Lightness (color)
Encyclopedia
Lightness is a property of a color
Color
Color or colour is the visual perceptual property corresponding in humans to the categories called red, green, blue and others. Color derives from the spectrum of light interacting in the eye with the spectral sensitivities of the light receptors...

, or a dimension of a color space
Color space
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...

, that is defined in a way to reflect the subjective brightness perception of a color for humans along a lightness–darkness axis. A color's lightness also corresponds to its amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...

.

Various color models
Color models
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. When this model is associated with a precise description of how the components are to be interpreted , the resulting set of...

have an explicit term for this property. The Munsell color model
Munsell color system
In colorimetry, the Munsell color system is a color space that specifies colors based on three color dimensions: hue, value , and chroma . It was created by Professor Albert H...

uses the term value, while the HSL color model and Lab color space
Lab color space
A Lab color space is a color-opponent space with dimension L for lightness and a and b for the color-opponent dimensions, based on nonlinearly compressed CIE XYZ color space coordinates....

use the term lightness. The HSV model uses the term value a little differently: a color with a low value is nearly black, but one with a high value is the pure, fully saturated color.

In subtractive color
Subtractive color
A subtractive color model explains the mixing of paints, dyes, inks, and natural colorants to create a full range of colors, each caused by subtracting some wavelengths of light and reflecting the others...

(i.e. paints) value changes can be achieved by adding black or white to the color. However, this also reduces saturation. Chiaroscuro
Chiaroscuro
Chiaroscuro in art is "an Italian term which literally means 'light-dark'. In paintings the description refers to clear tonal contrasts which are often used to suggest the volume and modelling of the subjects depicted"....

and Tenebrism
Tenebrism
Tenebrism, from the Italian tenebroso , is a style of painting using very pronounced chiaroscuro, where there are violent contrasts of light and dark, and darkness becomes a dominating feature of the image...

both take advantage of dramatic contrasts of value to heighten drama in art. Artists may also employ shading
Shading refers to depicting depth perception in 3D models or illustrations by varying levels of darkness.-Drawing:Shading is a process used in drawing for depicting levels of darkness on paper by applying media more densely or with a darker shade for darker areas, and less densely or with a lighter...

, subtle manipulation of value.

## Relationship between lightness, value, and luminance

The Munsell value has long been used as a perceptually uniform lightness scale. A question of interest is the relationship between the Munsell value scale and the relative luminance. Aware of the Weber–Fechner law
Weber–Fechner law
The Weber–Fechner law is a confusing term, because it combines two different laws. Some authors use the term to mean Weber's law, and others Fechner's law. Fechner himself added confusion to the literature by calling his own law Weber's law...

, Munsell remarked "Should we use a logarithmic curve or curve of squares?" Neither option turned out to be quite correct; scientists eventually converged on a roughly cube-root curve, consistent with the Stevens power law for brightness perception, reflecting the fact that lightness is proportional to the number of nerve impulses per nerve fiber per unit time. The remainder of this section is a chronology of lightness approximations, leading to CIELAB.

Note: Munsell's V runs from 0 to 10, while Y typically runs from 0 to 100 (often interpreted as a percent). Typically, the relative luminance is normalized so that the "reference white" (say, magnesium oxide
Magnesium oxide
Magnesium oxide , or magnesia, is a white hygroscopic solid mineral that occurs naturally as periclase and is a source of magnesium . It has an empirical formula of and consists of a lattice of Mg2+ ions and O2– ions held together by ionic bonds...

) has a tristimulus value of Y=100. Since the reflectance of magnesium oxide (MgO) relative to the perfect reflecting diffuser is 97.5%, V=10 corresponds to Y=100/97.5%≈102.6 if MgO is used as the reference.
1920 : Priest et al. provide a basic estimate of the Munsell value (with Y running from 0 to 1 in this case):

1933 : Munsell, Sloan, and Godlove launch a study on the Munsell neutral value scale, considering several proposals relating the relative luminance to the Munsell value, and suggest:

1943 : Newhall, Nickerson, and Judd prepare a report for the Optical Society of America
Optical Society of America
The Optical Society is a scientific society dedicated to advancing the study of light—optics and photonics—in theory and application, by means of publishing, organizing conferences and exhibitions, partnership with industry, and education. The organization has members in more than 100 countries...

. They suggest a quintic parabola (relating the reflectance in terms of the value):

1943 : Using Table II of the O.S.A. report, Moon and Spencer express the value in terms of the luminance:

1944 : Saunderson and Milner introduce a subtractive constant in the previous expression, for a better fit to the Munsell value. Later, Jameson and Hurvich claim that this corrects for simultaneous contrast effect
Contrast effect
A contrast effect is the enhancement or diminishment, relative to normal, of perception, cognition and related performance as a result of immediately previous or simultaneous exposure to a stimulus of lesser or greater value in the same dimension...

s.

1955 : Ladd and Pinney of Eastman Kodak
Eastman Kodak
Eastman Kodak Company is a multinational imaging and photographic equipment, materials and services company headquarted in Rochester, New York, United States. It was founded by George Eastman in 1892....

are interested in the Munsell value as a perceptually uniform lightness scale for use in television
Television
Television is a telecommunication medium for transmitting and receiving moving images that can be monochrome or colored, with accompanying sound...

. After considering one logarithmic and five power-law functions (per Stevens' power law
Stevens' power law
Stevens' power law is a proposed relationship between the magnitude of a physical stimulus and its perceived intensity or strength. It is often considered to supersede the Weber–Fechner law on the basis that it describes a wider range of sensations, although critics argue that the validity of the...

), they relate value to reflectance by raising the reflectance to the power of 0.352:

Realizing this is quite close to the cube root, they simplify it to:

1958 : Glasser et al. define the lightness as ten times the Munsell value (so that the lightness ranges from 0 to 100):

1964 : Wyszecki simplifies this to:

This formula approximates the Munsell value function for (it is not applicable for Y<1%) and is used for the CIE 1964 color space.

1976 : CIELAB uses the following formula:

where is the Y tristimulus value of a "specified white object" and is subject to the restriction . Pauli removes this restriction by computing a linear extrapolation which maps Y/Yn=0 to L*=0 and is tangent to the formula above at the point at which the linear extension takes effect. First, the transition point is determined to be , then the slope of is computed. This gives the two-part function:

The lightness is then .

At first glance, you might approximate the lightness function by a cube root, an approximation that is found in much of the technical literature. However, the linear segment near black is significant. The best-fit pure power function has an exponent of about 0.42, far from 1/3.

An 18% grey card, having a reflectance of 0.18, has lightness very close to 50. It is called "mid grey" because its lightness is midway between black and white.