DIN ISO 18314-2-2017 Analytical colorimetry - Part 2 Saunderson correction solutions of the Kubelka-Munk equation tinting strength hiding power (ISO 18314-2 2015)《分析比色法 第2部分 Saunde.pdf

1、April 2017 English price group 12No part of this translation may be reproduced without prior permission ofDIN Deutsches Institut fr Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).ICS 87.060.10!%c| 0 and x - x0 090 0 a

2、nd x - x00DIN ISO 18314-2:2017-04 13 a() are factors:aa KWKW KW() ()=+ +01 2323(33)Tables of coefficients K1, K2, and K3for standard shade depths 1/1, 1/3, 1/9, 1/25, and 1/200 are given in Annex A for standard illuminant D65 and a 10 standard observer and in Annex B for standard illuminant C and a

3、2 standard observer.W =0100(34)0is the closest angle in the table below the hue angle (in degrees). The coefficients K1, K2, and K3of 0are used in Formula (33).From Formula (6) and the Saunderson-corrected reflectance R()* for the test sample, calculate the corresponding Kubelka-Munk functions F() f

4、or the test and reference samples. Adjust the B values for the white reductions of the test and reference samples to the specified standard shade depth by varying the mass fractions mtand mr, and use the resulting values of mtand mrto determine modified Kubelka-Munk functions F() as follows:FFmmtttt

5、 ()=() (35)FFmmrrrr()=() (36)Solving Formula (6) for R, calculate modified reflectance spectra R()* from these modified Kubelka-Munk functions F() and subject the spectra to an inverse Saunderson correction (see Clause 3) to obtain modified R() that include surface effects. From these spectra calcul

6、ate the B values for the white reductions of the test and reference samples.Vary the mass fractions mtand mrindependently of one another, preferably by an iterative mathematical procedure, until the shade depth of the white reductions of the test and reference samples equals that of the specified st

7、andard shade depth, i.e. until:Bt= 0 for mt andBr= 0 for mrThen calculate the relative tinting strength from:Cmmrelrt=100 (37)Calculate the residual colour difference (see Reference 6) from those reflectance spectra Rt() and Rr() for the test and reference samples that result in equalization of the

8、shade depth.6 Determination of hiding power of pigmented media6.1 GeneralThe hiding power value indicates what area, in square metres, of a given contrast substrate can be coated with the unit of quantity of the sample in such a manner that a specified hiding criterion is achieved. The hiding criter

9、ion shall be an agreed colour difference between the two contrasting areas of the coated contrast substrate. A Eab*=1 is commonly applied. For achromatic coatings, a contrast ratio of 0,98 is used to take into account the 2 % threshold value for brightness perception by the human eye. DIN ISO 18314-

10、2:2017-04 14 The substrates have of course to be standardized for an exact method of determination. Values of reflectance close to zero for black and 0,8 for white substrates are employed.The parameter determined by all methods is the minimal film thickness hDnecessary to fulfill the criteria used.

11、The reciprocal of this parameter is equivalent to hiding power value D = 1/hD.The hiding power value can be determined and specified in the following ways: hiding power value Dvin square metres per litre; hiding power value Dm, in square metres per kilogram.Dvand Dmeach indicate the area of the cont

12、rast substrate concerned, in square metres, which can be coated with 1 l or 1 kg of the pigmented medium so as to ensure hiding (in the sense of the hiding criterion).Colourimetric methods for the determination of the hiding power use the general solutions for the Kubelka-Munk equation in combinatio

13、n with an iterative program to determine the necessary film thickness to fulfill the hiding power criteria chosen. This is the most straightforward way leading to the best results.It is possible to work with two non hiding layers on white and black substances or with a hiding layer in combination wi

14、th a non hiding one on a black or white substrate. The method should preferably be determined by reviewing the data available.6.2 Example for white or light coloured paints with a contrast ratio of 0,98 as hiding power criterionThe following equations specify a method applicable for white and light-

15、coloured paints where the colour differences between black and white substrates is determined by the lightness differences. In such cases R() can be replaced by R(Y) with R(Y) being the tristimulus value Y divided by 100.The following equations give the reflectance over a black R(Y)B* and white R(Y)

16、* substrate:RYYRYY YSYh*()1a( )()b() cothb( ) ()B=+0*(38)RYRY YY YSYhYRYY*()1()a( )b()cothb()()a( )()b()co=+00*tthb()()YSYh(39)A reflectance of 0,8 is assumed as RY()0*. So RY RY()B*/() is with a contrast ratio of 0,98:RYRYaY YYSYhaY bY*()()() 0, b( )cothb( )( )() ()cothB0,98=+8 b()() ()()coth ()()

17、)YSYh aY bY bY SYh09809810809, ,( ,+= 8 (40)this can be solved tohbY SYVYY098,=+1()()arccoth0,02 ()1,568 b( )(41)DIN ISO 18314-2:2017-04 15 withVY aY aY() 3,136 ()10,981 0,8( )2,5084= (42)The equations above give a result ofDYYSYVYbY()b( )( )arccoth0,02 ()1,568 ()=+(43)a(Y), b(Y), and S(Y) have the

18、same meaning as defined in Formulae 12 to 15.7 Repeatability and reproducibilityTypically the choice of the correct sampling and the preparation of the test specimen have influences on the result of the measurement far superior to those of the calculation applied. It shall be ascertained by suitable

19、 measurements and checked by mathematical analysis (error propagation) that the parameter determined are valid.8 Test reportThe equations outlined in the text above shall be properly cited in the national and international standards in which they are used so that the influence on the test results ca

20、n be investigated in case of interest.DIN ISO 18314-2:2017-04 16 Annex A (normative) Tables of coefficients for calculating a() values (standard illuminant D65 and 10 standard observer)The coefficients for different standard colour depths (SD) are given in Tables A.1 to A.5 for standard illuminant D

21、65 and 10 standard observer.Table A.1 1/1 SDRange 0a(0) K1K2K31 0,0 2,250 1,850 34 8,681 15 -11,632 82 60,0 3,973 1,512 13 -6,235 96 3,898 743 156,0 3,127 -1,218 51 5,390 38 -8,918 094 224,0 1,987 -4,006 96 -47,812 5 284,0235 240,0 1,285 7,426 88 -17, 554 7 8,955 086 268,0 2,185 0,822 426 0,741 241

22、-2,732 097 340,0 2,142 -1,032 000 8,056 27 -0,828 125Table A.2 1/3 SDRange 0a(0) K1K2K31 0,0 2,040 1,801 64 9,156 25 -12,686 52 52,0 3,669 1,445 9 -3,590 46 2,000 063 140,0 3,524 1,218 93 -8,803 59 7, 202 394 196,0 2,710 -0,562 195 -9,452 64 1,992 195 236,0 1,101 -4,187 35 16,971 7 118,6726 252,0 1,

23、351 7,984 62 -9,832 03 -14,277 37 276,0 2,504 1,549 35 -3,910 61 1,621 258 340,0 2,319 -2,578 89 -4,038 09 50,031 2Table A.3 1/9 SDRange 0a(0) K1K2K31 0,0 2,345 -0,634 155 11,219 2 -7, 883 792 52,0 3,94 2,405 70 -4,966 34 2,477 123 148,0 3,864 -1,289 06 1,005 37 -3,893 84 224,0 1,756 -4,939 51 -20,8

24、8 96 188,1175 244,0 1,438 5,801 15 -1,049 80 -12,962 96 280,0 2,785 1,678 51 -3,350 52 1,463 817 336,0 2,932 -1,5271 -15,6045 49,1836DIN ISO 18314-2:2017-04 17 Table A.4 1/25 SDRange 0a(0) K1K2K31 0,0 2,36 -3,051 67 11,086 4 30,080 12 28,0 3,035 8,938 35 -15,294 9 -9,648 443 56,0 4,126 8 -0,280 82 5

25、,083 5 -1,574 24 96,0 4,727 1 2,575 28 -6,646 51 2,610 055 148,0 4,636 -2,087 2 0,127 93 -3,271 976 224,0 1,687 3 -5,801 28,726 2 27, 294 17 244,0 1,894 5 6,096 1 -8,308 59 2,313 488 292,0 3,162 2 0,668 99 -3,245 85 0,796 387Table A.5 1/200 SDRange 0a(0) K1K2K31 0,0 5,68 -9,194 58 -19,978 5 95,984 4

26、2 28,0 3,646 -0,990 845 12,063 -1,349 613 80,0 6,203 14,131 8 -49,884 3 56,098 14 120,0 7,46 4 -1,578 55 1,258 79 -4,226 565 208,0 4,17 -8,990 36 23,008 8 15,734 46 232,0 3,555 4,269 04 215,078 -723,8447 248,0 6,779 10,693 2 -40,940 4 58,806 68 280,0 7,935 -0,109 528 0,637 939 -5,004 52DIN ISO 18314

27、-2:2017-04 18 Annex B (normative) Tables of coefficients for calculating a() values (standard illuminant C and 2 standard observer)The coefficients for different standard colour depths (SD) are given in Tables B.1 to B.5 for standard illuminant C and 2 standard observer.Table B.1 1/1 SDRange 0a(0) K

28、1K2K31 0,0 2,162 0 2,114 6 5,668 5 -7,691 42 56,000 3,773 0 2,298 2 -11,750 17,6853 88,000 3,885 0 -1,404 7 0,860 05 -0,547 974 200,00 2,620 5 -0,712 65 -7, 251 0 -6,423 85 228,00 1,711 0 -2,564 8 -57,746 316,036 244,00 1,117 0 3,679 6 -4,184 4 1,542 67 328,00 2,170 0 -1,019 0 4,703 6 -18,6458 344,0

29、0 2,051 0 -1,461 7 15,468 -12,263Table B.2 1/3 SDRange 0a(0) K1K2K31 0,0 1,971 0 1,885 4 7, 213 9 -9,808 12 52,000 3,523 0 0,569 64 -0,973 66 0,380 873 156,00 3,491 0 -0,369 32 -5,514 2 1,481 54 188,00 2,856 0 -2,812 6 -2,376 0 11,2545 216,00 2,130 0 -2,744 4 -25,405 62,6156 252,00 0,771 00 -0,421 1

30、4 70,062 -182,877 276,00 2,177 0 2,798 3 -12,018 17,0208 308,00 2,400 0 -0,492 71 3,156 1 -8,722 09 344,00 2,224 0 -2,955 8 -5,128 9 85,152Table B.3 1/9 SDRange 0a(0) K1K2K31 0,0 2,338 0 -0,899 72 11,961 -10,4902 48,000 3,502 0 5,248 4 -17,432 19,1653 92,000 4,069 0 -0,364 96 0,647 10 -1,417 44 188,

31、00 3,061 0 -1,781 9 -3,783 2 -4,893 65 224,00 1,701 0 -5,831 1 14,461 -12,9416 244,00 1,010 0 4,656 3 -0,212 40 -5,784 27 288,00 2,525 0 1,516 80 -1,577 2 -0,630 628 344,00 2,769 0 -0,853 58 -31,714 125,77DIN ISO 18314-2:2017-04 19 Table B.4 1/25 SDRange 0a(0) K1K2K31 0,0 2,399 0 -3,0667 16,380 -10,

32、9992 24,000 2,454 0 6,050 7 19,039 -87,7633 44,000 3,725 0 6,834 7 -38,741 69,4814 72,000 4,126 0 -0,303 89 5,607 9 5,655 35 104,00 4,788 0 3,503 0 -17, 579 20,2186 144,00 4,671 0 -1,600 6 -3,757 8 2,903 87 196,00 3,231 0 -3,991 8 -3,584 0 -7,414 18 220,00 1,964 0 -8,679 8 27, 377 -17,6339 236,00 1,

33、204 0 3,007 1 4,016 6 -7,156 210 296,00 2,908 0 0,416 89 -1,062 9 -1,298 5Table B.5 1/200 SDRange 0a(0) K1K2K31 0,0 5,781 0 -8,228 8 -7, 562 5 32,1882 20,000 4,090 0 -6,295 0 27,716 -28,7323 56,000 4,075 0 3,927 4 13,590 -14,1484 88,000 6,260 0 6,753 7 -11,422 -22,2585 104,00 6,957 0 2,353 2 -12,454

34、 14,9246 140,00 6,887 0 -2,557 2 4,140 1 -9,962 47 196,00 5,003 0 -4,135 0 -31,582 78,5708 216,00 3,542 0 -4,123 0 16,913 24,6029 232,00 3,416 0 0,285 16 121,20 -299,6910 248,00 5,336 0 19,078 -110,38 311,4411 264,00 6,839 0 4,345 8 -12,814 15,35212 304,00 7, 510 0 -1,007 3 1,254 4 -4,744 613 344,00

35、 7,004 0 -5,101 1 -17,707 10,250DIN ISO 18314-2:2017-04 20 Bibliography1 Brockes A Die Farbe. 9 (1/3). 1960. pp. 53622 VLZ Hans G Industrial Color Testing. Wiley-VCH Verlag. 20013 Kortm G Reflectance Spectroscopy Principles, Methods and Application . Springer Verlag. 19694 ISO 11664-1, Colorimetry P

36、art 1: CIE standard colorimetric observers5 ISO 11664-3, Colorimetry Part 3: CIE tristimulus values6 ISO 11664-4, Colorimetry Part 4: CIE 1976 L*a*b* Colour space7 DIN 53235-1, Testing of pigments Tests on specimens having standard depth of shade Part 1: Standard depths of shade8 DIN 55603:2003, Tes

37、ting of pigments Determination of relative tinting strength and of colour difference on reduction of inorganic pigments using the lightness method9 DIN 55986:1981, Testing of pigments; determination of relative tinting strength and colour difference after colour reduction; colorimetric method10 ISO 787-24, General methods of test for pigments and extenders Part 24: Determination of relative tinting strength of coloured pigments and relative scattering power of white pigments Photometric methodsDIN ISO 18314-2:2017-04 21