Accurate Color Measurment

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UNIVERSITY OF JOENSUU DEPARTMENT OF PHYSICS V ¨ AIS ¨ AL ¨ A 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

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UNIVERSITY OF JOENSUUDEPARTMENT OF PHYSICSVAISALA LABORATORYDISSERTATIONS 30Accurate Color MeasurementJouni HiltunenACADEMIC DISSERTATIONTo 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 2002Julkaisija Joensuun yliopistoPublisher University of JoensuuToimittaja Timo J a askelainen, Ph.D., ProfessorEditorOhjaajat Timo J a askelainen, Ph.D., ProfessorSupervisors Department of Physics, University of JoensuuJussi Parkkinen, Ph.D., ProfessorDepartment of Computer Science, University of JoensuuJoensuu, FinlandEsitarkastajat Mauri Aikio, Dr. Tech.Reviewers VTT ElectronicsOulu, FinlandErik Vartiainen, Ph.D., DocentDepartment of Electrical Engineering,Lappeenranta University of TechnologyLappeenranta, FinlandVastav aitt aja Harri Kopola, Dr. Tech., ProfessorOpponent VTT ElectronicsOulu, FinlandVaihto Joensuun yliopiston kirjasto, vaihdotPL 107, 80101 JOENSUUPuh. 013-251 2677, telefax 013-251 2691Email: [email protected] Joensuu University Library, exchangesP.O. Box 107, FIN-80101 JOENSUUTelefax +358 13 251 2691Email: [email protected] Joensuun yliopiston kirjasto, julkaisujen myyntiPL 107, 80101 JOENSUUPuh. 013-251 2652, 251 2677, telefax 013-251 2691Email: [email protected] Joensuu University Library, sale of publicationsP.O. Box 107, FIN-80101 JOENSUUTelefax +358 13 251 2691Email: [email protected] 1458-5332ISBN 952-458-077-2Joensuun yliopistopaino 2002Jouni Hiltunen; Accurate Color Measurement University of Joensuu, Depart-ment of Physics, Vais al a 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, FinlandAbstractIn 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 uorescent colors and shownto be useless. The thermochromic eect 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.ivPrefaceI am deeply indebted to my supervisors Prof. Timo J a askelainen 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 sta 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, 2002Jouni HiltunenContents1 Introduction 12 Colorimetry 42.1 Background to colorimetry . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 CIE Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.1 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 . . . . . . . . 172.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Measurement of surface color 213.1 General considerations on color measurement . . . . . . . . . . . . . . . 213.2 Intercomparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.3 Errors in surface color measurements . . . . . . . . . . . . . . . . . . . 243.3.1 Errors in absolute scales of diuse reectance and 0/45 radiancefactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3.2 Errors due to diering 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 . . . . . . . . . . . . . 30vvi3.3.10 Dierences in methods of calculating color data from spectral data 303.3.11 Geometry dierences between illumination and collection opticswithin the specied 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 Tristimulus integration 544.1 The ASTM weighting method . . . . . . . . . . . . . . . . . . . . . . . 554.2 Spectral bandpass error . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.3 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645 Thermochromism 655.1 Background of the study . . . . . . . . . . . . . . . . . . . . . . . . . . 655.2 Absorbance, transmittance, and optical density . . . . . . . . . . . . . 665.2.1 Transmitting samples . . . . . . . . . . . . . . . . . . . . . . . . 675.2.2 Opaque samples . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.3 Thermal eects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.5 Thermochromic measurements . . . . . . . . . . . . . . . . . . . . . . . 765.6 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796 Conclusions 82References 84Chapter IIntroductionSurface 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 specic 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 suciently similar to the desired one or whetherthe color is so dierent 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 dierences [58].For demanding color measurement, a spectral approach is denitely needed. Strictlyit is impossible to dene 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 dierences as small as 0.5 CIELAB units and, thus, distinguishmillions of colors. This 0.5 unit dierence should be the goal for precise color measure-ments. This limit is not a problem if we only want to measure the color dierence oftwo samples, but if we want to simultaneously know the exact color coordinate valuesaccuracy problems arise. The values of two instruments can be astonishingly dierent.The best accuracy in color measurement could be achieved by use of a spectropho-tometer. The only geometry for measuring real spectral reectance is normal/diuse(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 reected uxshould 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 accurate12 1. Introductionresults. 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 anecient 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 dierences [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 uorescentspecimen 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 dierences among people. Thus, some standard observers must be specied.The CIE 1931 standard observer is dened for a 2 eld of view by two equivalent setsof color matching functions [5]. The rst 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 rst one and remains positive for all wavelengths. The CIE 1964standard observer has been similarly dened for the 10 eld of view. These sets areused throughout industry.As well as standard observers, standard illumination conditions must be dened asthe form of tables of relative spectral power against wavelength. Illuminant A corre-sponds to the interior illumination by tungsten lament 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 19972000where 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 uorescent colorsand found to be useless. The results are rst time reported in this thesis and willbe published later. The thermochromic eect is discussed in detail and measured inChapter V. The rst idea of this phenomenon comes from the co-authors J a askelainen3and 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, 2123, 3032, 37, 38, 4648] but the topic of this thesis wasthe rst phase: How to measure spectral data accurately.Chapter IIColorimetryThe specication of basic standards used in colorimetry are based on denitions ofthe Commission Internationale de lclairage (CIE) by general consent in all countries.The rst 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 briey 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 colorimetryAt 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 scientic laboratories but therewas not color specication system that could be considered satisfactory for generalpractice. Later, it was agreed that eorts 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 rst majorrecommendations were made which laid the basis for modern colorimetry (CIE 1931).There was a total of ve recommendations. Recommendations 1, 4 and 5 establishedthe CIE 1931 standard observer and a colorimetric coordinate system, recommendation42.1 Background to colorimetry 52 specied three standard sources (A, B and C) and recommendation 3 standardizedthe illuminating and viewing conditions for the measurement of reective surfaces andthe standard of reectance in the form of a magnesium-oxide surface.The CIE 1931 standard colorimetric observer was dened by two dierent butequivalent sets of color-matching functions based on the photopic luminous eciencyfunction V (). These were already adopted by the CIE in 1924 and experimentalwork was carried out by Guild [13] in 1931 and Wright [59] 19281929. The rstset of color-matching functions, r(), g(), b(), was expressed in terms of spectralstimuli of wavelengths 700.0 nm (R), 546.1 nm (G), 435.8 nm (B) (Fig. 2.1), as thereectance 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 7000.40.30.20.10- 0.1Wavelength [nm]TristimulusvaluesrgbFigure 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(), y(), z() (Fig. 2.2), was rec-ommended for reasons of more convenient application in practical colorimetry. Itsderivation from the rst set was based on a proposal by Judd [24] in 1930 and involveda linear transformation. The coecients of the transformation were chosen so as toavoid negative values of x(), y(), z(), 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() is identical to V (). 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. Colorimetry400 450 500 550 600 650 700 75000.20.40.60.811.21.41.61.82Wavelength [nm]TristimulusvaluesxyzFigure 2.2: Color matching functions x, y and z [60].The new color-matching functions, x10(), y10(), z10(), dening the supplemen-tary standard colorimetric observer (CIE 1959) were ocially 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 eld by a direct method which did not involve an appeal to the CIE spectralluminous eciency 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. Manydierent 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 ocially 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 dierence formulae.These spaces are known as the CIE 1976 Luv color space and the CIE 1976 Labcolor 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 dierences are concerned [4,26,36,41,42].2.2 CIE Recommendations 7Among 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 [2729, 33, 35].For the color dierence evaluation, a new color dierence 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 RecommendationsThe terminology of the original recommendations has been altered to be consistent withmodern nomenclature and in some cases the original recommendations have also beenmodied in contents to bring them into line with present day thinking and practice.The recommendations are divided into the following ve 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 dataIlluminants for colorimetryStandard illuminants such as Illuminant A, B, C and D65 are recommended illuminantsfor color calculations. Here illuminant refers to a specic spectral power distribution,1According to The 9th Congress of the International Colour Association, June 2429, 2001,Rochester, NY.8 2. Colorimetrynot 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 Plancks 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 800Wavelength [nm]Radiantpower[a.u.]CCB BAAFigure 2.3: Standard illuminants A, B and C. The radiant power has been normalizedto the same value at 550 nm [60].Sources representing illuminantsIt is recommended that the following articial sources are used to realize the illuminantsdened above. Standard illuminant A is to be realized by a gas-lled tungsten lament2.2 CIE Recommendations 9400 500 600 700 800Wavelength [nm]Radiantpower[a.u.]D55D55D65D65D75D75Figure 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 lterconsisting of a layer of agreed solutions. At present, no articial sources have beenrecommended to realize illuminant D65 or any other D illuminants of various correlatedcolor temperatures.Standard of the reflectance factorThe perfect reecting diuser is recommended as a reference standard in 1986 in publi-cation CIE Standard Colorimetric Observers. It is dened as the ideal isotropic diuserwith a reectance 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 reecting diuser.Illuminating and viewing conditions for a reflecting specimenCIE recommends the use of one of the following illuminating and viewing conditions:45/normal , normal/45, diuse/normal and normal/diuse. 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 eective10 2. Colorimetryaxes are at the angle of 452 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 45/0Figure 2.5: Viewing geometries of 0/45 and 45/0.If the sample is illuminated diusely 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 reectingsphere 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 reected ux 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 baesto prevent light passing directly between the sample and the spot of the sphere wallilluminated or viewed.2.2 CIE Recommendations 11samplebeamdetectorgloss trapor whitesphere capsamplereferencebeamreferencebafflesFigure 2.6: Integrating sphere.In the 0/d and d/0 conditions, specular reection 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 reection. Note that only the 0/d geometry provides a spectral reectance. Theother conditions d/0, 0/45 and 45/0 give a specic radiance factor.Illuminating and viewing conditions for transmitting specimensIt is recommended that the colorimetric specication of transmitting species corre-spond to one of the following illuminating and viewing conditions: normal/normal,normal/diuse and diuse/diuse. 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 whoseeective 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 ux reachesthe detector. This condition gives the regular transmittance, r.In the normal/diuse (0/d) condition, the specimen is illuminated by a beam whoseeective 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 ux is usually measured with an integrating sphere. Thereectance of the sphere reecting surface or other material at the point of impingementof the regularly transmitted beam, or at the point of impingement of the illuminating12 2. Colorimetrybeam in the absence of a specimen, must be identical to the reectance of the remainderof the internal reecting sphere area. This condition gives the total transmittance, .If the regularly transmitted ux is excluded, for example by the use of a light trap, itgives the diuse transmittance, 0/d. If the positions of the light source and detectorare interchanged, the method gives the equivalent diuse/normal (d/0) quantities.In the diuse/diuse (d/d) condition, the specimen is illuminated diusely with anintegrating sphere and transmitted ux is collected using a second integrating sphere.This condition gives the double transmittance, dd.2.2.2 Standard observer dataCIE 1931 standard colorimetric observerIt is recommended that colorimetric specication of color stimuli be based on thecolor-matching functions x(), y(), z() given in the CIE Standard on ColorimetricObservers, whenever correlation with visual color matching of elds 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 signicant digits, and they dene 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 sucient for most applications.CIE 1964 supplementary standard colorimetric observerIt is recommended that colorimetric specication of color stimuli be based on the color-matching functions x10(), y10(), z10() given in the CIE Standard on ColorimetricObservers, whenever correlation with visual color matching of elds 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 signicant digits, and they dene the CIE 1964 standard colorimetric observer.2.2.3 Calculation of tristimulus values and chromaticity coordinatesCalculation of tristimulus valuesThe 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 () 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 by2.2 CIE Recommendations 13numerical summation at wavelength intervals, , equal to 1 nm,X = k

() x() Y = k

() y () (2.1)Z = k

() z () ,orX10 = k10

() x10 () Y10 = k10

() y10 () (2.2)Z10 = k10

() z10 () ,where X, Y , Z are tristimulus values, x(), y(), z(), are color-matching functions ofa standard colorimetric observer, and k is a normalizing constant dened below. Theseequations may be written without or with the subscript 10 to correspond to the CIE1931 or 1964 standard colorimetric system, respectively.For reecting or transmitting object colors, the color stimulus function, (), isreplaced by the the relative color stimulus function, (), evaluated as() = R()S()(2.3)() = ()S(),where R() is the spectral reectance factor (or spectral radiance factor or spectralreectance) of the object color, () is the spectral transmittance of the object color,and S() 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(), or () = 114 2. Colorimetryfor all wavelengths and hencek = 100

S()y()(2.4)k10 = 100

S()y10().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 ecacy. This valueis equal to 683 lumens per watt and () must be the spectral concentration of theradiometric quantity corresponding to the photometric quantity required.The use of abridged or truncated dataThe color stimulus function () 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 dierence 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 specication. 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.2.2 CIE Recommendations 15Calculation of chromaticity coordinatesThe chromaticity coordinates (x, y, z) should be calculated from the tristimulus values(X, Y, Z) as follows:x = XX + Y + Zy = YX + Y + Z (2.5)z = ZX + Y + Z.Because of the relation x + y + z = 1, it is sucient 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 spacingThe CIE 1976 UCS diagramThe 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

= 4XX + 15Y + 3Z (2.6)as abscissa and v

v

= 9YX + 15Y + 3Z (2.7)as ordinate, in which X, Y, Z are tristimulus values. The third chromaticity coordinatew

is equal to 1u

v

. This diagram is intended to apply to comparisons of dierencesbetween object colors of the same size and shape, viewed in identical white to middle-grey surroundings, by an observer photopically adapted to a eld of chromaticity nottoo dierent from that of average daylight.16 2. ColorimetryThe CIE 1976 uniform color spacesThe 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 Luv color space or CIELUV color space is dened by quantitiesL, u, vL = 116_YYn_1/316 when_YYn_> 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 speciedwhite object color stimulus. If Y/Yn is less than 0.008856, the above equations arechanged as follows_YYn_1/3is replaced by 7.787_YYn_+ 16116.The CIE 1976 Lab color space or CIELAB color space is dened by quantitiesLabL = 116_YYn_1/316 (2.11)a = 500__ XXn_1/3_YYn_1/3_ (2.12)b = 200__YYn_1/3_ ZZn_1/3_, (2.13)where X, Y, Z describe the color stimulus considered and Xn, Yn, Zn describe a specicwhite object color stimulus. If X/Xn, Y/Yn or Z/Zn is less than 0.008856, the above2.2 CIE Recommendations 17equations are changed as follows_ XXn_1/3is replaced by 7.787_ XXn_+ 16116_YYn_1/3is replaced by 7.787_YYn_+ 16116_ ZZn_1/3is replaced by 7.787_ ZZn_+ 16116.The dierences Euv or Eab between two color stimuli are calculated as theEuclidean distance between the points representing them in the space:Euv =_(L)2+ (u)2+ (v)2(2.14)Eab =_(L)2+ (a)2+ (b)2. (2.15)2.2.5 Miscellaneous colorimetric practices and formulaeDominant wavelengthThe dominant wavelength of a color stimulus d is a wavelength of the monochromaticstimulus that matches the color stimulus considered when additively mixed in suit-able proportions with the specied 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 speciedachromatic stimulus and the purple line.Complementary wavelengthThe complementary wavelength of a color stimulus c is a wavelength of the monochro-matic stimulus that matches the specic achromatic stimulus when additively mixedin suitable proportions with the color stimulus considered.18 2. ColorimetryColorimetric purityThe colorimetric purity pc is dened by the relationpc = LdLn + Ld, (2.16)where Ld and Ln are the luminances of the monochromatic stimulus and of the speci-ed 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 equationpc = peydy , (2.17)where yd and y are the y-chromaticity coordinates of the considered monochromaticstimulus and the color stimulus, respectively.Excitation purityExcitation purity pe is dened by the ratio NC/ND of two collinear distances on thechromaticity diagram of the CIE 1931 or 1964 standard colorimetric system. The rstdistance is that between point C and N which represents the considered color stimulusand the specied 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 denition leads to the following expressionspe = y ynydynor pe = x xnxdxn, (2.18)where (x, y), (xn, yn), (xd, yd) are the x, y-chromaticity coordinates of the points C, Nand D, respectively.Special metamerism indexTwo specimens having identical tristimulus values for a given reference illuminant andreference observer are metameric if their spectral radiance distributions dier within2.2 CIE Recommendations 19the 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 dierence 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 whitenessAccording to CIE recommendations, the formulae W or W10 for whiteness and TWor 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 dier much in color anduorescence, and that are measured on the same instrument at nearly the same time.W = Y + 800(xnx) + 1700(yny) (2.19)W10 = Y10 + 800(xn,10x10) + 1700(yn,10y10) (2.20)TW = 1000(xnx) 650(yny) (2.21)TW,10 = 900(xn,10x10) 650(yn,10y10), (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 perfectdiuser, 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 diuser W andW10 are equal to 100 and TW and TW,10 are equal to zero.Calculation of correlated color temperatureThe 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. Colorimetry2.3 SummaryThe recommendations of the CIE Colorimetry Committee are given for various col-orimetric practices and formulae such as recommendations for standard illuminants,for the standard reectance factor, for illuminating and viewing conditions, for thestandard colorimetric observers, for the calculation of tristimulus values, chromaticitycoordinates, and color dierences.Chapter IIIMeasurement of surface colorSurface 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 Eab 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 dierence 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 lters 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 reectances 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 measurementInternationally accepted illumination and observation angles should be standardisedfor use in instruments such as normal/diuse 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, ash lamp),one should be aware of uorescent samples. The source has to match a CIE standard or2122 3. Measurement of surface colorrecommended illuminant (A, D65, C etc.) as closely as possible to correctly determinecolor coordinates. If this is not accomplished, the surface color of a uorescent 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 theinstruments calibration standards. The same attention should be paid to integratingsphere coatings as well. Degradation of this coating produces several errors.The instruments 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 reectance standard. The low reectance standard is notas common as the white one. However, it is advisable to use another calibration set toindependently check the instruments performance. Ideally, this set should contain thefollowing elements: a surface mirror, a wavelength standard, two white standards (onematt and one glossy), a zero reectance standard and at least one grey standard withabout 50% reectance. 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 IntercomparisonThe human eye can perceive color dierences approximately 0.5 Eab in CIELABunits. The rst European intercomparison stopped in 1993 [45]. This intercomparisonsought to determine the state of the art of measurements of spectral reectance andcolor specication of surface colors using spectrophotometry. Four laboratories, eachfrom a dierent 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 objective3.2 Intercomparison 23in this project was to harmonise color measurements between 8 national laboratories toachieve a target of 95% agreement within 0.5Eab CIELAB units for non-uorescentcolors. This was achieved through the use of a system for determining and correctingerrors, followed by an intercomparison of non-uorescent surface color measurements.The second objective was to extend the capability for measurement of uorescent safetycolors using the two monochromator method to three countries within the EuropeanUnion, and carry out an intercomparison of uorescent colored materials to meet themetrological requirements of EN471, Specication 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 Cienticas (CSIC), Spain. Bundesanstalt f ur Materialforchung und-Pr ufung (BAM), Deutchland. University of Joensuu (UJ), Finland. Laboratoire National dEssais (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 rst 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 eectiveness of the methodologyfor harmonisation, and to give preliminary results on levels of agreement that mightbe achieved for non-uorescent colors.24 3. Measurement of surface color3.3 Errors in surface color measurementsSpectrophotometric 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 diuse reectance and 0/45 radiance factor. Errors due to diering 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. Dierences 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 dierence between illumination and collection optics within the speci-ed limits.At present, there is no method for quantifying the eects of geometry dierences(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 eective. Thus, it is now clear that there are signicant 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 baes inside the spherewhich prevent straight light from striking the detector.3.3 Errors in surface color measurements 253.3.1 Errors in absolute scales of diuse reectance and 0/45 radiancefactorThe 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 diering properties of white reference standardsWhen 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-linearityA 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 thereectance 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 eectssuch as inter-reection between glass surfaces within the instrument and a reductionin sphere response with dark samples.The simplest type of relationship between the true value of reectance R and theinstrumental value R

is a quadratic form. That means the dierence is biggest at the50% reectance level. Now the photometric non-linearity can be corrected by measuringonly one grey tile, about 50% of the reectance. Denition 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 classiedas the dark level error and, thus, treated separately.Assuming the quadratic relationship for the error we arrive atR = R

+ R= a + bR

+ cR2. (3.1)By this denition we nd that when R = 0 also R

= 0 and a = 0. In the same way26 3. Measurement of surface colorwhen R = 100, R

= 100 also. Now we have the equations100 = 100(b + 100c) (3.2)b = 1 100c. (3.3)For a grey tile, we can denote R = r and R

= r

. Thusr = br

+ cr2= (1 100c)r

+ cr2= r

100cr

+ cr2. (3.4)For a terms of c and b, we can solvec = r

r100r

r2 (3.5)b = 1 100c= 1 100r

100r100r

r2= 100r + r2100r

r2. (3.6)Hence,R =_100r r2100r

r2_R

+_ r

r100r

r2_R2, (3.7)where r is the certied 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 NPLs instruments non-linearitymay have been imposed on all values.3.3 Errors in surface color measurements 273.3.4 Incorrect zero levelAn integrating sphere dark level error is mainly due to light scattered inside the opticsof the spectrophotometer. This eect gives a halo around the main light beam, someof which falls on the sphere wall. There may also be a component due to an electronicoset. 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 reectance readingwith a wavelength. An optical wedge gives a reading k. Absolute diuse reectanceof a sample Ra isRa = aktkRt=a_1 ka_a_1 kt_Rt at_1 ka__1 + kt_Rt at_1 ka+ kt_Rt= atRt + k1_at1_, (3.8)where,k1 = ktRt. (3.9)a in Eq. 3.8 is the sample reading, t is the white standard reading, k is the darkreading and Rt is the calibrated value for a white standard.3.3.5 Wavelength scale errorWavelength error will lead to color errors, so the instruments wavelength scale shouldbe checked. Reectance values should be corrected, according to the expressionR() = Rm() + Rm() , (3.10)where R() is the correct reectance value, Rm is the measured reectance value and is the wavelength scale error, the dierence between the actual and displayed value.28 3. Measurement of surface colorWavelength error can be determined by using several wavelength standards: spectrallamps, reection tiles or transmission lters. The user must use the most appropriatestandard for the instrument type.3.3.6 Specular beam exclusion errorFor 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 reected 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 diuse reectance standard. A calibrated mirrorof reectance M gives a reading gm. In a case where a gloss trap is used to blockspecular reectance, a calibrated mirror M will give a readingg4 = 4Mgm. (3.11)The number 4 is used as a nominal value for the specular reectance of a typical glossysample. Absolute diuse reectance Ra of a sample isRa = ag4tg4Rt, (3.12)where , = 0 for a matt surface and , = 1 for a glossy surface. Using the sameapproximates as for the dark error correctionRa atRt + k2_at_, (3.13)where,k2 = g4tRt. (3.14)Here with the a reading of a sample, t is read when the white standard is measured,and Rt is the calibrated value for a white standard.3.3 Errors in surface color measurements 293.3.7 Specular beam weighting errorFor 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 eciency as the diusely reected light. A calibrated mirror of reectance Mplaced at the sample port gives a reading sm. If there is no specular beam error, themirror would give a readingtMRt, (3.15)where t 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 byem = smtMRt. (3.16)If we apply the nominal value of 4% specular reectance from a typical glossy samplewe arrive at the error in the specular beames = 4M_smtMRt_. (3.17)The absolute reectance Ra of a sample when applying a correction isRa = aestesRt at_1 esa+ est_Rt= atRt + ates_t a_Rt, (3.18)30 3. Measurement of surface colorwhere , = 0 is for a matt surface and , = 1 is for a glossy surface, where thesame approximates are used as before. Substituting es into the above equation we getRa = atRt + at4M_smtMRt__t a_Rt= atRt + 4_smt1M 1Rt__at_Rt= atRt + 4_smtRtM 1__at_= atRt + k3_at_, (3.19)where,k3 = 4_smtRtM 1_. (3.20)In Eqs. 3.19 and 3.20 a is a sample reading, sm is a reading for a calibrated mirrorin a sample port, t 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 spheresThe internal reectance of an integrating sphere will usually vary over its surface. Inaddition, baes included within the sphere lead to a variation in response to the angleof reectance. The reectance 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 geometrySeveral researchers have carried out studies on the eects of polarisation. However, noneed for a correction has arisen in typical surface color samples.3.3.10 Dierences in methods of calculating color data from spectral dataIn 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 dierent intervals.3.4 Measurements and corrections 313.3.11 Geometry dierences between illumination and collection opticswithin the specied limitsThe tolerances given in the CIE geometry specication are suciently large to resultin a wide range of implementation in instrumental design.3.3.12 Errors due to thermochromism in samplesIn 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 1C 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 timeA fast speed scan with slow integration time will generate a dierent result to a slowspeed, fast integration time scan, particularly in the resolution of slopes. The dierencebetween the two resulting spectra might appear as a wavelength shift and particularlyaect the results for the more chromatic tiles. The same is true for an instrument witha dierently shaped spectral bandwidth. The partners were investigating the eects ofthe scan speed and integration time and nally agreed to use same kind of parameters.3.4 Measurements and correctionsA double beam scanning spectrophotometer, Perkin Elmer -18, was used in reectancespectra recording. Measurements were performed with a bandwidth of 2 nm and with ascanning speed of 240 nm/min. The minimum temperature during the measurementswas 22.2C while the maximum was 23.4C. All samples were measured 6 times, 3times in the morning and 3 times in the afternoon after at least a 3 hour interval. Nosignicant dierences were noticed between the results. Error correction factors k1, k2and 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 dierence between the calibrated and the measured values was about0.56%-unit. As a matter of fact, the inuence 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 samples32 3. Measurement of surface colorshould be used. One interesting nding during this intercomparison was that a greytile and a neutral transmittance lter, at about the same level of 50% refelectance, donot necessarily have the same amount of non-linearity error. This was conrmed 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 80000.010.020.030.040.050.06Wavelength [nm]ValueFigure 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 resultsThe 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 reectance 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 33Matt 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 7500102030405060708090100Wavelength [nm]Reectance[%]Figure 3.2: Reectance spectra of a 8 matt color samples.Part of the results of the comparison are shown in the Tables 3.13.17. Table 3.1show the eect 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 dierences 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 dierences 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 that34 3. Measurement of surface colorTable 3.1: CIELAB Colorimetric dierences 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 GeometryTile Rd Rs Rnl Rd Rg RnlGlossy 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 0.273.5 Intercomparison results 35case there will be some uncertainty in all error corrections. From this aspect one cannot directly conclude that smaller dierences are always better.First of all, the purpose of this intercomparison was to harmonise measurementresults between all partners. This means that dierences are calculated from the meanvalue of all measurements. Tables 3.63.9 show the percentage of the measurements ofeach partner below three dierent E limits from the mean. However, there may besome minor disadvantages in this measure as well, since there are some large dierencesamong some colors. This will set the mean value as slightly false and distort the results.36 3. Measurement of surface colorTable 3.2: Partners colorimetric dierences 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 DELTAGlossyPale 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 1.78MattGrey 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 0.78Average|dierence| 0.44 0.38 1.74 0.43 0.71 0.42 0.49 0.833.5 Intercomparison results 37Table 3.3: Partners colorimetric dierences E from NPL for the set of 16 colortiles, specular included geometry. Fully corrected results, 10 degree observer, illuminantD65 [43].Tile UJ LNE BAM CETO CSIC SP BCRA DELTAGlossyPale Grey 0.05 0.31 0.12 0.18 0.20 0.05 0.08 0.24Mid Grey 0.05 0.41 0.37 0.21 0.24 0.07 0.06 0.40Black 0.17 0.33 2.72 0.33 0.57 0.17 0.20 0.28Red 0.72 0.69 2.67 0.42 0.89 0.55 0.82 1.48Bright Yellow 0.33 0.63 1.91 0.67 0.64 0.34 1.01 1.18Green 0.26 0.49 1.08 0.50 0.44 0.40 0.55 0.95Cyan 0.51 0.51 0.97 0.63 0.36 0.52 0.81 0.48Deep Blue 0.42 0.27 3.06 0.23 0.34 0.14 0.33 0.36MattPale Grey 0.13 0.11 0.33 0.09 0.13 0.14 0.06 0.20Mid Grey 0.10 0.20 0.19 0.28 0.10 0.29 0.10 0.47Black 0.16 0.16 1.64 0.21 0.23 0.05 0.08 0.47Red 0.57 0.78 1.84 0.46 2.49 0.46 0.80 1.33Bright Yellow 0.59 0.47 1.34 1.41 0.78 0.47 0.84 1.04Green 0.33 0.18 0.70 0.46 0.31 0.42 0.43 0.62Cyan 0.39 0.39 0.75 0.54 0.19 0.39 0.67 0.21Deep Blue 0.39 0.21 2.17 0.32 0.49 0.27 0.15 0.77Average|dierence| 0.32 0.38 1.30 0.43 0.52 0.30 0.44 0.6538 3. Measurement of surface colorTable 3.4: Partners colorimetric dierences E from NPL for the set of 8 color tiles,specular excluded geometry. Uncorrected results, 10 degree observer, illuminant D65 [43].Tile UJ LNE BAM CETO CSIC SP BCRA DELTAGlossyPale Grey 0.24 0.15 0.08 0.20 0.16 0.28 0.02 0.13Mid Grey 0.51 0.20 0.22 0.22 0.18 0.44 0.06 0.07Black 0.60 1.17 0.65 1.50 0.66 0.66 0.55 0.51Red 1.01 1.15 1.78 2.89 0.92 1.24 0.72 2.17Bright Yellow 0.99 0.48 0.85 0.60 0.59 0.97 0.60 1.08Green 0.66 0.33 0.53 0.22 0.42 0.68 0.64 0.86Cyan 0.57 0.45 0.30 0.63 0.58 0.79 1.16 1.13Deep Blue 1.70 0.98 0.35 0.90 1.48 1.57 0.80 0.90Average|dierence| 0.78 0.62 0.60 0.89 0.62 0.83 0.57 0.863.5 Intercomparison results 39Table 3.5: Partners colorimetric dierences E from NPL for the set of 16 colortiles, specular excluded geometry. Fully corrected results, 10 degree observer, illuminantD65 [43].Tile UJ LNE BAM CETO CSIC SP BCRA DELTAGlossyPale Grey 0.06 0.15 0.25 0.20 0.26 0.04 0.11 0.12Mid Grey 0.16 0.20 0.26 0.33 0.31 0.11 0.18 0.06Black 0.45 1.17 0.53 0.86 0.81 0.26 0.65 0.49Red 0.44 1.15 0.90 0.73 1.07 0.77 0.86 2.10Bright Yellow 0.66 0.48 0.47 0.99 0.72 0.72 0.69 1.09Green 0.54 0.33 0.24 0.64 0.48 0.70 0.64 0.86Cyan 0.56 0.45 0.27 0.73 0.57 0.93 1.07 1.15Deep Blue 0.92 0.98 1.37 1.35 1.64 1.11 0.86 0.98Average|dierence| 0.47 0.62 0.54 0.73 0.73 0.58 0.63 0.8640 3. Measurement of surface colorTable 3.6: Partners colorimetric dierences E from the mean dierence for the setof 16 color tiles, specular included geometry. Uncorrected results, 10 degree observer,illuminant D65 [43].UJ LNE BAM CETO CSIC SP BCRA DELTAAverage|dierence| 0.27 0.32 1.09 0.31 0.22 0.27 0.25 0.20% within 0.2E of mean 56.3 43.8 25.0 37.5 75.0 62.5 43.8 62.5% within 0.5E of mean 75.0 81.3 43.8 75.0 93.8 81.3 93.8 93.8% within 0.75E of mean 87.5 87.5 56.3 93.8 93.8 87.5 100 1003.5 Intercomparison results 41Table 3.7: Partners colorimetric dierences E from the mean dierence for the setof 16 color tiles, specular included geometry. Fully corrected results, 10 degree observer,illuminant D65 [43].UJ LNE BAM CETO CSIC SP BCRA DELTAAverage|dierence| 0.22 0.20 0.78 0.21 0.22 0.26 0.18 0.23% within 0.2E of mean 43.8 50.0 31.3 62.5 75.0 50.0 56.3 50.0% within 0.5E of mean 93.8 100 62.5 81.3 93.8 87.5 100 100% within 0.75E of mean 100 100 62.5 100 93.8 100 100 10042 3. Measurement of surface colorTable 3.8: Partners colorimetric dierences E from the mean dierence for the setof 16 color tiles, specular excluded geometry. Uncorrected results, 10 degree observer,illuminant D65 [43].UJ LNE BAM CETO CSIC SP BCRA DELTAAverage|dierence| 0.26 0.20 0.22 0.37 0.20 0.20 0.29 0.30% within 0.2E of mean 50.0 37.5 62.5 62.5 75.0 62.5 50.0 37.5% within 0.5E of mean 87.5 100 87.5 75.0 87.5 100 87.5 87.5% within 0.75E of mean 100 100 100 87.5 100 100 87.5 1003.5 Intercomparison results 43Table 3.9: Partners colorimetric dierences E from the mean dierence for the setof 16 color tiles, specular excluded geometry. Fully corrected results, 10 degree observer,illuminant D65 [43].UJ LNE BAM CETO CSIC SP BCRA DELTAAverage|dierence| 0.17 0.20 0.20 0.15 0.14 0.15 0.12 0.43% within 0.2E of mean 62.5 50.0 50.0 62.5 87.5 62.5 75.0 50.0% within 0.5E of mean 87.5 87.5 100 100 100 100 100 87.5% within 0.75E of mean 100 100 100 100 100 100 100 87.544 3. Measurement of surface color3.6 Determination of colorimetric uncertaintiesGenerally, the result of a measurement is only a approximation or estimate of thevalue of the specic quantity subject to measurement. Because of increasing demandsof measurement accreditation and quality systems there is a need to quote uncertaintieson all certied 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 diuse reectance 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 diuse reectance or radiancefactor comes from the traceability to the 100% levels. This is taken from a certicateof 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 eect is assessed using a skew of half the scale uncertainty.3.6 Determination of colorimetric uncertainties 45The dark uncertainty is a combination of the electronic oset of the instrument and,for diuse reectance, an optical oset 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 oset reading, because it does not quantify the eects 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 reectance in regions of spectral slope, wherereectance 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 dierences in eciency of collectionof the integrating sphere with angle of reectance. The error can be determined bymeasuring glossy samples against matt samples with dierent integrating spheres.The specularly reected light may not be collected with the same eciency as thediusely reected 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 rst divided by a coverage factor k, 1 or 2, which refers to condence level ofapproximately 65% or 95%, respectively. The total uncertainty was then combined inquadrature from the components of uncertainty asutotal =_(u21 + u22 + . . . ), (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 uncertainty46 3. Measurement of surface color gloss trap uncertainty specular beam uncertaintyUncertainties 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 eect wasneglected cause of agreed temperature limit 1C.All uncertainty components were calculated using the determined errors. If the errorwas corrected for in reectance calculations, the uncertainty was that after correction.If it was not corrected for, the uncertainty was the error itself.In Tables 3.103.12 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 3.133.14 partners colorimetric uncertaintiescombined to give Eab for the intercomparison are shown.3.6 Determination of colorimetric uncertainties 47Table 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 NPLGlossyPale 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 0.02b 0.00 0.5 0.5 0.07 0.75 0.34 0.19 0.2 0.02Mid 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 0.02b 0.00 0.5 0.5 0.04 0.57 0.26 0.34 0.2 0.02Black 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 0.02Red 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 0.13Bright 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 0.11b 0.18 0.8 0.5 1.76 0.55 0.28 1.13 0.2 0.19Green L 0.34 0.5 0.5 0.47 0.17 0.39 0.23 0.5 0.15a 0.00 0.5