THEORY AND PRINCIPLE OF COLOUR MANAGEMENT, APPLICATION AND COMMUNICATION 2

Reflectance Spectrophotometer
Reflectance spectrophotometers measure the amount of
light reflected by a surface as a function of wavelength to
produce a reflectance spectrum.

The reflectance of a sample is expressed between 0 and 1 (as
a fraction) or between 0 and 100 (as a %). It is important to
realize that the reflectance values obtained are relative values
and, for non-fluorescent samples, are independent of the
quality and quantity of the light used to illuminate the sample.
The operation of a spectrophotometer is basically to
illuminate the sample with white light and to calculate the
amount of light that is reflected by the sample at each
wavelength interval. Typically data are measured for 31
wavelength intervals centered at 400nm, 410nm, 420nm, and
700nm.
This is done by passing the reflected light though a
monochromatic device that splits the light up into separate
wavelength intervals. The instrument is calibrated using a
white tile whose reflectance at each wavelength is known
compared to a perfect diffuse reflecting surface.

Main component of a spectrophotometer are:
 Source of optical radiation
 An optical system defining the geometric conditions
for measurement
 Light dispersing system
 Detector
 Signal processing system that converts light into
signals suitable for analysis.

Block diagram of the subsystems comprising a spectrophotometer
designed for measurement.

A scanning spectrophotometer using a prism to disperse the light

An interface filter wheel spectrophotometer

A detector-array Spectrophotometer

The optical geometry of the instrument is important. In some
instruments an integrating sphere is used that enables the
sample to be illuminated diffusely (from all angles equally)
and the reflected light to be collected at an angle roughly
perpendicular to the surface of the sample. Alternatively, other
instruments illuminate the sample at a certain angle and
collect light at another angle. For example, typically the
sample may be illuminated at 45 degrees to the surface and
light reflected measured at 0 degrees - this is known as 45/0
geometry. The converse to this is 0/45. The sphere-based
geometries are known as D/0 and 0/D. It is extremely
difficult, if not impossible, to correlate measurements taken
between instruments if the optical geometry is not identical.
Optical Geometry of a
Spectrophotometer

 Colorimeters
 0/45° and 45/0° geometry spectrophotometers
 Integrating sphere geometry spectrophotometers
Colour Measuring Instruments
There are three major classes of measuring instruments
available to the coloring of textile industry. They are:

Colorimeters
Colorimeters were the pioneers of colour measuring
instruments. Colorimeters view a sample through at least three
filters measuring the quantity of light reflected from the
sample and passed through each of the filters. The filters were
originally designed to mimic the response of the red, blue and
green cones of the eye as closely as possible. This, at first
glance, would seem to have merit since it attempted to imitate
the eye of the standard observer. An important deficiency of
colorimeters is they cannot separate the pure colour from the
appearance of an object. Additionally, a colorimeter is unable
to detect if an object’s colour will appear differently under
different light sources. Therefore, colorimeters have limited
capability when compared with current technology.

Colorimeter
Uses three or four filters

 0/45° geometry spectrophotometers illuminate the sample
at an angle of 90° and the detector views the sample at a
45° angle.
 45/0° geometry illuminates the sample with a beam
striking the sample at an angle of 45° while the detector
views the sample at an angle of 90°.
0/45° and 45/0° Geometry
Spectrophotometers

Advantages
• Mimics visual observations.
• Minimizes gloss differences.
Disadvantages
• Unable to measure transparent samples.
• Cannot differentiate between colour and
appearance.
0/45° and 45/0° Geometry
Spectrophotometers

Integrating sphere geometry spectrophotometers utilize a
reflecting sphere to capture the reflected light from a
sample. The reflected light leaves the sphere through a
viewport and is analyzed by a detector array. The
detectors measure the percent reflectance across the
visible spectrum, usually at 10 nanometer increments.
Sphere spectrophotometers are the only instrument
capable of separating out surface and appearance effects
to measure only the colour of an object. Additionally, in
Specular Component Excluded (SCE) mode, a sphere
spectrophotometer can simulate visual assessment through
measurement of colour and appearance combined. Sphere
spectrophotometers dominate the market today.
Integrating Sphere Geometry
Spectrophotometers

When light strikes a surface some of the light penetrates where
it can then be absorbed, scattered, or even transmitted if the
layer is sufficiently thin. Nevertheless, because of the change
in refractive index between air and most substances, a certain
proportion of the incident light is reflected directly from the
surface. The angular distribution of this light depends upon the
nature of the surface but light that is reflected at the opposite
angle to the incident light is called specular reflectance. Light
that is reflected by the substance itself is called body
reflectance.
Sphere-based spectrophotometers often incorporate a so-
called gloss trap which allows the specular component of the
reflected light to be either included or excluded.
Specular Component of Reflectance

Specular Component of Reflectance

Inside these spectrophotometers, you'll find a light
source-generally a xenon-flash bulb or bank of super-
bright light-emitting diodes (LEDs), a holographic
diffraction grating that separates the light reflected from
the colour sample, a diode-based detector array that
measures the amount of light coming from the
diffraction grating, and the circuitry that handles the
mathematical tasks involved with colour measurement.
How Spectrophotometers Work

Minolta's Spectrophotometers
Together with their comprehensive
built in software, all models
conform perfectly to international
standards such as DIN5033, 5036,
6174; JISZ8722; ISO7724,
ISO2470; ASTMD2244; E308,
E313, E1164, BS6923 und
ASTMD1925, as well as the VDA
recommendations 280 part 1to.
CM-2600d
The CM-2600d offers great flexibility of use with two
interchangeable measurement apertures with Ø 8 mm (MAV)
and Ø 3 mm (SAV). These two apertures enable to measure
samples of all size and shapes and avoid taking time consuming
average measurements on structured surfaces.

GretagMacbeth Portable
Spectrophotometers
GretagMacbeth Color-Eye XTH
Basic Functionality
 Density
 Reflection spectrum
 Colour system CIE L*a*b*, CIE
L*C*h (a*b*), DE CIELAB
 Colour distance formulas
DE*94, DE CMC, DE FMCII
 BestMatch

Datacolour Portable Spectrophotometers
Technical Specifications
Measuring principle: Dual
beam sphere - Automatic
specular port
Measuring geometry: Diffuse
illumination 8º
Light source: Pulsed xenon
Spectral range: 360 to 700nm
Effective bandwidth: 10nm
Wavelength resolution: 2 nm
Spectrometer principle:
Concave holographic grating

X-Rite Portable Spectrophotometers
SP64 Reflection Spectrophotometer

MiniScan® XE Plus
• The xenon-flash portable
colour spectrophotometer.
• Available in d/8° or 45°/0°
optical geometry.
• 25mm (1.00") to 7.6mm
(0.30") measurement area
(Large Area View/Small
Area View) available.
• Fully portable, one-handed
operation with customizable
LCD display.
MiniScan XE Plus

• The standard 45/0 geometry,
perfectly suited for measurement
results to closely match visual
assessment.
• The CM-508c, with its' small
measurement area of 3mm,
commonly used in the graphic
arts industry, is perfectly suited
to measure packaging and
printed materials.

Ihara U.S. Inc.
• Colour measurement of very
small and curved parts with
4mm aperture
• Testing for colour fading by
wind and weather
• Comparison between colour
of raw materials and standard
colour
MODEL S600 SERIES

Specifications
Color-Tec™
 Measuring Geometry
45°/0°- (3mm, 12mm)
Hemisphere- (12mm)
 Measuring Area.
3mm, 12mm, 20mm or 26mm
 Measuring Time
>1 second (45/0 models)
>7 seconds (Hemisphere)
 Light Source
Light Emitting Diodes Array
 Short Term Repeatability
0.13 delta L*A*B* maximum
standard deviation (30
measurements on white standard,
< 0.05 typical)

GretagMacbeth color-Eye 7000A
NetProfiler
 Repeatability: Maximum
0.01 RMS DE CIELAB
 Inter-instrument agreement:
Max. 0.08 DE
 Illumination: Pulsed Xenon
 Spectral Range: 360nm to
750nm
 Wavelength interval: 10nm
GretagMacbeth Benchtop
Spectrophotometers

GretagMacbeth Softwares
NetProfiler
colour iQC colour
Quality Control
ProPalette Optiview
Quality Control
ProPalette
Textile Formulation

Datacolour Spectrophotometers
 Spectra Flash 600X High-precision, close-tolerance reference
grade Spectrophotometer with special capabilities to handle
fluorescent materials.
 Automated zoom lens, specular
port and UV control
 Multiple viewing apertures with
automatic aperture recognition

Datacolor
SF-650.pdf
 Haze measurements
 Regular transmittance, total transmittance and diffuse
transmittance measurements
 Automated zoom lens and specular port
 Automated UV control
 Multiple viewing apertures with automatic aperture
recognition
Features

Spectrophotometer CM-3700d has performance that
equals or exceeds that of most high-end bench-top
spectrophotometers, with 3 measuring areas, motorized
variable UV, and Specular Component Included or
Excluded. The CM-3700d offers both reflectance and
diffuses transmittance measurements.
CM-3700d

 Multiple areas of view in both
reflectance and transmittance for
the most versatility in measuring
non-uniform and variable size
samples.
GretagMacbeth
colour i 5
GretagMacbeth Benchtop
Spectrophotometers
 Designed with industry-leading features, the colour i 5 am
ideal for busy labs requiring high speed and throughput. Its
features include: Tri-Beam technology that simultaneously
measures specular component included and excluded for
simplified gloss assessment.

• The compact DF110 is one of the most powerful,
versatile and affordable compact spectrophotometers.
DataFlash 110
• Spherical design and automatic
gloss compensation.
• Exceptionally small aperture.

• CM-3600d can meet true "high-end" class standards
although it's at an affordable price.
• Simultaneous measurement of specular included and
excluded with "Numerical Gloss Control" without
mechanical moving parts.
• Simultaneous data for UV-
excluded, UV-included and
UV-adjusted.
• Instantaneous and trouble free
UV calibration with "Numerical
UV-Control" without mechanical
moving parts.
CM-3600d

ETA - ARC
Spectral measurement system for transparent layers
on curved surfaces

ETA - ARC
The ETA-ARC measuring system consists of a spectrometer
for the visible spectral range, a light source, and a newly
developed sensing head. Light source and spectrometer are
integrated in a desktop housing. The sensing head is
connected with this unit via optical fibers.
The light reflected at a transparent medium coated with anti-
reflective (AR) coatings and/or a protective varnish is
spectrally resolved in the spectrometer. The spectrometer is
based on a grating and a diode line array with 512 pixel and
16 bit dynamical resolution.

SpectraWiz software
EPP 2000C - 100
Stellarnet Fiber Optic Colour
Measurement System
• Measure reflectance of solid
samples
• Reflectance probe accessory for
small sample areas
• Display CIE L*a*b* values,
Delta E, Chroma, Hue
• Compare samples with standards
Main Features and Benefits
• Wavelength range: 350 to 850nm
• Spectral bandwidth: 4nm
• Real-time spectra displayed on PC screen
• Measure transmitted colour of liquids or solids

Non-contact colour
measurement
Normal to the sample surface (under
0°) the reflected light will be collected
and guided to a high resolution
spectrometer Simultaneously with the
sample measurement a reference
measurement of the lamp will be made
with a second high resolution
spectrometer (full dual beam design).
Online Spectrophotometer ER 50 PA
For a measurement the sample will be illuminated with white
light (Xenon flash lamp, daylight) with ultraviolet (UV) content.
The flash duration is around 1 / 1000 sec.

DigiEye
 DigiEye began as a concept from the University of
Derby’s Colour & Imaging Institute but has grown to
become a revolution in the field of digital colour
Imaging.
 It has flourished within the triangle of expertise
formed by The University of Derby's Colour Imaging
Institute (C&II), VeriVide Ltd and Global Colour
Solutions (GCS).

DigiEye
DigiEye is a revolutionary non-contact digital imaging
system that captures the total colour and appearance of 2D
and 3D objects in a unique controlled lighting environment. A
calibrated monitor gives true on-screen colour simulation of
the object and the profiled printer produces high quality hard
copies. DigiEye’s ability to select and retrieve colour data
from any pixel in the high- resolution image allows the
measurement of very small or irregular shaped samples.
Measured colours are represented by their
‘finger-prints’ in terms of colourimetric
values or spectral data. Electronic
communication of the image and colour
data is easy and fast over the World Wide
Web using standard formats

Colour Measurement
Textured Surfaces
DigiEye allows the capture of the total
appearance of the carpet tufts through
its non-contact measurement. The
ability to select small groups of pixels
allows colours from small areas of
pattern within the carpet to be
highlighted and measured without the
need of a skilled operator. Colour
recipes are formulated from the
DigiEye colourimetric data.

Simulated colorimeter response-
average colour over sample area
True image data used by digital
imaging system.
A colorimeter measures average colour but a digital
imaging system gives detailed colour information

Fluorescent Samples
Whiteness Measurement
Measurements of fluorescent samples are tied to the spectral
distribution of the actual light source of the instrument.
Contrary to colour measurements, where the reflectance
spectrum is independent on the light source of the instrument,
reflectance spectra of fluorescent samples are in general unique
and cannot be converted to other illuminants by software
manipulation. Here lies the reason that while there are a large
number of instruments designed to measure colour, they are not
suited to handle samples showing fluorescence. In fact the
correct way of measuring fluorescent samples is through the
use of the two-monochromator technique: samples are
illuminated with a monochromatic ray and the light from the
sample (containing reflected of the monochromatic ray and the
induced fluorescence) is analyzed by a second monochromator.

Fluorescence colorimeter
Features and Benefits
 Measure fluorescence and reflectance
 Supports both UV and VIS activated
fluorescence
 Measures in 10 nm intervals
a) Light excitation 300 - 780nm
b) Light emission 380 - 780nm
 Excellent Inter-instrument agreement
 Analyze colour under any illuminant
BFC- 450
Whiteness Measurement

Whiteness and yellowness are very important indicators
of product quality. While whiteness represents purity and
cleanliness, yellowness indicates degradation of material
or the presence of impurities.
WHITENESS ASSESSMENT

The White Colour
Highest Value and no Chroma
Significant attributes
• Neutrality: Non-aggression, void, peace
• High Value: Cleanliness, untouched
Yellowish-white: Old, used
Bluish-white: Coolness, freshness

Whiteness of Textile Samples
Perfect white is characterized by
• High level of luminosity (value)
• No saturation at all (Chroma)
• No hue
Actual white sample is characterized by
• High level of luminosity (value)
• Finite saturation (Chroma)
• Blue hue
Though the reflection whites is very high throughout the
visible wavelength, the substances reflecting more blue light
appear whiter than those reflecting more yellow light

Whiteness is a measurement of light reflectance across all
Wavelengths of light comprising the full visible spectrum
The perception of the whiteness of any ‘white’ product consists
of three components of the colour white (Almnet, 2012):
Base white is the contribution to the whiteness by the fabric
itself. It determines the extent by which the yellowness can
be compensated by physical means, i.e. bleaching and/or
optical brighteners.
Shaded white is the increased amount of whiteness due to
the compensation of yellowness by the addition of a product
such as bluing.
Fluorescent white is the addition of optical brighteners to
white, resulting in an increase in blue reflectance.

Bleaching alone cannot remove all traces of yellowish cast.
Therefore, an additional whitening stage, called colour
compensation, is essential the addition of complementary
colours of the substrate.
The age old practice is to treat the bleached material with a
very small amount of a blue or violet dye an operation
known as bluing to boost the visual impression of
whiteness. These dyes absorb light in the green yellow
portion of the spectrum that reduces lightness. Since, at the
same time, they shift the shade of the yellowish material
towards blue, the eye records an increase of whiteness. The
blue colour of the dye offsets the yellow colour of the
material, resulting in a neutral, very light grey, but the
greyness is not quickly noticed by the eye.

Whiteness Assessment
White Cloth
Cloth
Light
yellow
Observer
Blue

White Cloth + Bluing Agent
Cloth
Light Observer
Yellow
Blue
Bluing agent

Unlike dyes, FWAs offset the yellowish cast and at the same
time improve lightness, because they do not subtract green-
yellow light, but rather add blue light. FWAs are virtually
colourless compounds which, when present on a material,
have the ability to absorb mainly invisible ultraviolet light in
the 300-400 nm range and remit violet to blue fluorescent
light. The emitted fluorescent light is added to the light
reflected by the treated material, by that producing an
apparent increase of reflectance in the blue region.

White Cloth + Fluorescent Whitener
Cloth
Light Observer
Blue
FWA
Yellow
UV Light

Reflectance curves of cotton cloth at various stages of processing.

Primitive Formulas
• Whiteness = R470
• W = R700 - R450 / R700
• Stephansen formula
WI = 2 × R430 – R670
• Harrison formula
WI = 100 - R670 – R430
• Whiteness measured by Leukometer
WI = 2 × R459 – R614
R470 = % Reflectance at 470nm
(Yellow region)
R670 = % Reflectance at 670nm
(Blue region)

The interrelationship between the different contributions
is illustrated on the following diagram (L*, a*, b*) for a
fluorescent sample:

CIE Formulas
WCIE = Y + 800 (x0 – x) + 1700 (y0 – y)
TCIE = 900 (x0 – x) – 650 (y0 – y)
WCIE is for whiteness and TCIE is for tint factor for
daylight D65 and 100 observer.
(x0, y0) = (0.3127, 0.3290) for 100 observer

CIE Formulas in CIE-L*a*b* space
WCIE-L*a*b* = 2.41 L* -4.45 b* [1 -0.0090 (L* -96)] -141.4
TCIE-L*a*b* = -1..58 a* - 0.38 b*
CIE formulas have been adopted by many institutions
like ISO, Tappi, AATCC, DIN, ASTM, etc.
CIE formulas are valid only for illuminant D65 and for
UV amounts similar to daylight.

The tristimulus values (D65, 100 Observer) of two
samples of white cloth are given below:
X Y Z
Sample 1 81.29 85.19 95.98
Sample 2 81.59 85.77 87.68
Analyses these data to determine which of the two
samples will appear the better white when viewed
under average daylight (xo = 0.313, yo = 0.329)

METAMERISM
Metamerism occurs when two colours match under one
set of illumination and viewing conditions, but fail to
match under a second set of conditions. Such samples
are said to be metameric, or to form a metameric pair.

In dyeing, it is often possible to match a coloured object (under
one specified set of conditions) using a mixture of three dyes, but
the reflectance curve of the dyed sample will not necessarily be
the same as that of the object to be matched unless the same dyes
as used to produce the original sample can be used.

Metamerism is always the result of the fact that the reflectance
curves for the two coloured objects are different. Usually the
reflectance curves of a metameric pair of samples cross at least
three times.
Notice how the curves are twisting over each other. Whenever
two physical samples have curves that cross at least three
times, they are a metameric pair.
To avoid metamerism, the reflectance curves should coincide
at all wavelengths.
The reflectance curves of a metameric pair of samples
Reflectance
(log scale)
Wavelength (nm)

Metamerism can occur to
different degrees
Slightly metameric
A metameric pair may match perfectly under one set
of conditions, but be a slight mismatch under other
conditions.
Highly metameric
Another pair could match perfectly under one set of
conditions, but be a very bad mismatch under a third
set of conditions

Four types of metamerism are recognized:
 Illuminant metamerism, the most common
types of encountered
 Observer metamerism
 Field size metamerism
 Geometric metamerism

Illuminant metamerism is the most common type encountered.
In this case, a pair of samples matches when viewed under one
illuminant, but appear different when viewed under another
illuminant.
The reflectance curves for incandescent and daylight
Incandescent has a lot of energy in the red area, but not
much in blue. Because of the increased energy in the red
area, objects illuminated by incandescent lighting appear
redder than those under daylight, which peaks in blue.

Observer metamerism is exhibited when a metameric pair
matches for one person, but fails to match for a second person.
In this case, the wavelength sensitivities of the two people are
different and one, or both, may be significantly different.
Colour vision tests such as the Munsell 100 Hue Colour Vision
test should be used to check the colour vision of all personnel
professionally involved in assessing colour.
Field size metamerism occurs when the field viewing angle
changes with a single observer, for example from 2o to 10o. In
this case, a metameric pair may match when seen at a distance
(small field of view) but may no longer match when closer to
the eyes (large field of view).
Geometric metamerism occurs when the viewing geometry
changes. Metallic paints may match the target colour for one
particular angle of illumination and angle of viewing, but no
longer match if either angle is changed.

Fluorescent optical brighteners are also a common trigger for
metamerism in papers, fabrics, and liquids. In this process, a
chemical is added to absorb ultraviolet energy from below the
visible and re-emit it energy at longer wavelengths to make the
color appear whiter. OBAs can be difficult to manage and often
cause metameric pairs.
Although these shirts appear to
match under daylight, when
you flip on UV light you can
see that each of the pieces is
actually metameric pairs.

Colour Constancy
Colour constancy is a property of a single sample and is
the property of objects to appear to be more or less the
same colour when viewed under different light sources.
Metamerism and colour constancy are closely linked and
sometimes confused, but metamerism refers to differences
between two samples viewed under different conditions.

While most objects remain more or less colour constant
under normal light sources, some objects do change colour
appreciably.
For example, meat purchased from supermarket cabinets
illuminated by artificial light sources designed to accentuate
the redness of meat may appear a much less appealing grey-
brown when viewed in natural light coming through the
kitchen window.

COMPUTER COLOR MATCHING
SYSTEM (CCMS)
Computer Color Matching (CCM) is the instrumental
color formulation based on recipe calculation using the
spectrophotometric properties of dyestuff and fibers.
The basic three things are important in CCMS
 Color measurement Instrument (Spectrophotometers).
 Reflectance (R %) from a mixture of Dyes or Pigments
applied in a specific way.
 Optical model of color vision to closeness of the color
matching (CIE L*A*B).

Functions of Computer Color
Matching System
• Colour match prediction.
• Colour difference calculation.
• Determine metamerism.
• Pass / Fail option.
• Colour fastness rating.
• Cost Comparison. (Helps to choose the right dyes)
• Strength evaluation of dyes. (Effects the concentration
of dyes which will be used)
• Whiteness indices.
• Reflectance curve and K/S curve.
• Production of Shade library. (Store the recipe of the
dyeing for specific shade)
• Color strength

Advantages of Computer Color
Matching System (CCMS):
 Customers get the exact shade wanted
 Customers often have a choice of 10-20 formulation that
will match color. By taking costing, availability of dyes,
and auxiliaries into account, one can choose a best
swatch.
 3 to 300 times faster than manual color matching.
 Limited range of stock color needed.

As the concentration is increased the reflectance decreases very
rapidly at first, and at higher concentrations it asymptotically
approaches a limiting value.
Reflectance curves for different concentrations of CI Acid Black
60 on a nylon substrate

Reflectance of different concentrations of CI Acid Black 60 on a nylon
substrate at a wavelength of 600 nm

Textile dyes, can be considered to be dissolved in the fibre
and therefore have no scattering power of their own.
In textile recipe formulations the various K/S values, which
are specific to each dye on the given substrate are commonly
known as absorption coefficients.

𝑲/𝑺 𝝀 =
𝟏 − 𝑹𝝀
𝟐
𝟐𝑹𝝀
Kubelka-Munk Function
Where
R = reflectance of a sample of infinite thickness to
light of a given wavelength expressed in fractional form
K = absorption coefficient
S= scattering coefficient
Rλ = 1+ (K/S)λ - {(K/S)λ [(K/S)λ +2]}1/2

Relation between K/S and dye
Concentration
(K/S)dλ-(K/S)uλ α C
(K/S)λ’ α C
(K/S)λ’ = (K/S)dλ-(K/S)uλ
Where (K /S)dλ= (K/S)λ of the dyed sample
(K/S)uλ = (K/S)λ of undyed sample
C = concentration of the dye

(K/S)λ’ has a property of additivity
(K/S)mλ’ = (K/S)1λ’ + (K/S)2λ’ + (K/S)3λ’ ….. (K/S)nλ’
Where (K/S)1λ’ , (K/S)2λ’…. are the values of (K/S)λ’
obtained when the fabric is dyed with dyestuff 1,2,….
n separately in certain concentration, and the (K/S)mλ’
is the (K/S)λ’ of the fabric dyed with a mixture of these
1,2, ….. n dyes in the same concentration.

Where α is the proportionality constant also called the
dyeing absorbency co-efficient. It can be determined by
actual dyeing experiments (that is, dyeing the material
with known concentrations and measuring the reflectance
of the dyed samples.
𝜶 𝝀 =
𝑲/𝑺 𝝀,
𝑪
(K/S) λ’ αC
(K/S) λ’ = (α)λC

(K/S)mλ’ = (K/S)1λ’ + (K/S)2λ’ + (K/S)3λ’ ….. (K/S)nλ’
(K/S)λ’ = (α)λC
(K/S)mλ’ = (α1)λC1+ (α2)λC2+ (α3)λC3……… (αn)λCn
Where (α1)λ, (α2)λ, (α3)λ are the (α)λ values of dye 1,2
……………n.
C1, C2………… Cn are the concentrations of dyes 1, 2… n.
K/Smλ’ is the K/Sλ’ of the fabric dyed with a mixture of dyes
1, 2….n, concentrations C1, C2………… Cn.
These equations can be linked up to the concentration of the
dyes and tristimulus values
By varying the concentrationC1, C2………… Cn the
tristimulus values can also be made to vary.
What is required is calculation of these C1, C2………… Cn to
obtain, X,Y,Z values which approximate to the X,Y,Z values
of the sample to be matched.

Eλ = Spectral power distribution of standard source, Rλ =
Spectral reflectance of substrate and xλ. yλ. zλ = colour factor
of standard observer for red, blue and green.
Xs = ΣEλ.Rλ.xλ
Ys = ΣEλ.Rλ.yλ
Zs = ΣEλ.Rλ.zλ
Rλ= 1 + (K/S)λ - {(K/S)λ [(K/S)λ + 2]}1/2

Relative spectral energy (E) x Reflectance factor (R) x colorimetric functions (x,y,z)= 3
colorimetric values (xyz)

How to Calculate Concentration
(K/S)dλ = (K/S)uλ + (α1)λC1 + (α2)λC2 + (α3)λC3
Step 1: Assume certain values for C1, C2 and C3, pick up
corresponding α values and compute (K/S)dλ and then Rλ
Step 2: Using the computed values of Rλ calculate X,Y,Z.
Step 3: Designate the above values of X,Y,Z as X0,Y0,Z0

Step 4: Increase the value of C1by 2% and recalculate the
values of X,Y,Z as per the step 1 and 2. Designate these
values as X1,Y1,Z1.
Step 5: Increase the value of C2 by 2% and recalculate the
values as X2,Y2,Z2.
Step 6: Increase the value of C3 by 2% and recalculate the
values as X3,Y3,Z3.
Carry out such iterative procedure till the difference in
concentration of dyes is <0.001 or the difference between
the actual and predicted X,Y,Z values is < 0.05.

Xs ≅ Xp
Ys ≅ Yp
Zs ≅ Xp
The predicted concentrations of the three dyes,
namely C1, C2 and C3 can be taken as the predicted
recipe for the given sample.

DIFFERENT COLOUR SYSTEMS
AND COLOUR COMMUNICATION
IN REAL LIFE

PMS colors (also called Pantone® colors) are patented,
standardized color inks made by the Pantone company. Each
of the 1,755 solid PMS colors in their Formula Guide is a
Pantone proprietary blend and is sold to printers either
premixed or as a formula that printers mix on their premises.
PMS (Pantone® Matching System)
Use: Printing

Designers use the color swatches produced exclusively by
Pantone to pick the colors, and printers refer to the same
swatches. This ensures everyone works to the exact same
PMS color no matter where they are.
This standardization means most businesses and organizations
use PMS colors for their branding, especially logos, to ensure
the strictest color consistency across different print products
and across the globe.
In the past few years, Pantone has been expanding its color
matching system to fashion, plastics, home and lifestyle
products.

CMYK (Cyan, Magenta, Yellow, Black)
Use: Printing (Use in offset and digital printing)
CMYK color (also called four-color process) is actually a
method whereby a combination of tiny transparent dots of four
ink colors: Cyan, Magenta, Yellow and Black are printed.
Different combinations of large and small CMYK transparent
dots overlap each other to create a wide spectrum of colors.
Whereas a Pantone ink is one solid color throughout, a CMYK
color is not. When you look at a CMYK printed piece through a
magnifying glass, you can see a pattern of CMYK dots and
how they overlap to make the final color.
If you magnify our three CMYK colors, you can see how the
dots form the overall color. The cyan, magenta, yellow and
black inks absorb colored light, which is why CMYK is a
“subtractive” color model.

CMYK values of the original pantone swatches
CMYK transparent dots magnified

RGB (Red, Green, Blue)
RGB is the process by which colors are rendered onscreen by
using combinations of red, green and blue. RGB is the opposite
of CMYK because it is an “additive” process. When you mix
fully saturated versions of all three colors (red, green and blue)
together, you get pure white. When you remove all three colors
completely, you get black.
RGB is specific to digital applications only. This includes
mobile devices, computer monitors, laptops, TV and movie
screens, games and illuminated signs.
Use: Onscreen
RGB values of the
same three colors

Computer and display RGBs
All color computer monitors
are RGB monitors.
A display monitor capable of displaying many colors. In
contrast, a monochrome monitor can display only two colors,
one for the background and one for the foreground.
Color monitors implement the RGB color model by using
three different phosphors that appear red, green, and blue
when activated. By placing the phosphors directly next to
each other, and activating them with different intensities,
color monitors can create an unlimited number of colors.

Colour Gamut
A color 'gamut' means the entire range of colors a language
or technology can address.
• Can light-absorbing color inks on white paper always
match light- emitting diodes shining out from a computer
screen? Turns out the answer is No.
• Why we can discriminate between natural and artificial
images at a glance?
In fact, most gamut’s don not even address all the colors
possible in the real world.

Scientists back in 1931 established a mathematical definition of
every color possible for the human eye to see.
The CIE ‘LAB’ Gamut
Every colour it is possible
for the human eye to see

As RGB displays for TV and computers started becoming
a thing, electronics makers defined their own gamut for
all the colors an RGB device could possibly display,
which was a subset of the LAB gamut

Compare RGB (how most CAD programs define colors
on a screen) to CMYK (how most 2D printers define
colors on paper)

It's the areas where they don’t overlap that cause problems:
your printed part doesn't look like what it does on screen,
or vice versa. It’s like having a word in Russian that doesn't
exist in French-COLOUR COMMUNICATION!

Computer monitors which display RGB colors typically
have larger color gamut than printing devices which use
CMYK inks, especially in deep blues and blacks. This
means the printed image will be less vivid than the
original RGB image viewed on screen. Thus, printing the
image requires transforming the image from the original
RGB color space to the printer’s CMYK color space.
During this process, the colors from the RGB which are
out of gamut must be converted to approximate values
within the CMYK space gamut.

There are a wide range of colors that the human eye can see which
aren't defined by a Pantone. And there are a range of Pantones it's
not possible to even display on a computer screen. And finally,
there are a range of colors you CAN display on a computer screen
which can't be printed on a J750

ICC Profile
An ICC profile is a file that describes how colors can be
reproduced by a device.
It is a data file containing color information for devices
conducting color communication. It was developed by the
International Color Communication (ICC). Every device that
reproduces colors can be assigned a data set described by the
ICC profile. ICC profiles are used in color management
workflows to provide consistent color reproduction.

An working example of how and why to use an
ICC profile
The point of using an ICC profile is to achieve color consistency between
different devices. For example, if a photographer captures a particular
scene and wants to reproduce it on a photo printer in the studio, the colors
should be properly managed with ICC profiles. The photographer should
select the RGB color space on the camera when shooting, and use the
camera’s ICC profile to reproduce the colors on the printer. When editing,
the monitor should be calibrated to the RGB color gamut (and an ICC
profile for the RGB color gamut will be generated). When printing out
the photos, the printer’s ICC profile should be selected, and will reflect
the RGB color gamut, to get best results and consistent colors.

Shade Card
Shade card/color card are manufactured for paints, threads,
cosmetics and almost all the products in the world that vary in
color. Shade cards are like a mirror to a product. A consumer
does not essentially use and test the actual product before
purchasing it.

a. To specify a color, three elements are necessary and sufficient:
the hue, the luminance, and the luminance of the intermixed
white, which defines the saturation.
b. For every color, there is complementary color, which, when
mixed, becomes a colorless gray.
c. Two lights of different color with the same hue and saturation,
when mixed, produce another color with identical hue and
saturation independently of their power spectra.
d. The total luminance of any mixture of light is the sum of
each light's luminance.
Grassmann Laws (1853)
The basic laws for additional colors and color-matching
experiments were established by Grassmann (1853), who
attributed many of his ideas to Maxwell. The laws Grassmann
developed from these experiments state the following:

Standard Observer
20 Standard observers and 100 Supplementary standard observers
The color sensitivity of the eye changes according to the angle
of view (object size). The CIE originally defined the standard
observer in 1931 using a 2 field of view, hence the name 2
Standard Observer. In 1964, the CIE defined an additional
standard observer, this time based upon a 10 field of view; this
is referred to as the 10 Supplementary Standard Observers.
To give an idea of what a 2 field
of view is like compared to a 10
field of view, at a viewing
distance of 50cm a 2 field of view
would be a 1.7cm circle while a
10‫ذ‬field of view at the same
distance would be an 8.8cm circle

Colou-Matching
Functions
The color matching functions are
the tristimulus values of the
equal-energy spectrum as a
function of wavelength. These
functions are intended to
correspond to the sensitivity of
the human eye. Separate sets of
three color matching functions
are specified for the 20 Standard
Observer and 100 Supplementary
Standard Observers.

A hexadecimal color is specified with: #RRGGBB, where the RR (red), GG
(green) and BB (blue) hexadecimal integers specify the components of the
color.
For example, #ff0000 is displayed as red, because red is set to its highest
value (ff), and the other two (green and blue) are set to 00.
Another example, #00ff00 is displayed as green, because green is set to its
highest value (ff), and the other two (red and blue) are set to 00.
In HTML, a color can be specified using a hexadecimal value in the form:
#rrggbb
Where rr (red), gg (green) and bb (blue) are hexadecimal values between
00 and ff (same as decimal 0-255).
To display black, set all color
parameters to 00, like this: #000000.
To display white, set all color
parameters to ff, like this: #ffffff.
Experiment by mixing the HEX
values below.
HTML HEX Colors

Imaging Systems and Sensors
Vision and Imaging Sensors/Detectors are electronic
devices that detect the presence of objects or colors within
their fields of view and convert this information into a
visual image for display. They usually integrate a camera,
lights, and controller in a single unit, distinguishing them
from conventional vision inspection systems.

Device dependent and device
independent colour spaces
DEVICE INDEPENDENT
Mathematically described
CIE XYX
CIE LAB
DEVICE DEPENDENT
Use a specific device
RGB
CYMK

References
1. Allen, E. (1966). “Basic equations used in computer color matching“, Journal of the
Optical Society of America, 56.
2. Allen, E. (1974). “Basic equations used in computer color matching, II. Tristimulus
match, two-constant theory“. Journal of the Optical Society of America, 64.
3. Alman, D.H., Berns, R.S., Snyder, G.D. and Larsen, W.A. (1989). “Performance testing
of Color-difference metrics using a color tolerance dataset“. Col. Res. Appl., 14, 139–
151.
4. Aspland, J.R., Jarvis, C.W. and Jarvis, J.P. (1990). “A review and assessment of
numerical shade sorting methods“. Journal of the Society of Dyers and Colourists, 106,
315–320.
5. Berns, R. (2000). “Principles of Color Technology, 3rd Edition“, New York, NY: John
Wiley & Sons, Inc.
6. Bezerra, C.D.M. and Hawkyard, C.J. (2000). “Computer matching prediction for
fluorescent dyes by neural networks“. Journal of the Society of Dyers and Colourists,
116, 163–169.
7. CIE (1993). “Technical report. Parametric effects in colour-difference evaluation“. CIE
Publ. No. 101. Vienna, Austria: Central Bureau of the CIE.
8. CIE (1995). “Industrial colour-difference evaluation“, CIE Publ. 116, Central Bureau
of the CIE, Vienna, Austria.
9. CIE (2001). “Technical report: Improvement to industrial colour-difference
evaluation“. CIE Publ. No. 142. Vienna: Central Bureau of the CIE.

References
10. Guild, J. (1931). “The colorimetric properties of the spectrum“. Phil. Trans. Roy. Soc.
(London), A 230, 149–187.
11. Hans G. Volz (1995), “Industrial Colour Testing“, Will’s-VCH.
12. Hunt, R.W.G. (1991). “Measuring Colour“, 2nd edn. New York: Ellis Horwood.
13. J. Cegara (1992): “Dyeing of Textile materials“.
14. John H. Xin, “Total Colour Management in Textiles“, Woodhead publishing Limited,
Cambridge England
15. Judd, D.B. and Wyszecki, G. (1975). “Color in Business, Science and Industry, 3rd
edn“. New York: John Wiley.
16. Kuehni, R.G. (1975). “Computer Colourant Formulation“. Lexington, MA: DC Heath.
17. Kurt Nassan (2001), “The Physics and Chemistry of Colour“, John Willy’s &Sons.
18. Luo, M.R. and Rigg, B. (1986). “Chromaticity-discrimination ellipses for surface
colours“. Color Res. Appl., 11, 25–42.
19. Luo, M.R., Cui, G.H. and Rigg, B. (2001). “The development of the CIE 2000 colour
difference formula“. Color Res. Appl., 26, 340–350.
20. Pointer, M.R., Barnes, N.J., Clarke P.J. and Shaw, M.J. “Coloration Technology“, 121,
96–103 (2005).
21. Sluban, B. (1993). “Comparison of colorimetric and spectrophotometric algorithms for
computer matching prediction“, Color Research and Application, 18, 74–79.
22. Sluban, B. and Nobbs, J.H. (1997). “Colour correctability of a colour-matching
recipe“. Color Research and Application, 22, 88–95.

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