorimetry, metamerism or metameric failure is defined as a perceived matching of two
colours with different spectral power distributions (SPDs). Illuminant metamerism occurs when
two objects match in colour under a specific illuminant, but mismatch under another illuminant
with a different SPD. Likewise, observer metamerism (OM) is defined by two stimuli with
different SPDs that match in colour for a specific observer. However, the stimuli might not match
for another observer. OM is caused by the normal variations in the spectral responsivities of
various observers. In other words, observers do not have identical colour-matching functions
(CMFs). An observer model that takes into consideration the age and the field size of observers
with respect to a standard observer standard observer has already been standardised in the
CIE (CIE Pub. 170-1:2006).
Meanwhile, display manufacturers and users have required measurement methods of the OM
which occurs in display uses. For example, with the development of display technology and
grafting of display technology to various application fields and mass distribution, it has become
a common situation for users to use multiple displays at the same time. When using multiple
displays at the same time, a user can display the same colour through the calibration process.
However, this is only valid for certain observers because of OM. Also, when users watch a
single display, there could be observer dependency in colour perception even though the
display is calibrated.
Based on the CIE standards and research results of OM, a new Technical Specification is
suggested to measure the difference in display colour properties according to the observer in
an objective way, excluding subjective effects of evaluators.

MULTIMEDIA SYSTEMS AND EQUIPMENT –
COLOUR MEASUREMENT AND MANAGEMENT –

Part 13: Measurement method of display colour
properties depending on observers

1 Scope
This document defines an objective colour difference metric and a measurement method for
observer metamerism caused by displays with different spectral power distributions. This
document also specifies the measuring equipment, conditions and methods that are necessary
to obtain the metric. This document applies to light-emitting or backlit transmitting colour
displays measured under dark-room conditions.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies.
For undated references, the latest edition of the referenced document (including any
amendments) applies.
ISO/CIE 11664-1, Colorimetry – Part 1: CIE standard colorimetric observers
ISO/CIE 11664-4, Colorimetry – Part 4: CIE 1976 L*a*b* colour space
ISO/CIE 11664-6, Colorimetry – Part 6: CIEDE2000 colour-difference formula
CIE 170-1:2006, Fundamental chromaticity diagram with physiological axes – Part 1
CIE 170-2:2015, Fundamental chromaticity diagram with physiological axes – Part 2
3 Terms and definitions
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp
3.1.1
observer metamerism
differences in metameric matches when made by different observers
Note 1 to entry: Identical spectral pairs will be identified as the same colour for all observers with their individual
CMFs. However, when the spectral power distributions of the two stimuli differ, and only metameric matching is
possible, a match made by one observer will typically not match for other observers. This is also called metameric
failure. See entry [1] of the Bibliography.

– 8 – IEC TS 61966-13:2023 © IEC 2023
3.1.2
observer metamerism index
value of colour difference due to observer metamerism characteristics of a display
Note 1 to entry: Metamerism indices exist for illuminant metamerism but not for observer metamerism.
3.1.3
ORU
optical radiant unit
unit in a display from which light of a distinct spectral power distribution is radiated
Note 1 to entry: Unit can be present in direct-view and projection displays with temporally and/or spatially fused
colour. In the case of projection, spectral irradiance is measured.
3.1.4
multi-ORU
multi optical-radiant-unit display
display with more than three optical radiant units with different spectral power distributions
3.2 Abbreviations
ABC automatic brightness control
CCT correlated colour temperature
CIE Commission Internationale de L’Éclairage (International Commission on Illumination)
CIELAB CIE 1976 (L*a*b*) colour space
CMFs colour-matching functions
DUT device under test
FS field size
LMD light-measuring device
OM observer metamerism
ORU optical radiant unit
SPD spectral power distribution
4 Measuring equipment
4.1 Light-measuring devices
The system configurations and/or operating conditions of the measuring equipment shall comply
with the structure specified in each item.
To ensure reliable measurements, the spectroradiometer shall have a wavelength range of at
least from 380 nm to 780 nm, and the wavelength scale accuracy shall be less than 1 nm. The
relative luminance uncertainty of measured luminance (relative to CIE illuminant A source) shall
not be greater than 4 % for luminance values over 0,1 cd/m and not be greater than 10 % for
luminance values 0,1 cd/m and below. Note that errors from spectral stray light within a
spectroradiometer can be significant and shall be corrected. A simple matrix method may be
used to correct the stray light errors, by which stray light errors can be reduced for one to two
orders of magnitude. Details of this correction method are discussed in Reference [1] . If the
obtained luminance is lower than LMD limitation, the lower limit of the LMD shall be recorded
with measured luminance.
___________
Numbers in square brackets refer to the Bibliography.

4.2 Viewing direction coordinate system
The viewing direction is the direction under which the observer looks at the spot of interest on
the display. During the measurement, the LMD is replacing the observer, looking from the same
direction at a specified spot (i.e. measuring spot, measurement field) on the DUT. The viewing
direction is conveniently defined by two angles: the angle of inclination θ (related to the surface
normal of the DUT) and the angle of rotation φ (also called azimuth angle) as illustrated in
Figure 1. The azimuth angle is related to the directions on a watch-dial as follows: φ = 0° is
φ = 90° as the 12 o'clock direction ("top"), φ = 180°
referred to as the 3 o'clock direction ("right"),
as the 9 o'clock direction ("left") and φ = 270° as the 6 o'clock direction ("bottom").

Key
θ: incline angle from normal direction
φ: azimuth angle
3 o’clock: right edge of the screen as seen from the user
6 o’clock: bottom edge of the screen as seen from the user
9 o’clock: left edge of the screen as seen from the user
12 o’clock: top edge of the screen as seen from the user
Figure 1 – Representation of the viewing direction (equivalent to
the direction of measurement) by the angle of inclination, θ and the
angle of rotation (azimuth angle), φ in a polar coordinate system

– 10 – IEC TS 61966-13:2023 © IEC 2023
5 Measuring conditions
5.1 Standard measuring environmental conditions
Measurements shall be carried out under standard environmental conditions:
• Temperature: 25 ºC ± 3 ºC,
• Relative humidity: 25 % RH to 85 % RH,
• Atmospheric pressure: 86 kPa to 106 kPa.
When different environmental conditions are used, they shall be noted in the measurement
report.
5.2 Power supply
The power supply for driving the DUT shall be adjusted to the rated voltage ± 0,5 %. In addition,
the frequency of power supply shall provide the rated frequency ± 0,2 %.
5.3 Warm-up time
Measurements shall be carried out after sufficient warm-up. Warm-up time is defined as the
time elapsed from when the supply source is switched on, and a 100 % grey level of input signal
is applied to the DUT, until repeated measurements of the display show a variation in luminance
of no more than 2 % per minute and 5 % per hour.
5.4 Standard measuring dark-room conditions
The luminance contribution from the background illumination reflected off the test display shall
be < 0.01 cd/m . If these conditions are not satisfied, then background subtraction is required
and it shall be noted in the measurement report. In addition, if the sensitivity of the LMD is
inadequate to measure these low levels, then the lower limit of the LMD shall be noted in the
measurement report.
5.5 Standard set-up conditions
By default, the display shall be installed in the vertical position (Figure 2a), but the horizontal
alternative (Figure 2b) is also allowed. When the latter alternative is used, it shall be noted in
the measurement report.
The display shall be configured to the factory settings, default settings, or any viewing mode
agreed on by the supplier and the customer, and the settings recorded in the test report. These
settings shall be held constant for all measurements. It is important, however, to make sure that
not only the adjustments are kept constant, but also that the resulting physical quantities remain
constant during the measurement. This is not automatically the case because of, for example,
warm-up effects or auto-dimming features. Any automatic luminance or gain control shall be
turned off. Otherwise it should be noted in the report. The automatic brightness control (ABC)
or ambient light control, which can reduce the display luminance level with dim ambient
illumination, shall be turned off. If that is not possible, it is recommended to set it to turn on no
lower than 300 lx to minimize the influence of the ABC as specified in IEC 62087-3:2015, 6.4.4.
The state of the ABC shall be reported. In addition, if the display has an auto-dimming feature
which reduces to less than 95 % of original luminance when a static image is displayed after a
prolonged time, then a black frame shall be input and the display luminance shall be measured
with 1 s sampling time until the display recovers its original luminance with 5 % error prior to
rendering and measuring the desired test pattern. The measurements shall be completed before
the dimming feature is triggered. When the display has the option to be set for different viewing
modes, the viewing mode shall be defined by the test specification, and be used with
consistency for all measurements. Additional viewing modes can also be measured. The
viewing mode used during testing shall be reported. The display should be operated in a mode
that does not have over-scan.
a) Primary installation b) Alternative installation
Figure 2 – DUT Installation conditions
6 Measuring methods
6.1 Individual colour-matching functions
CIE presented XYZ tristimulus representation based on cone fundamentals from the technical
reports CIE 170-1 and CIE 170-2 in 2006 and 2015, respectively. In CIE 170-1, the cone
fundamentals are defined as the spectral sensitivity functions, which are the long-wave
sensitive (L-), medium-wave sensitive (M-) and short-wave sensitive (S-) cones, and effects of
age and field size are incorporated. In CIE 170-2, linear transformations of the cone
fundamentals in the form of cone-fundamental-based XYZ tristimulus values are presented for
2° and 10° field sizes. Thus, if the age and field size of an observer are given, corresponding
XYZ tristimulus values can be computed based on CIE 170-1 and 170-2 technical reports. In
this Technical Specification, the field size is set to 2°. The colour-matching functions of
individual observers transformed from the cone fundamentals will be defined as individual CMFs,
and they shall be used to compute the XYZ tristimulus values. Also, CIE CMFs which mean the
functions 𝑥𝑥̅(𝜆𝜆),𝑦𝑦�(𝜆𝜆), 𝑧𝑧̅(𝜆𝜆) in the CIE 1931 standard colorimetric system will be called standard
CMFs to distinguish them from the individual CMFs.
Since age is the only variable of the individual CMFs, age distribution data is necessary when
deciding the weight of each individual CMFs. For the data on age distribution, only officially
published data should be used. A representative example is the United Nations World
Population Prospects data. Annex A shows an example of generating an individual CMFs
dataset. Prepare a set of individual CMFs by referring to the method in Annex A and use it in
the evaluation method.
6.2 Reference colours
To evaluate the observer-dependent colour rendering properties of a display, a set of reference
colours to be compared with the DUT’s spectral response to input test signals, is required. In
this Technical Specification, the set is defined by the Macbeth colour checker patches 13-19
and the CIE D65 illuminant. Even though a variety of colour sets as reference colours have
been used in the previous studies [2][3], only seven colours were selected as the reference
colours. If it is necessary to evaluate a display using more colours, it is recommended to select
a set of colours uniformly sampled in the CIE 1976 L*a*b* colour space with D65 as reference
white.
– 12 – IEC TS 61966-13:2023 © IEC 2023
For the illuminant of the reference colours, CIE standard illuminant D65 is used. The SPDs of
the seven reference colours are summarised in Annex B. The D65 SPD in Annex B is
normalised data, and in this Technical Specification, D65 SPD should be rescaled to have
maximum luminance of the DUT.
6.3 Observer metamerism index
6.3.1 Purpose
The purpose of this method is to evaluate the observer metamerism of a display. See Annex E
for a working example regarding the measurement and calculation process.
6.3.2 Measuring conditions
The following measuring conditions apply:
a) Apparatus: an LMD to measure spectral radiance and luminance of the DUT; a driving power
source; a driving signal equipment; and a geometric mechanism as illustrated in Figure 2.
b) Standard measuring environmental conditions; dark-room conditions; standard setup
conditions.
6.3.3 Measurement method
6.3.3.1 General
The evaluation method of observer metamerism index consists of five steps: SPD measurement,
colour matching, XYZ computation, colour difference computation and reporting. The flowchart
of the overall evaluation method is shown in the Figure 3.

Figure 3 – Flowchart of the overall evaluation method

6.3.3.2 SPD measurement
1) Render the three area centre box patterns corresponding to normalised {R, G, B} input
signals {1,0,0}, {0,1,0}, and {0,0,1} or, for 8-bit grey quantization, {255,0,0}, {0,255,0}, and
{0,0,255}, respectively. Figure 4 shows an example of a centre box pattern with an APL of
4 %. If the DUT exhibits loading, reduce the APL with a requirement of minimum 0,5 %,
making sure that the measurement field covers subpixels corresponding to at least 500 input
pixels.
Figure 4 – 4 % area centre box patterns of primary colours
2) Align the LMD perpendicular to the display surface (θ = 0, φ = 0), and position it to the centre
of the display.
3) Measure the SPDs of the primary colours respectively at the screen centre.

– 14 – IEC TS 61966-13:2023 © IEC 2023
6.3.3.3 Colour matching
th
1) Calculate the XYZ values of i reference colour using individual CMFs, which stand for the
th
CMFs of j individual observer, as shown in Equation (1). See Annex A for individual CMFs
and Annex B for the SPDs of reference colours.
''
X =Lk⋅⋅Φ λx λ dλ
( ) ( )
ri, j sj ri j
( ) ∫ ()
''
Y =Lk⋅⋅Φ λy λ dλ (1)
( ) ( )
ri, j sj ri j
( ) ∫ ()
''
Z =Lk⋅⋅Φ λz λ dλ
( ) ( )
ri, j sj ri j
( ) ∫ ()
where
' ' '
th
X , Y and Z denote the XYZ values of i reference colour using individual CMFs
ri, j ri, j ri, j
( ) ( ) ( )
th
of j individual observer;
' ' '
th
x (λ) , y (λ) and z (λ) denote the CMFs of j individual observer;
j j j
th
Φλ denotes the SPD of i reference colour defined in Equation (2):
( )
ri
()
Φ (λ) S (λ)⋅Rλ( )
D65 i (2)
ri
()
where
S (λ) denotes the SPD of CIE Standard D illuminant;
D65 65
th
R (λ) denotes the spectral reflectance of the i reference colour;
i
is the scaling factor to match the normalised relative XYZ values of reference colours with
L
s
the absolute XYZ values of the test colours of the DUT. Here, use the maximum luminance of
th
the DUT as explained in 6.2; k is the normalisation constant for j individual observer and is
j
defined in Equation (3).
k =
j
780 (3)
'
S λy⋅ λ dλ
( ) ( )
D65 j
∫
2) Calculate the weighting factors of SPDs of the DUT response corresponding to the
normalised inputs {1,0,0}, {0,1,0}, and {0,0,1}. The colour-matching process can be
expressed as Equation (4) by adding up the SPDs to match the XYZ values of the DUT using
the individual CMFs with the reference XYZ values calculated in item 1). The weighting
factors can be calculated by solving the linear matrix in Equation (5) which is derived from
Equation (4).
' '' '
  
X X X X  
ri, j R j GBj j w
( ) ( ) ( ) ( )
R,ij
   ( )
 
  
' '' '
 
Y YY Y⋅ w
r ij, R j G j B j G,ij (4)
 ( ) ( ) ( ) ( ) ( )
 
  
 
' '' '
w
 Z  ZZ Z  B,ij
( )
ri, j R j GBj j  
( ) ( ) ( ) ( )
  
=
=
−1
'' ' '
  
  X X X X
w R j GBj j ri, j
( ) ( ) ( ) ( )
R,ij   
( )
 
  
'' ' '
 
(5)
w YY Y⋅ Y
G,ij  R j G j B j  r ij, 
( ) ( ) ( ) ( ) ( )
 
  
 
'' ' '
w
B,ij  ZZ Z  Z 
( )
  R j GBj j ri, j
( ) ( ) ( ) ( )
  
where
W , W W are the weighting factors calculated from the colour-matching;
R(i,j) G(i,j) and B(i,j)
' ' '
X , Y and Z (Q = R, G, B) are XYZ stimulus values of primary colours of the DUT
Qj Qj Qj
( ) ( ) ( )
th
using the j individual observer, and defined in Equation (6).
''
X 683 Φ (λx)⋅ (λ)dλ
Qj
Qj ∫
( )
''
Y 683 Φ (λy)⋅ (λ)dλ (6)
Q j
Qj ∫
( )
''
Z 683 Φ (λz)⋅ (λ)dλ
Qj
Qj ∫
( )
where
Φλ are the SPDs of the primary colours, and Q = R, G and B.
( )
Q
th
As a result, the SPD of the test colour of the DUT matched with the i reference colour can
be obtained by:
T
 
 
Φ (λ) w w w⋅ Φ (λΦ) (λΦ) (λ)
(7)
R GB
tij, R ij, G,ij B ij,  
( )  ( ) ( ) ( )
 
where
th th
Φλ is the SPD of the test colour matched with the i reference colour for j individual
( )
tij( , )
observer.
If the DUT has more than three ORUs, see Annex D.
6.3.3.4 XYZ computation
th
1) Calculate the XYZ values of the i reference colour using the CIE 1931 standard
colorimetric observer, as shown in Equation (8).
=
=
=
=
=
– 16 – IEC TS 61966-13:2023 © IEC 2023
X = Lk⋅ Φ λ⋅ xλdλ
( ) ( )
s
ri ∫ ri
() ()
Y = Lk⋅ Φ λ⋅ y λdλ (8)
( ) ( )
s
ri ∫ ri
() ()
Z = Lk⋅ Φ λ⋅ zλdλ
( ) ( )
ri s ∫ ri
() ()
where
th
X , Y , and Z are the XYZ values of i reference colour using the CIE 1931 standard
r(i) r(i) r(i)
colorimetric observer;
L is the scaling factor and k is the normalisation constant for the CIE 1931 standard
s
colorimetric observer, defined in Equation (9).

k=
780 (9)
Sy⋅ λλd
( )
D65
∫
2) Calculate the XYZ values of the test colour using the SPD of the test colour obtained in
Equation (7) and the CIE 1931 standard colorimetric observer as shown in Equation (10).
X 683 Φ λ⋅xλ dλ
( ) ( )
tij,,tij
( ) ∫ ( )
Y 683 Φ λ⋅y λ dλ (10)
( ) ( )
tij,,tij
( ) ∫ ( )
Z 683 Φ λ⋅zλ dλ
( ) ( )
tij,,tij
( ) ∫ ( )
where
th
X , Y and Z are the XYZ values of the test colour matched with i reference colour
t(I,j) t(I,j) t(I,j)
th
for j individual observer.
6.3.3.5 Colour difference computation
1) Transform both XYZ value sets obtained in steps 1) and 2) of 6.3.3.4 into the three-
dimensional CIELAB colour space (per ISO 11664-4). The CIELAB L*, a* and b* values are
calculated from the transformed tristimulus values using the following equations:
=
=
=

Y
*
Lf=116⋅−16

Y
n

 
  
XY
*
a=500⋅−ff
   
(11)
XY
 nn 
   
 
  
YZ
*
b=200⋅−ff
   
YZ
 
n  n
 
where

 6
1/3
tt<
 
  
ft =
() (12)


1 29 16
t+ otherwise
 
3 6 116
 

and X , Y and Z are defined as XYZ tristimulus values of the reference white multiplied by
n n n
the scaling factor L as shown in Equation (13);
s
 
X
X
 Ref_W
n
 

Y LY⋅ 
n s Ref_W (13)

 

Z  
Z
n
Ref_W
 
where
X , Y and Z are the normalised XYZ values of the reference white, that is the
Ref_W Ref_W Ref_W
CIE Standard D65 illuminant.
X k S λ⋅xλdλ
( ) ( )
Ref_W D65
∫
Y k S λ⋅y λdλ (14)
( ) ( )
Ref_W D65
∫
Z k S λ⋅zλdλ
( ) ( )
Ref_W D65
∫
2) Calculate the CIE DE2000 ∆E between the reference colour and the test colour according
to the following equations:
=
=
=
=
– 18 – IEC TS 61966-13:2023 © IEC 2023
* **
(15)
C ab+
i,ab ( i) ( i)
* **
C C+ C / 2
(16)
ab ( 1,ab 2,ab)
7
*
C

( ab)

G 0,5 1−
(17)
*7
C + 25
( ab)

'*
a 1+ Ga (18)
( )
ii
'' *
(19)
Ca+ b
ii( ) ( i)
*'

0 if ba0
ii

'
h =
(20)

i
−1 *'
tan ba, otherwise
( ii)

**
′ (21)
∆−LL= L
''
′ (22)
∆−CC= C
2 1
' '

00CC ≠

'' ' ' ''

hh− C C ≠ 0 hh−≤ 180°
21 2 1 21


' '' ' ' ''
∆=h hh−− 360 C C≠ 0 hh− > 180°
(23)
( ) ( )
i 21 2 1 21

'' ' ' ''

hh− + 360 C C ≠ 0 hh− <−180°
( 21) 2 1 ( 21)



′
∆h

' '
∆H′= 2 CC sin
(24)
21  
 
**
′
L LL− / 2
(25)
( )
''
′
C CC− / 2 (26)
( 2 1)
=
=
==
=
=
=
=
=
''

hh+
' ' '' ''
1 2
 h + h ≤°180 CC ≠ 0 CC ≠ 0
1 2 12 12

 ''
hh++ 360°
1 2 '' '' ' '

hh+ >°180 hh+ < 360° C C ≠ 0

1122( ) 12
h′=
2 (27)


''
hh+− 360°
'' '' ' '
1 2

hh+ >°180 hh+ ≥ 360° C C ≠ 0
( )
1 221 12


'' ' '
h + h CC ≠ 0

 1 2 12
T= 1− 0,17cos h′− 30°+ 0,24cos 2hh′′+ 0,32cos 3 + 6°− 0,2cos 4h′− 63°
(28)
( ) ( ) ( ) ( )

 
′
h− 275°
∆θ 30exp−
  (29)

 
   

'7
C
(30)
R = 2
C
'7 7
C + 25
'
0,015 L− 50
( )
S 1+
L (31)
'
20+−L 50
( )
'
(32)
SC1+ 0,045
C
'
(33)
S 1+ 0,015CT
H
R =−⋅sin(2 θR)
(34)
TC
2 2 2
        
∆L′ ∆C′ ∆H′ ∆CH′′∆
(35)
∆ER+ + +
   
     
00 T
k S kS k S kS k S
     
L L  CC H H  CC H H
3) Repeat the process 4) to 10) for each individual observer.
4) Repeat the process 4) to 11) for each reference colour.
Annex C describes the process for evaluating the OMI between different displays.
6.3.3.6 Reporting
1) Report maximum, minimum, average and standard deviation of CIE DE2000 ∆E values for
all the individual observers (see Table 1).
2) Report maximum, minimum, average and standard deviation of CIE DE2000 ∆E values for
all the individual observers and all the reference colours to provide a set of representative
OMI values (see Table 1).
=
=
=
=
=
– 20 – IEC TS 61966-13:2023 © IEC 2023
7 Reporting form
Report maximum, minimum, average and standard deviation values of OMI obtained in 6.3.3.6
using the form shown in Table 1. Also, present a graph showing the spectral plots of metameric
pairs of reference colour and DUT as shown in Figure 5.
Table 1 – Reporting form of observer metamerism index
Observer metamerism index
Reference colour
Standard
(i = 1 to 7)
Maximum Minimum Average
deviation
Macbeth white (1)
Macbeth red (2)
Macbeth green (3)
Macbeth blue (4)
Macbeth cyan (5)
Macbeth magenta (6)
Macbeth yellow (7)
Total
Figure 5 – Reporting example of a graph of colour-matched
metameric pair of reference colour and DUT

Annex A
(informative)
Generating a set of individual CMFs
A.1 Age distribution data
When generating a set of individual CMFs using CIE 170-1 and 2, age and field size (F ) data
s
are required. Among them, F can be selected by the standard user in consideration of the
s
application field and the use environment of the DUT. The 2° field size is recommended in this
Technical Specification.
For age distribution data, officially published data could be used such as the age distribution
data published by the United Nations World Population Prospects [4]. Users of this Technical
Specification can use various age distribution data depending on the purpose of measurement.
In the case of the CIE 170-1 model, only the age range of 20 to 80 is reflected. Therefore, it is
possible to reflect only the age range of 20 to 80 years of age distribution data.
Age distribution data determine the number of CMFs dataset. If the data is constructed with 1-
year intervals, the number of datasets would be more than 150 datasets. If the age interval is
10 years, you get 1/10 of the dataset compared to the first one. For a large number of datasets,
the appropriate number of datasets should be applied to the number of iterations of the
evaluation. Therefore, it is easy to use the evaluation method to reduce the number of datasets
without distorting the statistical significance of the age distribution. In this Technical
Specification, it is recommended to use at least 20 datasets.
A.2 Example of individual CMFs dataset
Table A.1 shows the example of age distribution data. The original data are distribution data
consisting of 5-year intervals from 20 to 79 years old, and the total is 100 %. The last column
is the data in which the number of iterations is reduced without statistical distortion to simplify
the measurement. If field size is fixed to 2° and using the reduced age distribution data, a total
of 20 individual CMFs is generated and the Table A.2 shows the result.
Table A.1 – Example of age distribution data
Age Original data [%] Reduced data [%]
20 to 24 5 % 1 %
25 to 29 15 % 3 %
30 to 34 15 % 3 %
35 to 39 10 % 2 %
40 to 44 10 % 2 %
45 to 49 15 % 3 %
50 to 54 5 % 1 %
55 to 59 5 % 1 %
60 to 64 5 % 1 %
65 to 69 5 % 1 %
70 to 74 5 % 1 %
75 to 79 5 % 1 %
Total 100 %
...