7/30/2019 Metamerism Index

1/2

METAMERISM INDEX

Note:

DIN 6172 multiplicative method is used in ColorTools 1.xx, and up to 3.0.5. (older method).

ColorTools 3.1 and newer and Datacolor Tools has both of the DIN 6172 methods included. (the newestmethod is additive).

DIN 6172 Metamerism Index

Algorithms/Equations:

DIN 6172 (August 1990) metamerism index is given the symbol MIT. The general equation for MIT is givenas:

( ) ( ) ( )MTT = + + + + +L L K a a K b b KT T L T T a T T b1 22

1 2

2

1 2

2* * * * * *

A new corrected color coordinate is calculated that is then differenced from the standard.

L L K a a K b b KT T L T T a T T b3 2 3 2 3 2* * * * * *, ,= + = + = +

and

( ) ( ) ( )MTT = + + L L a a b bT T T T T T 1 32

1 3

2

1 3

2* * * * * *

where the correction factors KL, Ka, Kb form an additive correction to the color coordinates of thesamples(sample 1 and sample 2) under the test illuminant (Testlichtart), when the sample pair is not anexact color match under the reference illuminant (Bezugslichtart). Then the additive correction factors aregiven by:

K L L K a a K b bL B B a B B b B B= = = 2 1 2 1 2 1* * * * * *, ,

7/30/2019 Metamerism Index

2/2

In an earlier version of this standard, a multiplicative correction to the tristimulus values of the batch wasrecommended. The multiplicative correction factors are given by:

fX

Xf

Y

Yf

Z

ZX

B

B

YB

B

ZB

B

= = =1

2

1

2

1

2

, ,

The new tristimulus values are:

X f X Y f Y Z f ZT X T T Y T T Z T 3 2 3 2 3 2= = = , ,

L*a*b* values are then calculated for the Test Illuminant and the MI T is again calculated.

The required measurement data are thus:

Reference Illuminant (B) Test Illuminant (T)

Sample 1 X1B Y1B Z1B X1T Y1T Y1T

Sample 1 L*1B a*1B b*1B L*1T a*1T b*1T

Sample 2 X2B Y2B Z2B X2T Y2T Z2T

Sample 2 L*2B a*2B b*2B L*2T a*2T b*2T

Curve Fit

Curve fit is calculated by taking the square root of the sum of the squares (the delta %R) between 2 curves (i.e. the of the squares of the differences between the 2 curves).

Curve fit is a number that will determine how close 2 curves are to being the same shape. The greater the number, t

greater the difference between the 2 curves.

Curve fit is not weighted by the illuminant/observer functions so it will treat all wavelengths equally(400nm has same effect as 550nm).

Compare curve fit to a metamerism index like "MI - Root Mean Square"

This index takes the square root of the sum of the squares (the DE under 3 illuminant/observer conditions) between samples. By using the DE, the curves are weighted by the illuminant/observer condition.