In colorimetry and color theory, colorfulness, chroma, and saturation are related concepts referring to the intensity of a specific color. Colorimetry or Colourimetry can refer to the quantitative study of Color perception Color Theory is the musical alter ego of American singer-keyboardist-songwriter Brian Hazard More technically, colorfulness is the perceived difference between the color of some stimulus and gray, chroma is the colorfulness of a stimulus relative to the brightness of a stimulus that appears white under similar viewing conditions, and saturation is the colorfulness of a stimulus relative to its own brightness. In Physiology, a stimulus is a detectable change in the internal or external environment Brightness is an attribute of Visual perception in which a source appears to emit or reflect a given amount of Light.  Though this general concept is intuitive, terms such as chroma, saturation, purity, and intensity are often used without great precision, and even when well-defined depend greatly on the specific color model in use. A color model is an abstract mathematical model describing the way Colors can be represented as Tuples of numbers typically as three or four values or color components
A highly colorful stimulus is vivid and intense, while a less colorful stimulus appears more muted, closer to gray. With no colorfulness at all, a color is a “neutral” gray. With three attributes—colorfulness (or chroma or saturation), lightness (or brightness), and hue—any color can be described. Lightness is a property of a Color, or a dimension of a Color space, that is defined in a way to reflect the subjective brightness perception of a color for humans Hue is one of the main properties of a Color described with names such as " Red " " Yellow " etc
Contrast and saturation increased
Saturation is one of three coordinates in the HSL and HSV color spaces. HSL and HSV are two related representations of points in an RGB color space, which attempt to describe perceptual color relationships more accurately than A Color model is an abstract mathematical model describing the way Colors can be represented as Tuples of numbers typically as three or four values or color components Note that virtually all computer software implementing these spaces use a very rough approximation to calculate the value they call "saturation", such as the formula described for HSV and this value has little, if anything, to do with the description shown here. HSL and HSV are two related representations of points in an RGB color space, which attempt to describe perceptual color relationships more accurately than
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 color is achieved by using just one wavelength at a high intensity, such as in laser light. If the intensity drops, so does the saturation. To desaturate a color in a subtractive system (such as watercolor), you can add white, black, gray, or the hue's complement. A subtractive color model explains the mixing of Paints Dyes Inks and natural colorants to create a range of Colors where each such color Watercolor ( US) or Watercolour ( UK) (and "aquarelle" in French is a Painting method White is a Color, the perception which is evoked by Light that stimulates all three types of color sensitive Cone cells in the Human eye Black is the Color of objects that do not emit or Reflect Light in any part of the Visible spectrum; they absorb all such frequencies of Complementary colors are pairs of Colors that are of “opposite” Hue in some Color model.
Various correlates of saturation follow.
where (u'n,v'n) is the chromaticity of the white point, and chroma is defined below. In Colorimetry, the CIE 1976 ( L*, u*, v*) color space, also known as the CIELUV color space, is a Color space adopted by 
By analogy, in CIELAB this would yield:
The CIE has not formally recommended this equation since CIELAB has no chromaticity diagram, and this definition therefore lacks direct correlation with older concepts of saturation. A Lab color space is a color-opponent space with dimension L for lightness and a and b  Nevertheless, this equation provides a reasonable predictor of saturation, and demonstrates that adjusting the lightness in CIELAB while holding (a * ,b * ) fixed does affect the saturation.
This definition is inspired by experimental work done with the intention of remedying CIECAM97s's poor performance. Published in 2002 by the CIE Technical Committee 8-01 ( Colour Appearance Modelling for Color Management Systems) as of 2008 CIECAM02 is the most recent Color appearance  It should be noted that M is proportional to the chroma C (), thus the CIECAM02 definition bears some similarity to the CIELUV definition. An important difference is that the CIECAM02 model accounts for the viewing conditions through the parameter FL. 
The excitation purity (purity for short) of a stimulus is its difference from the illuminant's white point relative to the furthest point on the chromaticity diagram with the same hue (dominant wavelength for monochromatic sources); using the CIE 1931 color space:
where (xI,yI) is the chromaticity of the white point and (xn,yn) is the point on the perimeter whose line segment to the white point contains the chromaticity of the stimulus. A white point (often referred to as reference white or target white in technical documents is a set of tristimulus values or Chromaticity coordinates In color science, the dominant wavelength and complementary wavelength are ways of describing non-spectral (polychromatic light mixtures in terms of the spectral Monochrome comes from the Greek μονόχρωμος ( monochromos) meaning “of one color” which is a combination In the study of the perception of Color, one of the first mathematically defined Color spaces was the CIE 1931 XYZ color space (also known as CIE 1931 color space Different color spaces, such as CIELAB or CIELUV may be used, and will yield different results.
The naïve definition of saturation does not specify its response function. In the CIE XYZ and RGB color spaces, the saturation is defined in term of additive color mixing, and has the property of being proportional to any scaling centered at white or the white point illuminant. However, both color spaces are nonlinear in terms of psychovisually perceived color differences. The difference or distance between two colors is a metric of interest in Color science. It is also possible, and sometimes desirable to define a saturation-like quantity that is linearized in term of the psychovisual perception.
In the CIE 1976 L*a*b* and L*u*v* color spaces, the unnormalized chroma is the radial component of the cylindrical coordinate CIE L*C*h (lightness, chroma, hue) representation of the L*a*b* and L*u*v* color spaces, also denoted as CIE L*C*h(a*b*) or CIE L*C*h for short, and CIE L*C*h(u*v*). A Lab color space is a color-opponent space with dimension L for lightness and a and b The transformation of (a * ,b * ) to (C * ,h) is given by:
and analogously for CIE L*C*h(u*v*).
The chroma in the CIE L*C*h(a*b*) and CIE L*C*h(u*v*) coordinates has the advantage of being more psychovisually linear, yet they are non-linear in terms of linear component color mixing. And therefore, chroma in CIE 1976 L*a*b* and L*u*v* color spaces is very much different from the traditional sense of "saturation".
Another, psychovisually even more accurate, but also more complex method to obtain or specify the saturation is to use the color appearance model, like CIECAM. The chroma component of the JCh (lightness, chroma, hue) coordinate, and becomes a function of parameters like the chrominance and physical brightness of the illumination, or the characteristics of the emitting/reflecting surface, which is also psychovisually more sensible.