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1
An Accurate Characterization of CRT Monitor (I)
Verifications of Past Studies and Clarifications of Gamma
Naoya Katoh
1, *
, Tatsuya Deguchi
1
and Roy S. Berns
2
1
PNC Development Center, Sony Corporation, 2-15-3, Konan, Minato-ku, Tokyo, 108-6201 Japan,
2
Munsell Color Science Laboratory,
Chester F. Carlson Center for Imaging Science, Rochester Institute of Technology, 54 Lomb Memorial Drive, Rochester, NY
14623-5604, USA
(Received October 4, 2000; Accepted April 18, 2001)
CRT monitors are widely used to view images on the Internet. The color images on the computer graphic display can be printed
out or displayed on other monitors through the Internet, and color matching between the original and the reproduction is very
important. The color management systems (CMSs) are useful for the color matching. CMSs utilize device profiles, in which color
characteristic information is stored, and these profiles are generated by device characterization. Thus, an accurate characterization
of the monitor is essential for better color matching. CRT monitor characteristics can be described by the tone reproduction curves
(TRCs) of each channel, and color additive matrix. In this paper, these characteristics were investigated from a physical point of
view. Various kinds of flare and the interdependence among the channels were also investigated and verified. The definition of the
term “gamma” is clarified, which is very often used to describe the TRC. Various definitions are compared and a new definition of
S-
γ
is proposed.
Key words: color management, device characterization, CRT monitor, gamma, tone reproduction, viewing flare
*
naoya@color.sony.co.jp
2
1. Introduction
Color characteristics of the CRT (cathode ray tube) monitor have recently been drawing people’s attention once again in the
color imaging field, since it is the most popularly used color imaging device today. According to the ICC (international color
consortium) specification
1)
, the monitor’s characteristics can be described by the chromaticity and the tone curve of each channel.
This idea is based on the research by Berns et al.
2)
which later became a CIE (commission internationale de l’eclairage) technical
report: CIE 122-1996
3)
and ASTM (American society for testing and materials) designation: E 1682-96
4)
. These models are based
on fundamental assumptions, such as color-additivity of RGB phosphors, and proportionality of phosphor spectral distributions.
However, in real situations, its characteristics deviate from the theoretical values. IEC (international electro-technical commission)
has issued standard IEC 61966-3
5)
, which describes a measurement procedure for the basic characteristics and deviations from
ideal conditions. In 1996, Hewlett-Packard and Microsoft proposed the sRGB Color Space
6)
, which is based on the “standard”
CRT monitor characteristics; in 1999 this was standardized as IEC standard 61966-2.1
7)
.
It was our great interest to survey past research on color reproduction, and to verify if those studies well represent physical
properties of the CRT monitor. Past studies on both the colorimetric research and physical properties of CRT monitors were
investigated, and measurements were performed to verify those results. We also investigated some of the possible causes for the
channel interdependence, which lead to deviations from theoretical colorimetric characterization.
Section 2 describes CRT’s tone curve characteristics based on the Child-Langmuir theory
8, 9)
on a vacuum tube. The subsequent
section will clarify the term “gamma”, that is often used to describe tone curve characteristics. Its use was originally proposed by
Hurter and Driffield
10)
in photography in 1890. Color-additivity matrix and various kinds of flare are described in Sect. 4 and 5.
Some additional terms regarding to the CIE 122 for the channel interdependence are also described.
3
2. Transfer characteristics of CRT monitor
The CRT monitor's overall system transfer characteristics can be expressed as a product of those of several parts. In this section,
the characteristics of each part are described. The transfer curves themselves are expressed as “
Γ
”
11, 12)
.
Display_
VideoCard_
Monitor_
VideoCard_ Set_ CRT_
VideoCard_ Set_ Gun_ Phosphor_
Γ
Γ
Γ
Γ Γ Γ
Γ Γ Γ Γ
=
=
=
×
× ×
× × ×
b g
b g
m r
(1)
where
Monitor_ Set_ CRT_
Γ
Γ
Γ
=
×
CRT_ Gun_ Phosphor_
Γ
Γ
Γ
=
×
Each transfer characteristic describes the following relationship, respectively.
Phosphor_
Γ
: Luminance:
Y
vs. Beam current:
I
k
Gun_
Γ
: Beam current:
I
k
vs. Cathode voltage:
E
d
CRT_
Γ
: Luminance:
Y
vs. Cathode voltage:
E
d
Set_
Γ
: Cathode voltage:
E
d
vs. Analogue video signal:
V
in
Monitor_
Γ
: Luminance:
Y
vs. Analogue video signal:
V
in
VideoCard_
Γ
: Analogue video signal:
V
in
vs. Digital data:
d
Display_
Γ
: Luminance:
Y
vs. Digital data:
d
First, input digital signal:
d
will be converted to analogue video signal:
V
in
by D/A (digital to analogue) converter in the video
card, and transferred to video amplifier. The RGB signal is properly adjusted channel by channel at the video amplifier circuit to
have the RGB signal white-balanced, and then applied to cathode voltage as
E
d
. Finally, electron beam:
I
k
is transmitted by
cathode voltage:
E
d
, and when the beam hits the proper phosphor, it will emit the visible light as
Y
.
4
2.1 Phosphor_
Γ
(
Y
vs.
I
k
)
Phosphor_
Γ
represents the relationship between the beam current:
I
k
and the output luminance:
Y
, and describes the
phosphor saturation characteristic. This relation can be closely represented by the power function with the exponent of
γ
phosphor
as
shown in Eq. (2). Figure 1 indicates the relationship between the beam current
I
k
and the output luminance
Y
of a typical P22
phosphor set that is commonly used in current CRTs. According to Fig. 1, the
γ
phosphor
is 0.97 for red, 0.90 for green, and 0.90 for
blue. These values differ from one channel to another. This characteristic depends on the chemical composition of the RGB
phosphors and the beam current density that is related to the monitor refresh rate, electron beam focus, screen size, anode voltage,
etc. This causes the overall RGB transfer curves to differ slightly from one channel to another.
Y I I
k
k
phosphor
∝ ≈
γ 0 9.
(2)
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
log
I
k
Y
Red
Green
Blue
Fig.1. Phosphor’s tone characteristics (Y vs. I
k
)
5
2.2 Gun_
Γ
(
I
k
vs.
E
d
)
Gun_
Γ
indicates the relationship between the cathode voltage:
E
d
and the beam current:
I
k
. Gun_
Γ
is a non-linear
transformation between the cathode voltage and the beam current of the electron gun and is sometimes called the
E
d
-
I
k
curve.
This relationship can also be represented by a power function, which describes the property of all cathode-ray tubes.
According to the Child-Langmuir law
8, 9)
, the current density reaching the anode from a thermionic cathode:
j
k
follows the
3/2 power law for a vacuum tube as in Eq. (3).
j E
k
d
∝
3 2/
(3)
Bessho derived total transmitted electron beam current:
I
k
by integrating over the cathode’s static region （inside diameter:
R
k
,
where
C
1
and
C
2
are the constants that are defined by the shape and the size of electrode）
13)
.
R
C E
C E
k
d
d
=
⋅
−
F
H
G
I
K
J
1
2
1 2/
(4)
I
k
=
2
π
j
k
r
( )
0
R
k
∫
r dr
(5)
When
R
k
can be viewed as small enough, the beam current density: j r
k
b
g
at the distance:
r
from the center can be
expressed as:
j
k
r
( )≈
j
k
0
( )
1
−
r
R
k
2
3
/
2
(6)
By substituting this into Eq. (5), we get:
6
I
k
≈
2
π
j
k
0
( )
1
−
r
R
k
2
3/ 2
r dr
0
R
k
∫
=
2
5
π
R
k
2
j
k
0
( )
(7)
and by substituting Eq. (3), we get:
I
C E
C E
k
d
d
∝
⋅
−
1
5 2
2
/
(8)
In the case of an electron gun, we usually have
C
E
d
2
>>
. Therefore, Eq. (8) can be approximated as:
I E E
k
d
d
gun
∝ ≈
γ 5 2/
(9)
and we see that electron beam current:
I
k
is approximately proportional to the 5/2 (=2.5) power of
E
d
. However, this is a
theoretical value for a vacuum tube, and real
γ
values of the CRT gun deviate from this theoretical value of 5/2 in real situations,
since the value depends on the type of electron beam gun and the cutoff voltage adjusted in the factory.
2.3 CRT_
Γ
(
Y
vs.
E
d
)
CRT_
Γ
indicates the relationship between the cathode voltage:
E
d
and the output luminance:
Y
. It is a product of Gun_
Γ
and Phosphor_
Γ
.
CRT_
Gun_
Phosphor_
Γ
Γ
Γ
=
×
(10)
Therefore, by substituting Eq. (9) into Eq. (2), the theoretical value of
γ
CRT
in CRT_
Γ
can be obtained as a product of
γ
gun
and
γ
phosphor
, and its value is approximately 2.25 (2.5 x 0.9).
7
Y E E E E
d d d d
CRT gun
phosphor
∝ ≈ ≈ =
×
γ γ
γ
d
i
5 2 0 9 2 25/ . .
(11)
It should be noted, however, that
γ
phosphor
differs from one channel to another. This will, in turn, cause CRT_
Γ
to differ from
one channel to another, and causes difficulty in grayscale adjustments. Grayscale is usually adjusted at two (light and dark) points
so that these two points will have the same CCT (color correlated temperature). This can be achieved by controlling the gain and
offset of each channel of the video amplifier circuit, which is described next.
2.4 Set
_
Γ
(
E
d
vs.
V
in
)
Set_
Γ
represents the relationship between the analogue video voltage:
V
in
and the cathode voltage:
E
d
. The analogue video
signal:
V
in
that is D/A converted from the video card will be amplified by the video amplifier circuit, and then applied to the
cathode voltage:
E
d
at an electron gun. The video amplifier circuit will control the CRT’s settings such as CCT of the white point
and grayscale, by adjusting the gain and offset terms for each channel.
E a a V b b E
E a a V b b E
E a a V b b E
d r r ch cnt in r brt r ch k co
d g g ch cnt in g brt g ch k co
d b b ch cnt in b brt b ch k co
, , , , ,
, , , , ,
, , , , ,
= ⋅ + + −
= ⋅ + + −
= ⋅ + + −
c
h
n
s
d i
o t
c h
n s
(12)
There are two types of gain and offset controls as shown above. RGB channel-independent gain a a a
r ch g ch b ch, , ,
, ,
d
i
and offset
b b b
r ch g ch b ch, , ,
, ,
d
i
terms are individually controlled by the video amplifier of the RGB channels and adjusted in the factory.
Usually user cannot change the values of these terms. On the other hand, the channel-nested gain:
a
cnt
and offset:
b
brt
terms are
usually controllable by the users by the user-controlled knobs of contrast and brightness.
E
k
,
co
is the voltage level at which the
electron beam barely begins to emit, and is called the cut-off voltage. Equation (12) can be simplified as below, and is expressed as
a linear transformation with gain
a
and offset
b
terms.
8
E a a V a b b E a V b
E a a V a b b E a V b
E a a V a b b E a V b
d r r ch cnt in r r ch brt r ch k co r in r r
d g g ch cnt in g g ch brt g ch k co g in g g
d b b ch cnt in b b ch brt b ch k co b in b b
, , , , , , ,
, , , , , , ,
, , , , , , ,
= ⋅ ⋅ + ⋅ + − = ⋅ +
= ⋅ ⋅ + ⋅ + − = ⋅ +
= ⋅ ⋅ + ⋅ + − = ⋅ +
c
h
c
h
d i d i
c h c h
(13)
Or, it can be expressed as shown below in general terms.
E
a
V
b
d
in
=
⋅
+
(14)
2.5 Monitor
_
Γ
(
Y
vs.
V
in
)
Monitor_
Γ
consists of CRT_
Γ
and Set_
Γ
and describes the relationship between the analogue video voltage:
V
in
and the
output luminance:
Y
.
Monitor_
Set_
CRT_
Γ
Γ
Γ
=
×
(15)
Monitor_
Γ
can be represented as below, from Eqs. (11) and (14).
Y a V b a V b a V b
in in in
CRT gun phosphor
∝ ⋅ + = ⋅ + ≅ ⋅ +
×
b
g
b
g
b
g
γ
γ
γ
2 25.
(16)
Here, we would like to investigate the effect of offset term
b
in the transfer characteristics. When
b
= 0, the monitor
characteristics in the log-log plot are linear and its slope becomes the S-
γ
value
15)
. However, when
b
> 0, it becomes slightly
non-linear and its slope becomes smaller. Similarly, when
b
< 0, the slope becomes greater. If we use the concept of S-
γ
by
approximating the monitor’s transfer characteristics by the power function, Eq. (16) can be rewritten as:
Y a V b V
in in
S
CRT
monitor
∝ ⋅ + ≅
−
b
g
γ
γ
(17)
9
The broadcast monitors that are usually seen in a dark (or very dim) room, are usually adjusted as
b
= 0, and the S-
γ
becomes
approximately 2.2. On the other hand, the simple gamma:
γ
monitor
of the past computer graphic display was generally around 2.5,
because these monitors are adjusted with a slightly negative offset
b
term in Set_
Γ
. This was because the computer displays
were usually seen in a light room, and the contrast of the image was the highest priority. These comparisons will be described in
detail in the next section.
Many color images are now being transmitted via networks and viewed on CRT monitors, so that some of the current CRT
monitors on the market have the capability to adjust the overall S-
γ
to 2.2, since most of these Internet images are now based on
the sRGB standard that has S-
γ
of 2.2.
2.6 VideoCard
_
Γ
(
V
in
vs.
d
)
VideoCard_
Γ
indicates the relationship between the digital data:
d
and the analogue video voltage:
V
in
. Equation (18)
indicates VideoCard_
Γ
transfer characteristic, where
LUT
VC
b
g
indicates the 1D-LUT (one dimensional-look up table) of the
video card.
V
in
=
LUT
VC
d
2
N
−
1
≅
d
2
N
−
1
γ
VC
(18)
1D-LUT in the video card is usually a linear transformation and thus can be ignored in most cases, but there are some exceptions.
For example, Macintosh and SGI have a non-linearity in their video card. It is reported that the exponent values: S-
γ
VC
values of
their video card are 1/1.4 and 1/1.7, respectively
14)
.
2.7 Display_
Γ
(
Y
vs.
d
)
Display_
Γ
represents the display’s overall transfer function that shows a relationship between the digital data
d
and the
output luminance
Y
, which is required for the ICC profile for the CRT display devices.
Display_
VideoCard_
Monitor_
Γ
Γ
Γ
=
×
(19)
10
If we substitute Eq. (18) into Eq. (17) and use the notion of S-
γ
, we get:
Y a LUT
d
b a
d
b
d d
VC
N N
N N
S
CRT
VC
CRT
VC
monitor
VC monitor
∝ ⋅
−
F
H
G
I
K
J
+
R
S
T
U
V
W
≅ ⋅
−
F
H
G
I
K
J
+
R
S
|
T
|
U
V
|
W
|
≅
−
F
H
G
I
K
J
R
S
|
T
|
U
V
|
W
|
=
−
F
H
G
I
K
J
× −
2 1 2 1
2 1 2 1
γ
γ
γ
γ
γ
γ γ
(20)
As mentioned previously, some of the OSs (operating systems) have non-linear characteristics built in. For example, the simple
gamma of Macintosh display is around 1.8 (
γ
VC
: 1/1.4 x S-
γ
monitor
: 2.5) and that of SGI is around 1.5 (
γ
VC
: 1/1.7 x S-
γ
monitor
:
2.5)
14)
. Note that the value of 2.5 is used for S-
γ
monitor
for computer graphic displays.
11
3. Tone Reproduction Curves and “Gamma”
3.1 Models to Describe TRCs (Tone Reproduction Curves)
The TRC describes the overall transfer function between RGB digital input data and output RGB linearized luminance data in
RGB channels, and can be approximately expressed by a power function with the exponent: gamma value “
γ
”. Various models
have been proposed in the literature
3, 5, 11, 12)
. Here, we compare four models that include some recently proposed standards to
represent the CRT monitor’s characteristics. In the equations shown below, “
ξ
” indicates the input signal of either of red, green
and blue channel normalized by its maximum input signal, and “
ψ
” represents the output luminance normalized by its maximum
luminance in each channel.
3.1.1 Simple Model
This is the simplest model and is often used in color management software. We refer to the “
γ
” in this model as “simple
gamma”.
ψ
ξ
γ
=
(21)
3.1.2 GOG (gain-offset-gamma) Model
This equation was introduced in CIE technical report CIE 122-1966
3)
. In this equation, coefficients
a
and
b
are called gain
and offset terms, respectively.
ψ
ξ
γ
= +a b
d
i
(22)
3.1.3 GOGO (gain-offset-gamma-offset) Model
This model has the additional offset term
c
, which is added to the GOG model, and mathematically equals the latest model
proposed by IEC in IEC 61966-3
5)
.
12
ψ
ξ
γ
= + +a b c
d
i
(23)
3.1.4 GGO (gain-gamma-offset) Model
This equation appeared in an earlier version of IEC/WD 61966-3.
ψ
ξ
γ
=
+
a
b
(24)
3.2 Clarification of the Term: “Gamma”
The tone characteristic of an imaging device is often called the “gamma” characteristic. However, the term “gamma” has been
used in various industries with different definitions
10, 16, 17)
, and thus has become a very ambiguous technical term
18, 19)
. Originally,
it was defined in the photography industry as the slope of the “linear” part extracted from the exposure-density (logE-D) curve
represented in the logarithmic domain
10)
, as indicated in Fig. 2. It is sometimes called the H-D curve using the initials of the two
proposers: Hurter and Driffield. CRT monitors also have non-linear characteristics between the input electronic signal and the
output luminance. The tone characteristics could be expressed approximately by the simple power function as
ψ
ξ
γ
=
, and its
exponent value:
γ
is often called “gamma”
by the TV industry
16, 17)
.
Basically, it is impossible to represent the whole TRC characteristic by a single value. However, it is very useful to have a single
index to describe the TRC, since the TRC changes image contrast and/or image appearance. Therefore, the concept of “gamma” is
very often used in different fields in the imaging industry. In the following sections, various definitions of gamma are briefly
described.
3.2.1 “Logarithmic Gamma (log-gamma)” – the Original Definition
This “gamma” is based on the original definition, and is regarded as the slope of the “linear” part in the tone characteristics
20)
.
We call this “log-gamma”. The power function:
ψ
ξ
γ
=
is represented as log log
ψ
γ
ξ
=
⋅
in the logarithmic scale.
Therefore, when the TRC is closely expressed by the power function, it becomes linear in the logarithmic scale, and its exponent
13
value becomes the slope of the line. Usually, the value of the slope is obtained by linear regression in the logarithmic space. This
sometimes causes a large error in the linear space in the lighter regions, since linear regression in the logarithmic domain puts much
more weight on the dark regions than on lighter regions by its nature. In actual situations, it deviates from the linear slope especially
at the very dark regions, and some of the data at the dark regions are usually neglected so that the linear part is extracted from the
total curve. However, the gamma value will depend on how we extract the linear part. In other words, how much of the data we
neglect at dark regions. Thus, it is difficult to determine an unambiguous value by this method.
Exposure vs. Density in Photo
log(Exposure)
γ =
log
f
(
x
2
)
−
log
f x
1
(
)
log
x
2
−
log
x
1
log f (x
1
)
log f (x
2
)
log x
2
log x
1
Fig.2. The definition of “gamma” in photography
3.2.2 Two-point Gamma
The “two-point gamma” can be calculated by Eq. (25), and several color management software on the market are using this due
to its simplicity. This method is simplified version of the above “log-gamma,” as it calculates the slope value only by two points.
One is at the maximum input and the other is chosen at some intermediate point. This “gamma” value is also dependent on the
choice of the second data, and has ambiguousness
21)
.
γ
ψ
ψ
ξ ξ
ψ
ψ
ξ ξ
=
−
−
=
log log
log log
log /
log /
max
max
max
max
b
g
d i
(25)
14
3.2.3 ”Point-gamma (local-gamma)”
We now would like to take the
γ
locally as indicated by Eq. (26)
22)
. The monitor’s TRCs are usually adjustable by the user
settings of contrast or brightness knobs, as shown Fig. 3(i). Setting (b) is the best setting where black is set to just zero and the tone
curve is not lost even in the dark area. In setting (a), brightness is set a little high and black is somewhat floating, whereas in a
setting (c) brightness is set a little low and black is somewhat sinking so that the tone in the dark region is lost.
Figure 3(ii) shows the same tone curves in the logarithmic domain, and Eq. (26) indicates the local slope of those curves.
γ ξ
ξ ξ ξ
ξ ξ ξ
d i
d
i
d i
=
+ −
+ −
log ( ) log
log log
f f∆
∆
(26)
Figure 3(iii) shows local gamma plotted at a given input signal. At setting (b), where CRT’s TRCs are given as
ψ
ξ
γ
= , its local
gamma remains the same. However, at the settings (a) and (c), the local gamma differs depending on the given input signals. This
local gamma is sometimes referred to as point-gamma
23)
.
In the logarithmic domain
log(Input Signal)
TRC in the linear domain
Input Signal
Point-gamma
for Input
Input Signal
c
a
b
c
a
c
a
b
b
(i) Tone characteristics in linear domain (ii) Tone characteristics in logarithmic domain (iii)Local gamma
Fig.3. CRT’s tone characteristics at different user settings
15
3.2.4 “Simple-gamma (S-
γ
)”
This method uses a non-linear optimization technique with several points of input/output data, directly in the linear domain. We
call this value “Simple-
γ
(S-
γ
)” as the exponent value of the simple model (
ψ
ξ
γ
= ). Using this method, error distribution
becomes smaller than using the Log-gamma method. The tone characteristics of the monitor can be clearly represented by a single
value. For instance, a monitor that displays high-contrast images, as in the case of (c) of, can be described by a high “S-
γ
”. It is
recommended that “S-
γ
” be used as an index to describe the tone characteristics of CRT monitors
15)
.
It should be noted, however, the approximation accuracy will greatly be decreased, when the tone curves deviate from
ψ
ξ
γ
=
as in other display devices such as LCDs.
16
4. Additive Color Mixture Matrix
4.1 Additive Color Mixture Matrix
After going through non-linear characteristics of the cathode ray tube, RGB phosphor will emit a light according to a given
signal, which is mixed to reproduce a desired color. Most current CRTs use P22-series phosphors and a typical spectral distribution
is shown in Fig. 4.
0
0.5
1
1.5
300 400 500 600 700 800
Wavelength (nm)
Red
Green
Blue
Fig.4. Typical spectral distribution of P22-series phosphors
When there is no interaction between the channels, the spectral distribution of the Radiance:
L
phosphor
λ
,
will be proportional and
the shape will not change independent of its luminance levels. Therefore, spectral distribution at given level is expressed as below,
using spectral distribution at a maximum signal level:
L
phosphorλ, ,max
and scalar: R, G, B.
L
L
L L
L L
r phosphor r phosphor
g phosphor g phosphor
b phosphor b phosphor
λ λ
λ λ
λ λ
, , , , ,max
, , , , ,max
, , , , ,max
=
⋅
= ⋅
= ⋅
R
G
B
(27)
17
Using Grassman’s law of additivity, the mixed color of RGB channels is expressed as:
L
L
L
L
L L L
pixel r phosphor g phosphor b phosphor
r phosphor g phosphor b phosphor
λ λ λ λ
λ λ λ
, , , , , , ,
, , ,max , , ,max , , ,max
=
+
+
= ⋅ + ⋅ + ⋅R G B
(28)
In a matrix notation, it is represented as:
L
L
L L L
L L L
n n n n
pixel
r phosphor g phosphor b phosphor
r phosphor g phosphor b phosphor
λ
λ
λ λ λ
λ λ λ
1 1 1 1
M
M
M M M
M M M
L
N
M
M
M
M
M
O
Q
P
P
P
P
P
=
L
N
M
M
M
M
M
O
Q
P
P
P
P
P
L
N
M
M
M
O
Q
P
P
P
, , ,max , , ,max , , ,max
, , ,max , , ,max , , ,max
R
G
B
(29)
On the other hand, tristimulus value of the red channel is given by:
X L x d
Y L y d
Z L z d
r phosphor r phosphor
vis
r phosphor r phosphor
vis
r phosphor r phosphor
vis
, , ,
, , ,
, , ,
=
=
=
z
z
z
683
683
683
λ λ
λ λ
λ λ
λ
λ
λ
(30)
where
x
λ
,y
λ
,
z
λ
are the CIE 1931 color matching functions. At a given intensity:
R
, the tristimulus values are:
X L x d X
Y L y d Y
Z L z d Z
r phosphor r phosphor
vis
r phosphor
r phosphor r phosphor
vis
r phosphor
r phosphor r phosphor
vis
r phosphor
, , , ,max , ,max
, , , ,max , ,max
, , , ,max , ,max
= ⋅ = ⋅
= ⋅ = ⋅
= ⋅ = ⋅
z
z
z
R R
R R
R R
683
683
683
λ λ
λ λ
λ λ
λ
λ
λ
(31)
Therefore, from Eq. (28), the mixed color of red, green and blue, is expressed as:
18
X L x d
L L L x d
pixel pixel
vis
r phosphor g phosphor b phosphor
vis
=
= ⋅ + ⋅ + ⋅
z
z
683
683
λ λ
λ λ λ λ
λ
λ
,
, , ,max , , ,max , , ,max
R G B
d i
(32)
From Eq. (31)
X
X
X
X
pixel r phosphor g phosphor b phosphor
=
⋅
+
⋅
+
⋅
R
G
B
, ,max , ,max , ,max
Similarly,
Y
Y
Y
Y
Z Z Z Z
pixel r phosphor g phosphor b phosphor
pixel r phosphor g phosphor b phosphor
=
⋅
+
⋅
+
⋅
= ⋅ + ⋅ + ⋅
R
G
B
R G B
, ,max , ,max , ,max
, ,max , ,max , ,max
(33)
In a matrix notation,
X
Y
Z
X X X
Y Y Y
Z Z Z
pixel
r phosphor g phosphor b phosphor
r phosphor g phosphor b phosphor
r phosphor g phosphor b phosphor
L
N
M
M
M
O
Q
P
P
P
=
L
N
M
M
M
O
Q
P
P
P
L
N
M
M
M
O
Q
P
P
P
, ,max , ,max , ,max
, ,max , ,max , ,max
, ,max , ,max , ,max
R
G
B
(34)
is obtained, and this will be the color additive mixture matrix
3)
. This equation indicates that the tristimulus values of the mixed
colors are obtained by adding the RGB phosphors in the given mixture ratio: R, G and B. This matrix can be used in ideal cases,
and is hereafter called the ideal matrix. As readily seen from the equation, chromaticity of the single channel will remain the same
in the ideal case when there are no interactions between the channels.
19
X
Y
Z
M
where
M
X X X
Y Y Y
Z Z Z
x y Y
Y
z y Y
x y Y
Y
z y Y
x y Y
pixel
ideal
ideal
r phosphor g phosphor b phosphor
r phosphor g phosphor b phosphor
r phosphor g phosphor b phosphor
r r r phosphor
r phosphor
r r r phosphor
g g g phosphor
g phosphor
g g g phosphor
b b b
L
N
M
M
M
O
Q
P
P
P
= ⋅
L
N
M
M
M
O
Q
P
P
P
=
L
N
M
M
M
O
Q
P
P
P
=
R
G
B
, ,max , ,max , ,max
, ,max , ,max , ,max
, ,max , ,max , ,max
, ,max
, ,max
, ,max
, ,max
, ,max
, ,max
b g
b g
d i
d i
b g
, ,max
, ,max
, ,max
, ,max
, ,max
, ,max
phosphor
b phosphor
b b b phosphor
r r
r r
g g
g g
b b
b b
r phosphor
g phosphor
b phosphor
Y
z y Y
x y
z y
x y
z y
x y
z y
Y
Y
Y
b g
b g
b g
d i
d i
b g
b g
L
N
M
M
M
O
Q
P
P
P
=
L
N
M
M
M
O
Q
P
P
P
L
N
M
M
M
O
Q
P
P
P
1 1 1 0
0
0
0
0
0
(35)
However, there are cases where the rule of additive mixture fails. The sum of the red, green and blue luminance usually becomes
more than the white luminance obtained by simultaneous radiation of the RGB phosphors. This is caused by various kinds of flare,
channel interactions and unwanted emissions.
20
5. Flare and Channel Interactions
5.1 Flare
CRT monitors are usually viewed in dim surroundings under ambient light, not in a dark room. Under such conditions, the
viewing flare caused by the reflection of the ambient light affects the color appearance of the monitor. According to CIE 122-1966
3)
, the viewing flare can be separated into an external flare and an internal flare, and monitor colors can be expressed by the
combination of colors produced by phosphor and these terms for various kinds of flare.
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
CRT pixel
external
flare
internal
flare
L
N
M
M
M
O
Q
P
P
P
=
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
(36)
5.1.1 External Flare
The external flare is defined as the reflection of the ambient illumination on the CRT surface. There exist three components of
reflection, i.e., Lambertian, haze and specular
24)
. However, most of the current CRT monitors have an anti-reflection filter on the
screen surface to reduce the specular and haze reflection, therefore the Lambertian reflection is dominant in the CRT monitor. The
amount of external flare depends not only on luminance levels of the surround, but also on the types of coating on the CRT surface.
The ambient light has a physical effect on the color appearance on a monitor. This influence is represented by the addition of
reflection of the ambient light to the color reproduced by the phosphor, as given by Eq. (36). The external flare can be described by
Eq. (37), if we assume that the CRT monitor surface is a Lambertian reflector. Here,
R
bk
is the reflection ratio of the CRT surface,
(
x
y
ambient
ambient
,
) is the color coordinate of the ambient light, and M (lux) is illuminance of the ambient light.
X
Y
Z
R
X
Y
Z
R
M
y
x
y
x y
external
flare
bk
ambient
bk
ambient
ambient
ambient
ambient ambient
L
N
M
M
M
O
Q
P
P
P
= ⋅
L
N
M
M
M
O
Q
P
P
P
= ⋅ ⋅
− −
L
N
M
M
M
O
Q
P
P
P
π
1
1
(37)
21
0
2
4
6
8
10
12
14
16
18
0 50 100 150 200 250 300 350
Ambient Light (= PRD's Value)
External Flare (=Reflection)
X: y = 0.0475x - 0.1579
Y: y = 0.0495x - 0.1751
Z: y = 0.0513x - 0.2321
(cd / m
2
)
(cd / m
2
)
Fig.5. External Flare vs. Ambient Light
There are many techniques to reduce this reflection using various kinds of surface coatings, but the reflectance is normally
between 3.0-5.0% in the current products on the market. Measurement procedure for the Lambertian reflection ratio is given in
Sect. 3.4 of IEC61966-3. Figure 5 indicates the relationship between the tristimulus values of the ambient light measured at a
perfect reflecting diffuser (PRD) located on the CRT and the reflection of the CRT surface under several luminance levels. In this
monitor, it was found that the reflectance:
R
bk
was about 5.0%.
It is expected that the CRT monitor’s gamut is reduced by the ambient illumination. Figure 6 shows the gamut volume of the
monitor at various ambient illuminance levels. Figure 7 shows the gamut shape in a*b* coordinates. For both calculations, ITU-R
BT. 709 phosphors and D65 white point were used. The viewing flare was assumed to be 5.0% with ambient illumination by a
CIE/F6 illuminant, which is a typical office lighting. The white point was redefined at each level to include the ambient flare. As
seen from the figures, the gamut of the CRT monitor is greatly reduced by the reflection of the ambient illumination.
22
Effect of Ambient Light on Monitor's Gamut
0
20
40
60
80
100
0 500 1000 1500 2000
Ambient Illuminance (lux)
Fig 6. Gamut volume of a monitor under different ambient lightings
a*
b*
2000 lux
500 lux
0 lux (dark)
Fig 7. Gamut under different ambient lightings in a*b* coordinate
5.1.2 Internal Flare
The internal flare is caused by the internal reflection in the CRT glass, when the phosphor around the area detected by the eyes
or the measurement instruments has some amount of emission. It can be separated into the three kinds shown below
25)
.
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
internal
flare
neighboring pixel
inter reflections
secondary
emissions
cross channel
emissions
L
N
M
M
M
O
Q
P
P
P
=
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
−
−
(38)
23
The first one is called neighboring pixel inter-reflections, and is caused by the reflection of the emission at the neighboring pixels
inside the front glass. The second is called secondary emissions, and is present when the electron beam is reflected back and hits
other pixels. These two kinds of flare become negligible when the proximal field of the measurement area is set to black. The
measurement procedure as the sum of these two is given in Sect. 3.5 of IEC61966-3.
The third one is called cross-channel emissions. This can be regarded as unwanted emission of the black level, when the signal is
detectable at the black level. This term is present only with three-color CRTs but not with single-color CRTs. When we measure
the red channel’s ramp data, for example, the red measurement data cannot be separated from the emission from minimum green
and minimum blue, which were present at black level. This term will be described in detail in the following sub-section.
5.1.3 Unwanted Emissions (Cross-channel Emissions)
The black level is usually set to a non-detectable range at the factory default setting. However, when the user adjusts the
brightness knob and increases the black luminance level, some amount of luminance will become detectable even if the digital
signal counts of all channels are set to zero. The tristimulus value of black:
XYZ
k , min
in this case can be expressed by the
equation below with each phosphor’s tristimulus values:
XYZ
r phosphor, min ,
,
XYZ
g phosphor, min ,
and
XYZ
b phosphor, min ,
.
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
k r phosphor g phosphor b phosphor
L
N
M
M
M
O
Q
P
P
P
=
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
,min , ,min , ,min , ,min
(39)
On the other hand, the measurement data of the single-channel already includes other channels’ minimum data such as
XYZ
r phosphor, min,
,
XYZ
g phosphor, min,
and
XYZ
b phosphor, min,
. Therefore, the measurements of tristimulus values of each color
of red:
XYZ
r meas,
, green:
XYZ
g meas,
and blue:
XYZ
b meas,
can be expressed as in Eq. (40).
24
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
r meas r phosphor g phosphor b phosphor
g meas g phosphor b phosphor r phosphor
b
L
N
M
M
M
O
Q
P
P
P
=
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
F
H
G
G
G
I
K
J
J
J
L
N
M
M
M
O
Q
P
P
P
=
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
F
H
G
G
G
I
K
J
J
J
L
N
M
M
M
O
Q
P
P
P
, , , ,min , ,min
, , , ,min , ,min
, , , ,min , ,minmeas b phosphor r phosphor g phosphor
X
Y
Z
X
Y
Z
X
Y
Z
=
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
F
H
G
G
G
I
K
J
J
J
(40)
XYZ
r phosphor
,
indicates the tristimulus values obtained by the red phosphor alone.
XYZ
g phosphor
,
and
XYZ
b phosphor
,
can be
expressed in the same manner as red. We call the emissions from other channels in parenthesis “unwanted emissions”.
Furthermore, we can express the tristimulus value of the any mixed color of RGB:
XYZ
pixel
at a given pixel, as below:
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
pixel r phosphor g phosphor b phosphor
L
N
M
M
M
O
Q
P
P
P
=
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
, , ,
(41)
From Eqs. (39), (40) and (41) we obtain Eq. (42)
26)
.
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
pixel r meas g meas b meas r phosphor g phosphor b phosphor
r meas g
L
N
M
M
M
O
Q
P
P
P
=
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
F
H
G
G
G
I
K
J
J
J
− ⋅
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
F
H
G
G
G
I
K
J
J
J
=
L
N
M
M
M
O
Q
P
P
P
+
L
N
M
M
M
O
Q
P
P
P
, , , , ,min , ,min , ,min
, ,
2
meas b meas k
X
Y
Z
X
Y
Z
+
L
N
M
M
M
O
Q
P
P
P
F
H
G
G
G
I
K
J
J
J
− ⋅
L
N
M
M
M
O
Q
P
P
P
, ,min
2
(42)
Or, by rearranging Eq. (42), we get:
25
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
pixel k r meas k g meas k b meas k
L
N
M
M
M
O
Q
P
P
P
−
L
N
M
M
M
O
Q
P
P
P
=
L
N
M
M
M
O
Q
P
P
P
−
L
N
M
M
M
O
Q
P
P
P
F
H
G
G
G
I
K
J
J
J
+
L
N
M
M
M
O
Q
P
P
P
−
L
N
M
M
M
O
Q
P
P
P
F
H
G
G
G
I
K
J
J
J
+
L
N
M
M
M
O
Q
P
P
P
−
L
N
M
M
M
O
Q
P
P
P
F
H
G
G
G
I
K
J
J
J
,min , ,min , ,min , ,min
(43)
This equation indicates that the color-additivity rule can be used, if we subtract the black level data from the measurement data.
5.2 Channel Interactions and Interaction Matrix
An insufficient power supply can be considered as one of the reasons for the channel interactions. If the power supply is not
sufficient for total current as in the maximum signal (i.e., white), the actual luminance of the white will be lower than the sum of
the red, green and blue signals. This is one reason why the color-additivity rule could fail. The secondary emissions described
earlier and the mis-landing of electron beams can be considered as other reasons. The mis-landing is caused when the monitors are
not well adjusted, i.e., when the convergence of the three colors were not properly adjusted.
As mentioned above, there are cases where the rule of additive mixture fails. This can be compensated by an interaction matrix
M
interactio
n
. In other words, we can characterize the relationship between linearized RGB and XYZ better with an introduction of
this matrix in addition to the matrix
M
ideal
. This matrix could be obtained by the linear regression technique from the
measurement values of several displayed colors. Several interaction matrices have been proposed, as given in Eqs. (44) to (46). In
some research
27)
, the square terms of R
2
, G
2
and B
2
were included in the matrix. Since the non-linearity within each channel should
have been compensated beforehand by the TRC, they would have no physical meaning. Nevertheless, these terms might be
effective for the monitor characterization if the compensating non-linearity of a single-channel is not sufficient. In these equations,
the cross terms of RG, GB, BR and RGB show the interdependence between the channels caused by insufficient power supply. The
non-diagonal terms of R, G and B might depict the influence of the secondary emissions and the electron beam mis-landings. The
offset term of “1” might describe the unwanted emissions and the various types of flare.
26
X
Y
Z
M M
pixel
ideal interaction
L
N
M
M
M
O
Q
P
P
P
= ⋅ ⋅
L
N
M
M
M
O
Q
P
P
P
×(3 3)
R
G
B
(44)
X
Y
Z
M M
pixel
ideal interaction
L
N
M
M
M
O
Q
P
P
P
= ⋅ ⋅
L
N
M
M
M
M
O
Q
P
P
P
P
×( )3 4
1
R
G
B
(45)
X
Y
Z
M M
pixel
ideal interaction
L
N
M
M
M
O
Q
P
P
P
= ⋅ ⋅
L
N
M
M
M
M
M
M
M
M
M
M
M
O
Q
P
P
P
P
P
P
P
P
P
P
P
×( )3 8
1
R
G
B
RG
GB
BR
RGB
(46)
5. Conclusions
Past studies on CRT color characteristics along with recently proposed methods were investigated with some measurements of
real CRT monitors. It was verified that the method in CIE122-1996 describes CRT physical representations at normal settings.
Also, the definition of the technical term “gamma” has been clarified, and the use of S-
γ
was recommended, if appropriate.
Several reasons for a failure of color-additivity were considered in the last section. It is important to know when and where these
kinds of flares are present, and to separate these terms in the colorimetric characterization of the CRT monitor. At proper settings
and under proper viewing conditions, most of these channel interactions are negligible. Therefore, CIE122 methods can be applied
in most cases. In the subsequent paper
28)
, the characterization methods are verified when the user setting deviates from a normal
position.
27
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