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LUMINANCE AND CHROMATICITY

On This Page:  • Luminance   • Chromaticity  • Limitations on Applications of Luminance and Chromaticity 


This page discusses the psychophysical concepts of luminance and chromaticity and their use in practical applications.

To achieve a standard, shared technical description of the perceptual effects of light stimuli on human observers, international organizations have developed a "standard observer". This is a hypothetical typical human visual system that is described in terms of equations relating its quantitative visual responses to measurable physical statistics of light stimuli. The descriptions are therefore "psychophysical". The equations that define the standard observer are based on averages of laboratory measurements of the visual responses of real human subjects to particular light stimuli under particular viewing conditions.

Luminance Back to the top of the page.

Spectral Dependence of Brightness. Luminance is simply a statistic designed to express the fact that lights of equal power but different wavelengths do not
all appear equally bright.

Graph of the CIE V-lambda photopic spectral sensitivity function. Relative sensitivity (0 to 1) is plotted as a function of visible wavelength (380 to 780 nm). The curve is bell-shaped with a maximum at 555 nm.

Even though the lights of the various wavelengths are equal in power from a physical standpoint, the visual system is not equally sensitive to them. For moderate-to-high light energies ("photopic" lights), brightness is greatest at wavelengths in the vicinity of 555 nm and decreases toward both ends of the spectrum. In 1924 the Commision Internationale d'Eclairage (CIE) adopted a standard photopic observer. Photopic luminance is defined as:

Equation for luminance as a function of spectral power, photopic spectral sensitivity, and wavelength.

where P is spectral power and V is the photopic spectral sensitivity of the standard observer.

Most of the lights in visual displays are at energies in the photopic range. Lights in the lowest part of the display output may be "mesopic". Still darker lights, in the "scotopic" range, play little role in information displays. The spectral sensitivity of the scotopic standard observer is similar in shape to that of the photopic observer, but with its peak at 505 nm.

Power Dependence of Brightness. The luminance statistic describes the variation of brightness with wavelength, but it says nothing about how the perceptual variable, brightness, varies when one changes the energy of a light of fixed wavelength. There have been many measurements of brightness as a function of luminance. They have produced a number of different quantitative descriptions of the function. For our purposes we will assume that brightness grows roughly in proportion to the cube root of luminance, a function that is built into the CIE L*u*v* system, discussed below.

Lightness. For graphics that have the appearance of surface colors (e.g., resembling colored or printed paper) lightness is the important intensitive variable. Several standard lightness variables are available. We will use two, L* and Munsell Value.

Figure showing color patches that span the gamut of a CRT display, arranged in CIE h*L*c* coordinates. All have the same red hue. The patches vary in lightness vertically (black to white) and in chroma horizontally (gray to saturated red).

L* is the lightness variable of the CIE L*u*v* system. For achromatic patches it spans the scale of grays from black to white. For more chromatic patches it varies from darker to lighter. In the illustration on the left L* increases from bottom to top in each column of patches.

Equation for CIE L* as a function of the luminance of the target and the luminance of a perfect diffuse reflector.

where Y is the luminance of the patch and Yn is the luminance of a perfect diffuse reflector (ideal white patch).

Figure showing color patches that span the gamut of a CRT display, arranged in Munsell HVC coordinates. All have the same red hue. The patches vary in lightness (Munsell Value) vertically (black to white) and in chroma horizontally (gray to saturated red).

Value is the lightness variable of the Munsell color order system. For achromatic patches it spans the scale of grays from black to white. In the illustration on the right Value increases from bottom to top.

In 1974 the CIE adopted the equationImage that shows the mathematical figure V=L*/10 for Munsell Value.

Chromaticity Back to the top of the page.

Color Matching. Color matching refers to a procedure in which an observer is presented with two spots of light. One spot, the test light, is fixed. The second spot, the matching light, contains light that is a variable mixture of several light sources of different colors. The observer's task is to adjust the intensity of each of the component sources in the matching light until the color appearance of the matching light equals that of the test light. Normal human observers are able to match any test light with a matching light made up of only three sources. (This description is highly simplified--a number of conditions must be met for the matching to work. See Wyszecki and Stiles (1982) for more details.)

This tridimensionality of color matching has a great advantage for both basic and applied color work: If we define three standard primary sources for the matching light and define a standard observer's color matching behavior, then any test light can be described by just three numbers, the intensities of the primaries that produce a color match for the standard observer. The 1931 CIE XYZ system implements this scheme. The CIE standard observer's color matching was defined by averaging color matching data from several real human observers in several research laboratories, using three real light sources for the matching light. To simplify the logic and computation in applications, the committee decided to mathematically transform the data in such a way that the red, green, and blue real light sources used in the laboratory measurements were replaced by three theoretical light sources. In this system, then, any test light is characterized by three numbers ("tristimulus values"), X, Y, and Z, which are the amounts of each of the three primaries needed by the standard observer to match the test light. Y, for example, was defined to be mathematically identical to the luminance of the test light. For convenience in plotting colors graphically, the chromatic variables are characterized by a two-dimensional derivative statistic (the "chromaticity coordinates") which are derived from X, Y, and Z by normalizing each to their sum:

x = X / (X + Y + Z)
y = Y / (X + Y + Z)
z = Z / (X + Y + Z) = 1 - (x + y)

Any two of these (conventionally x and y are used) plus the luminance, Y, fully capture the standard observer's color match to the test light. Graphs of the x and y coordinates of lights are called chromaticity diagrams. Chromaticity diagrams show two of the three dimensions of color, the third being luminance.

Graph of the 2D color gamut of a CRT display and two laptop LCDs. Small color patches show the locations of the three primary and three secondary colors. The CRT gamut is larger, especially in the blue region.

This is a chromaticity diagram on which we've plotted several familiar lights. The triangles show the (low-luminance) gamuts of two laptop LCDs and a SONY CRT monitor. All of these displays are nominally white-aligned to 6500K, and their chromaticities lie near the D65 chromaticity. The color patches in the figure have the indicated chromaticities on the SONY monitor. The smooth curve is the spectrum locus, with long wavelengths at the right-hand end.

One of the most useful properties of chromaticity diagrams is their convenient representation of mixtures of two lights. Under the assumed laws of color mixture that underlie this system, the chromaticities of all mixtures of any two lights lie on the straight line connecting the chromaticities of the two lights. For example, the magenta illustrated is a mixture of the red and blue primaries of the SONY display, so it lies on the line connecting the chromaticities of the red and blue primaries. A little thought shows that any light that the monitor can make is within the triangle connecting the primaries: Any mixture of the red and blue primaries lies on the lower side of the triangle. If the green primary is then added to any of those lights, the mixture lies on a line connecting that light to the green primary. These mixtures together populate the triangle which is therefore the (xy) gamut of the monitor.

By the same logic, all mixtures of any of the spectrum lights lie on straight lines interconnecting the points on the spectrum locus. These all lie within the area bounded by the spectrum locus, which therefore is the 2D gamut of physically realizable lights.

Limitations on Applications of Luminance and Chromaticity Back to the top of the page.

These concepts are extremely useful in both theoretical and applied work. For example, in principle, making two patches of color on different displays have the same xyY should be a good start toward identical apparent color. However, there are significant limitations you should keep in mind when using these tools. Their mathematical properties are derived from assumptions. If your situation deviates substantially from those assumptions, your practical results may differ significantly from predictions based on luminances and chromaticities. Some of these assumptions are described below. For a more complete technical treatment see Wyszecki and Stiles (1982).

Color Matching. Strictly speaking, chromaticities indicate which lights will match for the standard observer under the exact laboratory conditions that generated the data on which the system is based, given further assumptions about the mathematical properties of human color vision. The utility of the concepts would have been seriously limited if minor departures from the assumed conditions were to produce gross errors in the predictions. The CIE System has been widely regarded to be a practical success, with useful descriptions and predictions, but there are still some active disputes in the color community about the robustness of the system. Two patches of light with the same xyY will generally approximately appear the same color subject to the following considerations:

Size and Shape--The 1931 CIE System is based on matches for patches subtending two degrees of visual angle, or about 1.75 cm viewed from 50 cm (or 0.7 inches viewed from 20 inches). For much larger areas there is a second CIE system, the CIE 1964 System, based on matching with 10 degree patches. If the user's patches are very much smaller than two degrees other visual phenomena (e.g., small-field tritanopia) may produce poor predictions. If the shape departs radically from a blob the predictions might be affected. In information displays small or thin symbols (e.g., thin lines, small fonts) may be problematic for this reason.

Edges and uniformity--The matches strictly applies only to uniform areas. If the pattern in question is textured or has smooth gradients of color, the color appearance can be very different from a uniform patch with the same xyY.

Surrounding areas, previously viewed areas--If two patches with the same xyY are surrounded by different colors they may not match, and they may match when their xyY are different. This phenomenon is called "simultaneous color contrast." The same applies to two patches that are viewed immediately after viewing fields of different colors. The aftereffects of the preceding lights may differentially alter the response to the target patches in the phenomenon called "successive contrast."
More about Simultaneous and Successive Contrast

Observer characteristics--A significant fraction of the male European population has abnormal color vision. By definition they will accept a wider range of color matches than color normals. Older observers may have a significant yellowing of the pre-retinal optical media of their eyes which reduces their sensitivity to shortwave light.
More about Individual Differences in Color Vision

Color Appearance. Two patches with the same xyY will match (have the same appearance, subject to the above restrictions), but there is no guarantee about what that appearance will be. The appearance of any light is affected by a number of visual variables such as state of adaptation of the eye, size and contour sharpness, location on the retina, etc. For this reason the customary associations of regions of the chromaticity diagram with particular color appearances should be considered an approximation that requires reasonable approximations to standard viewing conditions. For most (but not all) computer graphics applications some conditions will be met, for example,

- Adaptation to a light near the center of the area within the spectral locus, e.g., around (0.3, 0.3)
- Photopic luminance, e.g., above 10 nits
- Color normal observer.

Others are frequently not met, for example,

- Gray or dark surround
- Patch larger than 0.5 deg.

Other Considerations. Other factors may get in the way of accurate matching by xyY. The matches depend on the light reaching the observer's retinas, not the light generated by the the display. If reflections or stray light are different in two viewing situations, patches with the same nominal xyY may not match across the viewing situations.


Related Topics:
go to this page Luminance Contrast
go to this page Designing with Luminance Contrast
go to this page Luminance Contrast in Color Graphics
go to this page Individual Differences in Color Vision
go to this page Luminance Contrast Color Guidelines



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