Newer display technologies, including microdisplay projection and LCD TV, are not limited by the color-gamut restrictions of phosphor-based displays, such as CRTs, and can have expanded color gamuts covering most natural colors. Evaluation and comparison of these expanded color gamuts is difficult, however, and no standard method is used by the display industry. In Part 1 of this two-part series, colorimetry issues associated with wide-color-gamut displays will be explained, covering the basics of colorimetry, color-difference formulas, and the color gamuts of video signals.

by Matthew S. Brennesholtz

HIGH-DEFINITION TELEVISION (HDTV) sets with color gamuts larger than the specified HDTV video color gamut are becom-ing common in the consumer-electronics industry. Everyone has heard a display maker boast, "I have a color gamut that is 105% of NTSC" or, perhaps more confusingly, "I havean expanded color gamut that is 75% of NTSC!" What do they mean by 105% of NTSC and how can 75% represent an "expanded" gamut? To understand the answers to these questions, it is necessary to look at three different technologies: basic color science, video-signal transmission encoding, and color gamuts of displays.

This article and the follow-on article to appear in the October issue of Information Display will review these three issues to the point where display engineers and consumers can begin to evaluate the claims of different manufacturers and put them in perspective.

Basic Colorimetry

The Commission Internationale de l'Eclairage¹ (CIE) is the international standards body that has established methods for measuring color. Several different methods have been established, with the two most commonly used by display engineers called CIE 1931 and CIE 1976.²

The CIE 1931 chromaticity diagram (two-degree standard observer) was the original system established in 1931 (Fig. 1³) and remains the most commonly used system by display engineers. The system is based on human-factors experiments in the 1920s and 1930s with a number of observers, so it represents an average of all observers, not an individual observer. It is most commonly called the x-y system,⁴ after the x and y symbols normally used to represent the color coordinates. Human vision is a three-dimensional system, and in display engineering the three coordinates most commonly used are the x-y color coordinates and Y (upper-case Y) representing luminance. The units for luminance depend on the exact geometry of the measurement system, but the two most important to display engineers are lumens (lum) and candelas per square meter (cd/m² ), also known as nits. The outer horseshoe-shaped boundary in the CIE 1931 diagram represents pure spectral colors, such as the ones made by a laser. The straight edge along the bottom represents a mixture of the longest wavelengths visible to humans, about 770 nm, with the shortest wavelengths visible, about 380 nm. The interior region represents mixtures of two or more wavelengths of light. White is near the center of the diagram. Natural white sunlight is formed by a mixture of all wavelengths, although "white" can also be made with only two or three wavelengths mixed together.

When two colors are slightly different from each other, they would plot on the x-y diagram at slightly different positions. In an ideal color diagram, if two different colors both, for example, in the green region, were just barely distinguishable from each other, and two other colors, both in the blue, were just barely distinguishable from each other, the distance between the two pairs of color points would be equal. The biggest problem with CIE 1931 is that barely distinguishable pairs of colors have radically different distances between them, depending on whether they are in the red, green, or blue portion of the color diagram. The ellipses in Fig. 1 represent distinguishable color pairs in different regions of the x-y color space. These ellipses are plotted 10 times their actual size to make them more visible. A color point on the ellipse, if plotted at true size, would be just barely distinguishable from the color point at the center of the ellipse.

This problem with the CIE 1931 diagram is also shown in Fig. 2(a) with four representative ellipses. The triangle in this figure represents the color gamut of HDTV video encoded with the ITU Recommendation 709 color gamut. An HDTV display with these primary colors could then make any additional color inside the triangle by blending two or three of the primary colors. Note that in the green region of the x-y diagram, the ellipse is long and thin, so two colors with a relatively large Δy but a small Δx could not be distinguished from each other by the human observer, while two green colors with a modest Δx and no Δy could be distinguished by the average observer. In addition, the ellipses are smaller in the blue region than in the red or green regions. In the ideal color space, all these ellipses would be circles of the same size. While color scientists have derived color spaces where this is nearly true, these color spaces are quite complex mathematically and difficult for a display engineer to use. Sometimes they are impossible to use because they require measurements not commonly made or items not under the control of the display engineer, such as the color of the areas surrounding the display.

The CIE 1976 color space is derived from the CIE 1931 color space through a simple coordinate transformation and uses the variables u′-v′ as color coordinates. Similar to the CIE 1931 system, the CIE 1976 system is actually a three-dimensional color space, and the same Y luminance measurements are used in both systems. This system is a compromise: It has most of the mathematical sim-plicity of the x-y space, the ellipses are more equal in area than they are in the x-y space, and the long and short axes of each ellipse are more nearly equal in length.

Figure 2(b) shows the CIE 1976 u′-v′ color diagram with the same four representative ellipses and the Rec. 709 gamut. Table 1 shows the calculated areas of the four representative color-difference ellipses in square x-y units and in square u′-v′ units. As can be seen, in x-y space, there is a vast difference in area between the largest and smallest ellipses: The green ellipse is about 62 times the area of the blue ellipse, or 5.5 times the area of the red ellipse. Therefore, comparing areas of two different color gamuts in x-y space, in terms of human perception, is primarily a comparison between the green areas of the color gamuts.

In u′-v′ space, the situation is better, although it is not perfect. The red ellipse is now the largest one, and it is only 3 times the size of blue, which is still the smallest one. More importantly from a display point of view, the red ellipse is only 1.4 times the size of the green ellipse. Therefore, if color gamuts are compared by their area in u′-v′ space, the red and green will roughly get equal weight. While the blue is still under-weighted, at least the error factor is only 3 times, not 62 times.

Most display engineers continue to use the x-y system and have not switched to the u′-v′ system. One reason for this is that while the u′-v′ system is improved compared to the x-y system when used to compare two colors, it still contains major errors. Unfortunately, some individuals and companies have switched and some have not, so data is available in both forms, and it is necessary for display engineers to be familiar with both systems.

Colorimetry of Video Signals

Broadcast video signals assume the video will be displayed on systems with certain red, green, and blue color points. These broadcast signals also assume the display will be set up to produce a certain white point, typically D65 (about 6550K). The actual colors for the system to display are not transmitted in a normal video signal. What is transmitted is the color difference, which is the difference between the color to be displayed and white. This portion of the video signal is called the "chrominance," and it is encoded in slightly different ways for the different video signal formats. There are actually two chrominance signals, corresponding to the two-dimensional color space shown in Figs. 1 and 2. The video signal also transmits the relative luminance to be displayed in the range from 0 to 100%, commonly called the "luminance" part of the video signal. For black-and-white TV, only the luminance signal is decoded and displayed – the chrominance signals are ignored. For color TV, the luminance and both chrominance signals are decoded. These color and luminance signals are then displayed as the full-color image.

For NTSC, these color difference signals are encoded onto the video signal in cylindrical coordinates as the amplitude and phase of the color sub-carrier. The color sub-carrier in NTSC is a 3.58-MHz signal added to the luminance signal. The amplitude of this color sub-carrier defines how different the color to be displayed is from "white," while the phase of the signal, relative to the phase of a color burst at the beginning of each video line, defines the direction of this color difference. This is illustrated in Fig. 3. If a pure-red color is to be displayed in an area of the image, the phase of the color sub-carrier in that region would be 103.5° and it would have the maximum amplitude. This would produce, or at least should produce, a drive on the red cathode of the cathode-ray tube (CRT) corresponding to the luminance signal in that area of the image and no drive on the blue or green cathodes.

When NTSC was established in 1953, all this would have been done with analog vacuum-tube circuits. Today, it would be done with digital circuits with the data adjusted to correct for the difference between the red primary of the liquid-crystal display (LCD) or other display, and the red primary of the CRT. Note that in this process of decoding and displaying colors, the x-y color coordinates play no role. All colors are defined in terms of white plus the red, green, and blue (RGB) primary colors. If the display primary colors are different than the video primary colors, the wrong colors will be displayed unless correction factors are applied to the signals. These correction techniques are well known and can be implemented in either analog or digital circuitry.

Note that the axes in Fig. 3 are labeled R-Y and B-Y, which are pronounced "R minus Y" and "B minus Y," respectively. The "Y" is the symbol for luminance, as discussed above. For a given luminance signal, with a color sub-carrier with 0 amplitude, the current in the cathodes would be divided up approximately equally so the CRT would produce the target white. Note that a pure R-Y signal, i.e., the color sub-carrier has a 90° phase angle relative to the color burst, does not, in fact, produce red, just a color close to red with a little blue added. R and B in R-Y and B-Y should be interpreted as "reddish" and "bluish," rather than literally as red and blue.

Other video signals such as PAL or SECAM use different primary colors and different encoding angles, but the basic principals are the same as NTSC. Digital TV signals encode the color-difference signals digitally rather than as the analog amplitude and phase of a color sub-carrier. For digital signals, Cartesian coordinates are used to encode the color differences rather than cylindrical coordinates. I do not want to say x-y coordinates because, similiar to NTSC and other analog signals, the x-y color coordinates do not play any role in decoding or displaying colors in a digital-transmission system.

Figure 4 shows the primary colors for three key video signals plotted on the CIE x-y diagram. Readers might question why, given the superiority of the u′-v′ space over the x-y space, Fig. 4 and Table 2 are both in terms of x-y. There are three primary reasons for this:

1. Habit. This is not just the author's habit, but also the habit in the display engineering community.
2. While u′-v′ is better than x-y, it is not that much better than x-y that it can be used for critical color work without a full understanding of its errors. If engineers have to account for errors in the system they are using in any event, they might as well use the more common and simpler system.
3. Color gamuts for video signals are defined in terms of x-y, not u′-v′.

Fig. 4: CIE 1931 color diagram with major video color gamuts

The x-y color coordinates used to encode video signals for each of these formats, plus several other color-encoding schemes, are shown in Table 2. In addition, the intended application for each video format is listed in the table.

A glance at Table 2 shows a couple of important features. First, if the size of each color gamut is compared to the size of the NTSC color gamut in x-y space, a lower area percentage is obtained than if compared in u′-v′ space. This occurs because NTSC defines a very "green" primary color compared to the other systems. The strong bias in the x-y system toward the green then makes the NTSC gamut seem larger than it actually is. This can be seen most easily by comparing the NTSC gamut to the DCI gamut. In x-y space, the DCI gamut is 96% of NTSC, while in u′-v′ space, it is 109% of NTSC. The second feature to note is that standard color gamuts are quite small compared to NTSC. For example, Rec. 709 is only 71% of NTSC in x-y units. This explains how a gamut 75% of NTSC can be called "expanded" – it is expanded compared to the video gamut that is actually defined for a high-definition video signal.

While there is no established standard for this, if a display manufacturer claims, "my display has a color gamut of 105%," with no qualification, typically (but unfortunately not always) it means that the area of its color gamut in x-y space is 105% of the area of the NTSC color gamut. If it claims 140% of NTSC, normally the manufacturer would be using x-y space and referring to Rec. 709 or some other current TV standard. When using u′-v′ space, most engineers, but not all, specify that they are using that space.

The DCI format is different from the others listed in Table 2 and deserves a little extra discussion. First of all, DCI is not a broadcast video format. The DCI color gamut was established by the Digital Cinema Initiative for use in digital-cinema theaters and cinema post-production systems. The specification for DCI encoding of feature films and other material for digital cinema was released in July 2005, and DCI-compliant equipment is currently being designed, built, and installed in cinema houses nationwide. Eventually, DCI-compliant electronic-cinema systems are expected to replace most or all film-based projectors for showing feature films. While DCI is a U.S. standard, it defines how Hollywood movies will be released in electronic format. If a non-U.S. movie house wants to show Hollywood-made electronic cinema movies, the projection system will need to be DCI compliant.

The encoding of color and luminance is fundamentally different for DCI compared to all the video broadcast formats. As discussed above, all the video formats define a luminance and color-difference signal, with color difference referenced to a white point and luminance referenced to 100%, which is whatever the maximum brightness the display can show. DCI transmits absolute color and brightness, in the form of the X, Y, and Z color values.⁵ Since luminance and color are in absolute terms, rather than compared to reference points, the defined primary colors and white point in the DCI specification are much less important than the primary colors and white in a normal video standard.

While this expanded color gamut is not currently used as a television gamut, Hollywood will produce all feature films in the future in digital form with this color gamut. I expect that this larger color gamut will eventually be encoded into high-definition or Blu-ray DVDs of feature films using xvYCC encoding.⁶ At that point, makers of DVDs and expanded-color-gamut TVs will advertise: "See the same colors seen in the movies." Competitive pressures will then force all signal providers and all HDTV manufacturers to follow suit and provide for expanded color gamuts.

Editor's Note: Part 2 of this article, to be published in the October issue of Information Display, will explore how the colorimetry and video signals discussed this month actually apply to wide-color-gamut displays. The limitations of measuring color-gamut area, even in u′-v′ space, will be discussed and an improved measure of color-gamut size will be proposed.

Table 2: Color gamuts for common video signals Standard

¹In English, this is the International Commission on Illumination. The organization is most commonly known by its French initials, CIE. http://www.cie.co.at/cie/.

²See, for example, G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data, and Formulae, 2nd ed., (John Wiley & Sons, New York, 1982) for far more detail on colorimetry than the average person can absorb.

³Figure from article on "MacAdam Ellipse" in Wikipedia, The Free Encyclopedia. Retrieved July 19, 2006, from http://en.wikipedia.org/w/ index.php?title=MacAdam_ellipse&oldid=44228211.

⁴The notation of this system distinguishes small letters such as x, y, and z used for normalized values and upper-case letters such as X, Y, and Z used for non-normalized values.

⁵See, Projection Displays by Ed Stupp and Matt Brennesholtz (John Wiley and Sons, New York, 1999) for an explanation of how x, y, and luminance are calculated from X, Y, and Z, which in turn are calculated from the spectrum of the light.

⁶See, for example, T. Matsumoto, et al., "xvYCC: A New Standard for Video Systems Using Extended-Gamut YCC Color Space," SID Symposium Digest Tech Papers 37, 1130–1133 (2006). •