Introduction
Color is an important aesthetic aspect of coated objects. Different persons have different perceptions of a specific color. Therefore, it is important to have an objective way to characterize colors of coatings, as well as to quantify differences between colors. The good news is that there is a standard system that is used all over the globe: the CIELAB color system. This article is about the fundamentals of this system.
The CIELAB Color Space
The color of (coated) objects is visualized and quantified by using the CIELAB color space. The 3-dimensional color space is built-up from three axes that are perpendicular to one another.
The L*-axis gives the lightness: a white object has an L* value of 100 and the L* value of a black object is 0. The so-called achromatic colors, the shades of grey, are on the L*-axis.
Chromatic (‘real’) colors are described by using the two axes in the horizontal plane. The a*-axis is the green-red axis and the b*-axis goes from blue (-b*) to yellow (+b*).
Each color is represented by a color point (L*, a*, b*) in the color space; L*, a* and b* are the color coordinates of the color point.
The asterisk (*) symbol of L*, a* and b* indicates that this is the new color system; it is the follow-up of the older CIELAB system. The new system is now universally used for the quantification of colors, even though often the simplified notation of the Lab-values, without the * symbol, is used.
Color differences
The color difference between two colors is the distance between the color points of the two colors. ΔE*ab is the color difference of two colors, ‘1‘ and ‘2’, that have color coordinates L*1, a*1, b*1 and L*2, a*2, b*2, respectively. A small ΔE*ab value implies that the colors are close to one another. The color difference can be calculated by using the mathematical theorem of Pythagoras:
The concept and quantification of color differences is important when a color must be matched or when a new batch of a paint must have a color that is close to the color of the standard paint, the reference. But, how well must the color of the new batch match with the color of the reference? The answer to this question is a criterion in the quality control of a new batch of paint. The color coordinates of the batch and the reference are measured and the color difference ΔE*ab is calculated. Depending on the industry, the criterion for color approval can be strict, for example ΔE*ab < 0.3, or much milder, for example ΔE*ab < 1.5.
In the daily practice of those who work with paints, the representation of a color difference is often simplified as ΔE* or ΔE.
Hue and Chroma
Hue is the color tone or color name of a color. Chroma is the amount of saturation of a color. Colors of high chroma are said to be clear, bright or brilliant. Dull (pastel) colors have a low chroma.
Hue and chroma can be visualized and quantified by using the a*b*-plane of the CIELAB color space.
The hue of a color is quantified by its hue angle hab (without * symbol) in the a*b*-plane, given in degrees (°). The hue angle range starts, by definition, at the positive side of the a*-axis and goes counter-clockwise. This implies that red has a hue angle of 0°. A full circle goes from 0° to 360°. Cyan blue (an organic blue pigment with color index PB 15), for example, has a hue angle of about 240°. The hue angle of a color can be calculated from the color coordinates:
The chroma of a color is quantified by C*ab; it is the distance of the color point to the L*-axis. Chroma can be calculated from the color coordinates by using Pythagoras’ theorem:
A saturated (or brilliant) color is represented by a color point that is far away from the lightness axis. The color point of a pale (or dull, or pastel) color, a color of low saturation, is close to the L*-axis.
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The formulas are the simple CIE76 formuls.
CIE94 and CIEDE2000 are a bit more complicated.
https://en.wikipedia.org/wiki/Color_difference#CIE94
Dear Dr Jochum … DE is something more complex than Pitagoras nowadays. DE in CIE2000 is the most acurate way to get a color difference.
Nice refresher article, Jochum!
As a color scientist I have a few points of clarification:
“The color difference can be calculated by using the mathematical theorem of Pythagoras”:
This is actually Euclidean not Pythagorean.
“The new system is now universally used for the quantification of colors, even though often the simplified notation of the Lab-values, without the * symbol, is used.”
This statement isn’t entirely true universally used is the challenge. ASTM also allows the use of Hunter LAB space. Many other industries outside coatings prefer the CIELUV system or the RGB system(graphics) or CMYK system (print).
You did not discuss white point which defines CIELAB space. White point is critical as if you adjust this the entire space shifts to accommodate. This is how one can adjust the light source or observer. Likewise there is no discussion of how to move from measured data to CIELAB coordinates. Though most modern software will do this for you it is a crucial step in understanding the space. Though perhaps brevity prevented this explanation.
Over all a very concise description.
This is a great article! Thanks for writing it !
With respect to the three topics addressed by Mrs. Schwen:
– Pythagoras’ theorem is used to calculate the distance between 2 points in space. The type of geometry used in the CIELAB methodology is called Euclidean; the CIELAB color space, as described in the article, is a so-called Euclidean 3-dimensional space. Also, Euclid was one of the persons proving that the theorem of Pythagoras was correct.
– Indeed, other color systems are used as well. The CIELAB system is the system that is most often used in coating industry.
– The objective of the article is to briefly explain the CIELAB color space for coating people. Calibration, light sources, observers and how devices convert measuring results into color coordinates is beyond the scope of the article.
Thanks for reading,
Jochum Beetsma
The remarks made by Mr. Zapata and Mr. Nielsen are true and important. Indeed, newer models, like CIE94 and CIEDE2000, are also used to calculate color differences. The development of these new calculation methods was done to obtain better agreement with human perception when judging color differences. To prevent misunderstanding, it is important to use the right subscripts for delta E* values: ‘ab’ when using the CIELAB76 calculation method, ‘94’ when using the CIE94 calculation method and ’00‘ when using the CIEDE2000 calculation method. In coating industry, the CIELAB76 calculation method, as described in the article, is (still) the method that is most often used.
Thank you so much for such a great article!
I have a question if you don’t mind …. As I am writing my thesis in a chromometry subject, can you please let me know if the parameters a*, b* using the (CIELAB, 1974) system are related with each other and with the parameter L* (brightness)?
For example if we have 2 objects: Object A–> L*=43, a*=47.63, b*=14.12 and Object B—> L*=43, a*=44,58, b*=15,16 then the object A is darker than the object B because the redness of A is greater than the redness of B and the yellowness of A is less than the yellowness of B?
Thanks for your positive feedback.
The system described in the article is CIELAB76; it was introduced in 1976.
The 3 axis in the L*a*b* color space are independent from each other. In practice, however, it is difficult to change only one of the 3 parameters when, for example, adding a colorant to a paint.
If we take your example, look at the color coordinates and visualize the color of the 2 objects in the color space, the following can be concluded:
– The lightness of the objects is the same, because they have the same L* value.
– Object A is more red, because object A has a higher a* value.
– Object A is less yellow, because object A has a lower b* value.
Dear Dr
Thank you for such indepth explanation.The concept color quantification is now not limited to Paint industyr.It has spread its wings ino pharma aswell.The color appearance of liquid injectables is the most crucial phenomenon -Because it links to quality as many liquid injectables tend to change color upon stability studies.
I am very much interested to know how to convert the actual transmission values into CIELAB values.Any reference is highly appreciated.
Dear RC:
I do not know how to transfer color properties of liquid injectables into L*a*b* coordinates. In the paint industry, the CIELAB system is used to quantify the color of (mostly) solid films. I presume that liquid injectables are partly transparent. I expect that the color properties of such liquids are described via the absorption or transmission spectrum. Possibly, another reader of the articles could shine her/his light on this.
Thanks for reading!
Hi Doctor,
Thanks for such an informative article.
I am associated with a recycled PET manufacturing plant and we are searching for any suitable additive to improve B value and whitening index of Polyester Chips made from extrusion of plastic bottles.
Can you suggest any suitable chemical against aforementioned issue.? Thanking in advance
Dear Mr/Mrs Haider Awan,
I advise you to contact one of the plastic experts, that you can find on the Prospector Knowledge Center.
Greetings, Jochum Beetsma.