Accurate Color Measurment

UNIVERSITY OF JOENSUU

DEPARTMENT OF PHYSICS

VAISALA LABORATORY

DISSERTATIONS 30

Accurate Color Measurement

Jouni Hiltunen

ACADEMIC DISSERTATION

To be presented, with permission of the Faculty of Science of the Univer-sity of Joensuu, for public criticism in Auditorium M1 of the University,Yliopistonkatu 7, Joensuu, on February 8th, 2002, at 12 noon.

JOENSUU 2002

Julkaisija Joensuun yliopistoPublisher University of Joensuu

Toimittaja Timo Jaaskelainen, Ph.D., ProfessorEditor

Ohjaajat Timo Jaaskelainen, Ph.D., ProfessorSupervisors Department of Physics, University of Joensuu

Jussi Parkkinen, Ph.D., ProfessorDepartment of Computer Science, University of JoensuuJoensuu, Finland

Esitarkastajat Mauri Aikio, Dr. Tech.Reviewers VTT Electronics

Oulu, Finland

Erik Vartiainen, Ph.D., DocentDepartment of Electrical Engineering,Lappeenranta University of TechnologyLappeenranta, Finland

Vastavaittaja Harri Kopola, Dr. Tech., ProfessorOpponent VTT Electronics

Oulu, Finland

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ISSN 1458-5332ISBN 952-458-077-2

Joensuun yliopistopaino 2002

Jouni Hiltunen∗; Accurate Color Measurement – University of Joensuu, Depart-ment of Physics, Vaisala Laboratory, Dissertation 30, 2002. - 88 p.ISBN 952-458-077-2Keywords: accurate color measurement, tristimulus integration, thermochromism.

∗ Address: Department of Physics, University of Joensuu, P.O. Box 111, FIN-80101,Joensuu, Finland

Abstract

In this thesis studies on accurate surface color measurements are considered. Errors ina spectrophotometric measurements are discussed and correction methods introduced.The wavelength interval in a tristimulus integration is considered next. The ASTMweighting functions are tested with a large data set of non fluorescent colors and shownto be useless. The thermochromic effect is also discussed in detail and measured. Thisthesis shows how thermochromism is based on physical processes. Simple formulas arederived, and shown to explain the experimental data. In conclusion, this thesis showshow commercial instruments should be calibrated for precision color measurements, ifone aims at achieving the highest level for measuring accuracy.

iv

Preface

I am deeply indebted to my supervisors Prof. Timo Jaaskelainen and Prof. JussiParkkinen for their guidance, encouragement and patience during my studies. I amgrateful for the opportunity to work at the Department of Physics.

I want to express my special thanks to all my co-workers during these years, espe-cially Merja, Kimmo and Jarkko. Furthermore, I wish to express my gratitude to thecolleagues and staff of the department, and the members of the color group.

To my referees, Dr. Mauri Aikio and Docent Erik Vartiainen, I am greatly indeptedfor their careful review and constructive comments. For revising the language of themanuscript I express my gratitude to Dr. Greg Watson.

Finally, I want to express my warmest thanks to my dear parents and to my sisterwith her family, and to Liisa for her love and support.

Joensuu January 23, 2002

Jouni Hiltunen

Contents

1 Introduction 1

2 Colorimetry 42.1 Background to colorimetry . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 CIE Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 Standard physical data . . . . . . . . . . . . . . . . . . . . . . . 72.2.2 Standard observer data . . . . . . . . . . . . . . . . . . . . . . . 122.2.3 Calculation of tristimulus values and chromaticity coordinates . 122.2.4 Uniform color spacing . . . . . . . . . . . . . . . . . . . . . . . 152.2.5 Miscellaneous colorimetric practices and formulae . . . . . . . . 17

2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Measurement of surface color 213.1 General considerations on color measurement . . . . . . . . . . . . . . . 213.2 Intercomparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.3 Errors in surface color measurements . . . . . . . . . . . . . . . . . . . 24

3.3.1 Errors in absolute scales of diffuse reflectance and 0/45 radiancefactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3.2 Errors due to differing properties of white reference standards . 253.3.3 Photometric non-linearity . . . . . . . . . . . . . . . . . . . . . 253.3.4 Incorrect zero level . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.5 Wavelength scale error . . . . . . . . . . . . . . . . . . . . . . . 273.3.6 Specular beam exclusion error . . . . . . . . . . . . . . . . . . . 283.3.7 Specular beam weighting error . . . . . . . . . . . . . . . . . . . 293.3.8 Errors due to non-uniformity of collection of integrating spheres 303.3.9 Polarisation errors in the 0/45 geometry . . . . . . . . . . . . . 30

v

vi

3.3.10 Differences in methods of calculating color data from spectral data 303.3.11 Geometry differences between illumination and collection optics

within the specified limits . . . . . . . . . . . . . . . . . . . . . 313.3.12 Errors due to thermochromism in samples . . . . . . . . . . . . 313.3.13 Errors due to the dependence of spectral resolution on band-

width, scan speed and integration time . . . . . . . . . . . . . . 313.4 Measurements and corrections . . . . . . . . . . . . . . . . . . . . . . . 313.5 Intercomparison results . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.6 Determination of colorimetric uncertainties . . . . . . . . . . . . . . . . 443.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4 Tristimulus integration 544.1 The ASTM weighting method . . . . . . . . . . . . . . . . . . . . . . . 554.2 Spectral bandpass error . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.3 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5 Thermochromism 655.1 Background of the study . . . . . . . . . . . . . . . . . . . . . . . . . . 655.2 Absorbance, transmittance, and optical density . . . . . . . . . . . . . 66

5.2.1 Transmitting samples . . . . . . . . . . . . . . . . . . . . . . . . 675.2.2 Opaque samples . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.3 Thermal effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.5 Thermochromic measurements . . . . . . . . . . . . . . . . . . . . . . . 765.6 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6 Conclusions 82

References 84

Chapter I

Introduction

Surface color measurement is important for a very wide range of industrial applicationsincluding paint, paper, printing, photography, textiles, plastics [43,45]. Let us consideran example. A manufacturer wants to produce goods with specific color appearance.He can design the appearance of the product and he can measure it. After the produc-tion process the appearance of the product might be changed or it can vary betweenmanufacturing batches because of noise inherent in the process. Now a manufacturerwould like to know if the actual color is sufficiently similar to the desired one or whetherthe color is so different that it is not economically advisable to sell the products be-cause of fear of consumer complaints. From this point of view, it is very important tobe able to handle measurements and calculations of small color differences [58].

For demanding color measurement, a spectral approach is definitely needed. Strictlyit is impossible to define the absolute color values of a sample, that is why we alwayswork with some kind of approximations, some of us closer than others. The humaneye can perceive color differences as small as 0.5 CIELAB units and, thus, distinguishmillions of colors. This 0.5 unit difference should be the goal for precise color measure-ments. This limit is not a problem if we only want to measure the color difference oftwo samples, but if we want to simultaneously know the exact color coordinate valuesaccuracy problems arise. The values of two instruments can be astonishingly different.The best accuracy in color measurement could be achieved by use of a spectropho-tometer. The only geometry for measuring real spectral reflectance is normal/diffuse(0/d) geometry where the specimen is illuminated by a beam whose axis at an anglewhich does not exceed 10◦ from the normal to the specimen [5, 60]. The reflected fluxshould be collected by means of an integrating sphere.

The accuracy of the spectrophotometer used in color measurement may dependon various errors such as photometric non-linearity, wavelength error, and integratingsphere dark level error, integrating sphere error in both specular included and specularexcluded modes. Thus, correction formulas should be used to obtain more accurate

1

2 1. Introduction

results. Another question is how many channels i.e. wavelengths were used to measurea spectrum. It is obvious that the sampling interval should be short enough to gainmore precise results. Furthermore, the result we attain is always a compromise betweenmeasuring time, conditions and cost. Sometimes, one has to use a portable system orthe shape and the size of a sample makes it impossible to be able to use sensitiveequipment.

Regardless of how good an instrument one has, we need to point out that ultimatelycolor is a sensation produced in the human brain. It is evident that the informationprocessing system of the human has learned to process, e.g. visual information, in anefficient way. The human eye is able to distinguish several million colors, and thus colormeasuring instruments should accurately match the sensitivity of the eye to be ableto detect small color differences [18]. The basic sensory system of the eye is known,but the operation of the process is an open question. The color of any non fluorescentspecimen can be matched with a mixture of red, green and blue primaries, becausethere are only three types of color sensitive receptor on the retina. Human color visionshows differences among people. Thus, some standard observers must be specified.The CIE 1931 standard observer is defined for a 2◦ field of view by two equivalent setsof color matching functions [5]. The first set is expressed in terms of spectral stimuli ofwavelengths 700 nm (R), 546.1 nm (G), and 435.8 nm (B). The second set is a lineartransformation of the first one and remains positive for all wavelengths. The CIE 1964standard observer has been similarly defined for the 10◦ field of view. These sets areused throughout industry.

As well as standard observers, standard illumination conditions must be defined asthe form of tables of relative spectral power against wavelength. Illuminant A corre-sponds to the interior illumination by tungsten filament lamps, C represents averagedaylight with a correlated color temperature of 6774 K, and the D sources aim todescribe for other phases of daylight. For instance, the most widely used daylight stan-dard is D65, which represents a source whose correlated color temperature is 6504 K.There are a number of other illuminants which are used, too.

This thesis contains studies on accurate surface color measurements. First, somebasic background is introduced in Chapter II. Errors in a spectrophotometric measure-ments are discussed and correction methods introduced in Chapter III. This work waspart of the European Union color measurement harmonisation project in 1997–2000where 9 laboratories in Europe were involved. The author was responsible for measur-ing, analysing and reporting the results made in University of Joensuu [15, 20, 43, 44].In Chapter IV the wavelength interval in a tristimulus integration is considered. TheASTM weighting functions are tested with a large data set of non fluorescent colorsand found to be useless. The results are first time reported in this thesis and willbe published later. The thermochromic effect is discussed in detail and measured inChapter V. The first idea of this phenomenon comes from the co-authors Jaaskelainen

3

and Silfsten. However, formulaes introduced here, were derived by the author with co-authors and entirely calculated numerically by the author [16, 19]. This thesis showshow thermochromism is based on physical processes. Simple formulas are derived, andshown to explain the experimental data. Such an explanation has not been publishedin literature before.

In conclusion, this thesis shows how commercial instruments should be calibratedfor precision color measurements, if one aims at achieving the highest level for mea-suring accuracy. In addition, the precise color measuring technique developed duringthe preparation of this thesis, has been applied to a number of industrial projects.Use of spectral data is increasing in a wide range of applications, too. The authorscontribution is shown in [17,21–23,30–32,37,38,46–48] but the topic of this thesis wasthe first phase: How to measure spectral data accurately.

Chapter II

Colorimetry

The specification of basic standards used in colorimetry are based on definitions ofthe Commission Internationale de l’clairage (CIE) by general consent in all countries.The first major recommendations regarding colorimetric standards were made by theCIE in 1931. The original recommendations made in 1931 are reviewed from timeto time by the CIE Colorimetry Committee and changes are made when considerednecessary. In this chapter, the CIE recommendations are briefly introduced since theyessentially form the basis of modern color research. The original and more preciserecommendations can be found from [5]. General and historical views of color visioncan be found from [3,18,57,60].

2.1 Background to colorimetry

At the 6th Session of the CIE held at Geneva in 1924 it was decided to set up a StudyGroup on Colorimetry (CIE 1924). The reason was the fact that the measurement ofcolor had become an important factor in industry and scientific laboratories but therewas not color specification system that could be considered satisfactory for generalpractice. Later, it was agreed that efforts should be made to reach agreements on

• colorimetric nomenclature

• a standard daylight for colorimetry

• the “sensation curves” of the average human observer with normal color vision.

At the 8th Session of the CIE held at Cambridge, England, in 1931, the first majorrecommendations were made which laid the basis for modern colorimetry (CIE 1931).There was a total of five recommendations. Recommendations 1, 4 and 5 establishedthe CIE 1931 standard observer and a colorimetric coordinate system, recommendation

4

2.1 Background to colorimetry 5

2 specified three standard sources (A,B and C) and recommendation 3 standardizedthe illuminating and viewing conditions for the measurement of reflective surfaces andthe standard of reflectance in the form of a magnesium-oxide surface.

The CIE 1931 standard colorimetric observer was defined by two different butequivalent sets of color-matching functions based on the photopic luminous efficiencyfunction V (λ). These were already adopted by the CIE in 1924 and experimentalwork was carried out by Guild [13] in 1931 and Wright [59] 1928–1929. The firstset of color-matching functions, r(λ), g(λ), b(λ), was expressed in terms of spectralstimuli of wavelengths 700.0 nm (R), 546.1 nm (G), 435.8 nm (B) (Fig. 2.1), as thereflectance stimuli, with the units adjusted so that the chromaticity coordinates of theequi-energy spectrum are equal. The equi-energy spectrum is a stimulus whose spectralconcentration of power as a function of wavelength is constant.

400 500 600 700

0.4

0.3

0.2

0.1

0

- 0.1

Wavelength [nm]

Tri

sti

mu

lus

valu

es

r

g

b

Figure 2.1: Color matching functions r, g and b in terms of spectral stimuli of wave-lengths 700.0 nm (R), 546.1 nm (G) and 435.8 nm (B), respectively [60].

The second set of color-matching functions, x(λ), y(λ), z(λ) (Fig. 2.2), was rec-ommended for reasons of more convenient application in practical colorimetry. Itsderivation from the first set was based on a proposal by Judd [24] in 1930 and involveda linear transformation. The coefficients of the transformation were chosen so as toavoid negative values of x(λ), y(λ), z(λ), at all wavelengths and so that the luminancesLX , LY , LZ of unit quantities of the stimuli were equal to 0, 1, 0 respectively, result-ing in a set of color matching functions in which y(λ) is identical to V (λ). The unitsof the new reference stimuli (X), (Y ), (Z) were adjusted to make the chromaticitycoordinates x, y, z also equal for the equi-energy spectrum.

6 2. Colorimetry

400 450 500 550 600 650 700 7500

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Wavelength [nm]

Tri

stim

ulu

svalu

es

xy

z

Figure 2.2: Color matching functions x, y and z [60].

The new color-matching functions, x10(λ), y10(λ), z10(λ), defining the supplemen-tary standard colorimetric observer (CIE 1959) were officially adopted in 1964. Theywere derived from experimental data supplied by Stiles and Burch [51] in 1959 andby Speranskaya [49] in 1959. The experimental color-matching data were obtained fora 10◦ field by a direct method which did not involve an appeal to the CIE spectralluminous efficiency function, but depend on the actual measurement of the relativepower distribution of the spectrum studied.

One of the important problems the Colorimetric Committee has dealt with overseveral years concerns a coordinate system which would provide a three dimensionalcolor spacing that would be perceptually more uniform than the XY Z system. Manydifferent proposals have been forwarded over the years. In the 14th Session of the CIEat Brussels in 1959 the committee considered a number of the systems. The MacAdamuniform chromaticity scale diagram of 1937 was adopted as a standard UCS diagram.The proposal was officially approved by the CIE in 1960, so the diagram is nowadaysknown as the CIE 1960 UCS diagram.

At the 18th Session of the CIE in London in 1975 the Colorimetry Committeeapproved the adoption of two new color spaces and associated color difference formulae.These spaces are known as the CIE 1976 L∗u∗v∗ color space and the CIE 1976 L∗a∗b∗

color space. The former was mainly used for TV and illumination industries and thelatter was used for surface color industries.

A lot of work has been done for decades to generate more uniform color spaces suchas CMC(l : c), BFD(l : c), CIE94, since the linearity of the CIE 1976 color spaces is notsatisfactory enough, at least where small color differences are concerned [4,26,36,41,42].

2.2 CIE Recommendations 7

Among the imaging industry there was still a need for a single color appearance modelthat could be used throughout the industry to promote uniformity of practice andcompatibility between various components in a modern imaging system. The CIE wasable to respond these needs. In 1997 CIECAM97s color appearance model was adoptedby the CIE for color imaging applications [27–29,33,35].

For the color difference evaluation, a new color difference formula CIEDE2000 [34]was developed, which is based on CIELAB space. It includes not only lightness, chroma,and hue weighting functions but also an interactive term between chroma and hue dif-ferences for improving the performance for blue colors and a scaling factor for CIELABa∗ scale for improving the performance for grey colors. It has been approved by theCIE and published as a CIE Technical Report [6].

The present colorimetric recommendations were published in CIE Publication 15.2,Colorimetry [5], in 1986. The new and up-to-date recommendations will be publishedin 2002 as CIE Publication 15.31.

2.2 CIE Recommendations

The terminology of the original recommendations has been altered to be consistent withmodern nomenclature and in some cases the original recommendations have also beenmodified in contents to bring them into line with present day thinking and practice.The recommendations are divided into the following five groups:

1. Recommendations concerning standard physical data.

2. Recommendations concerning standard observer data.

3. Recommendations concerning the calculation of tristimulus values and chromatic-ity coordinates.

4. Recommendations concerning uniform color spacing.

5. Recommendations concerning miscellaneous colorimetric practices and formulae.

2.2.1 Standard physical data

Illuminants for colorimetry

Standard illuminants such as Illuminant A, B, C and D65 are recommended illuminantsfor color calculations. Here “illuminant” refers to a specific spectral power distribution,

1According to The 9th Congress of the International Colour Association, June 24–29, 2001,Rochester, NY.

8 2. Colorimetry

not necessarily realized by a “source” which refers to a physical light emitter, such asa lamp, the sun and the sky. Illuminant A represents light from a full radiator atabsolute temperature 2856 K according to The International Practical TemperatureScale, 1968. The relative spectral power distribution of illuminant A has been derivedin accordance with Planck’s radiation formula.

Illuminant B was intended to represent direct sunlight with a correlated color tem-perature of approximately 4900 K. Illuminant C was intended to represent averagedaylight with a correlated color temperature of about 6800 K. In Fig. 2.3 standardilluminants A,B and C are shown, where the radiant power has been normalized to thesame value at 550 nm. Illuminant D65 was intended to represent a phase of daylightwith a correlated color temperature of approximately 6500 K. The illuminant D65 isrecommended for use whenever possible. Illuminants D50, D55 and D75 can still be usedto realize a phase of daylight having correlated color temperatures of approximately5000 K, 5500 K, and 7500 K, respectively. In Fig. 2.4 examples of the standard day-light illuminants D55, D65 and D75 are shown. The radiant power has been normalizedto the same value at 550 nm.

400 500 600 700 800

Wavelength [nm]

Rad

ian

tp

ow

er[a

.u.]

C

C

B B

A

A

Figure 2.3: Standard illuminants A, B and C. The radiant power has been normalizedto the same value at 550 nm [60].

Sources representing illuminants

It is recommended that the following artificial sources are used to realize the illuminantsdefined above. Standard illuminant A is to be realized by a gas-filled tungsten filament


400 500 600 700 800

Wavelength [nm]

Rad

ian

tp

ow

er

[a.u

.]

D55

D55

D65D

65D

75

D75

Figure 2.4: Standard illuminants D55, D65 and D75. The radiant power has beennormalized to the same value at 550 nm [60].

lamp operating at a correlated color temperature of 2856 K. A lamp with a fused-quartz envelope or window is recommended if the spectral power distribution of theultraviolet radiation of illuminant A is to be realized more accurately.

Illuminant B and C are to be realized using the source A, combined with a filterconsisting of a layer of agreed solutions. At present, no artificial sources have beenrecommended to realize illuminant D65 or any other D illuminants of various correlatedcolor temperatures.

Standard of the reflectance factor

The perfect reflecting diffuser is recommended as a reference standard in 1986 in publi-cation CIE Standard Colorimetric Observers. It is defined as the ideal isotropic diffuserwith a reflectance equal to unity. Smoked magnesium oxide was superseded from Jan-uary 1, 1969. A secondary reference standard, such as pressed barium sulphate, mustbe calibrated in terms of the perfect reflecting diffuser.

Illuminating and viewing conditions for a reflecting specimen

CIE recommends the use of one of the following illuminating and viewing conditions:45◦/normal , normal/45◦, diffuse/normal and normal/diffuse. For these conditions thefollowing symbols are used 45/0, 0/45, d/0 and 0/d, respectively.

In the 45/0 geometry the sample is illuminated by one or more beams whose effective

10 2. Colorimetry

axes are at the angle of 45◦ ± 2◦ from the normal to the sample surface. The viewingangle from the normal to the sample should be less than 10◦. There is also a restrictionin the viewing and illuminating beams: the angle between the axis and ray should notexceed 8◦.

In the 0/45 geometry the illumination is in the direction normal to the sample, andthe viewing angle is 45◦ from the normal. Now normal illumination is within 2◦, andthe angle between the axis and any ray should not exceed 8◦. The same restrictionshould be observed in the viewing beam. The illuminatig conditions 0/45 and 45/0 areshown in Fig. 2.5.

0/45 45/0

Figure 2.5: Viewing geometries of 0/45 and 45/0.

If the sample is illuminated diffusely by an integrating sphere and the viewingangle does not exceed 10◦ from the direction normal to the surface of the sample,one is referring to the d/0 geometry. The integrating sphere may be of any diameterprovided the total area of the ports do not exceed 10 percent of the internal reflectingsphere area. The angle between the axis and arbitrary ray of the viewing beam shouldnot exceed 5◦.

If the specimen is illuminated by a beam whose axis does not exceed 10◦ from thenormal to the specimen one is referring to 0/d geometry. The reflected flux is collectedby means of an integrating sphere. The angle between the axis and any ray of theilluminating beam should not exceed 5◦.

In Fig. 2.6, a typical setup of 0/d geometry is shown using an integrating sphere.When integrating spheres are used, they should be equipped with white coated bafflesto prevent light passing directly between the sample and the spot of the sphere wallilluminated or viewed.


sample

beam

detector

gloss trap

or white

sphere cap

sample

reference

beam

reference

baffles

Figure 2.6: Integrating sphere.

In the 0/d and d/0 conditions, specular reflection can be excluded or included bythe use of a gloss trap. In the 0/d condition, the sample should not be measured witha strictly normal axis of illumination if it is required to include the regular componentof reflection. Note that only the 0/d geometry provides a spectral reflectance. Theother conditions d/0, 0/45 and 45/0 give a specific radiance factor.

Illuminating and viewing conditions for transmitting specimens

It is recommended that the colorimetric specification of transmitting species corre-spond to one of the following illuminating and viewing conditions: normal/normal,normal/diffuse and diffuse/diffuse. The following symbols are used 0/0, 0/d and d/d,respectively.

In the normal/normal (0/0) condition, the specimen is illuminated by a beam whoseeffective axis is at a angle not exceeding 5◦ from the normal to its surface and with theangle between the axis and any ray of the illuminating beam not exceeding 5◦. Thegeometric arrangement of the viewing beam is the same as that of the illuminatingbeam. The specimen is positioned so that only the regularly transmitted flux reachesthe detector. This condition gives the regular transmittance, τr.

In the normal/diffuse (0/d) condition, the specimen is illuminated by a beam whoseeffective axis is at an angle not exceeding 5◦ from the normal to its surface and withthe angle between the axis and any ray of the illuminating beam not exceeding 5◦. Thehemispherical transmitted flux is usually measured with an integrating sphere. Thereflectance of the sphere reflecting surface or other material at the point of impingementof the regularly transmitted beam, or at the point of impingement of the illuminating

12 2. Colorimetry

beam in the absence of a specimen, must be identical to the reflectance of the remainderof the internal reflecting sphere area. This condition gives the total transmittance, τ .If the regularly transmitted flux is excluded, for example by the use of a light trap, itgives the diffuse transmittance, τ0/d. If the positions of the light source and detectorare interchanged, the method gives the equivalent diffuse/normal (d/0) quantities.

In the diffuse/diffuse (d/d) condition, the specimen is illuminated diffusely with anintegrating sphere and transmitted flux is collected using a second integrating sphere.This condition gives the double transmittance, τdd.

2.2.2 Standard observer data

CIE 1931 standard colorimetric observer

It is recommended that colorimetric specification of color stimuli be based on thecolor-matching functions x(λ), y(λ), z(λ) given in the CIE Standard on ColorimetricObservers, whenever correlation with visual color matching of fields of angular subtensebetween about 1◦ and about 4◦ at the eye of the observer is desired. These color-matching functions are given in the Standard as values from 360 nm to 830 nm at1 nm intervals with seven significant digits, and they define the CIE 1931 standardcolorimetric observer. The values at 5 nm intervals over the range 380 nm to 780 nmare consistent with the Standard and are sufficient for most applications.

CIE 1964 supplementary standard colorimetric observer

It is recommended that colorimetric specification of color stimuli be based on the color-matching functions x10(λ), y10(λ), z10(λ) given in the CIE Standard on ColorimetricObservers, whenever correlation with visual color matching of fields of angular subtensegreater than about 4◦ at the eye of the observer is desired. These color-matchingfunctions are given in the Standard as values from 360 nm to 830 nm at 1 nm intervalswith six significant digits, and they define the CIE 1964 standard colorimetric observer.

2.2.3 Calculation of tristimulus values and chromaticity coordinates

Calculation of tristimulus values

The CIE Standard on Colorimetric Observers recommends that the CIE tristimulusvalues of a color stimulus be obtained by multiplying at each wavelength the value ofthe color stimulus function φλ(λ) by that of each of the CIE color matching functionsand integrating each set of products over the wavelength range corresponding to theentire visible spectrum 360 nm to 830 nm. The integration may be carried out by


numerical summation at wavelength intervals, ∆λ, equal to 1 nm,

X = k∑

λ

φλ (λ) x (λ) ∆λ

Y = k∑

λ

φλ (λ) y (λ) ∆λ (2.1)

Z = k∑

λ

φλ (λ) z (λ) ∆λ,

or

X10 = k10

∑λ

φλ (λ) x10 (λ) ∆λ

Y10 = k10

∑λ

φλ (λ) y10 (λ) ∆λ (2.2)

Z10 = k10

∑λ

φλ (λ) z10 (λ) ∆λ,

where X, Y , Z are tristimulus values, x(λ), y(λ), z(λ), are color-matching functions ofa standard colorimetric observer, and k is a normalizing constant defined below. Theseequations may be written without or with the subscript 10 to correspond to the CIE1931 or 1964 standard colorimetric system, respectively.

For reflecting or transmitting object colors, the color stimulus function, φλ(λ), isreplaced by the the relative color stimulus function, φ(λ), evaluated as

φ(λ) = R(λ)S(λ)

(2.3)

φ(λ) = τ(λ)S(λ),

where R(λ) is the spectral reflectance factor (or spectral radiance factor or spectralreflectance) of the object color, τ(λ) is the spectral transmittance of the object color,and S(λ) is the relative spectral power distribution of the illuminant. In this case, theconstants k and k10 are chosen so that Y = 100 for objects for which R(λ), or τ(λ) = 1

14 2. Colorimetry

for all wavelengths and hence

k =100∑

λ S(λ)y(λ)∆λ

(2.4)

k10 =100∑

λ S(λ)y10(λ)∆λ.

For self-luminous objects and illuminants the constants k and k10 are usually chosenon the grounds of convenience. However, if in the CIE 1931 standard colorimetricsystem the Y value is required to give the absolute value of photometric quantity theconstant k must be equal to Km, the maximum spectral luminous efficacy. This valueis equal to 683 lumens per watt and φλ(λ) must be the spectral concentration of theradiometric quantity corresponding to the photometric quantity required.

The use of abridged or truncated data

The color stimulus function φλ(λ) should be known at 5 nm intervals over the wave-length range from 380 nm to 780 nm. In practical applications, all the required datamay not be available. Data may have been measured at greater intervals than 5 nm orit may not be equally divided. Many times it is possible to predict unmeasured data.It is important to use the same wavelength interval and range throughout for any setof precise color difference calculations.

Abridgement of the data may lead to errors in the computed tristimulus values.Data with 10 nm or 20 nm intervals should be used only when it can be demonstratedthat these errors are negligibly small for the intended use of the tristimulus values.If this is not the case it is recommended to interpolate needed but unmeasured val-ues. Such a prediction should be made with a polynomial interpolation formula or byLagrange interpolation.

In some cases the measurement range is less than the practical range of summationfrom 380 nm to 780 nm. Omission of the values at these limits of the measurementrange may lead to errors while computing tristimulus values. Such truncation shouldbe used only if it can be demonstrated that these errors are negligibly small. If theseerrors are not negligibly small adequate extrapolation is recommended. The rangeof the summation is an essential part of the tristimulus specification. As a roughapproximation, in the absence of other information, unmeasured values may be setequal to the nearest measured value of the appropriate quantity in truncation.


Calculation of chromaticity coordinates

The chromaticity coordinates (x, y, z) should be calculated from the tristimulus values(X,Y, Z) as follows:

x =X

X + Y + Z

y =Y

X + Y + Z(2.5)

z =Z

X + Y + Z.

Because of the relation x + y + z = 1, it is sufficient to quote x and y only. Thechromaticity coordinates x10, y10, z10 are computed similarly from the tristimulus valuesX10, Y10, Z10.

2.2.4 Uniform color spacing

The CIE 1976 UCS diagram

The CIE 1976 UCS chromaticity diagram is recommended for use whenever a pro-jective transformation of the (x, y)-diagram yielding color spacing perceptually morenearly uniform than that of the (x, y)-diagram is desired. The chromaticity diagram isproduced by plotting u′

u′ =4X

X + 15Y + 3Z(2.6)

as abscissa and v′

v′ =9Y

X + 15Y + 3Z(2.7)

as ordinate, in which X,Y, Z are tristimulus values. The third chromaticity coordinatew′ is equal to 1−u′−v′. This diagram is intended to apply to comparisons of differencesbetween object colors of the same size and shape, viewed in identical white to middle-grey surroundings, by an observer photopically adapted to a field of chromaticity nottoo different from that of average daylight.

16 2. Colorimetry

The CIE 1976 uniform color spaces

The use of the following color spaces is recommended whenever a three-dimensionalspacing perceptually more nearly uniform than that provided by the XY Z system isdesired.

CIE 1976 L∗u∗v∗ color space or CIELUV color space is defined by quantitiesL∗, u∗, v∗

L∗ = 116

(Y

Yn

)1/3

− 16 when

(Y

Yn

)> 0.008856 (2.8)

u∗ = 13L∗(u′ − u′n) (2.9)

v∗ = 13L∗(v′ − v′n), (2.10)

where Y, u′, v′ describe the color stimulus considered and Yn, u′n, v′

n describe a specifiedwhite object color stimulus. If Y/Yn is less than 0.008856, the above equations arechanged as follows

(Y

Yn

)1/3

is replaced by 7.787

(Y

Yn

)+

16

116.

The CIE 1976 L∗a∗b∗ color space or CIELAB color space is defined by quantitiesL∗a∗b∗

L∗ = 116

(Y

Yn

)1/3

− 16 (2.11)

a∗ = 500

[(X

Xn

)1/3

−(

Y

Yn

)1/3]

(2.12)

b∗ = 200

[(Y

Yn

)1/3

−(

Z

Zn

)1/3]

, (2.13)

where X,Y, Z describe the color stimulus considered and Xn, Yn, Zn describe a specificwhite object color stimulus. If X/Xn, Y/Yn or Z/Zn is less than 0.008856, the above


equations are changed as follows

(X

Xn

)1/3


(X

Xn

)+

16

116(Y

Yn

)1/3


(Y

Yn

)+

16

116(Z

Zn

)1/3


(Z

Zn

)+

16

116.

The differences ∆E∗uv or ∆E∗

ab between two color stimuli are calculated as theEuclidean distance between the points representing them in the space:

∆E∗uv =

√(∆L∗)2 + (∆u∗)2 + (∆v∗)2 (2.14)

∆E∗ab =

√(∆L∗)2 + (∆a∗)2 + (∆b∗)2. (2.15)

2.2.5 Miscellaneous colorimetric practices and formulae

Dominant wavelength

The dominant wavelength of a color stimulus λd is a wavelength of the monochromaticstimulus that matches the color stimulus considered when additively mixed in suit-able proportions with the specified achromatic stimulus. A monochromatic stimulusis monochromatic radiant power of given magnitude and wavelength, entering the eyeand producing a sensation of light or color. An achromatic stimulus is the color stim-ulus chosen because it usually yields a color perception which is devoid of hue underthe desired observing conditions. Complementary wavelength is used instead of dom-inant wavelength for stimuli whose chromaticities lie between those of the specifiedachromatic stimulus and the purple line.

Complementary wavelength

The complementary wavelength of a color stimulus λc is a wavelength of the monochro-matic stimulus that matches the specific achromatic stimulus when additively mixedin suitable proportions with the color stimulus considered.

18 2. Colorimetry

Colorimetric purity

The colorimetric purity pc is defined by the relation

pc =Ld

Ln + Ld

, (2.16)

where Ld and Ln are the luminances of the monochromatic stimulus and of the speci-fied achromatic stimulus that match the color stimulus considered in an additive mix-ture, respectively. In the case of stimuli characterized by a complementary wavelengthsuitable mixtures of light from the two end of the spectrum are used instead of themonochromatic stimuli. In the CIE 1931 standard colorimetric system, colorimetricpurity is related to excitation purity pe by the equation

pc = peyd

y, (2.17)

where yd and y are the y-chromaticity coordinates of the considered monochromaticstimulus and the color stimulus, respectively.

Excitation purity

Excitation purity pe is defined by the ratio NC/ND of two collinear distances on thechromaticity diagram of the CIE 1931 or 1964 standard colorimetric system. The firstdistance is that between point C and N which represents the considered color stimulusand the specified achromatic stimulus, respectively. The second distance is betweenpoint N and point D on the spectrum locus at the considered dominant wavelength ofthe color stimulus. The definition leads to the following expressions

pe =y − yn

yd − yn

or pe =x − xn

xd − xn

, (2.18)

where (x, y), (xn, yn), (xd, yd) are the x, y-chromaticity coordinates of the points C,Nand D, respectively.

Special metamerism index

Two specimens having identical tristimulus values for a given reference illuminant andreference observer are metameric if their spectral radiance distributions differ within


the visible spectrum. It is recommended that two specimens whose correspondingtristimulus values (X1 = X2, Y1 = Y2, Z1 = Z2) are identical with respect to a referenceilluminant and observer, the metamerism index, Mt is set to be equal to the indexof color difference ∆E between the two specimens computed for the test illuminantt. The preferred reference illuminant is the CIE standard illuminant D65. If anotherilluminant is used as reference this should be noted.

The evaluation of whiteness

According to CIE recommendations, the formulae W or W10 for whiteness and TW

or TW,10 for tint, given below, are used for comparisons of the whiteness of samplesevaluated for CIE standard illuminant D65. The application of the formulae is restrictedto samples that are called “white” commercially, that do not differ much in color andfluorescence, and that are measured on the same instrument at nearly the same time.

W = Y + 800(xn − x) + 1700(yn − y) (2.19)

W10 = Y10 + 800(xn,10 − x10) + 1700(yn,10 − y10) (2.20)

TW = 1000(xn − x) − 650(yn − y) (2.21)

TW,10 = 900(xn,10 − x10) − 650(yn,10 − y10), (2.22)

where Y is the Y -stimulus value of the sample, x and y are the x, y chromaticitycoordinates of the sample, and xn, yn are the chromaticity coordinates of the perfectdiffuser, all for the CIE 1931 standard colorimetric observer. Y10, x10, y10, xn,10 and yn,10,are similar values for the CIE 1964 supplementary standard colorimetric observer. Thehigher the value of W or w10 the greater is the indicated whiteness. The more positivethe value TW or TW,10 the greater is the indicated greenishness. The more negative thevalue TW or TW,10 the greater is the indicated reddishness. For perfect diffuser W andW10 are equal to 100 and TW and TW,10 are equal to zero.

Calculation of correlated color temperature

The correlated color temperature of a given stimulus is the temperature of the Planck-ian radiator whose perceived color most closely resembles that of the stimulus at thesame brightness and under the same viewing conditions. The recommended methodfor calculating the correlated color temperature of a stimulus is to determine on a chro-maticity diagram the temperature corresponding to the point on the Planckian locusthat is intersected by the agreed isotemperature line containing the point representingthe stimulus.

20 2. Colorimetry

2.3 Summary

The recommendations of the CIE Colorimetry Committee are given for various col-orimetric practices and formulae such as recommendations for standard illuminants,for the standard reflectance factor, for illuminating and viewing conditions, for thestandard colorimetric observers, for the calculation of tristimulus values, chromaticitycoordinates, and color differences.

Chapter III

Measurement of surface color

Surface color measurements are of great importance in the production of a very widerange of manufactured goods in industry. Industry needs to be able to measure surfacecolor to within the discrimination limits of the human eye of 0.5 ∆E∗

ab CIELAB units.The basic idea is to measure the absolute spectrum as accurately as possible [25].The spectrum is then used with the stored numerical data to derive desired results.The algorithms should include the commonly used illuminants together with variouscoordinate systems, whiteness formulas, and color difference formulas.

There are two main classes of color measuring instruments, which are used forsurface color measurements, colorimeters and spectrophotometers. Colorimeters aretrichromatic devices, where the illuminant is simulated by a light source and the colormatching functions are simulated by (interference) colored filters in combination witha photodetector. These instruments have a simple construction, but they are notaccurate enough for typical quality control tasks in industry.

Spectrophotometers allow accurate measurement, because they measure the spec-tral reflectances of the samples. The disadvantage of traditional scanning spectropho-tometers is that they are slow. In addition, because of vibration sensitivity and otherenvironmental requirements they can not be used outside of laboratory conditions.These disadvantages have recently been avoided by constructing non-scanning spec-trophotometers, which are based on use of diode array detectors.

3.1 General considerations on color measurement

Internationally accepted illumination and observation angles should be standardisedfor use in instruments such as normal/diffuse with including or excluding the specularcomponent, or 0/45. Tolerances on these angles along with the maximum angle ofacceptance are given in CIE Publication 15.2 [5].

If wide spectrum illumination is used (incandescence lamp, xenon lamp, flash lamp),one should be aware of fluorescent samples. The source has to match a CIE standard or

21

22 3. Measurement of surface color

recommended illuminant (A, D65, C etc.) as closely as possible to correctly determinecolor coordinates. If this is not accomplished, the surface color of a fluorescent samplehas to be measured by the double monochromator method [40, 44]. Fluorescence ispresent in many objects, even in some white standards.

There are some general principles to follow in order to obtain reliable measurementresults. Color measurement instruments have to be maintained as advised in theirmanuals. It is necessary to pay special attention to the handling and maintance of theinstrument’s calibration standards. The same attention should be paid to integratingsphere coatings as well. Degradation of this coating produces several errors.

The instrument’s start up routine should be done as indicated by the manufacturer.Currently this is automatically done by most spectrophotometers and colorimeters.The warm-up time should also be followed as indicated in the manual. At the veryleast the warm up should be thirty minutes in every case. Samples should be measuredat the same room temperature as the instrument.

Many instruments have their own calibration set, which contains a white standardand a black standard or zero reflectance standard. The low reflectance standard is notas common as the white one. However, it is advisable to use another calibration set toindependently check the instrument’s performance. Ideally, this set should contain thefollowing elements: a surface mirror, a wavelength standard, two white standards (onematt and one glossy), a zero reflectance standard and at least one grey standard withabout 50% reflectance. The function of these elements is given later in this chapter.

It is good policy to measure a sample a few times and, to calculate the meanvalue of those measurements. One can rotate the sample between each measurementto avoid directional dependency from surface inhomogeneties. For as accurate resultsas possible, the performance and potential error sources in the instrument must beknown [7,8, 15,20,43].

3.2 Intercomparison

The human eye can perceive color differences approximately 0.5 ∆Eab in CIELABunits. The first European intercomparison stopped in 1993 [45]. This intercomparisonsought to determine the state of the art of measurements of spectral reflectance andcolor specification of surface colors using spectrophotometry. Four laboratories, eachfrom a different country within the European Community, participated. Sets of four-teen ceramic color standards were calibrated by each laboratory. The intercomparisoncovered the specular excluded, specular included and 0/45 geometries. The result wasthat approximately half of the measurements made by the laboratories with respon-sibility for national standards did not agree on the limit of the human eye. This isinadequate for industrial requirements.

The second European intercomparison was started in 1997 [43]. The main objective

3.2 Intercomparison 23

in this project was to harmonise color measurements between 8 national laboratories toachieve a target of 95% agreement within 0.5∆Eab CIELAB units for non-fluorescentcolors. This was achieved through the use of a system for determining and correctingerrors, followed by an intercomparison of non-fluorescent surface color measurements.The second objective was to extend the capability for measurement of fluorescent safetycolors using the two monochromator method to three countries within the EuropeanUnion, and carry out an intercomparison of fluorescent colored materials to meet themetrological requirements of EN471, Specification of High Visibility Warning Cloth-ing. Partners in this project entitled “Harmonisation of National Scales of SurfaceColor Measurements”, Contract SMT4-CT96-2140, European Commission StandardsMeasurements and Testing Programme, were as follows:

• National Physical Laboratory (NPL), United Kingdom.

• Consejo Superior de Investigatines Cientificas (CSIC), Spain.

• Bundesanstalt fur Materialforchung und-Prufung (BAM), Deutchland.

• University of Joensuu (UJ), Finland.

• Laboratoire National d’Essais (LNE), France.

• Centro de Ciencias e Technologias Opticas (CETO), Portugal.

• Swedish National Testing Research Institute (SP), Sweden.

• British Ceramic Researc Ltd (BCRA), United Kingdom.

• Danish Electronic Light and Acoustics (DELTA), Denmark.

NPL worked as a co-ordinator of the project. During the first year, all partnersmet at NPL. They agreed upon which errors in the measurements of surface colorthat could be determined and corrected, and the principles of the methodology forachieving this. NPL calibrated and dispatched to partners a set of calibrated artefactsfor determining correcting errors. Partners then determined the errors within theirinstruments and reported their result to the co-ordinator. NPL also measured sets of 4color standards to be used by partners for testing the effectiveness of the methodologyfor harmonisation, and to give preliminary results on levels of agreement that mightbe achieved for non-fluorescent colors.


3.3 Errors in surface color measurements

Spectrophotometric errors are discussed in this section on a qualitative basis. In orderto achieve the target level of agreement of 0.5 ∆Eab CIELAB units, it is necessaryto determine and correct errors in the measurement color and to adopt a commonprocedure where relevant. The following is a list of the principal errors:

• Errors in absolute scales of diffuse reflectance and 0/45 radiance factor.

• Errors due to differing properties of white reference standards.

• Non-linearity of the photodetector.

• Incorrect zero level.

• Wavelength scale error.

• Specular beam exclusion error.

• Specular beam weighting error.

• Errors due to non-uniformity of collection of integrating spheres.

• Polarisation errors in the 0/45 geometry.

• Differences in methods for calculating color data from spectral data.

• Errors due to thermochromism in samples.

• Errors due to the dependence of spectral resolution on bandwidth, scan speedand integration time.

• Geometry difference between illumination and collection optics within the speci-fied limits.

At present, there is no method for quantifying the effects of geometry differences(last item) and applying corrections. The method used to minimise error due tonon-uniformity of collection by integrating spheres, which is to measure matt sam-ples against matt masters and glossy samples against glossy masters, has not provedvery effective. Thus, it is now clear that there are significant undetermined errorswhich remain uncorrected, limiting agreement at present.

Integrating sphere errors are due to the fact that the integrating sphere is not anideal sphere but a hemispherical sphere. There are also some baffles inside the spherewhich prevent straight light from striking the detector.

3.3 Errors in surface color measurements 25

3.3.1 Errors in absolute scales of diffuse reflectance and 0/45 radiancefactor

The method used for this intercomparison relies on the stability of the white referencetiles to accurately transfer common absolute scales to all participants with a high degreeof accuracy. All standards were calibrated by NPL, providing a common scale for thematt and glossy calibrations. These scales contain an inherent uncertainty associatedwith the NPL calibration.

3.3.2 Errors due to differing properties of white reference standards

When making measurements of matt samples using spectrophotometers with a inte-grating sphere accessory, errors may be introduced if the instrument is calibrated usinga glossy standard. The same is also true for glossy measurement against a matt stan-dard. To minimize these errors a matt standard should be used for matt samples anda glossy standard for glossy samples.

3.3.3 Photometric non-linearity

A lack of linearity in a detection system causes errors in results. Photometric non-linearity error assumes that the response of the photodetector is not linear over thereflectance scale from 0% to 100%. Towards the higher end of the signal range, satura-tion of the detector or electronics may occur. There may also be some additional effectssuch as inter-reflection between glass surfaces within the instrument and a reductionin sphere response with dark samples.

The simplest type of relationship between the true value of reflectance R and theinstrumental value R′ is a quadratic form. That means the difference is biggest at the50% reflectance level. Now the photometric non-linearity can be corrected by measuringonly one grey tile, about 50% of the reflectance. Definition of the non-linearity erroris based on the assumption that the error is zero at 100% and 0%. The 100% levelcorresponds to a sample being measured against itself and 0% level errors are classifiedas the dark level error and, thus, treated separately.

Assuming the quadratic relationship for the error we arrive at

R = R′ + δR

= a + bR′ + cR′2. (3.1)

By this definition we find that when R = 0 also R′ = 0 and a = 0. In the same way


when R = 100, R′ = 100 also. Now we have the equations

100 = 100(b + 100c) (3.2)

b = 1 − 100c. (3.3)

For a grey tile, we can denote R = r and R′ = r′. Thus

r = br′ + cr′2

= (1 − 100c)r′ + cr′2

= r′ − 100cr′ + cr′2. (3.4)

For a terms of c and b, we can solve

c =r′ − r

100r′ − r2(3.5)

b = 1 − 100c

= 1 − 100r′ − 100r

100r′ − r′2

=100r + r′2

100r′ − r′2. (3.6)

Hence,

R =

(100r − r′2

100r′ − r′2

)R′ +

(r′ − r

100r′ − r′2

)R′2, (3.7)

where r is the certified value for the grey tile, and r′ is the corresponding measuredvalue. Now the linearity corrected spectrum R can be calculated for any color whenthe uncorrected spectra R′ is measured.

As the tiles used in this intercomparison were calibrated against a white master ona sphere instrument at NPL, it is possible that the NPL’s instrument’s non-linearitymay have been imposed on all values.


3.3.4 Incorrect zero level

An integrating sphere dark level error is mainly due to light scattered inside the opticsof the spectrophotometer. This effect gives a halo around the main light beam, someof which falls on the sphere wall. There may also be a component due to an electronicoffset. The error is determined by placing a black glass wedge at the sample port, whichabsorbs the light in the main beam and by measuring the variation of reflectance readingwith a wavelength. An optical wedge gives a reading ρk. Absolute diffuse reflectanceof a sample Ra is

Ra =ρa − ρk

ρt − ρk

Rt

=ρa

(1 − ρk

ρa

)ρa

(1 − ρk

ρt

)Rt

≈ ρa

ρt

(1 − ρk

ρa

)(1 +

ρk

ρt

)Rt

≈ ρa

ρt

(1 − ρk

ρa

+ρk

ρt

)Rt

=ρa

ρt

Rt + k1

(ρa

ρt

− 1

), (3.8)

where,

k1 =ρk

ρt

Rt. (3.9)

ρa in Eq. 3.8 is the sample reading, ρt is the white standard reading, ρk is the darkreading and Rt is the calibrated value for a white standard.

3.3.5 Wavelength scale error

Wavelength error will lead to color errors, so the instrument’s wavelength scale shouldbe checked. Reflectance values should be corrected, according to the expression

R(λ) = Rm(λ) +∂Rm(λ)

∂λ∆λ, (3.10)

where R(λ) is the correct reflectance value, Rm is the measured reflectance value and∆λ is the wavelength scale error, the difference between the actual and displayed value.


Wavelength error can be determined by using several wavelength standards: spectrallamps, reflection tiles or transmission filters. The user must use the most appropriatestandard for the instrument type.

3.3.6 Specular beam exclusion error

For a glossy sample measured in the specular excluded mode, the specular beam fallson a gloss trap. Ideally, none of the light entering the trap should be reflected back intothe sphere and none of the beam should meet an integrating sphere wall. In practice,these ideal conditions are not often achieved and, thus, correction is needed. Thesimplest method is to use a calibrated front surface mirror to give a strong specularbeam with the white tile used as the diffuse reflectance standard. A calibrated mirrorof reflectance M gives a reading ρgm. In a case where a gloss trap is used to blockspecular reflectance, a calibrated mirror M will give a reading

ρg4 =4

Mρgm. (3.11)

The number 4 is used as a nominal value for the specular reflectance of a typical glossysample. Absolute diffuse reflectance Ra of a sample is

Ra =ρa − αρg4

ρt − βρg4

Rt, (3.12)

where α, β = 0 for a matt surface and α, β = 1 for a glossy surface. Using the sameapproximates as for the dark error correction

Ra ≈ ρa

ρt

Rt + k2

(β

ρa

ρt

− α

), (3.13)

where,

k2 =ρg4

ρt

Rt. (3.14)

Here with the ρa reading of a sample, ρt is read when the white standard is measured,and Rt is the calibrated value for a white standard.


3.3.7 Specular beam weighting error

For a glossy sample measured in the specular included mode, non uniformity of theintegrating sphere may mean that the specular component is not collected with thesame efficiency as the diffusely reflected light. A calibrated mirror of reflectance Mplaced at the sample port gives a reading ρsm. If there is no specular beam error, themirror would give a reading

ρtM

Rt

, (3.15)

where ρt is a reading of a calibrated matt white tile Rt is placed at the sample port.Thus, the error in the mirror reading em is given by

em = ρsm − ρtM

Rt

. (3.16)

If we apply the nominal value of 4% specular reflectance from a typical glossy samplewe arrive at the error in the specular beam

es =4

M

(ρsm − ρt

M

Rt

). (3.17)

The absolute reflectance Ra of a sample when applying a correction is

Ra =ρa − αes

ρt − βes

Rt

≈ ρa

ρt

(1 − αes

ρa

+βes

ρt

)Rt

=ρa

ρt

Rt +ρa

ρt

es

(β

ρt

− α

ρa

)Rt, (3.18)


where α, β = 0 is for a matt surface and α, β = 1 is for a glossy surface, where thesame approximates are used as before. Substituting es into the above equation we get

Ra =ρa

ρt

Rt +ρa

ρt

4

M

(ρsm − ρt

M

Rt

)(β

ρt

− α

ρa

)Rt

=ρa

ρt

Rt + 4

(ρsm

ρt

1

M− 1

Rt

)(β

ρa

ρt

− α

)Rt

=ρa

ρt

Rt + 4

(ρsm

ρt

Rt

M− 1

) (β

ρa

ρt

− α

)

=ρa

ρt

Rt + k3

(β

ρa

ρt

− α

), (3.19)

where,

k3 = 4

(ρsm

ρt

Rt

M− 1

). (3.20)

In Eqs. 3.19 and 3.20 ρa is a sample reading, ρsm is a reading for a calibrated mirrorin a sample port, ρt is a reading for the calibrated white standard, M is the calibratedvalue for a mirror and Rt is the calibrated value for a white standard.

3.3.8 Errors due to non-uniformity of collection of integrating spheres

The internal reflectance of an integrating sphere will usually vary over its surface. Inaddition, baffles included within the sphere lead to a variation in response to the angleof reflectance. The reflectance of samples, particularly materials such as metals andpaper, varies considerably with the direction of view. This, linked with the non-uniformangular response of the sphere, may lead to errors.

3.3.9 Polarisation errors in the 0/45 geometry

Several researchers have carried out studies on the effects of polarisation. However, noneed for a correction has arisen in typical surface color samples.

3.3.10 Differences in methods of calculating color data from spectral data

In the calculation of colorimetric values some errors may occur. Usually, the CIEstandard observer data are available at 5 nm intervals. Errors may occur if calculationis made at different intervals.

3.4 Measurements and corrections 31

3.3.11 Geometry differences between illumination and collection opticswithin the specified limits

The tolerances given in the CIE geometry specification are sufficiently large to resultin a wide range of implementation in instrumental design.

3.3.12 Errors due to thermochromism in samples

In common with all materials, the ceramic tiles used in the intercomparison will changecolor with temperature. Thus, samples should be measured at the same temperature.It was agreed to measure samples in 23 ± 1◦C in this comparison. In this thesis,thermochromism is discussed in more detail in Chapter V.

3.3.13 Errors due to the dependence of spectral resolution on bandwidth,scan speed and integration time

A fast speed scan with slow integration time will generate a different result to a slowspeed, fast integration time scan, particularly in the resolution of slopes. The differencebetween the two resulting spectra might appear as a wavelength shift and particularlyaffect the results for the more chromatic tiles. The same is true for an instrument witha differently shaped spectral bandwidth. The partners were investigating the effects ofthe scan speed and integration time and finally agreed to use same kind of parameters.

3.4 Measurements and corrections

A double beam scanning spectrophotometer, Perkin Elmer λ-18, was used in reflectancespectra recording. Measurements were performed with a bandwidth of 2 nm and with ascanning speed of 240 nm/min. The minimum temperature during the measurementswas 22.2◦C while the maximum was 23.4◦C. All samples were measured 6 times, 3times in the morning and 3 times in the afternoon after at least a 3 hour interval. Nosignificant differences were noticed between the results. Error correction factors k1, k2

and k3 were determined as described earlier in Eqs 3.9, 3.14 and 3.20. Quantities ofconstants ki for a PE-18 instrument are shown in Fig. 3.1 as a function of wavelength.The correction constants were then used to apply the needed corrections. Wavelengtherror was determined by measuring the emission spectrum of a deuterium lamp. Thiserror was noticeably negligible. The amount of linearity correction was also determinedby measuring the mid-grey calibration sample which was compared to the calibratedvalues. The difference between the calibrated and the measured values was about0.56%-unit. As a matter of fact, the influence of the photometric linearity correctionwas biggest among all applied corrections in our case. One has to point out that byusing only one grey tile a quadratic relationship is assumed for the linearity error. Toensure the nature of the behavior of the photodetector, more calibrated grey samples


should be used. One interesting finding during this intercomparison was that a greytile and a neutral transmittance filter, at about the same level of 50% refelectance, donot necessarily have the same amount of non-linearity error. This was confirmed bymeasurement between UJ and NPL. Later, in 1998 the co-ordinator received a letterfrom Japan as part of the work of a CIE Technical Committee, giving completelyindependent results.

350 400 450 500 550 600 650 700 750 8000

0.01

0.02

0.03

0.04

0.05

0.06

Wavelength [nm]

Valu

e

Figure 3.1: Error correction factors for the PE-18 spectrophotometer. Solid, dashed,and dot-dashed lines correspond to the correction factors k1, k2 and k3, respectively.

3.5 Intercomparison results

The main objective of the project was to harmonise color measurements between 8national laboratories within discrimination limits of the human eye. A target wasset to 95% agreement within 0.5 ∆E CIELAB units. Each laboratory measured andapplied corrections for a set of 16 samples, 8 matt samples and 8 glossy samples. Allof the measurements and calculations of Joensuu cite were done by the author. Allthe samples were ceramic tiles which are known to be very stable [12]. The mattsamples were measured against a matt white tile and, similarly, glossy tiles against aglossy white tile. Fig. 3.2 shows the reflectance spectra of the 8 matt color samples.The colors of the tiles were pale grey, mid grey, black, red, bright yellow, green, cyanand deep blue. These samples were provided and calibrated by the NPL. Partnersdid not have a priori knowledge of the spectral data of the samples while makingmeasurements. Each laboratory tried to measure samples as accurately as they could.

3.5 Intercomparison results 33

Matt samples were measured in specular included geometry and glossy samples weremeasured both in specular included and excluded geometry. Some of the laboratoriesmeasured the samples in 0/45 geometry, as well.

400 450 500 550 600 650 700 7500

10

20

30

40

50

60

70

80

90

100

Wavelength [nm]

Refl

ecta

nce

[%]

Figure 3.2: Reflectance spectra of a 8 matt color samples.

Part of the results of the comparison are shown in the Tables 3.1–3.17. Table 3.1show the effect of the applied error corrections for the data measured at the Universityof Joensuu. In specular included geometry corrections are made in the following order:dark error correction (Rd), specular beam error correction (Rs) and non-linearity cor-rection (Rnl). Each correction was added cumulatively to the previous corrections. Inthe specular excluded geometry a gloss trap error correction (Rg) was applied insteadof the specular beam correction.

The colormetric differences from the NPL-data were calculated for each partner.The results for the specular included geometry are shown in Tables 3.2 and 3.3 beforeand after the corrections, respectively. In Tables 3.4 and 3.5 corresponding results areshown for the specular excluded geometry. By comparing the results between 3.2 and3.3 or 3.4 and 3.5 one can see the impact of applied corrections. In most corrections theresults improve. Surprisingly, there are quite large differences with black, red and deepblue samples. It is hard to say whether the reason lies in the instrument or if thereis human error in the measurements. Nevertheless, the UJ-results are the only oneswhere the impact of error corrections did not change results in the wrong direction, i.e.in every case better results were achieved after corrections were applied. This indicatesthat NPL and us were the best among the participating laboratories. However, weneed to point out that in this kind of experimental investigation the “right” results donot exist. It is possible that there may be some error in the NPL-data as well. In that


Table 3.1: CIELAB Colorimetric differences ∆E for the UJ-data after applied cumu-lative corrections in the order of dark error (Rd) correction, specular beam error (Rs)or gloss trap error (Rg) correction and non-linearity error (Rnl) correction, 10 degreeobserver, illuminant D65.

Specular Included Specular ExcludedGeometry Geometry

Tile Rd Rs Rnl Rd Rg Rnl

Glossy Grey 0.00 0.01 0.23 0.00 0.00 0.25Glossy Mid Grey 0.01 0.02 0.33 0.01 0.00 0.35Glossy Black 0.03 0.08 0.20 0.11 0.14 0.21Glossy Red 0.03 0.02 0.27 0.12 0.26 0.31Glossy Bright Yellow 0.03 0.02 0.31 0.04 0.14 0.33Glossy Green 0.01 0.03 0.35 0.02 0.07 0.37Glossy Cyan 0.01 0.02 0.34 0.01 0.06 0.37Glossy Deep Blue 0.04 0.15 0.36 0.15 0.90 0.87Matt Grey 0.00 0.23Matt Mid Grey 0.01 0.34Matt Black 0.03 0.25Matt Red 0.02 0.29Matt Bright Yellow 0.02 0.29Matt Green 0.01 0.33Matt Cyan 0.01 0.32Matt Deep Blue 0.03 0.27


case there will be some uncertainty in all error corrections. From this aspect one cannot directly conclude that smaller differences are always better.

First of all, the purpose of this intercomparison was to harmonise measurementresults between all partners. This means that differences are calculated from the meanvalue of all measurements. Tables 3.6–3.9 show the percentage of the measurements ofeach partner below three different ∆E limits from the mean. However, there may besome minor disadvantages in this measure as well, since there are some large differencesamong some colors. This will set the mean value as slightly false and distort the results.


Table 3.2: Partners’ colorimetric differences ∆E from NPL for the set of 16 color tiles,specular included geometry. Uncorrected results, 10 degree observer, illuminant D65 [43].

Tile UJ LNE BAM CETO CSIC SP BCRA DELTA

Glossy

Pale Grey 0.23 0.31 0.09 0.19 0.15 0.27 0.02 0.21Mid Grey 0.37 0.41 0.59 0.14 0.28 0.34 0.13 0.59Black 0.17 0.33 4.06 0.33 1.27 0.32 0.78 1.46Red 0.73 0.69 4.04 0.68 1.45 0.70 0.92 1.58Bright Yellow 0.59 0.63 3.25 0.46 1.19 0.66 0.63 1.48Green 0.34 0.49 1.70 0.33 0.73 0.43 0.63 0.72Cyan 0.47 0.51 1.37 0.57 0.50 0.49 0.80 0.51Deep Blue 0.20 0.27 4.47 0.44 1.14 0.29 0.45 1.78

Matt

Grey 0.12 0.11 0.19 0.09 0.22 0.10 0.08 0.26Mid Grey 0.43 0.20 0.09 0.25 0.06 0.11 0.26 0.37Black 0.43 0.16 1.76 0.23 0.12 0.35 0.11 0.37Red 0.71 0.78 1.01 0.56 2.55 0.62 0.79 1.30Bright Yellow 0.84 0.47 1.56 1.31 0.71 0.76 0.82 0.96Green 0.49 0.18 0.75 0.40 0.32 0.47 0.47 0.62Cyan 0.42 0.39 0.70 0.48 0.22 0.40 0.73 0.31Deep Blue 0.55 0.21 2.16 0.37 0.48 0.46 0.22 0.78

Average|difference| 0.44 0.38 1.74 0.43 0.71 0.42 0.49 0.83


Table 3.3: Partners’ colorimetric differences ∆E from NPL for the set of 16 colortiles, specular included geometry. Fully corrected results, 10 degree observer, illuminantD65 [43].


Glossy


Matt




Table 3.4: Partners’ colorimetric differences ∆E from NPL for the set of 8 color tiles,specular excluded geometry. Uncorrected results, 10 degree observer, illuminant D65 [43].


Glossy




Table 3.5: Partners’ colorimetric differences ∆E from NPL for the set of 16 colortiles, specular excluded geometry. Fully corrected results, 10 degree observer, illuminantD65 [43].


Glossy




Table 3.6: Partners’ colorimetric differences ∆E from the mean difference for the setof 16 color tiles, specular included geometry. Uncorrected results, 10 degree observer,illuminant D65 [43].

UJ LNE BAM CETO CSIC SP BCRA DELTA


% within 0.2∆E of mean 56.3 43.8 25.0 37.5 75.0 62.5 43.8 62.5

% within 0.5∆E of mean 75.0 81.3 43.8 75.0 93.8 81.3 93.8 93.8

% within 0.75∆E of mean 87.5 87.5 56.3 93.8 93.8 87.5 100 100


Table 3.7: Partners’ colorimetric differences ∆E from the mean difference for the setof 16 color tiles, specular included geometry. Fully corrected results, 10 degree observer,illuminant D65 [43].



% within 0.2∆E of mean 43.8 50.0 31.3 62.5 75.0 50.0 56.3 50.0

% within 0.5∆E of mean 93.8 100 62.5 81.3 93.8 87.5 100 100

% within 0.75∆E of mean 100 100 62.5 100 93.8 100 100 100


Table 3.8: Partners’ colorimetric differences ∆E from the mean difference for the setof 16 color tiles, specular excluded geometry. Uncorrected results, 10 degree observer,illuminant D65 [43].



% within 0.2∆E of mean 50.0 37.5 62.5 62.5 75.0 62.5 50.0 37.5

% within 0.5∆E of mean 87.5 100 87.5 75.0 87.5 100 87.5 87.5

% within 0.75∆E of mean 100 100 100 87.5 100 100 87.5 100


Table 3.9: Partners’ colorimetric differences ∆E from the mean difference for the setof 16 color tiles, specular excluded geometry. Fully corrected results, 10 degree observer,illuminant D65 [43].



% within 0.2∆E of mean 62.5 50.0 50.0 62.5 87.5 62.5 75.0 50.0

% within 0.5∆E of mean 87.5 87.5 100 100 100 100 100 87.5

% within 0.75∆E of mean 100 100 100 100 100 100 100 87.5


3.6 Determination of colorimetric uncertainties

Generally, the result of a measurement is only a approximation or estimate of thevalue of the specific quantity subject to measurement. Because of increasing demandsof measurement accreditation and quality systems there is a need to quote uncertaintieson all certified quantities. The result is complete only when accompanied a quantitativestatement of its uncertainty [8, 53].

The uncertainty of the result of a measurement generally consists of several compo-nents. These components may be grouped into two categories according to the methodused to estimate their numerical values:

• Type A, evaluated by statistical methods.

• Type B, evaluated by other means.

The only Type A uncertainty in this intercomparison was the repeatability [43]. TheType B uncertainties were:

• Uncertainty in the level of the absolute scales of diffuse reflectance and radiancefactor.

• Uncertainty in the spectral slope of the scales.

• Dark uncertainty.

• Linearity uncertainty.

• Wavelength scale uncertainty.

• Thermochromism uncertainty.

• Glossy to matt ratio uncertainty.

• Specular beam uncertainty.

• Gloss trap uncertainty.

The repeatability was determined by making several measurements. The standarddeviation was then used in the calculation of of the standard uncertainty.

Uncertainty in the level of the absolute scales of diffuse reflectance or radiancefactor comes from the traceability to the 100% levels. This is taken from a certificateof calibration for a white standard. Uncertainty in the spectral slope of scales isconnected to absolute scale uncertainty. The scale may have a slope on it within theuncertainty limits. This effect is assessed using a skew of half the scale uncertainty.

3.6 Determination of colorimetric uncertainties 45

The dark uncertainty is a combination of the electronic offset of the instrument and,for diffuse reflectance, an optical offset due to a halo of scattered light surrounding thesample beam and falling on the integrating sphere. Dark errors can be measured byplacing a gloss trap at the sample port of integrating sphere. Blocking the beam doesnot give a true offset reading, because it does not quantify the effects of the halo ofstray light.

Photometric linearity uncertainty is connected to non-linearity of the detector. Itcan be assessed from measurements of a white and a grey standards. Non-linearityerror was modelled using a polynomial and was set to zero at 0% and 100%.

Wavelength error cause changes in reflectance in regions of spectral slope, wherereflectance changes with wavelength. Wavelength error can be measured using a wave-length standard or a known spectral line of a lamp. Thermochromism causes shift intospectral data in a similar way as wavelength error.

Errors in the glossy to matt ratio are due to differences in efficiency of collectionof the integrating sphere with angle of reflectance. The error can be determined bymeasuring glossy samples against matt samples with different integrating spheres.

The specularly reflected light may not be collected with the same efficiency as thediffusely reflected light in the specular included geometry. Specular beam uncertaintycan be determined using a mirror and a calibrated matt white standard. In the specularexcluded geometry, the error due to incomplete absorption of the specular beam in thegloss trap is known as the gloss trap error. This error can also be determined with amirror and a calibrated matt white standard.

Each uncertainty is characterised by assessed probability distribution for the un-certainty. In a case of Gaussian (normal) distribution each component of uncertaintywas first divided by a coverage factor k, 1 or 2, which refers to confidence level ofapproximately 65% or 95%, respectively. The total uncertainty was then combined inquadrature from the components of uncertainty as

utotal =√

(u21 + u2

2 + . . . ), (3.21)

which was then multiplied by a coverage factor. In here coverage factor of k = 2 wasused.

The following components of uncertainties were determined for a UJ-data:

• repeatability

• photometric linearity uncertainty

• dark level uncertainty


• gloss trap uncertainty

• specular beam uncertainty

Uncertainties in the level of the absolute scales and in the spectral slope of thescales were left to calculate by co-ordinator since they provide partners absolute scales.The wavelength uncertainty was not determined because of zero wavelength error inmeasurement of the emission line of deuterium lamp. Also thermochromism effect wasneglected cause of agreed temperature limit ±1◦C.

All uncertainty components were calculated using the determined errors. If the errorwas corrected for in reflectance calculations, the uncertainty was that after correction.If it was not corrected for, the uncertainty was the error itself.

In Tables 3.10–3.12 partners’ colorimetric uncertainties are shown for both specularincluded and specular excluded geometries. For the UJ-data the most of the uncertaintylies in a luminosity coordinate L∗. This is due the fact that the photometric linearitywas the biggest error source. In Tables 3.13–3.14 partners’ colorimetric uncertaintiescombined to give ∆E∗

ab for the intercomparison are shown.


Table 3.10: Colorimetric uncertainties for partners tiles for a coverage factor of k = 2,specular included geometry [43].

Tile UJ LNE BAM CETO CSIC SP BCRA DELTA NPL

Glossy

Pale L∗ 0.23 0.5 0.5 0.01 0.24 0.36 0.26 0.5 0.21Grey a∗ 0.01 0.5 0.5 0.24 1.44 0.11 0.10 0.2 0.02

b∗ 0.00 0.5 0.5 0.07 0.75 0.34 0.19 0.2 0.02

Mid L∗ 0.35 0.5 0.5 0.00 0.18 0.40 0.29 0.5 0.16Grey a∗ 0.01 0.5 0.5 0.14 1.10 0.08 0.18 0.2 0.02

b∗ 0.00 0.5 0.5 0.04 0.57 0.26 0.34 0.2 0.02

Black L∗ 0.28 0.5 0.5 0.27 0.12 0.32 0.81 0.5 0.16a∗ 0.01 0.5 0.5 0.95 0.75 0.55 0.28 0.2 0.02b∗ 0.00 0.5 0.5 0.98 0.38 0.17 0.79 0.2 0.02

Red L∗ 0.28 0.8 0.5 0.39 0.14 0.39 0.82 0.5 0.16a∗ 0.02 0.8 0.5 1.45 1.04 0.25 0.38 0.2 0.15b∗ 0.02 0.8 0.5 1.26 0.41 0.29 1.54 0.2 0.13

Bright L∗ 0.20 0.8 0.5 0.65 0.27 0.38 0.45 0.5 0.21Yellow a∗ 0.14 0.8 0.5 2.23 1.70 0.32 0.47 0.2 0.11

b∗ 0.18 0.8 0.5 1.76 0.55 0.28 1.13 0.2 0.19

Green L∗ 0.34 0.5 0.5 0.47 0.17 0.39 0.23 0.5 0.15a∗ 0.00 0.5 0.5 1.56 0.96 0.20 0.65 0.2 0.08b∗ 0.01 0.5 0.5 1.58 0.46 0.28 1.13 0.2 0.13

Cyan L∗ 0.33 0.5 0.5 0.47 0.17 0.37 0.21 0.5 0.16a∗ 0.03 0.5 0.5 1.60 0.95 0.32 0.73 0.2 0.13b∗ 0.01 0.5 0.5 1.86 0.60 0.36 0.52 0.2 0.13

Deep L∗ 0.28 0.8 0.5 0.00 0.17 0.33 1.09 0.5 0.16Blue a∗ 0.03 0.8 0.5 0.05 0.96 0.32 0.73 0.2 0.06

b∗ 0.05 0.8 0.5 0.02 0.46 0.26 0.64 0.2 0.11


Table 3.11: Colorimetric uncertainties for partners tiles for a coverage factor of k = 2,specular included geometry [43].


Matt

Pale L∗ 0.23 0.5 0.5 0.01 0.26 0.43 0.26 0.5 0.21Grey a∗ 0.01 0.5 0.5 0.24 1.57 0.11 0.10 0.2 0.05

b∗ 0.00 0.5 0.5 0.07 0.82 0.34 0.19 0.2 0.05

Mid L∗ 0.34 0.5 0.5 0.00 0.18 0.40 0.29 0.5 0.16Grey a∗ 0.00 0.5 0.5 0.14 1.10 0.08 0.18 0.2 0.05

b∗ 0.00 0.5 0.5 0.04 0.57 0.26 0.34 0.2 0.05

Black L∗ 0.27 0.5 0.5 0.00 0.13 0.32 0.81 0.5 0.16a∗ 0.00 0.5 0.5 0.01 0.77 0.55 0.28 0.2 0.05b∗ 0.01 0.5 0.5 0.00 0.41 0.17 0.79 0.2 0.05

Red L∗ 0.30 0.8 0.5 0.00 0.15 0.39 0.82 0.5 0.16a∗ 0.03 0.8 0.5 0.02 1.11 0.25 0.38 0.2 0.15b∗ 0.03 0.8 0.5 0.01 0.46 0.29 1.54 0.2 0.11

Bright L∗ 0.20 0.8 0.5 0.00 0.29 0.38 0.45 0.5 0.21Yellow a∗ 0.13 0.8 0.5 0.05 1.82 0.32 0.47 0.2 0.11

b∗ 0.19 0.8 0.5 0.02 0.60 0.28 1.13 0.2 0.19

Green L∗ 0.34 0.5 0.5 0.00 0.19 0.39 0.23 0.5 0.15a∗ 0.01 0.5 0.5 0.02 1.07 0.20 0.65 0.2 0.08b∗ 0.00 0.5 0.5 0.01 0.52 0.28 1.13 0.2 0.13

Cyan L∗ 0.33 0.5 0.5 0.00 0.18 0.37 0.21 0.5 0.16a∗ 0.02 0.5 0.5 0.02 1.03 0.32 0.73 0.2 0.13b∗ 0.02 0.5 0.5 0.01 0.65 0.36 0.52 0.2 0.13

Deep L∗ 0.28 0.8 0.5 0.00 0.13 0.33 1.09 0.5 0.16Blue a∗ 0.02 0.8 0.5 0.01 0.78 0.32 0.73 0.2 0.06

b∗ 0.07 0.8 0.5 0.00 0.45 0.26 0.64 0.2 0.11


Table 3.12: Colorimetric uncertainties for partners tiles for a coverage factor of k = 2,specular excluded geometry [43].


Glossy

Pale L∗ 0.25 0.5 0.5 0.00 0.23 0.40 0.26 0.5 0.20Grey a∗ 0.00 0.5 0.5 0.04 1.38 0.10 0.14 0.2 0.02

b∗ 0.00 0.5 0.5 0.02 0.71 0.33 0.17 0.2 0.02

Mid L∗ 0.35 0.5 0.5 0.00 0.16 0.43 0.23 0.5 0.15Grey a∗ 0.00 0.5 0.5 0.04 0.96 0.08 0.15 0.2 0.02

b∗ 0.00 0.5 0.5 0.01 0.50 0.25 0.22 0.2 0.02

Black L∗ 0.14 0.5 0.5 0.11 0.06 0.39 0.54 0.5 0.41a∗ 0.04 0.5 0.5 0.36 0.35 0.04 0.26 0.2 0.02b∗ 0.04 0.5 0.5 0.41 0.17 0.14 0.38 0.2 0.02

Red L∗ 0.22 0.8 0.5 0.13 0.16 0.39 0.74 0.5 0.18a∗ 0.10 0.8 0.5 0.50 1.12 0.29 0.30 0.2 0.21b∗ 0.03 0.8 0.5 0.45 0.53 0.44 1.59 0.2 0.47

Bright L∗ 0.21 0.8 0.5 0.00 0.26 0.39 0.37 0.5 0.20Yellow a∗ 0.15 0.8 0.5 0.04 1.64 0.40 0.66 0.2 0.12

b∗ 0.07 0.8 0.5 0.01 0.56 0.60 0.39 0.2 0.27

Green L∗ 0.33 0.5 0.5 0.00 0.17 0.38 0.23 0.5 0.15a∗ 0.05 0.5 0.5 0.02 0.93 0.25 0.43 0.2 0.10b∗ 0.04 0.5 0.5 0.01 0.44 0.32 0.84 0.2 0.15

Cyan L∗ 0.32 0.5 0.5 0.00 0.16 0.37 0.37 0.5 0.16a∗ 0.06 0.5 0.5 0.02 0.91 0.26 1.03 0.2 0.16b∗ 0.02 0.5 0.5 0.01 0.56 0.33 0.63 0.2 0.14

Deep L∗ 0.19 0.8 0.5 0.00 0.18 0.32 0.61 0.5 0.39Blue a∗ 0.05 0.8 0.5 0.02 1.02 0.38 1.01 0.2 0.48

b∗ 0.13 0.8 0.5 0.01 0.47 0.47 0.97 0.2 0.46


Table 3.13: Partners’ colorimetric uncertainties combined to give a ∆E for the inter-comparison for a coverage factor of k = 2, specular included geometry [43].


Glossy


Matt


3.7 Summary 51

Table 3.14: Partners’ colorimetric uncertainties combined to give a ∆E for the inter-comparison for a coverage factor of k = 2, specular excluded geometry [43].


Glossy


3.7 Summary

Although not all possible errors for the color measurements have been addressed, theerror correction method employed within the project has considerably improved theagreement regarding measurements carried out by the partners for the 16 color tiles. Atthe end of the project, over 92% of the measurements made by all the partners for allthe tiles agreed to within 0.5 ∆E∗

ab. This result fell slightly short of the target set at theoutset of the project but is considerably better than those agreements achieved in allprevious intercomparisons. In Tables 3.15–3.17 summary of percentage of colorimetricdifferences are shown with errors within 0.2, 0.5 and 0.75 ∆E from the mean difference,respectively.


Table 3.15: Summary of percentage of Partners’ colorimetric differences ∆E from themean difference for the set of 16 color tiles, 10 degree observer, illuminant D65. Totalpercentage of errors within 0.2 ∆E from the mean difference [43].

Specular Included Specular ExcludedCorrection applied geometry geometry

Uncorrected results (R1) 51% 55%R1 + Wavelength correction (R2) 50% 58%R2 + Sphere error correction (R3) 42% 63%R3 + Linearity correction (R4) 52% 63%




3.7 Summary 53




Chapter IV

Tristimulus integration

The permanent CIE Colorimetry Committee reviews from time to time the originalrecommendations and makes those changes considered necessary. The work is done indifferent working groups which are divided into technical committees. A working groupof USTC-1.3 of the CIE prepared, between 1981 and 1983, new recommendations forthe calculation of CIE tristimulus values. These recommendations state that the stan-dard method of performing the integration forming the basic definition of tristimulusvalues shall be by summation at a wavelength interval of 1 nm over the wavelengthrange 360–830 nm, but that for most colorimetric purposes the approximation of sum-mation at a 5nm interval over the range 380–780 nm should suffice. Recommendationswere also made concerning abridgement, interpolation, extrapolation, truncation andthe calculation of weighting factors, since measured data does not always fulfill therequirements. Weighting factors are used in the calculation of color coordinates withintervals which are not so dense, such as 10nm or 20 nm. Although tables of weightingfactors were not included in the recommendations to the CIE, they have since beencalculated in cooperation with the Working Group and published by the AmericanSociety for Testing and Materials, ASTM [1].

CIE recommends the use of the method of calculation of weight sets for tristimulusintegration published by the ASTM in its Method E-308-85. In this method, the prepa-ration of weight sets for any measurement interval or wavelength range by Lagrangeinterpolation from standard tables of data at other intervals is described [2,10,11,54].In this chapter, we show that this recommendation is useless and that it should not beused. Furthermore, its use may confuse the user and may lead to miscalculation.

54

4.1 The ASTM weighting method 55

4.1 The ASTM weighting method

The tristimulus values are defined by the equations

X = k

∫β(λ)S(λ)x(λ)dλ

Y = k

∫β(λ)S(λ)y(λ)dλ (4.1)

Z = k

∫β(λ)S(λ)z(λ)dλ.

The analytical functions of the three factors in the product are not known, so theintegrals should be evaluated alternatively. CIE recommends this be done by 1 nmsummation. Now the equations for such a summation are of the form

Y = k∑

β(λ)S(λ)y(λ)∆λ, (4.2)

where the values have the same meaning as in Eqs. 4.1. In order to solve Eq. 4.2 allinput values of the three functions should also be obtained at 1 nm intervals. Mostcolorists will not wish to resort to measurement of the spectral radiance factors at 1nm interval. In many cases, it would be sufficient to measure these functions at 10 nmor 20 nm intervals. Those unmeasured 9 or 19 unit wavelengths radiance factors can beinterpolated by Lagrange interpolation, method recommended by the Working GroupVIII. The first and the last missing intervals should be interpolated quadratically usingthree measured values and all interior values should be interpolated cubically using fourmeasured values. Lagrange interpolating coefficients may be calculated from

Lj(r) =n∏

i=0i�=j

(r − ri)

(rj − ri)for j = 0, 1, . . . n, (4.3)

where n signifies the degree of the coefficients being calculated. The values of i and rare the indices denoting the location on the abscissa of the tabular values among whichinterpolation is to be carried out.

In the usual case where the measurement interval is uniform across the spectrum

56 4. Tristimulus integration

Eq. 4.3 simplifies to

L0 =(r − 1)(r − 2)(r − 3)

−6(4.4)

L1 =r(r − 2)(r − 3)

2(4.5)

L2 =r(r − 1)(r − 3)

−2(4.6)

L3 =r(r − 1)(r − 2)

6(4.7)

in the cubic case and to

L0 =(r − 1)(r − 2)

2(4.8)

L1 =r(r − 2)

−1(4.9)

L2 =r(r − 1)

2(4.10)

in the quadratic case. In each of the above equations, indices r are substituted togenerate the necessary set of Lagrange interpolating coefficients. Suppose we have 20nm data and we want to calculate Lagrange coefficients for those missing 19 values.For intermediate intervals indices r now ranges from 1 + 1/20 to 2 − 1/20 at 1/20steps. For last interval indices r ranges the same way, but for a first interval r takesvalues from 0 + 1/20 to 1 − 1/20 again at 1/20 steps. Table 4.1 shows an example ofcalculated Lagrange coefficients L0, L1, L2, and L3 in a cubic interpolation for the caseof prediction of 19 values missing.

In Fig. 4.1 calculated Lagrange coefficients are shown both for the cubic and thequadratic cases where data interval was 20 nm. The missing intermediate values maybe predicted from

P (r) =n∑

i=0

Limi, (4.11)

where P is the value being interpolated, L is the Lagrange interpolation coefficient andm is the measured value corresponding to the indices.

4.1 The ASTM weighting method 57

0 2 4 6 8 10 12 14 16 18 20−0.2

0

0.2

0.4

0.6

0.8

1

1.2

i

coeffi

cien

tvalu

e

L0

L1

L2

0 2 4 6 8 10 12 14 16 18 20

−0.2

0

0.2

0.4

0.6

0.8

1

i

coeffi

cien

tvalu

e

L0

L1

L2

L3

Figure 4.1: Lagrange coefficients for the cubic case and the quadratic case where 19missing values are interpolated.


Table 4.1: Lagrange coefficients L0, L1, L2, and L3 in a cubic case for 20 nm intervaldata where 19 missing values are interpolated.

L0 L1 L2 L3

-0.0154 0.9726 0.0512 -0.0083-0.0285 0.9405 0.1045 -0.0165-0.0393 0.9042 0.1596 -0.0244-0.0480 0.8640 0.2160 -0.0320-0.0547 0.8203 0.2734 -0.0391-0.0595 0.7735 0.3315 -0.0455-0.0626 0.7239 0.3898 -0.0512-0.0640 0.6720 0.4480 -0.0560-0.0639 0.6181 0.5057 -0.0598-0.0625 0.5625 0.5625 -0.0625-0.0598 0.5057 0.6181 -0.0639-0.0560 0.4480 0.6720 -0.0640-0.0512 0.3898 0.7239 -0.0626-0.0455 0.3315 0.7735 -0.0595-0.0391 0.2734 0.8203 -0.0547-0.0320 0.2160 0.8640 -0.0480-0.0244 0.1596 0.9042 -0.0393-0.0165 0.1045 0.9405 -0.0285-0.0083 0.0512 0.9726 -0.0154

4.2 Spectral bandpass error

Spectral bandpass dependence occurs whenever the width of the passband is other thaninfinitesimal [50]. The passband must be of sufficient width that the power passed tothe detector of the instrument is sufficient to lie within the dynamic range of thedetector. The most common situation in industrial equipment is that the bandpassis both symmetrical and triangular in shape, and that the half-peak width is equalto the measurement interval. This leads to a result where linear spectral radiancewithin bandpass range does not cause any bandpass error. Instead, bandpass erroroccurs if the spectral radiance is either concave or convex within the range of bandpassfunction. This is because the instrument with a finite bandpass always measures the

4.2 Spectral bandpass error 59

spectral values too high in a concave situation compared to linear a extrapolant. Ina convex case, the situation is exactly opposite. An example of a triangular shapebandpass and of a concave radiance function is shown in Fig. 4.2.

-9 -5 0 5 9

Figure 4.2: The representation of the triangular bandpass at one nanometer intervalsand its relationship to a concave radiance function. The dashed line represents the linearextrapolant of the value of the function at the central wavelength.

Stearns has proposed that any wavelength index i can be estimated by

Rc(i) = −kRm(i − 1) + (1 + 2k)Rm(i) − kRm(i + 1), (4.12)

where Rc is the corrected radiance and the Rm is the measured radiance [50]. Accordingto Venable [54] the correct value for coefficient k is 0.083 in the case of a symmetricalbandpass with a half-peak bandwidth equal to measurement interval. When correctingeither the first or last measured passband the correction is made by

Rc(i) = (1 + k)Rm(i) − kRm(i ± 1). (4.13)

The ASTM field test was done by Fairman [11]. In that research, 140 spectra wereused provided by cooperators. Wavelength range was from 380 nm to 780 nm with 10


nm intervals. The spectra were considered to be arbitrarily corrected without regardto their origin or geometry of measurement. In Table 4.2 summary of the results madeby Fairman are shown.

Table 4.2: Summary of the results of all color difference ∆E∗ab calculations with and

without the ASTM weighting for 10 nm and 20 nm data [11].

Median 80-percentile

Interval None Weighting None Weighting

10 nm 0.145 0.004 0.253 0.01120 nm 0.605 0.015 1.053 0.075

4.3 Materials and methods

Two data sets were used to analyze the ASTM weighting sets in the case of nonfluorescent color spectra. The first data set was measured with a Perkin Elmer Lambda9 UV/VIS/NIR spectrophotometer with an external integrating sphere attached. Thisdata set consists of 1269 reflectance spectra of the matt Munsell chips. The seconddata set was measured with a Perkin Elmer Lambda 18 UV/VIS spectrometer witha Labsphere RSA-PE-18 reflectance spectroscopy accessory. In this set, there was atotal of 922 spectra of Pantone colors. Therefore the total number of spectra was 2191.Both data sets were measured at 1 nm intervals from 380 nm to 780 nm. This data isconsidered to be arbitrarily correct and free of bandpass error. Of course, this can bedone if we simply consider the original data to be correct, theoretically.

Let us first consider the effect of calculating CIELAB color coordinates with dif-ferent wavelength intervals. In table 4.3, some statistics are shown for the calculatedcolor differences ∆E∗

ab with different wavelength intervals. Data intervals other than1 nm was achieved by picking data with the appropriate interval from the originaldata. The first value of the wavelength is 380 nm in every case. The last value is notnecessarily 780 nm if the new interval is not evenly divided within the original 400nm wide wavelength band. Color differences are then compared with the original 1nm data. Two different illuminants and observers were used which provided a total of8764 differences for each interval.

4.3 Materials and methods 61

Table 4.3: Color difference ∆E∗ab with different data intervals, each interval compared

to 1 nm reference data. There were a total of 8764 calculated color differences in eachinterval.

Interval Mean Max Std Median 80-percentile

2 0.006 0.038 0.006 0.003 0.0103 0.012 0.227 0.017 0.007 0.0174 0.010 0.096 0.009 0.007 0.0155 0.002 0.016 0.002 0.001 0.0026 0.018 0.303 0.020 0.012 0.0267 0.023 0.336 0.025 0.015 0.0368 0.024 0.742 0.029 0.015 0.0369 0.029 0.558 0.032 0.019 0.04410 0.031 0.433 0.034 0.018 0.04615 0.074 0.616 0.064 0.054 0.11620 0.126 1.205 0.103 0.099 0.18725 0.251 1.671 0.217 0.187 0.38830 0.397 2.375 0.275 0.331 0.59835 0.614 3.315 0.495 0.472 0.97940 0.938 6.264 0.797 0.689 1.50245 1.302 7.478 1.081 0.959 2.03750 1.665 9.564 1.331 1.325 2.663

One can see that the mean difference ∆E∗ab is still less than 0.5 when the wavelength

interval is over 30 nm. If all measurements should go under the limit of the human eyediscrimination, 10 nm data would still be usable. The maximum ∆E∗

ab error is 0.433with a 10 nm interval. The last statistic 80− percentile tells us under what limit 80%of the data goes. Again the data interval can be almost 30 nm when 20% of the resultsare over the 0.5 ∆E∗

ab limit value.

Let us now apply the ASTM weighting into the previous sets. Table 4.4 shows theresults with the ASTM weighting. If we now compare the results of Table 4.3 and Table4.4 one can note only minimal changes. The weighting does not give significantly betterresults. The situation is completely different in the results calculated by Fairman [11]Table 4.2, where the effect of weighting was about tenfold. The reason may be inthe way in which the calculation was made. The starting point was the data of 140


Table 4.4: Color difference ∆E∗ab with different data intervals with ASTM weighting,

8764 differences in each interval.

Interval Mean Max Std Median 80-percentile

2 0.006 0.039 0.006 0.003 0.0104 0.009 0.094 0.009 0.006 0.0155 0.001 0.016 0.001 0.001 0.0018 0.023 0.744 0.029 0.013 0.03510 0.031 0.432 0.034 0.018 0.04716 0.055 0.942 0.049 0.044 0.08020 0.122 1.247 0.095 0.104 0.17925 0.185 1.380 0.159 0.139 0.28740 1.149 7.984 0.958 0.869 1.79150 1.925 10.475 1.538 1.451 3.059

spectra with 10 nm intervals. From that data a new data set was formed by Lagrangeinterpolation which was then set as the reference data to which the color differencecalculations were done.

Let us now simulate the calculations of the Fairman’s paper. First, 10 nm data isacquired by picking every tenth reflectance value from the original 1 nm interval dataof the 2191 non fluorescent color spectra. Then, 1 nm reference data is interpolatedfrom the former 10 nm data. There is no need for any bandpass weighting if we assumethe original 1 nm data to be free of bandpass errors. Table 4.5 shows the results of thestatistics of the color differences with the ASTM weighted and unweighted data. Colordifferences are calculated by comparing the 10 nm ASTM weighted and unweighteddata with the 1 nm data which was obtained by interpolation.

If we calculate the same color differences but use 1 nm original data as the referencewe obtain the results shown in Table 4.6. The difference between weighted and un-weighted data is minimal. In fact, weighting has only a minor effect on the 10 nm data.This is demonstrated in Table 4.7 where ∆E color difference is calculated between the10 nm original and 10 nm the ASTM weighted data.

Furthermore, one can notice by comparing Tables 4.5 and 4.6 that the interpolated1 nm data is much closer to the 10 nm data than to the original 1 nm data. Thereforeinterpolation does not lead to the right original data. This can be realized by comparingcolor differences of the original 1 nm data and the interpolated 1 nm data, as shown

4.3 Materials and methods 63

Table 4.5: Color difference ∆E∗ab for the ASTM weighted and unweighted data, total

of 8764 differences. Color differences were calculated by comparing 10 nm data with 1nm data which was obtained by interpolation.

Weighting Mean Max Std Median 80-percentile

None 0.0065 0.0793 0.0063 0.0046 0.0022ASTM 0.0006 0.0028 0.0004 0.0005 0.0003

Table 4.6: Color difference ∆E∗ab for the ASTM weighted and unweighted data, 8764

differences total. Color differences were calculated by comparing 10 nm data with theoriginal 1 nm data.

Weighting Mean Max Std Median 80-percentile

None 0.0309 0.4331 0.0342 0.0183 0.0271ASTM 0.0310 0.4318 0.0342 0.0183 0.0278

Table 4.7: Color difference ∆E∗ab for the original 10 nm data compared to the ASTM

weighted 10 nm data, 8764 differences in total.

Mean Max Std Median 80-percentile

0.0068 0.0805 0.0063 0.0049 0.0025


in Table 4.8.

Table 4.8: Color difference ∆E∗ab for the original 1 nm data compared to the 1 nm

interpolated data, 8764 differences in total.

Mean Max Std Median 80-percentile

0.0308 0.4319 0.0343 0.0180 0.0276

4.4 Results

It was shown that the use of the ASTM weighting functions in the case of non fluores-cent reflectance spectra of matt color samples may not greatly affect the accuracy oftristimulus integration with different wavelength intervals. However, the results in theFairman paper were shown to depend on the starting point of that research. It can notbe assumed that Lagrange interpolation can reliably accomplish 1 nm reference datafrom the original 10 nm data in every case. Even with our instrument, which provedto perform well in the previous chapter, it is not possible to interpolate correct 1 nmdata from correct 10 nm data. Hence, this becomes even more difficult with the 10 nminterval instruments.

The error of absolute color coordinates of a given reflecting sample is mainly de-pendent on the instrument that is used in the measurement. If accurate color valuesare needed the performance of the instrument must be carefully studied at first, asshown in the intercomparison study presented in the previous chapter. This makes theASTM standard E-308-85 useless, and we recommend it not be used. Furthermore, inmany quality control tasks where no exact absolute values are needed no weighting isneeded either.

Chapter V

Thermochromism

The color of an object depends on the temperature of the object. This phenomena isknown as the thermochromic effect and it may be already noticed at room tempera-ture if the temperature varies a few centigrades. Red and orange samples are especiallysensitive to temperature variation and may cause difficulties in precise color measure-ments. This chapter shows, how the phenomenon is based on physical processes andnot only reflects the instability of red color pigments. Simple formulas are derived,which explain the experimental data. We discuss the meaning of thermochromismfor color measurements, measure the magnitude of it and propose the experimentalconditions to avoid this effect [16,19].

5.1 Background of the study

As pointed out in the previous chapters, accurate color measurements have becomemore and more important during the past few decades. This is valid not only inphysical research, but also in industrial production, where the importance of accuratemeasurements is mainly due to increased quality requirements set by the customersof various goods. The development of technology enables more and more accuratemeasuring systems. While the accuracy has improved one has noticed, that many un-expected factors affect the color of an object. One of these factors is the temperatureof the sample. It is known that, for example, the reflectance of the ceramic referencetiles used for calibration of colorimeters and spectrophotometers is temperature de-pendent. This phenomenon is called thermochromism, which is a reversible changeof color of the sample as a function of temperature. Wyszecki and Stiles state somegeneral principles of thermochromism in the case of transmitting filters [60]. Theyconclude that the spectral transmittance at a given wavelength that increases with in-creasing wavelength usually decreases with increasing temperature. The more positivethe slope of the spectral transmittance curve, the greater the temperature effects as arule. Spectral transmittance that decreases with increasing wavelength is, in general, of

65

66 5. Thermochromism

minor importance, but if it becomes important it often causes a transmittance increasewith increasing temperature. Spectral transmittance curves varying only slightly withwavelength are usually not sensitive to temperature variations. The data sheets forSCHOTT colored glass filters give the shift of the half value of maximum transmit-tance of the rising edge with increasing wavelength towards longer wavelengths in theunits of nm/K [52]. This value gradually increases with increasing wavelength from0.07 nm at 400 nm to 0.17 nm/K at 700 nm. Malkin et al. have studied reflectancespectra of ceramic color standards as a function of temperature [39]. They reportedthat increasing the temperature of a sample caused a fall in reflectance which wasconcentrated in the steeply rising or falling parts of the spectral reflectance. The partof the spectral curve rising with increasing wavelengths was displaced towards longerwavelengths, while the part falling with increasing wavelengths was displaced towardsshorter wavelengths on heating. The slope moves typically 0.1 nm/K. It is worth point-ing out that the reflectance usually decreases as the temperature increases. The longwavelengths reflecting e.g. yellow, orange and red samples are found to be affectedmost, leading to the largest color differences in the CIELAB ∆E values. On the otherhand, neutral samples (grey, white, black) do not exhibit thermochrmism. The rea-son is that the spectral reflectance curves of neutral colors have a small or zero slope.Similar results for color differences of reflectance standards has been earlier reportedby Verrill et. al. [56] and Fairchild and Grum [9]. Instead of the wavelength shiftper nanometer or the color difference per centigrade, a third measure also exists: therelative change of the optical density of the sample as a function of wavelength [55].However, independent of the measure one likes to use, the main point is how much theobserved color depends on temperature.

The aim of this chapter is to derive a simple mathematical model for thermochromism,and to investigate the magnitude of the effect. The experiments done for this investi-gation as well as the published data discussed above confirm our model.

5.2 Absorbance, transmittance, and optical density

One knows from the standard literature that the color of an object under a givenillumination depends on the reflectance or transmittance spectrum of the sample. Re-flectance and transmittance are the only quantities which, through absorbance dependon temperature. In the following, we consider how the spectral properties may dependon temperature, to see if the long wavelength end of the spectrum is affected more thanthe short wavelength end of the spectrum. Luminescent materials might also exhibitthermochromism, but they are not considered in this thesis. When light reaches a sur-face of a nonfluorescent material, where neither nonlinear nor abnormal polarisation

5.2 Absorbance, transmittance, and optical density 67

effects appear, it holds that

1 = R(λ) + A(λ) + T (λ), (5.1)

where R(λ) is reflectance, A(λ) is absorption and T (λ) is transmittance of the sample.In the following, we separately consider transmitting and opaque samples.

5.2.1 Transmitting samples

Let us consider external quantities. Light passing through an absorbing material at-tenuates as

I(λ) = I0(λ)e−µ(λ)d, (5.2)

where I0(λ) is the incoming intensity on the front surface of the sample, I(λ) is theintensity transmitted through the sample, d is the thickness of the sample and µ(λ) isthe absorption coefficient of the sample at wavelength λ. Definitely, µ(λ) is the mainquantity responsible for thermal effect.

We have the following relation between the transmittance and optical density

D = − log(T (λ)) = − log

(I(λ)

I0(λ)

)

= µ(λ)d log e =µ(λ)d

ln 10. (5.3)

Hence, the changes in the absorption coefficient change the optical density, the ab-sorbance and, thus, the transmittance of the sample.

5.2.2 Opaque samples

In the case of a glossy opaque sample, T (λ) is zero and the changes in absorbance di-rectly change the reflectance. Now, the reflected part is comparable to the transmittedpart in transmitting samples and the optical density can be calculated from

D = − log

(IR(λ)

I0(λ)

), (5.4)


where IR(λ) is the reflected intensity.On the other hand, the intensity of light falling upon some material attenuates

exponentially and, in the case of opaque materials, the light reflected from the materialexperiences similar attenuation. Thus, Eq. (5.3) holds for the reflected light if d is thedistance the reflected light has passed in the material.

For translucent materials, the thickness of the material as well as the backgroundover which the sample is viewed affect the reflectance and the opacity of the material.For all matt samples, the scattering properties of the material should be taken intoaccount through the Kubelka-Munk theory, although there is not a requirement fora specimen to be matt for the Kubelka-Munk theory to hold. However, the simpleformulas given above are enough to investigate the thermochromism of the material.

We conclude that, as a good approximation, investigation of the thermal propertiesof absorbance gives correct information on thermochromism for opaque, transmitting,and translucent samples independent of whether the sample is glossy or matt.

5.3 Thermal effects

The depth from which the reflected light is coming is probably not affected by smallchanges in temperature, but if µ(λ) changes as a function of temperature, it also affectsthe reflected light distribution [14]. The absorption in the visible range is causedby low level electron transitions, where an absorbed photon excites an electron fromone energy level to another with higher energy. The general case of an undisturbedabsorbing unit leads to two general solutions, which are of a Lorentzian and Gaussianshape of µ(λ) and, hence, also of the absorption band. The Lorentzian band appearsat low temperatures and the Gaussian at high temperatures. The absorption peakis homogeneously broadened if the absorbing units are indistinguishable. This meansthat the absorption peak is symmetric in the energy scale, and in the frequency scale,but not in the wavelength scale. Because the photon energy ε = hν where ν is thefrequency and h is the Planck’s constant, we will get a very simple relation betweenenergy and wavelength

ε[eV] =1239.8

λ[nm]. (5.5)

Properties of the absorption band are usually given in electron volts. The Gaussianshape of the absorption coefficient and hence the absorption band is [14] given by

µ (ε) = µmax exp

(−4 ln 2 (ε − ε0)

2

(∆ε)2

), (5.6)

5.3 Thermal effects 69

where ε0 is the energy of the absorption peak maximum and ∆ε is the full width athalf maximum absorption (called half width). In Fig. 5.1, an example of the Gaussianpeak is shown as a function of energy. Here ε0=2.5 eV and ∆ε=0.4 eV. This meansthat the left half width point (ε−1/2) is at energy 2.3 eV and the right half widthpoint (ε+1/2) corresponds to the energy 2.7 eV. In Fig. 5.2, the change of equi-energy

1.5 2 2.5 3 3.5

0

0.05

0.1

0.15

0.2

0.25

Energy [eV]

Abso

rbance

ε0

ε−1/2 ε+1/2

∆ε

Figure 5.1: Example of a Gaussian peak where ε=2.5 eV and ∆ε=0.4 eV. The positionsof the left and the right half width points are also shown.

absorbance peaks from the energy scale to the wavelength scale is demonstrated. Ifthermal changes appear in the absorption band, they appear so that the integratedabsorption, which is the area of the absorption band, remains constant. In the case ofboth line shapes this means that ∆εDmax remains constant. Here, Dmax is the peakheight. Gebhardt and Kuhnert first reported the change of the absorption bands asa function of temperature [14]. The general behaviour of ∆ε at low temperatures(near room temperature) is found to be proportional to T 1/2, where T is the absolutetemperature in Kelvin. Thus, the temperature change from 20◦C to 40◦C (from 293K to 313 K) causes that ∆ε of the absorption band becomes 1.034 times broader andthe peak height 1/1.034 = 0.968 times lower. In addition the peak maximum tends tochange towards smaller energies i.e, longer wavelengths as the temperature increases.This increases the change of rising edge towards longer wavelengths and decreases thechanges of falling edge towards shorter wavelengths. The effect of this phenomenonis usually small and the change of the position of absorption bands is not taken intoaccount in this study. The discussion above is valid only to a single absorption line.Generally, a color spectrum in the energy-absorbance scale might be considered as


1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Energy [eV]

Abso

rbance

400 450 500 550 600 650 700 750 8000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Wavelength [nm]

Abso

rbance

Figure 5.2: Absorbance peaks changed from energy scale to wavelength scale.

a linear combination of Gaussian peaks given by Eq. (5.6). Figs. 5.3 and 5.4 giveexamples of two different spectra, which are formed from a few Gaussian absorbancecurves.

These figures demonstrate how Gaussian absorption lines form absorbance spectrain the energy scale, how they convert to the wavelength scale, and finally what theresulting transmittance is in the wavelength scale. Note, that single absorption linesare not symmetric in the wavelength scale. The rising and falling edges of a spectrum


1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2

0

0.5

1

1.5

2

2.5

Energy [eV]

Abso

rbance

400 450 500 550 600 650 700 750 800

0

0.5

1

1.5

2

2.5

Wavelength [nm]

Abso

rbance

400 450 500 550 600 650 700 750 800

0

0.2

0.4

0.6

0.8

1

Wavelength [nm]

Tra

nsm

itta

nce

Figure 5.3: An example on the formation of the absorption and transmittance spectrafrom three individual Gaussian Peaks.


1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2

0

0.5

1

1.5

2

2.5

Energy [eV]

Abso

rbance

400 450 500 550 600 650 700 750 800

0

0.5

1

1.5

2

2.5

Wavelength [nm]

Abso

rbance

400 450 500 550 600 650 700 750 800

0

0.2

0.4

0.6

0.8

1

Wavelength [nm]

Tra

nsm

itta

nce

Figure 5.4: An example on the formation of the absorption and transmittance spectrafrom three individual Gaussian Peaks.


may be thought to consist of a single Gaussian peak. Thus, to understand the generalprinciples of thermochromism it is enough to study the properties of a single Gaussianabsorbance peak instead of a linear combination of them. The peaks forming the edgeshave the major influence on the thermal properties of a spectrum whereas the otherpeaks have a minor effect or none at all.

Let us consider in detail the properties of Gaussian absorbance curves. Absorbanceand optical density in the energy scale are

D(ε) = Dmax exp

(−4 ln 2(ε − ε0)

2

(∆ε)2

)(5.7)

where Dmax = µmaxd/ ln 10. In the visible range (1.59–3.3 eV) one can integrate theabsorption peak, and the result is area

A = Dmax

√π

4 ln 2∆ε. (5.8)

If the temperature changes, A remains constant and ∆ε = u√

T , where u is a constantand T is given in Kelvins. Let ∆ε0 be the halfwidth of the peak at a temperature T0.Then at another temperature T the left and right halfwidth points ε±1/2 as a functionof temperature are

ε±1/2(T ) = ε0 ± ∆ε0

√T

T0

. (5.9)

Thus, the shift of the halfwidth points is

δε±1/2(T ) = ε±1/2(T ) − ε±1/2(T0)

= ±1

2∆ε0

(√T

T0

− 1

)

≈ ±1

4∆ε0

∆T

T0

, (5.10)

where T = T0 + ∆T . The approximation at the last line of Eq. (5.10) is quite valid upto ∆T = 30 K.


Let us next derive the shift formula in the wavelength scale, where the absorptionbands are not symmetric. Let λ±1/2(T ) be the wavelengths corresponding to the pointsε±1/2(T ). One can easily confirm that

1

λ±1/2(T )=

1

λ0

± 1

2

∆ε0

hc

√T

T0

, (5.11)

where λ0 is the wavelength corresponding to the peak maximum. The shift of the slopeis

δλ±1/2(T ) = λ±1/2(T ) + λ±1/2(T0)

=k

(λ±1/2(T0)

)2

1 − kλ±1/2(T0), (5.12)

where,

k = ±1

2

∆ε0

hc

(1 −

√T

T0

). (5.13)

Eqs. (5.12) and (5.13) describe exactly the slope shift in the wavelength scale. How-ever, in many practical situations k is small and one gets from Eq. (5.12) as a firstapproximation

δλ±1/2(T ) ∼= ∓1

4

∆T

T0

∆ε0

hc

(λ±1/2 (T0)

)2. (5.14)

Let us finally calculate the shift of the transmittance curve by determining the shiftof the 50% transmittance points. For these points

1

2= exp (− ln 10D) . (5.15)

Taking into account that√

T0Dmax(T0) =√

TDmax(T ) for two temperatures T0 and Tone can easily show that the half width point reduces to

ε±1/2 (T ) = ε0 ±1

2∆ε0w (T )

√T

T0

, (5.16)

5.4 Numerical results 75

where

w(T ) =1√ln 2

√ln Dmax +

1

2ln

T

T0

+ 1.20055. (5.17)

Thus, one can directly use Eqs. (5.9)–(5.13) for transmittance (or reflectance) curvesby replacing ∆ε0 in these formulas by ∆ε0w(T ).

5.4 Numerical results

We have calculated the change of reflectance and transmittance curves by generatingGaussian absorption bands with different heights and half widths. We have also modi-fied absorbance curves so that the integrated absorption remains constant so that halfwidth and maximum absorbance changes. The position of the peak maximum washeld constant. Modifications corresponded to temperature change from 300 K to 400K. We used 0.2 eV and 0.4 eV as half widths, which are quite typical in solid mate-rials. Maximum absorbance used was 2.0 and 4.0. This value effects the dynamics ofthe transmitting filter. Maximum absorption 4.0 gives four orders of magnitude dy-namics. Absorption curves were then converted to reflectance or transmittance curvesand the change of the rising or falling edge are read from half value of reflectance ortransmittance curves.

Fig. 5.5 shows the absolute shift of the halfwidth points of absorbance peaks asa function of temperature change for three peak widths and two wavelengths. Thesolid lines and the dashed lines correspond the shift of the rising and falling parts ofthe peaks, respectively. The calculations were done using Eq. 5.12. One notes thatshift in nanometers is much higher for the edges in the red region than for a similarpeak in blue region. One also notes that there is a slight difference how the fallig andrising parts of the peaks are moving. The reason is seen from Eq. 5.12. Note thataccording to the approximative formula (Eq. 5.14) positive and negative slope exhibitan equal shift. Figure 5.6 shows the absolute shift of the absorbance half width pointsas a function of wavelength. The reference temperature is 300 K, and the peak widthat this temperature was set to 0.4 eV. The curves a–e correspond the behavior of thematerial when the temperature change is 50–10 K. The solid lines and the dashed linescorrespond the shift of the rising and falling parts of the peaks, respectively. Fig. 5.6shows clearly, that blue samples are not as sensitive as the red samples for temper-ature changes. Again, exact formulas were used to show the difference between thepositive and negative slopes. On the other hand, the approximative formulas, whichdo not show any difference between the negative and positive slopes, are valid only on alimited temperature range. Fig. 5.7 shows the shift of the halfwidth points in nanome-ters/K. The curves were calculated for a temperature change 10 K when the reference


temperature is 300 K. The effect of the peak height and width is demonstrated, too.As can be seen, by increasing the half widths of the absorption band or height of theabsorption peak, the changes in rising and falling edges become bigger.

0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8

9

10

Temperature change [K]

Shift

ofth

ehalfw

idth

poin

ts[n

m]

a

b

c

d

e

f

a) λ = 600 nm, ∆ε = 0.4 eV

b) λ = 600 nm, ∆ε = 0.2 eV

c) λ = 400 nm, ∆ε = 0.4 eV

d) λ = 600 nm, ∆ε = 0.1 eV

e) λ = 400 nm, ∆ε = 0.2 eV

f) λ = 400 nm, ∆ε = 0.1 eV

T0 = 300 K

Figure 5.5: Shift of the halfwidth points as a function of temperature. The solidand dashed curves correspond to the shift of the rising and falling parts of the spectra,respectively.

5.5 Thermochromic measurements

Red colored Pantone� paper samples, red, orange, and yellow Labsphere� secondarystandards and cyan, green, yellow and red ceramic tiles were the samples used in thisstudy. These samples have a common spectral feature: they reflect less or about 10percent for short wavelengths before the steeply rising part of the spectrum. For longwavelengths these samples reflect well over 70 percent. The reflectance measurementsat different temperatures were made on a Perkin Elmer Lambda 18 spectrophotometerequipped with a 150 mm integrating sphere. All of the measurements were made inthe 0/d geometry and in the specular included mode. The scanning speed was 480nm/min, bandwidth 2 nm, and the measuring range 380–780 nm.

Before measuring the thermochromic samples, the errors of the spectrophotometerwere carefully investigated and the instrument were calibrated using the NPL stan-dards. Sample imperfections (size and position of the illuminating beam on the sam-ple) were investigated but found to be negligible in this study. The purpose of thiscalibration procedure was to guarantee that the spectrophotometer is reliable in the

5.5 Thermochromic measurements 77

300 350 400 450 500 550 600 650 700 750 8000

1

2

3

4

5

6

7

8

9

Wavelength [nm]

Shift

ofth

ehalfw

idth

poin

ts[n

m]

a

b

c

d

e

a) ∆T = 50 K

b) ∆T = 40 K

c) ∆T = 30 K

d) ∆T = 20 K

e) ∆T = 10 K

T0 = 300 K, ∆ε = 0.4 eV

Figure 5.6: Shift of the halfwidth points as a function of wavelength. The solid anddashed curves correspond to the shift of the rising and falling parts of the spectra,respectively.

300 350 400 450 500 550 600 650 700 750 8000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Wavelength [nm]

Shift

ofth

ehalfw

idth

poin

ts[n

m/K

]

a

b

c

d

a) ∆ε = 0.4 eV, Dmax = 4 eV

b) ∆ε = 0.4 eV, Dmax = 2 eV

c) ∆ε = 0.2 eV, Dmax = 4 eV

d) ∆ε = 0.2 eV, Dmax = 2 eV

T0 = 300 K, ∆T = 10 K

Figure 5.7: Shift of the halfwidth points in nanometers/Kelvins as a function of wave-length. The solid and dashed curves correspond to the shift of the rising and falling partsof the spectra, respectively.


measurements of the thermochromic effect. The measurements at different temper-atures were made as follows. Pantone� samples were heated with a brass cylinderusing an electric resistor. Labsphere SCS standards were heated with another heatingplate and a thermo resistor system was used with the ceramic tiles. The samples wereheated up to 94 centigrades outside the photometer to avoid heating of the instrument.The temperature of the samples was measured with a calibrated thermopile during thespectral measurements. The average measurment accuracy of the surface temperatureof the samples was less than one degree in all measurements. The repeatability of ourmeasurements became excellent after these calibration and temperature checking pro-cedures. Spectral and colorimetric changes caused by the thermochromic effect werenoticed if the temperature was changed by about two degrees. The corrected spectrawere used to calculate the CIELAB coordinates and the color differences by standardmeans. We need to point out, that although it is well known that CIELAB is notlinear it is generally accepted for the expression of color differences. In this coordinatesystem, an average human eye is able to distinguish ∆E differences higher than 0.5units, as pointed out in the beginning of this thesis.

5.6 Experimental results

Table 5.1 shows the results for a typical Pantone� sample (red 032 U). One can notethat all of the CIELAB coordinates decrease while the temperature increases. Thecolor of this typical paper sample changes 0.093 ∆E units per centigrade. If we definethe wavelength shift observing the reflectance value 50 percent at the steeply growingpart of the spectrum we found that that this part linearly moves towards the longerwavelengths 0.1 nm/deg, which is of the same order as that for the ceramic tiles.Tables 5.2 and 5.3 shows the results for two typical Labsphere secondary standards.One can see decreasing luminance coordinate values with an increase in temperature.Note, that especially in case of the red sample, the color difference compared to thereference temperature increases very rapidly, and in typical living surroundings thecolor change of this kind of samples can be noticed by any person with normal colorvision. The average ∆E/deg change of the red and orange samples was 0.107 and 0.088∆E/deg, respectively. The color change of our yellow samples was clearly smaller.The wavelength change of the red, orange, and yellow sample was 0.11, 0.09, and 0.06nm/deg, respectively. Both the wavelength change and the color difference change arelinear functions of temperature on the temperature range measured.

In Table 5.4 the results of the thermochromic measurements of the ceramic tiles ofcyan, green, yellow and red are shown. Calculated changes for the wavelength shift forthe rising edge were approximately 0.05, 0.12, 0.18 and 0.15 nm/K, respectively. Fig.5.8 shows the measured reflectance spectra for the red ceramic tile at temperatures27◦C–80◦C.

5.7 Conclusions 79

Table 5.1: CIELAB values for the Pantone Red 032 U sample at four temperatures[◦C]. Color difference ∆E was calculated from the lowest temperature curve.

Temperature[◦C] L∗ a∗ b∗ ∆E

28 55.75 58.42 27.6335 55.46 58.17 27.26 0.5340 55.20 57.98 26.88 1.0345 55.00 57.78 26.55 1.46

Table 5.2: CIELAB values for the red Labsphere secondary standard SCS-R-010 sampleat six different temperatures [◦C]. Color difference ∆E was calculated from the lowesttemperature curve.


26 47.31 50.38 25.5330 47.40 49.76 25.04 0.8035 47.04 49.51 24.75 1.2040 46.79 49.27 24.43 1.6545 46.65 48.92 24.11 2.1450 46.46 48.50 23.68 2.77

5.7 Conclusions

The magnitude of the thermochromic effects of transmitting and reflecting materialshas been calculated. If only the change of half width of the absorption curve as afunction of temperature is considered, we will obtain the result that the rising edge withincreasing wavelength shifts towards longer wavelengths and the falling edge towardsshorter wavelengths. The greater the slope (high absorbance) is, the bigger the change


Table 5.3: CIELAB values for the orange Labsphere secondary standard SCS-O-010sample at six different temperatures [◦C]. Color difference ∆E was calculated from thelowest temperature curve.


26 65.28 53.60 52.6830 65.10 53.74 52.55 0.2635 64.83 53.89 52.20 0.7240 64.65 53.98 51.63 1.2745 64.45 54.06 51.28 1.6950 64.29 54.17 51.02 2.02

Table 5.4: CIELAB ∆E color difference values for the ceramic tiles at six differenttemperatures [◦C]. Color difference ∆E was calculated from the lowest temperature.

Cyan Green Yellow Red

T [◦C] ∆E T [◦C] ∆E T [◦C] ∆E T [◦C] ∆E

27 28 28 2738 0.45 40 0.95 40 1.73 39 1.2648 0.83 50 1.47 50 2.95 52 3.1462 1.39 60 2.17 60 4.03 60 3.9072 1.67 70 2.77 70 5.08 68 4.8082 1.99 83 4.24 80 6.41 80 6.17

is. If we take into account the shift of the peak position this enhances the shift ofthe rising edge and diminishes the change of falling edge. In some cases, the effect ofpeak a position change towards longer wavelengths can be greater than a shift in the

5.7 Conclusions 81

400 450 500 550 600 650 700 7500

10

20

30

40

50

60

70

80

90

Wavelength [nm]

Refl

ecta

nce

[%]

600 605 610 615 620 625 630 635 64040

41

42

43

44

45

46

47

48

49

50

Wavelength [nm]

Refl

ecta

nce

[%]

Figure 5.8: Curves from left to right represent the reflectance spectra of a red ceramictile measured at temperatures of 27, 39, 52, 60, 68 and 80◦C, respectively.

falling edge towards longer wavelengths. This can happen if the slope of the fallingedge is small (low absorption) and total shift can be even towards long wavelengths asproposed by Wyszecki and Stiles [60]. In the case of a rising edge the shift is alwaystowards longer wavelengths. The changes become bigger as the wavelength increases.This means the biggest color differences occur for yellow, orange and red samples asfound in other studies.

In conclusion the thermal shift of a transmittance or reflectance curve edge is di-rectly proportional to the temperature change and the slope of the spectrum as well asdirectly proportional to the square of the wavelength. Because of thermochromism, newrecommendations for color measurements require the temperature during measurementto be set to a predefined temperature e.g. (25 ± 1)◦C.

Chapter VI

Conclusions

Surface color measurement is of importance in a very wide range of industrial appli-cations including paint, paper, printing, photography, textiles and plastics. For de-manding color measurement the spectral approach is often needed. The most accuratemeasurements of non fluorescent surface color are made with a spectrophotometer. Themethod used internationally for specifying color has been recommended by the CIE.These recommendations were shortly described and presented in this thesis.

The human eye can perceive color difference as small as 0.5 CIELAB units and thusdistinguish millions of colors. This 0.5 unit difference should be a goal for precise colormeasurements. By the CIE recommendations the only geometry for reflectance mea-surement is 0/d geometry, other geometries give only values of reflectance factors. Theuse of a 0/d geometry will require the use of an integrating sphere to collect reflectedflux. In practical color measurement situations, an integrating sphere is never idealbut hemispherical. Thus, absolute reflectance can not be collected either, ideally. Inthis thesis, methodologies for measuring and correcting errors in color measurementsare discussed. These results are part of the European surface color measurement har-monisation project. It was shown that it is possible to improve upon the agreement ofcolor measurement results where 16 samples of the same colors were measured in ninelaboratories of EU countries.

The sampling interval in a tristimulus integration affects the accuracy of a colorcoordinate performance. In a publication of the American Society for Testing andMaterials, ASTM, in its method E-308-85 a method for the preparation of weightsets for any measurement interval or wavelength range by Lagrange interpolation fromstandard tables of data at other intervals is described. This method is recommendedby the CIE, although it is not included in CIE recommendations. In this thesis, thisASTM method is tested with a large set of non fluorescent reflectance colors fromthe Munsell and Pantone basis. The usefulness of this method was found to be quiteminimal and we recommended not to use it.

82

83

The color of an object depends on the temperature of the object. This phenomenais known as the thermochromic effect and it may be noticed already at room tem-perature if the temperature varies by a few centigrade. Red and orange samples areespecially sensitive to temperature variation and may cause difficulties in precise colormeasurements. In this thesis, it has been shown how this phenomenon is based onphysical processes and, that it does not only reflect the instability of color pigments.Simple formulas are derived, which explain the experimental data. The meaning ofthermochromism for color measurements is also discussed, the magnitude of it is mea-sured and experimental conditions to avoid this effect is proposed to be ±1◦C.

References

[1] ASTM Standards on Color and Appearance measurement, Standard Test Methodfor Computing the Colors of Objects by Using the CIE System, 4th ed., 233–259,(ASTM, Philadelphia, 1994).

[2] J. F. W. Billmeyer and H. S. Fairman, “CIE Method for Calculating TristimulusValues,” Color Research and Application 12, 27–36 (1987).

[3] R. M. Boynton, Human Color Vision (Holt, Rinehart & Winston, New York,1979).

[4] K. M. Braun and M. D. Fairchild, “Testing Five Color-Appearance Models forChanges in Viewing Conditions,” Color Research and Application 22, 165–173(1997).

[5] CIE Publication 15.2, Colorimetry, 2nd Edition, Central Bureau of the CIE, (Vi-enna, 1986).

[6] CIE Publication No 142-2001, CIE Technical Report: Improvement to IndustrialColour-Difference Evaluation, Central Bureau of the CIE, (Vienna, 2001).

[7] F. J. J. Clarke and J. A. Compton, “Correction methods for integrating-spheremeasurement of hemispherical reflectance,” Color Research and Application 11,253–262 (1986).

[8] P. J. Clarke, A. R. Hanson, and J. F. Verrill, “Determination of colorimetric un-cerntainties in the spectrophotometric measurement of colour,” Analytica ChimicaActa 380, 363–367 (1999).

[9] M. D. Fairchild and M. Grum, “Thermochromism of ceramic reflectance tiles,”Applied Optics 24, 3432–3433 (1985).

84

References 85

[10] H. S. Fairman, “The Calculation of Weight Factors for Tristimulus Integration,”Color Research and Application 10, 199–203 (1985).

[11] H. S. Fairman, “Results of the ASTM Field Test of Tristimulus Weighting Func-tions,” Color Research and Application 20, 44–49 (1995).

[12] H. S. Fairman and H. Hemmendinger, “Stability of Ceramic Color ReflectanceStandards,” Color Research and Application 23, 408–415 (1998).

[13] J. Guild, “The colorimetric properties of the spectrum,” Philosophical Transac-tions of the Royal Society A 230, 149–187 (1931).

[14] W. Hayes and A. M. Stoneham, Defects and Defect Processes in NonmetallicSolids (Wiley & Sons, New York, 1991).

[15] J. Hiltunen, T. Jaaskelainen, and J. P. Parkkinen, “Accurate spectral color mea-surements,” Intelligent Robots and Computer Vision XVIII: Algorithms, Tech-niques, and Active Vision, Proc. SPIE 3837, 202–209 (1999).

[16] J. Hiltunen, J. Mutanen, T. Jaaskelainen, and J. Parkkinen, “Thermochromismin color measurement,” in Proceedings of the 9th Congress of the InternationalColour Association (Rochester, 2001), in press.

[17] J. Hiltunen, R. Silvennoinen, T. Jaaskelainen, K. Nygren, and J. Parkkinen, “Re-flectance spectra of pine grown in polluted environment,” in Proceedings of theXXVIII annual conference of the Finnish physical society, M. Hyvonen-Dabek,ed. (Helsinki, 1994).

[18] R. W. G. Hunt, Measuring Colour (Ellis Horwood Ltd., Chichester, 1987).

[19] J. Hiltunen, P. Silfsten, T. Jaaskelainen, and J. P. S. Parkkinen, “A Qualita-tive Description of Thermochromism in Color Measurement”, Color Research andApplication, in press.

[20] T. Jaaskelainen, J. Hiltunen, H. Laamanen, and J. Parkkinen, “Accurate Spec-tral Measurement and Reconstruction,” in Proceedings of the Second Interna-tional Symposium on Multispectral Imaging and High Accurate Color reproduction(Chiba, 2000).

[21] T. Jaaskelainen, J. Hiltunen, R. Silvennoinen, K. Nygren, and J. Parkkinen, “Spec-tral forest monitoring on VIS-NIR region,” in International Symposium on Meth-ods and Equipment for Environmental Monitoring (St. Petersburg, 1995).

86 References

[22] T. Jaaskelainen, J. Parkkinen, J. Hiltunen, and M. Hauta-Kasari, “Spectral ap-proach to color and color images,” in Proceedings of the ICO Topical Meeting onOptics for Sustainable Development (Dakar, 2000).

[23] T. Jaaskelainen, R. Silvennoinen, J. Hiltunen, and J. P. S. Parkkinen, “Classifica-tion of reflectance spectra of pine, spruce and birch,” Applied Optics 33, 2356–2362(1994).

[24] D. B. Judd, “Reduction of data on mixture on color stimuli,” Bureau of StandardsJournal of Research 4, 515–548 (1930).

[25] S. J. Kishner, “Effect of spectrophotometric errors on color difference,” Journalof the Optical Society of America 67, 772–779 (1977).

[26] R. G. Kuehni, “Hue Uniformity and the CIELAB Space and Color DifferenceFormula,” Color Research and Application 23, 314–322 (1998).

[27] R. G. Kuehni, “Analysis of Five Sets of Color Difference Data,” Color Researchand Application 26, 141–150 (2001).

[28] R. G. Kuehni, “Color Space and Its Divisions,” Color Research and Application26, 209–222 (2001).

[29] R. G. Kuehni, “From Color-Matching Error to Large Color Differences,” ColorResearch and Application 26, 384–393 (2001).

[30] R. Lenz, M. Osterberg, J. Hiltunen, T. Jaaskelainen, and J. Parkkinen, “Exploringcolor spaces with unsupervised filters and gaussian quadrature,” in Proc. SSABConference (Linkoping, 1995).

[31] R. Lenz, M. Osterberg, J. Hiltunen, T. Jaaskelainen, and J. Parkkinen, “Unsuper-vised filtering of color spectra,” in Proceedings of the 9th Scandinavian Conferenceof Image Analysis (Uppsala, 1995).

[32] R. Lenz, M. Osterberg, J. Hiltunen, T. Jaaskelainen, and J. Parkkinen, “Unsu-pervised filtering of color spectra,” Journal of the Optical Society of America A13, 1315–1324 (1996).

[33] C. J. Li, M. R. Luo, and R. W. G. Hunt, “A Revision of the CIECAM97s,” ColorResearch and Application 25, 260–266 (2000).

[34] M. R. Luo, G. Cui, and B. Rigg, “The Development of the CIE 2000 Colour-Difference Formula: CIEDE2000,” Color Research and Application 26, 340–350(2001).

References 87

[35] M. R. Luo and R. W. G. Hunt, “The Structure of the CIE 1997 Colour AppearanceModel (CIECAM97s),” Color Research and Application 23, 138–146 (1998).

[36] M. R. Luo, M.-C. Lo, and W.-G. Kuo, “The LLAB(l:c) Colour Model,” ColorResearch and Application 21, 412–429 (1996).

[37] J. Luostarinen and J. Hiltunen, “On-line spectral measurement for grading ofbeech parquet blocks,” in Proceedings of the Finnish optics days 1998 (Oulu, 1998).

[38] J. Luostarinen, J. Hiltunen, and K. Paukkonen, “Use of colour data in grading ofbeech parquet blocks,” in 3rd International Wood Scanning Seminar (Skelleftea,1998).

[39] F. Malkin, J. A. Larkin, J. F. Verrill, and R. H. Wardman, “The BCRA-NPLCeramic Standards, Series II - Master spectral reflectance and thermochromismdata,” Journal of the Society of Dyers and Colourists 113, 84–94 (1997).

[40] H. Minato, M. Nanjo, and Y. Nayatani, “Colorimetry and its Accuracy in the Mea-surement of Fluorescent Materials by the Two-Monochromator Method,” ColorResearch and Application 10, 84–91 (1985).

[41] Y. Nayatani, “Examination of Adaptation Coefficients for Incomplete ChromaticAdaptation,” Color Research and Application 22, 156–164 (1997).

[42] Y. Nayatani, H. Sobagaki, K. Hashimoto, and T. Yano, “Field Trials of a NonlinearColor-Appearance Model,” Color Research and Application 22, 240–258 (1997).

[43] NPL report COEMS33, Harmonisation of National Scales of Surface Colour Mea-surements, (Luxembourg, 2000).

[44] Project report EUR 19552EN, Good Practice Guide to Surface Colour Measure-ments, (Luxembourg, 2000).

[45] Report EUR 14982EN, Intercomparison of colour measurements, Synthesis report,(Luxembourg, 1993).

[46] R. Silvennoinen, T. Jaaskelainen, K. Nygren, J. Hiltunen, and J. Parkkinen, “Clas-sification of Reflectance Spectra of Pine, Spruce and Birch,” in First Finnish Con-ference of Environmental Sciences, J. Tuomisto and J. Ruuskanen, eds. (Kuopio,1993).

[47] R. Silvennoinen, T. Jaaskelainen, K. Nygren, J. Hiltunen, and J. Parkkinen, “Re-flectance spectra of pine, spruce and birch grown in polluted environment,” inOptical Methods in Biomedical and Environmental Sciences, H. Ohzu and S. Ko-matsu, eds. (Elsevier Science B. V., Tokyo, 1994).

88 References

[48] R. Silvennoinen, T. Jaaskelainen, K. Nygren, J. Hiltunen, and J. P. S. Parkkinen,“Temporal, spatial and environmental classification of pine reflectance spectra,”Environmental Science and Technology 29, 1456–1459 (1995).

[49] N. I. Speranskaya, “Determination of spectrum colour coordinates for twenty-seven normal observers,” Optics and Spectroscopy 7, 424–428 (1959).

[50] E. I. Stearns and R. E. Stearns, “An example of a method for correcting data forbandpass error,” Color Research and Application 13, 257–259 (1988).

[51] W. S. Stiles and J. M. Burch, “N. P. L. Colour-matching investigation: Finalreport,” Optica Acta 6, 1–26 (1959).

[52] URL: http://www.besoptics.com/html/schott color filters.html (valid15th October 2001).

[53] URL: http://www.ukas.com/pdfs/LAB12.PDF (valid 11th December 2001).

[54] W. H. Venable, “Accurate tristimulus values from spectral data,” Color Researchand Application 14, 260–267 (1989).

[55] J. Verrill, “Advances in spectrophotometric transfer standards at NPL,” in Spec-trophotometry, Luminescence and Colour; Science and Compliance, C. Burgessand D. G. Jones, eds. (Amsterdam, 1995).

[56] J. F. Verrill, J. A. Compton, and F. Malkin, “Thermochromism of ceramic colorstandards,” Applied Optics 25, 3011 (1986).

[57] N. J. Wade, A Natural History of Vision, 2nd ed. (The MIT Press, Cambridge,1999).

[58] B. A. Wandell, “Measurement of Small Color Diffrences,” Psychological Review89, 281–302 (1982).

[59] W. D. Wright, “A re-determination of the trichromatic coefficients of the spectralcolours,” Transactions of the Optical Society 30, 141–164 (1929).

[60] G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, QuantitativeData and Formulae, 2nd ed. (John Wiley & Sons, New York, 1982).

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