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CIELAB
CMCCIELCH
Standard
a*b*
Ligh
tness (L*)
Yellow
Blue
RedGreen
Tolerance ellipsoidsare tightly packed inthe orange region.
Tolerance ellipsoidsare larger in the
green region.
h˚L*
C*
Standard
Lig
htn
ess
Chroma
a*
b*
C*
C*
C*
h˚
h˚
h˚
b* A
B
C
a*
Hue
Chroma
Lig
htn
ess
Tolerance ellipsoid ∆Ecmc tolerance vs. visually acceptableCIELCH tolerance vs. visually acceptableCIELCH tolerance wedge
Numerically correct vs. visually acceptableCIELAB tolerance box
400nm 700nmVisible Spectrum
X-Rite® is a trademark of X-Rite, Incorporated. L10-281 (03/07)
CMC tolerancing is a modification ofCIELCH which provides better agree-ment between visual assessment andinstrumentally measured color differ-ence. The CMC ∆ E calculation definesan ellipsoid, around the standard color,with semi-axes corresponding to hue(SH), chroma (SC) and lightness (SL). Theellipsoid represents the volume ofacceptance and varies in size andshape depending on position in colorspace.
In commercial situations, the amountof color differences that is consideredacceptable is accounted for by applyinga commercial factor (cf) to all dimen-sions of the ellipsoid. In this case,∆ E CMC < cf is considered acceptable.
∆ E CMC = [(∆ L*/ SL)2 + (∆ Cab*/c SC)2
+ ∆ Hab*/SH)2]1/2
CIELCH tolerancing uses polarcoordinates to give direct numericalcolor differences as they relate toHue (∆ H*) and Chroma (∆ C*):
L* = 116 (Y/Yn)1/3 -16C* = (a*2 + b*2)1/2
h˚ab = arctan (b*/a*)∆ L* = LT* - LS*∆ C* = CT* - CS*∆ H* = [∆ Eab*)2 - (∆ L*)2 - (∆ C*)2]1/2
(If X/Xn, Y/Yn or Z/Zn is < .008856,modified formulas are applied.)
(Subscript T indicates trial andsubscript S indicates standard.)
CIELAB Tolerancing
+b*Yellow
-a*Green
+a*Red
-b*Blue
A
C
B
CIELAB tolerancing usesrectangular coordinates basedon the following formulas:
L* = 116 (Y/Yn)1/3 -16a* = 500[(X/Xn)1/3 - (Y/Yn)1/3]b* = 200[(Y/Yn)1/3 - (Z/Zn)1/3]∆ E*ab = [(∆ L*)2 + (∆ a*)2 + ∆ b*)2]1/2
∆ L* = LT* - LS*∆ a* = aT* - aS*∆ b* = bT* - bS*
(If X/Xn, Y/Yn or Z/Zn is < .008856,modified formulas are applied.)
(Subscript T indicates trial andsubscript S indicates standard.)
a*
b*
a*
b*
Samples withinthe ellipsoid are visually acceptable
Samples within the box and not in the ellipsoid are numerically correct but visually unacceptable
CMC TolerancingCIELCH Tolerancing
To learn more about how X-Rite can improve yourcolor management, call (877) 979-7483 ext.309 orvisit xrite.com/industrial.
Hue
90˚+ b*Yellow
A
C*
h˚ h˚
h˚
C*
C* C
B
– a*Green
+ a*Red
– b*Blue
270˚
0˚180˚
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