Editing Colorfulness (section)

== Saturation ==
The saturation of a color is determined by a combination of light intensity and how much it is distributed across the spectrum of different wavelengths. The purest (most saturated) color is achieved by using just one wavelength at a high intensity, such as in laser light. If the intensity drops, then as a result the saturation drops.  To desaturate a color of given intensity in a [[Subtractive color|subtractive]] system (such as [[watercolor]]), one can add white, black, [[Grey|gray]], or the hue's [[Complementary color|complement]].

Various correlates of saturation follow.

=== CIELUV and CIELAB ===

In [[CIELUV]], saturation is equal to the ''chroma'' normalized by the ''lightness'':
<math display=block>s_{uv} = \frac{C^*_{uv}}{L^*} = 13 \sqrt{(u' - u'_n)^2 + (v' - v'_n)^2}</math>
where <math>\left(u_n, v_n\right)</math> is the chromaticity of the white point, and chroma is defined below.<ref>{{Cite book|last=Schanda|first=János|title=Colorimetry: Understanding the CIE System|publisher=[[Wiley Interscience]]|year=2007|isbn=978-0-470-04904-4|url=https://books.google.com/books?id=g8VDAgAACAAJ|url-status=live|archive-url=https://web.archive.org/web/20170117120237/https://books.google.com/books?id=g8VDAgAACAAJ&dq=intitle:Colorimetry+intitle:Understanding+intitle:the+intitle:CIE+intitle:System|archive-date=2017-01-17}}, page 88.</ref>

By analogy, in [[CIELAB]] this would yield:
<math display=block>s_{ab} = \frac{C^*_{ab}}{L^*} = \frac{\sqrt{{a^*}^2 + {b^*}^2}}{L^*}</math>

The CIE has not formally recommended this equation since CIELAB has no chromaticity diagram, and this definition therefore lacks direct connection with older concepts of saturation.<ref>{{cite book|url=https://archive.org/details/focalencyclopedi00lesl|url-access=registration|title=The Focal Encyclopedia of Photography|publisher=Focal Press|editor=Leslie D. Stroebel, Richard D. Zakia|isbn=0-240-51417-3|year=1993|page=[https://archive.org/details/focalencyclopedi00lesl/page/124 124]|first=Robert William Gainer|last=Hunt}}</ref> Nevertheless, this equation provides a reasonable predictor of saturation, and demonstrates that adjusting the lightness in CIELAB while holding {{nobr|(''a''*, ''b''*)}} fixed does affect the saturation.

But the following verbal definition of Manfred Richter and the corresponding formula proposed by Eva Lübbe are in agreement with the human perception of saturation:
Saturation is the proportion of pure chromatic color in the total color sensation.<ref>{{Cite book|last=Lübbe|first=Eva|title=Colours in the Mind - Colour Systems in Reality- A formula for colour saturation|publisher=[Book on Demand]|year=2010|isbn=978-3-7881-4057-1 }}</ref>
<math display=block>S_{ab} = \frac{C^*_{ab}}{\sqrt{{C^*_{ab} }^2 + {L^*}^2}} 100\%</math>
where <math>S_{ab}</math> is the saturation, <math>L^*</math> the  lightness and <math>C^*_{ab}</math> is the chroma of the color.

=== CIECAM02 ===

In [[CIECAM02]], saturation equals the square root of the ''colorfulness'' divided by the ''brightness'':
<math display=block>s = \sqrt\frac{M}{Q}</math>

This definition is inspired by experimental work done with the intention of remedying [[CIECAM97s]]'s poor performance.<ref name=ciecam02>{{cite conference|conference=The CIECAM02 Color Appearance Model|title=IS&T/SID Tenth Color Imaging Conference|last=Moroney|first=Nathan|author2=Fairchild, Mark D. |author3=Hunt, Robert W.G. |author4=Li, Changjun |author5=Luo, M. Ronnier |author6= Newman, Todd |url=http://www.polybytes.com/misc/Meet_CIECAM02.pdf|location=[[Scottsdale, Arizona]]|isbn=0-89208-241-0|date=November 12, 2002|publisher=The [[Society for Imaging Science and Technology]]|url-status=dead|archive-url=https://web.archive.org/web/20111002195211/http://www.polybytes.com/misc/Meet_CIECAM02.pdf|archive-date=Oct 2, 2011}}
</ref><ref>{{cite conference|title=Magnitude estimation for scaling saturation|first=Lu-Yin G.|last=Juan|author2=Luo, Ming R.|conference-url=http://spiedl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PSISDG004421000001000575000001&idtype=cvips&gifs=yes| work=[[Proceedings of SPIE]]|volume=4421|conference=9th Congress of the International Colour Association|editor=Robert Chung |editor2=Allan Rodrigues|date=June 2002|pages=575–578|doi=10.1117/12.464511}}</ref> <math>M</math> is proportional to the chroma <math>C,</math> thus the CIECAM02 definition bears some similarity to the CIELUV definition.<ref name=ciecam02/>

=== HSL and HSV===

Saturation is also one of three coordinates in the [[HSL and HSV]] [[color space]]s. However, in the HSL color space saturation exists independently of lightness. That is, both a very light color {{em|and}} a very dark color can be heavily saturated in HSL; whereas in the previous definitions&mdash;as well as in the HSV color space&mdash;colors approaching white all feature low saturation.