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Lightness is a visual perception of the
luminance Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls wit ...
$\left(L\right)$ of an object. It is often judged relative to a similarly lit object. In
colorimetry Colorimetry is "the science and technology used to quantify and describe physically the human color perception". It is similar to spectrophotometry, but is distinguished by its interest in reducing spectra to the physical correlates of color ...
and
color appearance model A color appearance model (CAM) is a mathematical model that seeks to describe the perceptual aspects of human color vision, i.e. viewing conditions under which the appearance of a color does not tally with the corresponding physical measurement o ...
s, lightness is a prediction of how an illuminated
color Color (American English) or colour (British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are associ ...
will appear to a standard observer. While luminance is a linear measurement of light, lightness is a linear prediction of the human perception of that light. This is because human vision's lightness perception is non-linear relative to light. Doubling the quantity of light does not result in a doubling in perceived lightness, only a modest increase. The symbol for perceptual lightness is usually either $J$ as used in
CIECAM02 In colorimetry, CIECAM02 is the color appearance model published in 2002 by the International Commission on Illumination (CIE) Technical Committee 8-01 (''Color Appearance Modelling for Color Management Systems'') and the successor of CIECAM97s ...
or $L^*$ as used in
CIELAB The CIELAB color space, also referred to as ''L*a*b*'' , is a color space defined by the International Commission on Illumination (abbreviated CIE) in 1976. (Referring to CIELAB as "Lab" without asterisks should be avoided to prevent confusio ...
and
CIELUV In colorimetry, the CIE 1976 ''L''*, ''u''*, ''v''* color space, commonly known by its abbreviation CIELUV, is a color space adopted by the International Commission on Illumination (CIE) in 1976, as a simple-to-compute transformation of the 1931 ...
. $L^*$ ("Lstar") is not to be confused with $L$ as used for luminance. In some color ordering systems such as Munsell, Lightness is referenced as value.
Chiaroscuro Chiaroscuro ( , ; ), in art, is the use of strong contrasts between light and dark, usually bold contrasts affecting a whole composition. It is also a technical term used by artists and art historians for the use of contrasts of light to ach ...
and
Tenebrism Tenebrism, from Italian ' ("dark, gloomy, mysterious"), also occasionally called dramatic illumination, is a style of painting using especially pronounced chiaroscuro, where there are violent contrasts of light and dark, and where darkness becom ...
both take advantage of dramatic contrasts of value to heighten drama in art. Artists may also employ
shading Shading refers to the depiction of depth perception in 3D models (within the field of 3D computer graphics) or illustrations (in visual art) by varying the level of darkness. Shading tries to approximate local behavior of light on the obje ...
, subtle manipulation of value.

# Lightness in different colorspaces

In some colorspaces or color systems such as Munsell, HCL, and CIELAB, the lightness (value) achromatically constrains the maximum and minimum limits, and operates independently of the hue and chroma. For example Munsell value 0 is pure black, and value 10 is pure white. Colors with a discernible hue must therefore have values in between these extremes. In a
subtractive color Subtractive color or subtractive color mixing predicts the spectral power distribution of light after it passes through successive layers of partially absorbing media. This idealized model is the essential principle of how dyes and inks are u ...
model (e.g. paint, dye, or ink) lightness changes to a color through various tints, shades, or tones can be achieved by adding white, black, or grey respectively. This also reduces saturation. In HSL and HSV, the displayed luminance is relative to the hue and chroma for a given lightness value, in other words the selected lightness value does not predict the actual displayed luminance nor the perception thereof. Both systems use coordinate triples, where many triples can map onto the same color. In HSV, all triples with value 0 are pure black. If the hue and saturation are held constant, then increasing the value increases the luminance, such that a value of 1 is the lightest color with the given hue and saturation. HSL is similar, except that all triples with lightness 1 are pure white. In both models, all pure saturated colors indicate the same lightness or value, but this does not relate to the displayed luminance which is determined by the hue. I.e. yellow is higher luminance than blue, even if the lightness value is set at a given number. While HSL, HSV, and similar spaces serve well enough to choose or adjust a single color, they are not perceptually uniform. They trade off accuracy for computational simplicity, as they were created in an era where computer technology was restricted in performance. If we take an image and extract the hue, saturation, and lightness or value components for a given color space, we will see that they may differ substantially from a different color space or model. For example, examine the following images of a fire breather (). The original is in the sRGB color space. CIELAB $L^*$ is a perceptually uniform lightness prediction that is derived from luminance $Y$, but discards the $X$ and $Z$, of the CIE XYZ color space. Notice this appears similar in perceived lightness to the original color image. Luma $\left(Y^\prime\right)$ is a gamma-encoded luminance component of some video encoding systems such as $\left(Y^\prime IQ\right)$ and $\left(Y^\prime UV\right)$. It is roughly similar, but differs at high chroma, deviating most from an achromatic signal such as linear luminance $Y$ or non-linear lightness $L^*$. HSL $L$ and HSV $V$ are neither perceptually uniform, nor uniform as to luminance.

# Relationship to value and relative 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 Relative luminance Y follows the photometric definition of luminance L including spectral weighting for human vision, but while luminance L is a measure of light in units such as cd/m^2, Relative luminance Y values are normalized as 0.0 to 1.0 ...
. Aware of the
Weber–Fechner law The Weber–Fechner laws are two related hypotheses in the field of psychophysics, known as Weber's law and Fechner's law. Both laws relate to human perception, more specifically the relation between the actual change in a physical stimulus an ...
, Albert 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's 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 models, leading to
CIECAM02 In colorimetry, CIECAM02 is the color appearance model published in 2002 by the International Commission on Illumination (CIE) Technical Committee 8-01 (''Color Appearance Modelling for Color Management Systems'') and the successor of CIECAM97s ...
. ''Note.'' – Munsell's ''V'' runs from 0 to 10, while ''Y'' typically runs from 0 to 100 (often interpreted as a percentage). Typically, the relative luminance is normalized so that the "reference white" (say,
magnesium oxide Magnesium oxide ( Mg O), or magnesia, is a white hygroscopic solid mineral that occurs naturally as periclase and is a source of magnesium (see also oxide). It has an empirical formula of MgO and consists of a lattice of Mg2+ ions and O2− io ...
) has a tristimulus value of . Since the reflectance of magnesium oxide (MgO) relative to the perfect reflecting diffuser is 97.5%, corresponds to if MgO is used as the reference.

## 1920

Irwin Priest, Kasson Gibson, and Harry McNicholas provide a basic estimate of the Munsell value (with ''Y'' running from 0 to 1 in this case): :$V = 10 \sqrt.$

## 1933

Alexander Munsell, Louise Sloan, and Isaac Godlove launch a study on the Munsell neutral value scale, considering several proposals relating the relative luminance to the Munsell value, and suggest: :$V^2 = 1.4742 Y - 0.004743 Y^2.$

## 1943

Sidney Newhall, Dorothy Nickerson, and Deane Judd prepare a report for the
Optical Society of America Optica (formerly known as The Optical Society (OSA) and before that as the Optical Society of America) is a professional society of individuals and companies with an interest in optics and photonics. It publishes journals and organizes conferen ...
(OSA) on Munsell renotation. They suggest a quintic parabola (relating the reflectance in terms of the value): :$Y = 1.2219 V - 0.23111 V^2 + 0.23951 V^3 - 0.021009 V^4 + 0.0008404 V^5.$

## 1943

Using Table II of the OSA report, Parry Moon and Domina Spencer express the value in terms of the relative luminance: :$V = 5\left\left(\frac\right\right)^ = 1.4 Y^.$

## 1944

Jason Saunderson and B.I. Milner introduce a subtractive constant in the previous expression, for a better fit to the Munsell value. Later, Dorothea Jameson and Leo Hurvich claim that this corrects for simultaneous contrast effects. :$V = 2.357 Y^ - 1.52.$

## 1955

Ladd and Pinney of
Eastman Kodak The Eastman Kodak Company (referred to simply as Kodak ) is an American public company that produces various products related to its historic basis in analogue photography. The company is headquartered in Rochester, New York, and is incorpor ...
are interested in the Munsell value as a perceptually uniform lightness scale for use in
television Television, sometimes shortened to TV, is a telecommunication medium for transmitting moving images and sound. The term can refer to a television set, or the medium of television transmission. Television is a mass medium for advertisin ...
. After considering one logarithmic and five power-law functions (per Stevens' power law), they relate value to reflectance by raising the reflectance to the power of 0.352: :$V = 2.217 Y^ - 1.324.$ Realizing this is quite close to the
cube root In mathematics, a cube root of a number is a number such that . All nonzero real numbers, have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. ...
, 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

Günter Wyszecki simplifies this to: ''Note:'' The asterisks are not used in the paper. : This formula approximates the Munsell value function for (it is not applicable for ) and is used for the CIE 1964 color space.

## 1976

CIELAB The CIELAB color space, also referred to as ''L*a*b*'' , is a color space defined by the International Commission on Illumination (abbreviated CIE) in 1976. (Referring to CIELAB as "Lab" without asterisks should be avoided to prevent confusio ...
uses the following formula: :$L^\star = 116\left\left(\frac\right\right)^\frac13 - 16.$ where ''Y''n is the CIE XYZ ''Y'' tristimulus value of the reference
white point A white point (often referred to as reference white or target white in technical documents) is a set of tristimulus values or chromaticity coordinates that serve to define the color " white" in image capture, encoding, or reproduction. Depending ...
(the subscript n suggests "normalized") and is subject to the restriction . Pauli removes this restriction by computing a linear extrapolation which maps to 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: :$f\left(t\right) = \begin t^\frac13 & \text t > \left\left(\frac\right\right)^3 \\ \frac\left\left(\frac\right\right)^2 t + \frac & \text \end$ The lightness is then: :$L^\star = 116 f\left\left(\frac\right\right) - 16.$ 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, and so the 116 and 16 coefficients. The best-fit pure power function has an exponent of about 0.42, far from . An approximately 18% grey card, having an exact reflectance of ()3, has a lightness value of 50. It is called " mid grey" because its lightness is midway between black and white.

## 1997

As early as in 1967 a hyperbolic relationship between light intensity and cone cell responses was discovered in fish, in line with the
Michaelis–Menten kinetics In biochemistry, Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics. It is named after German biochemist Leonor Michaelis and Canadian physician Maud Menten. The model takes the form of an equation describing the ra ...
model of biochemical reactions. In the 70s the same relationship was found in a number of other vertebrates and in 1982, using microelectrodes to measure cone responses in living rhesus macaques, Valeton and Van Norren found the following relationship: :1 / V ~ 1 + (σ / I)0.74 where V is the measured potential, I the light intensity and σ a constant. In 1986 Seim and Valberg realised that this relationship might aid in the construction of a more uniform colour space. This inspired advances in colour modelling and when the
International Commission on Illumination The International Commission on Illumination (usually abbreviated CIE for its French name, Commission internationale de l'éclairage) is the international authority on light, illumination, colour, and colour spaces. It was established in 1913 a ...
held a symposium in 1996, objectives for a new standard colour model were formulated and in 1997
CIECAM97s A color appearance model (CAM) is a mathematical model that seeks to describe the perceptual aspects of human color vision, i.e. viewing conditions under which the appearance of a color does not tally with the corresponding physical measurement o ...
(International Commission on Illumination, colour appearance model, 1997, simple version) was standardised. CIECAM97s distinguishes between lightness, how light something appears compared to a similarly lit white object, and brightness, how much light appears to shine from something. According to CIECAM97s the lightness of a sample is: :J = 100 (Asample / Awhite)cz In this formula, for a small sample under bright conditions in a surrounding field with a relative luminance n compared to white, c has been chosen such that: :$\text = \frac$ This models that a sample will appear darker on a light background than on a dark background. See contrast effect for more information on the topic. When n = , cz = 1, representing the assumption that most scenes have an average relative luminance of compared to bright white, and that therefore a sample in such a surround should be perceived at its proper lightness. The quantity A models the achromatic cone response; it is colour dependent but for a grey sample under bright conditions it works out as: :$\frac = \frac + 1$ :Nbb is a fudge factor that is normally 1; it's only of concern when comparing brightness judgements based on slightly different reference whites. Here Y is the relative luminance compared to white on a scale of 0 to 1 and LA is the average luminance of the adapting visual field as a whole, measured in cd/m2. The achromatic response follows a kind of S-curve, ranging from 1 to 123, numbers which follow from the way the cone responses are averaged and which are ultimately based on a rough estimate for the useful range of nerve impulses per second, and which has a fairly large intermediate range where it roughly follows a square root curve. The brightness according to CIECAM97s is then: :Q = (1.24 / c) (J / 100)0.67 (Awhite + 3)0.9 The factor 1.24 / c is a surround factor that reflects that scenes appear brighter in dark surrounding conditions. Suggestions for a more comprehensive model, CIECAM97C, were also formulated, to take into account several effects at extremely dark or bright conditions, coloured lighting, as well as the
Helmholtz–Kohlrausch effect The Helmholtz–Kohlrausch effect (after Hermann von Helmholtz and V. A. Kohlrausch) is a perceptual phenomenon wherein the intense saturation of spectral hue is perceived as part of the color's luminance. This brightness increase by saturation ...
, where highly chromatic samples appear lighter and brighter in comparison to a neutral grey. To model the latter effect, in CIECAM97C the formula for J is adjusted as follows: :JHK = J + (100 – J) (C / 300) , sin(½h – 45°), , where C is the chroma and h the hue angle Q is then calculated from JHK instead of from J. This formula has the effect of pulling up the lightness and brightness of coloured samples. The larger the chroma, the stronger the effect; for very saturated colours C can be close to 100 or even higher. The absolute sine term has a sharp V-shaped valley with a zero at yellow and a broad plateau in the deep blues.

## 2002

The achromatic response in CIECAM97s is a weighted addition of cone responses minus 2.05. Since the total noise term adds up to 3.05, this means that A and consequentially J and Q aren't zero for absolute black. To fix this, Li, Luo & Hunt suggested subtracting 3.05 instead, so the scale starts at zero. Although CIECAM97s was a successful model to spur and direct colorimetric research, Fairchild felt that for practical applications some changes were necessary. Those relevant for lightness calculations were to, rather than use several discrete values for the surround factor c, allow for linear interpolation of c and thereby allowing the model to be used under intermediate surround conditions, and to simplify z to remove the special case for large stimuli because he felt it was irrelevant for imaging applications. Based on experimental results, Hunt, Li, Juan and Luo proposed a number of improvements. Relevant for the topic at hand is that they suggested lowering z slightly. Li and Luo found that a colour space based on such a modified CIECAM97s using lightness as one of the coordinates was more perceptually uniform than CIELAB. Because of the shape of the cone response S-curve, when the luminance of a colour is reduced, even if its spectral composition remains the same, the different cone responses don't quite change at the same rate with respect to each other. It is plausible therefore that the perceived hue and saturation will change at low luminance levels. But CIECAM97s predicts much larger deviations than are generally thought likely and therefore Hunt, Li and Luo suggested using a cone response curve which approximates a power curve for a much larger range of stimuli, so hue and saturation are better preserved. All these proposals, as well as others relating to chromaticity, resulted in a new colour appearance model, CIECAM02. In this model, the formula for lightness remains the same: :J = 100 (Asample / Awhite)cz But all the quantities that feed into this formula change in some way. The parameter c is now continuously variable as discussed above and z = 1.48 + √n. Although this is higher than z in CIECAM97s, the total effective power factor is very similar because the effective power factor of the achromatic response is much lower: :$\frac = \frac$ As before, this formula assumes bright conditions. Apart from 1220, which results from an arbitrarily assumed cone response constant, the various constants in CIECAM02 were fitted to experimental data sets. The expression for the brightness has also changed considerably: :$Q = \frac \frac \left(A_ + 4\right) \left\left(\frac\right\right)^$ Note that contrary to the suggestion from CIECAM97C, CIECAM02 contains no provision for the Helmholtz–Kohlrausch effect.CIE technical committee: Colour Appearance Models for Color Management Applications
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# Other psychological effects

This subjective perception of luminance in a non-linear fashion is one thing that makes gamma compression of images worthwhile. Beside this phenomenon there are other effects involving perception of lightness. Chromaticity can affect perceived lightness as described by the
Helmholtz–Kohlrausch effect The Helmholtz–Kohlrausch effect (after Hermann von Helmholtz and V. A. Kohlrausch) is a perceptual phenomenon wherein the intense saturation of spectral hue is perceived as part of the color's luminance. This brightness increase by saturation ...
. Though the CIELAB space and relatives do not account for this effect on lightness, it may be implied in the Munsell color model. Light levels may also affect perceived chromaticity, as with the Purkinje effect.