Lightness

Also known as luminance or intensity of a colour. It is the visual perception of the Luminance (\(L\)) of an object. In Colorimetry and Colour Appearance Models, lightness is a prediction of how an illuminated colour will appear to a standard observer. While luminance is a linear measurement of light, lightness is a linear prediction of the human perception of light.

But human vision's lightness perception is non-linear relative to light, so we have to use some alternative for perceptual lightness. Change of luminance can change the colour of light.

In colour spaces like Munsell, HCL and CIELAB, the lightness value achromatically constrains the maximum and minimum limits, and operates independently of the Hue and Chroma.

The Munsell value has long been used as a perceptually uniform lightness scale. CIELAB and CIELUV use \(L^*\) as the symbol for perceptual lightness (in contrast with luminance \(L\)). CIECAM02 uses \(J\).

In a subtractive colour model, the lightness changes to a colour through various tints, shades or tones can be achieved by adding white, black or grey respectively. This also reduces Saturation.

Relationship of Munsell value to the relative luminance

Munsell-Sload-Godlove value function (1933)

They launched a study on the Munsell neutral value scale, considering several proposals relating the Relative Luminance to the Munsell value, and they suggest:
\(V^2=1.4742Y-0.004743Y^2\)

Newhall-Nickerson-Judd value function (1943)

They suggest a quintic parabola (relating the reflectance in terms of value):
\(Y=1.2219V-0.23111V^2+0.23951V^3-0.021009V^4+0.0008404V^5\)

1976 CIELAB

CIELAB uses the following formula:
\(L^*=116(\frac{Y}{Y_n})^\frac{1}{3}-16\)
where \(Y_n\) is the CIE 1931 XYZ Colour Space Y tristimulus value of the reference White Point (the n subscript suggests "normalized") and is subject to the restriction \(\frac{Y}{Y_n}>0.01\). Pauli removes this restriction by computing a linear extrapolation which maps \(\frac{Y}{Y_n}=0\) to \(L^*=0\) and is tangent to the formula above at the point at which the linear extension takes effect.