Grassmann's laws describe empirical results about how the perception of mixtures of colored lights (i.e., lights that co-stimulate the same area on the retina) composed of different
spectral power distributions can be algebraically related to one another in a color matching context. Discovered by
Hermann Grassmann
Hermann Günther Grassmann (german: link=no, Graßmann, ; 15 April 1809 – 26 September 1877) was a German polymath known in his day as a linguist and now also as a mathematician. He was also a physicist, general scholar, and publisher. His mat ...
these "laws" are actually principles used to predict color match responses to a good approximation under
photopic
Photopic vision is the vision of the eye under well-lit conditions (luminance levels from 10 to 108 cd/m2). In humans and many other animals, photopic vision allows color perception, mediated by cone cells, and a significantly higher visua ...
and
mesopic
Mesopic vision, sometimes also called twilight vision, is a combination of photopic and scotopic vision under low-light (but not necessarily dark) conditions. Mesopic levels range approximately from 0.01 to 3.0 cd/m2 in luminance. Most nig ...
vision. A number of studies have examined how and why they provide poor predictions under specific conditions.
Modern interpretation
The four laws are described in modern texts with varying degrees of algebraic notation and are summarized as follows (the precise numbering and corollary definitions can vary across sources):
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These laws entail an algebraic representation of colored light.
Assuming beam 1 and 2 each have a color, and the observer chooses
as the strengths of the primaries that match beam 1 and
as the strengths of the primaries that match beam 2, then if the two beams were combined, the matching values will be the sums of the components. Precisely, they will be
, where:
:
:
:
Grassmann's laws can be expressed in general form by stating that for a given color with a
spectral power distribution the RGB coordinates are given by:
:
:
:
Observe that these are linear in
; the functions
are the
color matching function
The CIE 1931 color spaces are the first defined quantitative links between distributions of wavelengths in the electromagnetic visible spectrum, and physiologically perceived colors in human color vision. The mathematical relationships that defin ...
s with respect to the chosen primaries.
See also
*
Color space
A color space is a specific organization of colors. In combination with color profiling supported by various physical devices, it supports reproducible representations of colorwhether such representation entails an analog or a digital represen ...
*
CIE 1931 color space
The CIE 1931 color spaces are the first defined quantitative links between distributions of wavelengths in the electromagnetic visible spectrum, and physiologically perceived colors in human color vision. The mathematical relationships that defin ...
References
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Color
Visual system