Metamerism is a colorimetric term used to describe the phenomenon where color stimuli with different spectral compositions produce the same color perception (i.e., have the same tristimulus values). The English word for this is “metamerism,” which was originally a chemical term referring to isomerism (the phenomenon where molecules have the same types and numbers of atoms but different molecular structures due to different chemical bonds). Whether used as a colorimetric term or in its original chemical context, “metamerism” might initially sound far removed from our daily lives. But is that really the case? In this article, we will uncover the truth about metamerism together.

The Essence of the Metamerism Phenomenon

Any color stimulus existing in the form of optical radiation has a corresponding frequency spectrum, commonly referred to as its spectral (power) distribution. If we “decompose” this distribution into numerous single frequency components, it can be regarded as a vector in a high-dimensional linear space. When light emitted from a light source interacts with certain materials, its spectral power distribution is altered by these materials due to absorption, scattering, and other effects. This process can be viewed as the rotation and scaling of vectors in a high-dimensional space. From this perspective, a color stimulus at the physical level is a high-dimensional concept.

For individuals with normal color vision, there are three types of cone cells on the retina of the human eye. The outer segments of these cells contain light-sensitive substances called visual pigments. The molecular structures of the visual pigments in the three types of cells differ slightly, leading to differences in their spectral characteristics. Under photopic vision conditions, the pigments decompose under the action of color stimuli, triggering a series of photochemical reactions. The cone cells become excited by the light stimulation, generating nerve impulses. The degree of excitation of the cone cells is directly related to the spectral power distribution of the color stimulus and the spectral response characteristics of the human eye (which include the spectral transmittance of the physiological structures themselves, as well as the degrees of light and chromatic adaptation of the cone cells). Here, the spectral response of the human eye can also be regarded as a vector in a high-dimensional linear space.

Thanks to the differences in the spectral characteristics of the three types of cells, their degrees of excitation in response to color stimuli also differ, and color vision is precisely the product of these differences. Clearly, color vision is a three-dimensional concept, so color can be considered a vector in a three-dimensional linear space. Therefore, mathematically, the process of color formation can be viewed as the inner product (dot product) of the color stimulus vector and the human eye's spectral response vector in a high-dimensional linear space. In other words, it is a dimensionality reduction from a high-dimensional linear space to a three-dimensional linear space. Dimensionality reduction is a many-to-one operation, meaning that many different vectors in the high-dimensional space become identical vectors in the low-dimensional space after reduction. This is the essence of the metamerism phenomenon.

The above explanation may inevitably seem obscure. To intuitively demonstrate metamerism, let us conduct a small experiment. First, we define a cosine-shaped spectrum as color stimulus A, covering the visible light band from 360 nm to 830 nm, with a peak at 595 nm. Then, using the CIE 1931 standard colorimetric observer, we can calculate the tristimulus values (XYZ) of color stimulus A. If color stimulus A originates from a uniform color patch, it will appear yellow. Next, we select monochromatic light at three wavelengths: 420 nm, 550 nm, and 620 nm, and match the tristimulus values (XYZ) of A based on their respective tristimulus values, thereby obtaining the spectral power distribution of color stimulus B. From Figure 2, it is easy to see that color stimuli A and B have completely different spectral power distributions, meaning they differ spectrally; however, for the standard colorimetric observer, the tristimulus values (colors) of the two patches are identical, meaning they match in color.

Applications and Evaluation of the Metamerism Phenomenon

In the previous section, metamerism might still seem like a phenomenon far removed from daily life. However, the following examples may refresh your understanding of metamerism.

(1) Driven by the need to save electrical energy, the luminous efficacy of lighting sources is increasingly higher. Mainstream indoor lighting sources have gradually transitioned from incandescent and fluorescent lamps to semiconductor light sources represented by LEDs. Due to different light-emitting mechanisms, the differences in the spectral power distributions of various light sources are quite significant. Nevertheless, we can always purchase light sources with very similar emitted colors on the market.
(2) A bicycle may simultaneously use components made of materials such as metal, plastic, and carbon fiber. The spectral reflection characteristics of these components are all different, but from an industrial design perspective, the color style of a bicycle should not be limited by the materials of its components. In short, we want components made of different materials to have very similar colors.
(3) A national flag is an iconic banner representing a country and is widely used. The pattern of the national flag may appear on various materials such as textiles, paper, plastic, metal, and glass, as well as on cinema screens or electronic displays, and even in drone performances in the night sky. The spectral characteristics of these different media, pigments, and dyes are all different, yet ideally, the colors of the national flag should be very similar. (4) When we take a photo with a camera or a mobile phone and reproduce it, the most basic requirement is that the scene in the photo should look very similar to the original scene. However, whether it is traditional photo printing, printing with a digital printer, or direct viewing on an electronic display, their spectra will inevitably be different. From traditional printing, photography, film, and television to modern cross-media color reproduction and replication, they all essentially belong to the same category of processes. The above four examples are all typical applications of metamerism and are ubiquitous in our daily lives. Many of the above examples concern object color, the formation of which is directly related to the light source, the object, and the observer. When two color samples with different spectral power distributions (in the visible light band) exhibit the same color or have the same tristimulus values for a given illuminant and a given observer, they are called metameric colors. If a change in the illuminant (spectral power distribution) causes their colors or tristimulus values to no longer match, this phenomenon is called illuminant metamerism.

As mentioned earlier, object color metamerism is one of the core requirements in many applications. In these applications, we typically want multiple object colors to remain as consistent as possible under various lighting conditions. To this end, the CIE (International Commission on Illumination) published Supplement No. 1 to Technical Report CIE 15-1971, “Special metamerism index: Change in illuminant,” in 1972, which explains the calculation method and usage of the special metamerism index Milm. Similar explanations can also be found in reports or standards such as CIE 015:2018, ISO 18314-4:2024, and GB/T 7771-2008. By definition, for a specified reference illuminant and reference observer, there is no color difference between the reference sample and the test sample; at this point, the color difference between the two samples under the test illuminant is Milm. Among them, CIE standard illuminant D65 is recommended as the reference illuminant, while the test illuminant can be an application-related illuminant, such as CIE standard illuminant A, as well as FL (representative fluorescent lamps), HP (representative high-pressure gas discharge lamps), or LED (representative blue/violet-excited, multi-color mixed LED light sources) illuminants. With the help of Milm, we can evaluate the ability of a pair of color samples to maintain color consistency under different illuminants; the more consistent the color, the smaller the Milm.

In addition to evaluating color samples, Milm can also be used to evaluate the capability of light sources. In this case, we need to find several sets of metameric color samples under reference illuminants (for a reference observer), and then calculate the color differences of these samples under the test illuminant. Technical Report CIE 051.2, “A method for assessing the quality of daylight simulators for colorimetry,” published in 1999, describes a method based on Milm for evaluating the quality of daylight illuminants. A similar method also appears in the ISO/CIE 23603:2024 standard.

Metamerism — The Cornerstone of Modern Colorimetry

Having read this far, you will certainly not consider metamerism to be a concept far removed from our daily lives. However, we often overlook a more important fact: metamerism is actually the cornerstone of modern colorimetry.

In September 1931, at the 8th Session held in Cambridge, UK, the CIE Colorimetry Committee adopted the famous CIE 1931 standard colorimetric observer image.png. This observer was designed to simplify calculations and facilitate usage. In fact, the CIE 1931 standard observer was derived from the color matching functions image.png, which in turn were based on the results of color matching experiments independently designed and conducted by two British scholars. The color matching experiment is a psychophysical experiment, and the matching method is a psychophysical method. Unlike physical quantities such as length, time, and mass, color is a psychological quantity and cannot be measured directly. The original intention of conducting color matching experiments was to indirectly measure psychological quantities using measurable physical quantities. The essence of the color matching experiment is to mix the colored light produced by three known light sources (with known spectral power distributions) in different proportions, attempting to match monochromatic light of any wavelength within the visible light band. In other words, what is to be matched is monochromatic light, and according to the CIE definition, the three known colored lights used to achieve the match are blue light at a wavelength of 435.8 nm, green light at 546.1 nm, and red light at 700 nm.

Color matching is performed within a 2° bipartite field (i.e., a circular field divided into two equal halves), where one half of the field is filled with the monochromatic light to be matched, and the other half is filled with a mixture of the three known colored lights. During the color matching experiment, the subject continuously adjusts the luminance of the three known colored lights so that the result of the three-color mixture matches the color of the monochromatic light at a given wavelength. Consulting the image.png color matching functions reveals that to match 1 part of 600 nm monochromatic light [C], 0.34429 parts of red light [R], 0.06246 parts of green light [G], and -0.00049 parts of blue light [B] are required. The negative value here indicates that the corresponding light must be moved to the side of the color being matched. In other words, 1 [C] + 0.00049 [B] ≡ 0.34429 [R] + 0.06246 [G]. When the color match is successful, the spectrum in one half of the field contains two spectral lines at 600 nm and 435.8 nm, while the spectrum in the other half contains two spectral lines at 700 nm and 546.1 nm. Clearly, metamerism appears before us once again.

It is not hard to see that metamerism is the foundation of color matching experiments, and the results of these experiments—the color matching functions—are in turn the foundation of modern colorimetry. Therefore, we can say that the three-dimensional nature of human color vision makes the phenomenon of metamerism possible, and metamerism, in turn, serves as the cornerstone for building modern colorimetry.