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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