A 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.

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