## Wednesday, January 11, 2012

### Q: If I mix 700nm (red) light and 400nm (green) light, is the result a color that can't be made by a single wavelength?

The answer is yes -- if you mix light from a laser (monochromatic light) at 700 nm with another laser at 400 nm, the resulting radiation will be different from any monochromatic light.

That's true in two ways:
• The resulting radiation is radiometrically (or physically) distinct from any monochromatic light. Adding two sine waves of different frequencies won't make a sine wave.
• The resulting radiation is photometrically (or perceptually) distinct from any monochromatic light, when observed by a human with normal (trichromatic) vision.

You can see this on the CIE standard observer colorimetry diagram:

(from http://en.wikipedia.org/wiki/CIE_1931_color_space)

This horseshoe-shaped figure represents the human perception of color near the area of focus (where cones predominate), once overall brightness (luminance) is factored out.

The top outside of the horseshoe (with the numbers going from "380" on the lower left to "700" on the lower right) is known as the "spectral locus": it represent the colors you can get with monochromatic light, e.g. by varyting a laser in wavelength from 380 nanometers to 700 nanometers.

The bottom line that directly connects "380" and "700" is known as the line of purples. These colors (all shades of purple) cannot be made by any single laser! And the entire interior of the horseshoe, including the middle where "white" is, also requires more than one laser.

Your color -- a combination of light at 400 nm and 700 nm -- will be found somewhere very close to the line of purples. (The more 400 nm, the more it will be closer to that side, and vice versa.) You can tell from the diagram that these colors aren't on the spectral locus, and therefore can't be made with a single laser.

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The standard "R'G'B'" color spaces work by picking three illuminants from the inside of this diagram. (These can be three phosphors on a CRT, three filters on an LCD, three slices on the color wheel of a DLP display, three layers of emulsion on a piece of color film, etc.) Each illuminant's color has a point within the horseshoe, and the three points form a triangle. By varying the amount of R, G, and B, we can make a color that is perceived the same as any color that lies within the triangle.

Here's one of the most popular triangles, known as the ITU-R Rec. BT.709 or sRGB primaries. The three colors on your computer monitor are probably close to these points on the triangle, meaning your monitor can make any color within the triangle. But as you can see, it takes three illuminants to have any nonzero area in this "perceptual" space of colors (again, with luminance already factored out).
No single laser can do it.