Is Metamerism Far from Our Daily Lives?
Metamerism is a colorimetric term describing the phenomenon where color stimuli with different spectral compositions produce the same color (tristimulus values). The English word "metamerism" was originally a chemical term referring to isomerism (i.e., molecules with identical atom types and counts but different chemical bonds). Whether as a colorimetric term or its former chemical usage, "metamerism" might seem distant from daily life—but is this truly the case? This article reveals the reality of metamerism.

Figure 1 Metamerism. Two color stimuli appear identical but have distinct spectral power distributions.

The Essence of Metamerism

Any color stimulus in the form of light radiation has a corresponding spectrum, often called the spectral power distribution (SPD). If we decompose this distribution into individual frequency components, it can be viewed as a vector in high-dimensional linear space. When light interacts with matter (via absorption, scattering, etc.), the SPD is altered—equivalent to vector rotation/scaling in high-dimensional space. Thus, physical color stimuli are high-dimensional concepts.

For people with normal color vision, three types of cone cells exist in the retina. These contain photopigments with slightly different structures, resulting in distinct spectral sensitivities. Under photopic conditions, light triggers photochemical reactions that excite cone cells, generating neural signals. The excitation level depends on the SPD of the stimulus and the eye’s spectral response (including physiological transmission properties and adaptation states). Here, the eye’s spectral response also acts as a vector in high-dimensional space.

Becasue of the cones’ spectral differences, their excitation levels vary, creating color perception—a three-dimensional phenomenon. Mathematically, color formation is the dot product between the stimulus vector and the eye’s response vector in high-dimensional space. This is a dimensionality reduction from high-dimensional to 3D linear space. Such reduction is many-to-one: different high-dimensional vectors map to identical 3D vectors. This is metamerism.

The above explanation may inevitably seem obscure; to intuitively demonstrate metamerism, let us conduct a small experiment. First, we define a cosine-function-shaped spectrum as color stimulus A, covering the visible light band from 360 nm to 830 nm, with its peak at 595 nm. Then, using the CIE 1931 standard colorimetric observer, we calculate the tristimulus values (XYZ) of color stimulus A. If color stimulus A originates from a uniform color patch, it appears yellow. Next, we select monochromatic lights of three wavelengths—420 nm / 550 nm / 620 nm—and match their respective tristimulus values to those of A (XYZ), thereby obtaining the spectral power distribution of color stimulus B. From Figure 2, we can clearly see that stimuli A and B exhibit entirely different spectral power distributions (heterospectral); however, for the standard observer, the tristimulus values (color) of both color patches are identical (metameric).

As shown in Figure 2, stimuli A and B have entirely different SPDs (heterospectral) yet identical tristimulus values (metameric) for the standard observer.

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Figure 2 Metamerism. Stimuli A and B have different SPDs but identical color for the CIE 1931 observer.

Applications and Evaluation of Metamerism

In the previous section, metamerism may still seem like a phenomenon distant 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 continues to increase. Mainstream indoor lighting sources have transitioned from incandescent and fluorescent lamps to semiconductor sources represented by LEDs. Due to differences in light-emitting mechanisms, the spectral power distributions of various sources differ significantly, yet we can always purchase sources with very similar emitted colors on the market.

2. A bicycle may use components made of metal, plastic, carbon fiber, and other materials. The spectral reflectance characteristics of these components all differ, yet from an industrial design perspective, a bicycle’s color scheme should not be limited by component materials. In short, we desire components of different materials to exhibit highly similar colors.

3. A national flag is an iconic symbol of a country, used extensively across contexts. Its design may appear on textiles, paper, plastic, metal, glass, and other materials, as well as on cinema screens or electronic displays, even in drone performances in the night sky. The spectral characteristics of these different media, pigments, and dyes all differ, yet ideally, the flag’s colors should remain highly consistent.

4. When capturing a photo with a camera or smartphone and reproducing it, the fundamental requirement is that the scene in the photo should closely resemble the original subject. However, whether through traditional photo development, digital printing, or direct display viewing, their spectra inevitably differ. From traditional printing, photography, film, and television to modern cross-media color reproduction, all essentially belong to the same category of processes.

The above four examples are all typical applications of metamerism, ubiquitous in our lives. Many involve object colors, whose formation directly relates to the light source, object, and observer. When two color samples with different spectral power distributions (within the visible band) exhibit identical color or tristimulus values under a given illuminant and observer, we call them a metameric color pair. If a change in illuminant (spectral power distribution) causes their colors or tristimulus values to diverge, this phenomenon is termed illuminant metamerism.

Figure 3 Illuminant metamerism. Two metameric samples under CIE D65 show color differences under other illuminants.

As mentioned, object-color metamerism is a core requirement in many applications. Typically, we aim for multiple object colors to maintain consistency across varied lighting conditions. To address this, CIE (International Commission on Illumination) published Supplement No. 1 to Technical Report CIE 15-1971—Special metamerism index: Change in illuminant—in 1972, detailing the calculation and application of the special metamerism index MilmMilm. Similar specifications appear in reports/standards like CIE 015:2018, ISO 18314-4:2024, and GB/T 7771-2008. By definition, under a specified reference illuminant and observer, if a reference sample and test sample exhibit no color difference, then the color difference under a test illuminant is MilmMilm. CIE Standard Illuminant D65 is recommended as the reference illuminant, while test illuminants may include application-relevant sources such as CIE Standard Illuminant A, FL (representative fluorescent lamp), HP (representative high-pressure gas-discharge lamp), or LED (representative blue/violet-excited, multi-color mixed LED sources). Using MilmMilm, we evaluate a color pair’s ability to maintain consistency across illuminants: smaller MilmMilm indicates better consistency.

Beyond evaluating color samples, MilmMilm can assess light source capabilities. Here, we identify several metameric sample pairs under a reference illuminant (for a reference observer), then calculate their color differences under a test illuminant. The 1999 Technical Report CIE 051.2—A method for assessing the quality of daylight simulators for colorimetry—describes a MilmMilm-based method for evaluating daylight simulator quality; a similar method appears in the ISO/CIE 23603:2024 standard.

Metamerism: The Cornerstone of Modern Colorimetry

Metamerism is not remote—it underpins modern colorimetry.

At this point, you certainly will not consider metamerism a concept far removed from daily life. However, we often overlook a more crucial 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 renowned CIE 1931 standard colorimetric observerimage.png, designed to simplify calculations and enhance usability. In practice, the CIE 1931 standard observer derives from color-matching functions image.png, which are based on color-matching experiments independently designed and conducted by two British scholars. Color-matching experiments are psychophysical tests, and the matching method is a psychophysical technique. Unlike physical quantities such as length, time, and mass, color is a psychological quantity that cannot be directly measured. The original intent of color-matching experiments was to indirectly quantify psychological quantities through measurable physical parameters. The essence of color-matching experiments is to mix three known (spectrally defined) primary lights in varying proportions to match monochromatic light at any wavelength within the visible spectrum. In other words, the target being matched is monochromatic light, while the three primaries defined by CIE are: blue light at 435.8 nm, green light at 546.1 nm, and red light at 700 nm.

Figure 4 Color-matching experiment. Metamerism enables matching monochromatic light with primary mixtures, yielding CMFs.

Color matching occurs within a 2° bipartite field (i.e., a circular field divided into two equal halves). One half is filled with the target monochromatic light, while the other contains a mixture of the three known primaries. During the experiment, observers continuously adjust the intensities of the three primaries until the mixture matches the color of the monochromatic light at a given wavelength. Retrievingimage.png the color-matching functions reveals that matching 1 unit of 600 nm monochromatic light [C] requires 0.34429 units of red light [R], 0.06246 units of green light [G], and –0.00049 units of blue light [B]. The negative value indicates that the corresponding light must be added to the target side. In other words: 1 [C] + 0.00049 [B] ≡ 0.34429 [R] + 0.06246 [G]. Upon successful matching, one half-field contains spectral lines at 600 nm and 435.8 nm, while the other half contains lines at 700 nm and 546.1 nm. Clearly, metamerism reappears before us.

Evidently, metamerism underlies color-matching experiments, and the outcome of these experiments—the color-matching functions—forms the foundation of modern colorimetry. Therefore, we can state: the three-dimensional nature of human color vision makes metamerism possible, and metamerism in turn becomes the cornerstone for constructing modern colorimetry.

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