Grassmann's Law (optics)
Encyclopedia
In optics
, Grassmann's law is an empirical result about human color perception: that chromatic sensation can be described in terms of an effective stimulus consisting of linear
combinations of different light colors. It was discovered by Hermann Grassmann
.
In other words, if beam 1 and 2 are the initial colors, 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 law 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 functions with respect to the chosen primaries.
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
, Grassmann's law is an empirical result about human color perception: that chromatic sensation can be described in terms of an effective stimulus consisting of linear
Linear
In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...
combinations of different light colors. It was discovered by Hermann Grassmann
Hermann Grassmann
Hermann Günther Grassmann was a German polymath, renowned in his day as a linguist and now also admired as a mathematician. He was also a physicist, neohumanist, general scholar, and publisher...
.
Statement
An early statement of law, attributed to Grassmann, is:Modern interpretation
If a test color is the combination of two other colors, then in a matching experiment based on mixing primary light colors, an observer's matching value of each primary will be the sum of the matching values for each of the other test colors when viewed separately.In other words, if beam 1 and 2 are the initial colors, 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 law can be expressed in general form by stating that for a given color with a spectral power distribution
Spectral density
In statistical signal processing and physics, the spectral density, power spectral density , or energy spectral density , is a positive real function of a frequency variable associated with a stationary stochastic process, or a deterministic function of time, which has dimensions of power per hertz...
the RGB coordinates are given by:Observe that these are linear in
; the functions are the color matching functions with respect to the chosen primaries.