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CRT chromaticity

gamut is in simple terms the "

**colorspace**" that a given CRT is able to display: The set of all colors in the

**CIE (x,y)** space that the monitor is capable of displaying.

This set, or gamut, is defined by three unique points on the CIE (x,y) plane: The reddest red, the greenest green, and the bluest blue. White is a combination of all light, thus it is a equal combination of red, green, and blue; somewhere in the middle of the space. These three points define a triangle and the given CRT can

**not** display any color outside the triangle.

To find this triangle we first must measure the output of the CRT. Each CRT is made up of a 2D hexagonal matrix where each line has a sequence of red, green, and blue

phosphors in order: RGBRGBRGBRGB. Each line is offset such that the R of one line falls directly below and between the GB of the previous line. In this way, a

pixel is defined by three phosphors which are in a sort of triangle. An

electron gun fires a certain amount of

electrons (vary the amount of electrons, vary the "

brightness" of the color) at each phosphor about once every 1/60th of a second. Three guns are used to fire at the three different phosphor sets: red green and blue. Each phosphor has a certain "

spectrum" of wavelengths it emits within the visible range (and probably some in the non-visible range, but we don't care about that). By using a measuring the CRT output at different colors, the spectrum can be approximated from a smooth curve to a set of points on that curve, given enough points. Call the number of points N_lambda. Now, a Nx1 matrix can represent the

illumination spectrum. For red phosphors this matrix can be called Pr. For Green and Blue use Pg and Pb. Combining these columns into a Nx3 matrix gives us P.

Now that a matrix of phosphor constants have been found for the given CRT, multiply it by e where e is the electron gun intensity and ranges over {0,1} (where zero is when the gun is off, one when it is on full blast). P*e is now a representation of every color the given CRT can display.

Taking the new matrix set, multiply it by the

CIE_XYZ matrix developed in 1931 to map these colors to the CIE XYZ colorspace. This is a 3D space and therefore it must be reduced to a 2D space in order to get (x,y) values. CIE set a standard of projecting (

perspective projection) the 3D space onto the plane X=Y=Z given a

center of projection at (0,0,0). This (new) 2D space can now be transformed into the

unit square {(0,0) (1,0) (1,1) (0,1)}. These final coordinates are the CIE (x,y) chromaticity coordinates. In this space is where the R, G, and B points are defined and a triangle can be drawn with these three points that defines the colorspace which a CRT monitor is capable of displaying.