With the increasingly widespread application of digital images, the colorimetric term “color gamut” has gradually entered the public eye. In the introductions of mobile computing devices (such as smartphones and tablets), computer display devices (desktop and head-mounted), televisions, projectors, and other products, the term color gamut and its corresponding specifications (e.g., 95% sRGB) are frequently seen. Indeed, the larger the color gamut, the wider the range of colors a display device can reproduce, and the better the reproduction of highly saturated colors. Consequently, concepts like extended gamut and wide color gamut have emerged. In computer terminology, display devices, printers, and the like are all output devices, and the color gamut can partially reflect the color reproduction capability of the output device (and medium). So, we cannot help but ask: as the primary source of digital images, do input devices represented by digital cameras and scanners also have a color gamut? Today, we will discuss this interesting question together.

What is a Color Gamut?

According to the definition in the International Lighting Vocabulary (https://cie.co.at/eilvterm/17-32-007), a color gamut refers to a set (volume, area, or solid) of specified colors in a color space. Here, the “entirety” can refer to all the colors contained in an objectively existing medium (such as a scene, a painting, a photograph, a book, etc., under certain conditions), or all the colors that a device or medium can reproduce (under certain conditions). Clearly, this article discusses the latter, which is a characteristic of the device. Furthermore, we find that one of the keywords here is “reproduce,” a concept closely related to output devices. In addition, another keyword in the above definition is color space. We know that human color vision is a three-dimensional concept based on the LMS three types of cone cells; therefore, the color space, and the color gamut as a part of it, is also three-dimensional.

For example, the widely used sRGB standard (IEC 61966-2-1:1999) defines a color space for digital image encoding. When the normalized values of the RGB tristimulus values range from [0,1], all the corresponding colors form a color gamut. Observed in the sRGB color space, this cube-shaped gamut is located in the first octant, with one of its vertices coinciding with the origin, and the three edges connected to this vertex coinciding with the three coordinate axes, as shown in Figure 1. If the sRGB color gamut is represented and observed in the CIE 1931 XYZ color space, the result will be a parallelepiped, as shown in Figure 2. Obviously, a color gamut is a three-dimensional concept, one dimension of which is related to luminance (lightness), which we will temporarily call the luminance gamut. If we project the sRGB color gamut in Figure 2 onto the unit plane (X+Y+Z=1), we obtain the projection of the sRGB color gamut on the CIE 1931 xy chromaticity diagram, as shown in Figure 3, where the horseshoe-shaped region covers the chromaticity range visible to the human eye. If the three primaries of a digital image display device conform to the definition of the sRGB standard, then its color gamut corresponds to the triangle in Figure 3, which we will temporarily call the chromaticity gamut.

To summarize, we have the following understanding of the color gamut:

1. The color gamut is a concept closely related to output devices;
2. The color gamut is three-dimensional; in different color spaces, the same color gamut has different shapes;
3. The range of luminance (lightness) and the range of chromaticity (chroma) together determine the boundaries of the color gamut.

It is worth noting that in some color spaces (such as XYZ or sRGB), the color gamut and its boundaries can be accurately depicted given the luminance gamut and chromaticity gamut of sRGB, whereas in certain color spaces (such as CIE 1976 L*u*v* or ICtCp), the shape of the sRGB color gamut is relatively complex, and the luminance gamut and chromaticity gamut themselves do not have an explicit and direct relationship with the shape of its three-dimensional color gamut. Secondly, a color gamut is a range; it is only one metric for evaluating the color characteristics of an output device, and the accuracy of color reproduction is often a more important metric. Additionally, the impact of quantization bit depth should not be underestimated, as it determines the maximum number of colors a digital output device can reproduce, or rather, the number of samples obtained after sampling the color gamut. With a constant quantization bit depth, the larger the color gamut, the greater the difference between reproducible color samples, and the less continuous the color transitions.

What Factors Affect the Color Gamut of Digital Image Display Devices?

As typical output devices, digital image display devices often use additive color mixing for color reproduction. The principle is the temporal and spatial mixing of colored light; therefore, the color gamut of a digital image display device is related to its own physical characteristics and environmental factors. Under ideal conditions, the darkest color a display device can show is inevitably black (i.e., no light emission). However, in actual use, the display device may be affected by ambient light or its own physical characteristics (such as the reflection of ambient light on the screen surface, light leakage in LCD panels, etc.), making it unable to display absolute black, which in turn determines the lower limit of display luminance. The upper limit of luminance, apart from environmental influences, is mainly determined by the maximum spectral radiance that can be achieved when the display primaries are superimposed at their maximum radiant flux. The upper and lower limits of displayable luminance together determine the luminance gamut of the display device. A digital image display device has at least three primaries, and the spectral power distribution of the primaries determines their chromaticity coordinates, which in turn defines the boundaries of its chromaticity gamut. Obviously, in the chromaticity diagram, the purer the color, the closer its position is to the edge of the horseshoe-shaped region. The area of the polygon formed by connecting the primaries as vertices determines the chromaticity gamut of the display device.
In short, a digital image display device has both a luminance gamut and a chromaticity gamut.

Do Digital Cameras Also Have a Color Gamut?

Digital cameras and scanners are both typical input devices. So, do input devices have a color gamut? Let us take the digital camera as an example and compare it with the concepts of luminance gamut and chromaticity gamut in digital image display devices. The imaging sensors in common digital cameras are mostly semiconductor imagers, which consist of an array of a large number of identical pixel circuits. The pixel circuits are responsible for converting incident photons into charges and storing them. The charge is then converted into a voltage signal, and the finally digitized voltage signal becomes a pixel value reflecting luminance. The brightest color the imager can “see” mainly depends on the conversion efficiency from photons to charges (often called quantum efficiency) and the capacity of the potential well used to store charges (often called full-well capacity). Ideally, the imager can “see” colors with extremely low luminance, including black. In practice, the random generation of carriers in the semiconductor produces dark current. Although this current is very weak, the current generated by light with sufficiently low luminance will still be overwhelmed by this dark current. Therefore, the darkest color the imager can “see” is mainly determined by the quantum efficiency and the level of dark current. The ratio of the luminance of the brightest and darkest colors the camera can “see” is often called the dynamic range. In addition, some camera parameters (such as sensitivity, exposure time, lens relative aperture, etc.) as well as the reflection, scattering, diffraction, and absorption of light in the camera's optical path, all affect the brightest and darkest colors the camera can “see”, which we will temporarily ignore here. From this perspective, the camera does have a luminance gamut, similar to a display device.

As mentioned earlier, the width of the spectral power distribution of the display device's primaries directly affects the size of the chromaticity gamut; in other words, there are always some highly saturated colors that the display device cannot reproduce. However, as long as the radiation of the scene is within the spectral detection range of the camera's imager, and as long as the luminance of the scene is within the camera's dynamic range, the camera can “see” it. From this angle, the concept of chromaticity gamut does not seem to apply to cameras. However, careful consideration reveals that “seeing” a color and “seeing” it accurately are not the same thing. Although a camera does not directly reproduce colors, when observing the same scene, the colors seen by an ideal camera and the human eye should be completely identical or mutually convertible, i.e., satisfying the Luther condition. The design goal of colorimeters is to satisfy the Luther condition, but actual cameras generally do not meet this condition. That is to say, actual cameras operate in a different color space from the human eye, and there is no unique, definitive color space transformation relationship between the two. Therefore, digital cameras use methods such as correction matrices and lookup tables to make this transformation as accurate as possible, and this “accuracy” is generally optimized for a given camera, a given light source, given color samples, and a given color style.

It can be said that the essence of a camera is to map the spectral power distribution of electromagnetic radiation to a standard, device-independent color space (such as CIE 1931 XYZ or sRGB). The result of the camera's mapping will inevitably differ from the mapping result of a colorimeter (or a standard colorimetric observer). Imagine what would happen if monochromatic light of all wavelengths in the visible spectrum were mapped to the CIE 1931 XYZ color space through a camera and then reprojected onto the unit plane to obtain a chromaticity diagram. Generally speaking, spectral colors are not the primary focus of camera users and developers; therefore, the color space transformation will not be specifically optimized for monochromatic light. As a result, spectral colors are highly likely to be mapped to incorrect positions by the camera. At this time, the horseshoe-shaped spectral locus in the chromaticity diagram will be distorted, and may even extend beyond the horseshoe-shaped region. Although the distorted spectral locus still represents a boundary and can be called a gamut in a sense, what matters for a camera is the accuracy of color mapping, not the range covered by the gamut.

Summary
To summarize, the dynamic range of a digital camera's imager determines that it has a luminance gamut. However, as an input device, a camera does not have a chromaticity gamut similar to that of an output device.