AATCC 173 CMC：小色差合格率计算

Copyright 2005 American Association of Textile Chemists and Colorists AATCC Technical Manual/2006TM 173-2005311 Developed by AATCC Committee RA36 in 1989; reaffirmed 1990; editorially re- vised and reaffirmed 1991, 2005; re- vised and reaffirmed 1992; revised 1998. Partly related to ISO 105-J03. 1. Purpose and Scope 1.1 The CMC (?:c) formula is a modi- fication of the corresponding CIELAB color-difference formula. It has color- difference symbol Ecmc. Even though use of the CIE 1976 L*a*b* (CIELAB) equa- tion provides industry with a standard means of calculating and communicating color differences of trials from their stan- dards (see 8.1), it is recognized that CIELAB color-difference values (E*) correlate poorly with visual assessments. The lack of correlation is caused by the non-uniformity of CIELAB color space (see Fig. 1). Significantly improved cor- relation between visual assessments and instrumentally measured color differ- ences is given by the CMC (?:c) color- difference formula (see 7.1 to 7.3). The improvement in correlation between vi- sual and instrumental color-difference re- ports yielded by the CMC (?:c) equation will usually permit the adoption of a sin- gle-number tolerance for judging the ac- ceptability of a color match in most situa- tions, regardless of both the color of the standard and the direction of the color difference of any trial from it. Another equation, CIE94 has been considered, but it has not shown any significant improve- ment over CMC (see 8.2). 1.2 The CMC (?:c) formula retains, in modified form, the partitioning of overall color difference into differences in light- ness, chroma, and hue components (see Fig. 2) which is present in the CIELAB color-difference formula. Using the ellip- soidal semi-axes (?SL, cSC, and SH) makes the CMC (?:c) equation suitable for a wide range of uses. 2. Principle 2.1 The CMC (?:c) modification to CIELAB provides a unit of measurement for the acceptance volume about a stan- dard color. This volume takes the shape of an ellipsoid whose semi-axes are ?SL, cSC, and SH in the directions of lightness, chroma, and hue differences, respec- tively, in CIELAB color space. The CMC (?:c) formula varies the ratio of the lengths of these three semiaxes system- atically throughout CIELAB color space according equality of lengths with visu- ally equal color differences, regardless of both the color of the standard and direc- tion of difference of any trial from it. Around any given standard color, the ra- tio SL:SC:SH is fixed regardless of the end use of the trials. 3. Terminology 3.1 CIE 1976 L*a*b* equation, n. a commonly used equation which trans- forms CIE tristimulus values into a three- dimensional opposed color space. Gener- ally abbreviated as CIELAB (see 8.1). 3.2 CMC unit, n.in color difference evaluation, a measure of acceptability ex- pressed in terms of the boundary for the CMC acceptability ellipsoid of Ecmc = 1.0. 3.2.1 CMC is an acronym for the Colour Measurement Committee of The Society of Dyers and Colourists which was largely responsible for the develop- ment of the CMC (?:c) equation. 3.3 commercial factor (cf), n.in color difference evaluation, a tolerance (specified in terms of Ecmc units) which adjusts all axes of the unit CMC volume equally to create a volume of acceptance for commercial use. 3.4 Ecmc, n.in color difference eval- uation, a single number defining the total color difference in CMC units of a trial from a standard. AATCC Test Method 173-2005 CMC: Calculation of Small Color Differences for Acceptability Fig. 1CMC(? ?:1) Unit ellipsoid cross sections in CIELAB a*b* diagram. If CIELAB were uniform, these sections would be equal-sized circles. Fig. 2Unit volume of acceptance. Distance from standard to surface is one CMC(? ?:c) unit. Copyright 2005 American Association of Textile Chemists and Colorists 312TM 173-2005AATCC Technical Manual/2006 3.5 semi-axes (? ?SL, cSC, and SH), n. in color difference evaluation, individual dimensions of the CMC volume which are used to calculate a Ecmc value. 3.6 volume of acceptability, n.in color difference evaluation, the volume of the ellipsoid obtained when each semi- axis (?SL, cSC, and SH) is multiplied by cfcreating an agreed upon volume de- scribing the limits of commercial accept- ability for the color difference about a standard. 4. Procedure of Calculation 4.1 Calculation of CIELAB values. 4.1.1 Calculate the CIELAB L*,Cab*, and hab values from the CIE tristimulus values X, Y, Z of each specimen using equations 1, 2, 3 and 4: L* = 116 (Y/Yn)1/3 16(1) if Y/Yn 0.008856 but L* = 903.3 (Y/Yn)(2) if Y/Yn 0.008856 a* = 500f(X/Xn) f(Y/Yn) b* = 200f(Y/Yn) f(Z/Zn) where f(X/Xn) = (X/Xn)1/3 if X/Xn 0.008856 but f(X/Xn) = 7.787(X/Xn) + 16/116 if X/Xn 0.00856 f(Y/Yn) = (Y/Yn)1/3 if Y/Yn 0.008856 but f(Y/Yn) = 7.787(Y/Yn) + 16/116 if Y/Yn 0.008856 f(Z/Zn) = (Z/Zn)1/3 if Z/Zn 0.008856 but f(Z/Zn) = 7.787(Z/Zn) + 16/116 if Z/Zn 0.008856 C*ab = (a*2 + b*2)1/2(3) hab = arct