In photometry, a light's color rendering capacity is a measure of how broad a color space can be perceived under that light's illumination. Color rendering is measured on a scale of 1 to 100, where 100 is equivalent to sunlight. See color rendering index.

Colors are perceived because objects reflect only some frequencies of incoming light; the rest is absorbed. A red object reflects red light. However, a light source missing some frequencies of light will not be able to show colors as well as sunlight, because objects can not reflect frequencies of light that are not emitted by the light source. Sources of artificial light that heat a piece of wire until it glows (standard incandescent lamps, or halogen lamps) emit a smooth distribution of light from low "red" frequecies to high "blue" frequencies, so these light sources have very good color rendering. These lamps are "black body" light sources.

Many artificial light sources use more efficient light generation techniques, but do not produce light of all frequencies. A well-known example is the orange light of a low pressure sodium lamp that is used in older street lighting; green objects and black objects both appear black since the orange light emits very little of the light that is required to make green. All gas-discharge lamps (including fluorescent lamps) have this problem, but to lesser degrees than low-pressure sodium, and some of them are quite acceptable for shop and television studio usage.

Note that light sources are often rated with a "color temperature" which is a measure of the average color of the light based on the temperature of an equivalent "black body", but color temperature does not measure the distribution of light frequencies. A light source with a low color temperature (a standard incandescent lamp) can easily have much better color rendering than a "whiter" fluorescent lamp.

To put this in the context of a standard, simple color science model, refer to HSV color space. The colors perceivable under a particular illumination will form a continuous solid in the HSV color space (and in all the other transformations of color space, e.g. RGB, CIE, etc.). For a bright white light, this solid fills nearly the entire color space, while for a dim red light, the solid is a small, squished segment of the total space. The rendering capacity is thus usually defined as the volume of the solid representing all the colors perceivable, divided by the total volume of the color space.

Other measures of color rendering properties of a light source are:

How closely the color appearances of colored samples lit by a given light resemble those of the same samples lit by a reference Planck radiator.

How different the color appearance of eight colored samples lit by a given light look in comparison with each other. This is called the Color Discrimination Index (CDI)

References

CIE Publication 13.3. Method of measuring & specifying colour rendering properties of light sources. CIE,1995.

Thornton WA. Colour-discrimination index. J. Opt. Soc. Am. 1972, 62(2), 191-194. PMID 5009385

Xu H. Colour rendering capacity and luminous efficiency of a spectrum. Lighting Res. Technol. 1993, 25, 131-132

Xu H. Colour rendering capacity of illumination. J. Opt. Soc. Am. 1983, 73(12), 1709-1713. PMID 6663375