Metamerism

Definition

Two light spectra that appear identical despite being physically different are called metamers.

Mathematical Condition

Two spectra $L_1(\lambda)$ and $L_2(\lambda)$ are metamers if:

$\int L_1(\lambda) S_L(\lambda) d\lambda = \int L_2(\lambda) S_L(\lambda) d\lambda$

$\int L_1(\lambda) S_M(\lambda) d\lambda = \int L_2(\lambda) S_M(\lambda) d\lambda$

$\int L_1(\lambda) S_S(\lambda) d\lambda = \int L_2(\lambda) S_S(\lambda) d\lambda$

where $S_L$, $S_M$, $S_S$ are the cone sensitivity functions.

Why Metamerism Occurs

Dimension Reduction

• Visible light spectrum: Infinite dimensions (continuous function)
• Human cone response: Only 3 values (L, M, S)
• Information is lost in the transformation

One-Way Mapping

Many different spectra map to the same cone responses:

$\text{Spectrum} \xrightarrow{\text{cones}} (L, M, S)$

The reverse mapping is not unique.

Practical Importance

Displays

Displays exploit metamerism:

• A display emits a narrow RGB spectrum
• This matches the perception of natural objects with broad spectra
• The viewer cannot tell the difference

Example: A sunset captured by a camera is reproduced by mixing three narrow-band LEDs. The spectrum is completely different, but the colour matches perceptually.

Colour Reproduction

All colour reproduction relies on metamerism:

• Printing: CMYK inks spectrum ≠ original reflectance
• Photography: Sensor spectrum ≠ eye sensitivity
• Digital displays: RGB primaries ≠ natural light

Conditions for Metamerism

Two spectra are metamers if and only if they have identical tristimulus values:

$X_1 = X_2, \quad Y_1 = Y_2, \quad Z_1 = Z_2$

Metameric Failure

Metamers may not match under different conditions:

Observer Metamerism

Different observers have slightly different cone sensitivities:

• Age-related changes (lens yellows)
• Genetic variation in cone pigments
• Colour vision deficiency

Illuminant Metamerism

Two surfaces that match under one light may not match under another:

Light Source	Surface A	Surface B	Match?
D65 (daylight)	Spectrum A	Spectrum B	Yes
A (tungsten)	Spectrum A	Spectrum B	No

This is critical for:

• Textile industry (fabrics must match under store lighting)
• Automotive (interior materials under various light conditions)
• Printing (proofing under standard illuminant)

Applications

Colour Matching

• Paint mixing: Find a formulation that matches a target under specified lighting
• Quality control: Spectral matching vs metameric matching

Colour Science Research

• Study of observer variation
• Development of colour difference metrics
• Design of colour spaces

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Summary

• Metamers are different spectra that produce identical colour perception
• Occurs because spectrum has infinite dimensions but cone response has only 3
• Displays rely on metamerism to reproduce colours
• Metameric matches may fail under different observers or illuminants

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Past Paper Questions

2024 Paper 3 Question 3: Explain metamerism. Why is it important for displays?

2023 Paper 3 Question 4: Why can two different spectra appear the same colour?

2022 Paper 3 Question 3: What is illuminant metamerism? Give a practical example.