Metamerism (color)

In colorimetry, metamerism is a perceived matching of the colors that, based on differences in spectral power distribution, do not actually match. Colors that match this way are called metamers.

A spectral power distribution describes the proportion of total light given off (emitted, transmitted, or reflected) by a color sample at each visible wavelength; it defines the complete information about the light coming from the sample. However, the human eye contains only three color receptors (three types of cone cells), which means that all colors are reduced to three sensory quantities, called the tristimulus values. Metamerism occurs because each type of cone responds to the cumulative energy from a broad range of wavelengths, so that different combinations of light across all wavelengths can produce an equivalent receptor response and the same tristimulus values or color sensation. In color science, such sensations are numerically represented by color matching functions.

Sources of metamerism

Metameric matches are quite common, especially in near neutral (grayed or whitish colors) or dark colors. As colors become brighter or more saturated, the range of possible metameric matches (different combinations of light wavelengths) becomes smaller, especially in surface colors.

Metameric matches made between two light sources provide the trichromatic basis of colorimetry. For any given light stimulus, regardless of the form of its spectral emittance curve, there always exists a unique mixture of three "primary" lights that when added together, or added to the stimulus, will be an exact metameric match.

The basis for nearly all commercially available color image reproduction processes such as photography, television, printing, and digital imaging, is the ability to make metameric color matches.

Making metameric matches using reflective materials is more complex. The appearance of surface colors is defined by the product of the spectral reflectance curve of the material and the spectral emittance curve of the light source shining on it. As a result, the color of surfaces depends on the light source used to illuminate them.

Metameric failure

The term illuminant metameric failure is sometimes used to describe situations where two material samples match when viewed under one light source but not another. Most types of fluorescent lights produce an irregular or peaky spectral emittance curve, so that two materials under fluorescent light might not match, even though they are a metameric match to an incandescent "white" light source with a nearly flat or smooth emittance curve. Material colors that match under one source will often appear different under the other.

Normally, material attributes such as translucency, gloss or surface texture are not considered in color matching. However geometric metameric failure can occur when two samples match when viewed from one angle, but then fail to match when viewed from a different angle. A common example is the color variation that appears in pearlescent automobile finishes or "metallic" paper; e.g., Kodak Endura Metallic, Fujicolor Crystal Archive Digital Pearl.

Observer metameric failure can occur because of differences in color vision between observers. The common source of observer metameric failure is colorblindness, but it is also not uncommon among "normal" observers. In all cases, the proportion of long-wavelength-sensitive cones to medium-wavelength-sensitive cones in the retina, the profile of light sensitivity in each type of cone, and the amount of yellowing in the lens and macular pigment of the eye, differs from one person to the next. This alters the relative importance of different wavelengths in a spectral power distribution to each observer's color perception. As a result, two spectrally dissimilar lights or surfaces may produce a color match for one observer but fail to match when viewed by a second observer.

Finally, field-size metameric failure occurs because the relative proportions of the three cone types in the retina vary from the center of the visual field to the periphery, so that colors that match when viewed as very small, centrally fixated areas may appear different when presented as large color areas. In many industrial applications, large field color matches are used to define color tolerances.

The difference in the spectral compositions of two metameric stimuli is often referred to as the degree of metamerism. The sensitivity of a metameric match to any changes in the spectral elements that form the colors depend on the degree of metamerism. Two stimuli with a high degree of metamerism are likely to be very sensitive to any changes in the illuminant, material composition, observer, field of view, and so on.

The word metamerism is often incorrectly used to indicate a metameric failure rather than a match, or incorrectly used to describe a situation in which a metameric match is easily degraded by a slight change in conditions, such as a change in the illuminant.

Measuring metamerism

The best-known measure of metamerism is the color rendering index (CRI), which is a linear function of the mean Euclidean distance between the test and reference spectral reflectance vectors in the CIE 1964 color space. A newer measure, for daylight simulators, is the MI, CIE Metamerism Index^[1] which is derived by calculating the mean color difference of eight metamers (five in the visible spectrum and three in the ultraviolet range) in CIELAB or CIELUV. The salient difference between CRI and MI is the color space used to calculate the color difference, the one used in CRI being obsolete and not perceptually uniform.

MI can be decomposed into MI_vis and MI_UV if only part of the spectrum is being considered. The numerical result can be interpreted by rounding into one of five letter categories:^[2]

Category	MI (CIELAB)	MI (CIELUV)
A	< 0.25	< 0.32
B	0.25–0.5	0.32–0.65
C	0.5–1.0	0.65–1.3
D	1.0–2.0	1.3–2.6
E	> 2.0	> 2.6

Metamerism and industry

Using materials that are metameric color matches rather than spectral color matches is a significant problem in industries where color matching or color tolerances are important. A classic example is in automobiles: the interior fabrics, plastics and paints may be manufactured to provide a good color match under a standard light source (such as the sun), but the matches can disappear under different light sources (fluorescent or halide lights). Similar problems can occur in apparel manufactured from different types of dye or using different types of fabric, or in quality color printing using different types of inks. Papers manufactured with optical brighteners are especially susceptible to color changes when lights differ in their short wavelength radiation, which can cause some papers to fluoresce.

Color matches made in the paint industry are often aimed at achieving a spectral color match rather than just a tristimulus (metameric) color match under a given spectrum of light. A spectral color match attempts to give two colors the same spectral reflectance characteristic, making them a good metameric match with a low degree of metamerism, and thereby reducing the sensitivity of the resulting color match to changes in illuminant, or differences between observers.

See also

• Tetrachromacy
• Hyperspectral imaging

References

1. CIE Publication 15
2. CIE Standards for assessing quality of light sources, J Schanda, Veszprém University, Department for Image Processing and Neurocomputing, Hungary

• Wyszecki, Günter & Stiles, W.S. (2000). Color Science - Concepts and Methods, Quantitative Data and Formulae (2nd ed.). New York: Wiley-Interscience. ISBN 0-471-39918-3.
• R.W.G Hunt. The Reproduction of Color (2nd ed.). Chichester: John Wiley & Sons, 2004.
• Mark D. Fairchild. Color Appearance Models Addison Wesley Longman, 1998.

External links

• Java applet demonstrating metamers
• Stanford University CS 178 interactive Flash demo demonstrating color matching.
• Explanation of Metamerism in color