Lightness and Luminance
Images from a video display are a combination of color and light. Video calibration allows us to address both aspects because the meters we use to measure our displays return both color data and brightness data. However, information about the brightness of your display can be represented in three ways: lightness, absolute luminance, and relative luminance.
Absolute luminance is a linear unit of light intensity measured by color analyzers and luminance meters. It is reported in either metric candelas per square meter (cd/m2) or imperial foot lamberts (ft-L). Either measures the intensity of light emitted from a diffuse surface, such as from a flat panel display or projector screen. SMPTE has established standards for luminance of reference displays. This is 120 cd/m2 (35 ft-L) for flat panels and 48 cd/m2 (14 ft-L) for front projection.
Relative luminance is also a linear measurement of light output and is typically represented as a number between 0-1.0, with 1.0 offered as the intensity of white. All other values are expressed as percentages of white using the symbol Y. Video calibration data is presented typically in the xyY format, with xy being coordinates that define color and Y representing the light output. If a green color, for example, has a Y value of 0.7134 that simply means that the green is 71.34% as intense as white at the same level of stimulus.
Lightness is also a measurement of light output, but it is not linear because it is perceptually weighted. Human vision is much more sensitive to small changes in light perception under low light conditions than we are of the same change under higher light conditions. To illustrate the non-linear nature of lightness, see the chart below.
We have already perceived 50% of the difference between black and peak output when only approximately 18% of the stimulus is received.
The lightness measurement is useful in two ways. First, it is the method for quantifying light output that is used for calculating dE. Both CIELUV and all of the LAB-based dE formulas use lightness (it is the 'L' in LUV and LAB). Second, lightness is useful for understanding the need for gamma. As you may have perhaps noticed, the lightness curve above is almost exactly the inverse of the gamma curve we measure from commercial displays. It is the canceling out of the gamma of the display by the inverse sensitivity of human vision that produces a natural perception of light output from our televisions. What gamma value is closest to a perfect inverse of the lightness function? This source reports it as 2.32. Others recommend 2.35.
ChromaPure reports absolute luminance for the grayscale, absolute and relative luminance for the gamut and color decoding modules, and lightness for the color management module.