Quantifying Colour

Across the globe, billions of digital displays can render the exact same hue when given the same command. While this is a staggering achievement of modern engineering, it masks a fundamental requirement: the existence of a universal, standardized definition for colour.

Historically, humans relied on a sparse vocabulary to describe the visual spectrum. Most languages possess only about a dozen words for colours. While these labels suffice for casual conversation, they lack the granularity needed for high-fidelity reproduction.

The Limitation of Labels: "Same Name, Different Colours"

Consider the variety of shades that fall under a single umbrella term. For instance, the label green is used for a vast array of distinct visual experiences:

One might attempt to solve this by adding modifiers (e.g., light-green or dark-green), but this system is efficient clunky and unsustainable. To accurately render a complex image, we cannot rely on an infinitely expanding list of adjectives.

From Words to Numbers

Instead of mapping colours to millions of unique names, it is far more logical to use numerical units. Precision is then simply a matter of increasing the number of digits used.

While assigning numbers to colours may seem abstract, it follows the precedent of other physical measurements. For example, we quantify temperature or mass; therefore, if colour is a physical phenomenon, it can be quantified.

The Implications of Numerical Colour Mapping colours to numbers allows us to explore complex questions:

• What happens when we add or multiply colours?
• Why are 16,777,216 hexcode values still insufficient to capture all visible colours?
• How do biological differences lead to colour blindness?
• Why did a single photograph of a dress spark a global internet debate?

Goals of Quantification

• Move beyond linguistic labels.
• Establish a physical basis for colour.
• Create a mathematical framework for reproduction.

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The Physics of Light: Spectral Power Distribution

To quantify colour, we must first treat it as a physical entity. The fact that humans generally agree on the colour of an object suggests an objective physical reality. This reality is rooted in light.

Light consists of wave-like particles known as photons. Each photon carries a specific amount of energy, which is determined by its frequency or wavelength.

![Image: A conceptual representation of a photon as a wave-particle duality]

Because photons exhibit both particle and wave-like properties, visualizing them is notoriously difficult. However, we can categorize them via the Electromagnetic Spectrum, which is the total range of photon energies ordered by their wavelength.

Measuring the Energy

We can quantify light by measuring the energy of these photons. To make these measurements useful for comparison, we apply two levels of normalization:

1. Power: Energy normalized per unit of time.
2. Intensity: Power normalized per unit of area (the total area of the radiating body).

Mathematically, the energy $E$ of a photon is inversely proportional to its wavelength $\lambda$:

$E = \frac{hc}{\lambda}$

(Where $h$ is Planck's constant and $c$ is the speed of light)

Rather than a single intensity value, light is more accurately represented by measuring intensity across different wavelengths. This resulting distribution is known as the Spectral Power Distribution (SPD).

In an SPD graph, the intensity at any given wavelength depends on both the number of photons present and the energy of those specific photons.

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The Biological Interface: Photoreceptor Cells

Quantifying light is only half the battle; we must also quantify how the human eye perceives that light. Colour perception is a biological process involving specialized cells.

Human eyes have evolved to be sensitive to the specific wavelengths emitted by the sun, roughly between 380nm and 750nm.

![Image: Approximation of the Sun's Spectral Power Distribution]

How We See

The eye utilizes two primary types of photoreceptor cells to translate photons into signals:

• Rod Cells: Primarily for low-light vision.
• Cone Cells: Three distinct types, each sensitive to different wavelength ranges.

These cone cells do not react uniformly. Some are highly responsive to shorter wavelengths, while others respond more strongly to longer ones. This varying sensitivity is what allows the brain to distinguish between different colours.

# Conceptual representation of cone sensitivity
def cone_response(wavelength):
    if 400 <= wavelength <= 500:
        return "S-Cone (Short/Blue) Active"
    elif 500 <= wavelength <= 600:
        return "M-Cone (Medium/Green) Active"
    elif 600 <= wavelength <= 700:
        return "L-Cone (Long/Red) Active"
    else:
        return "No significant response"

The relationship between the physical Spectral Power Distribution and the normalized sensitivity curves of these cone cells is the key to truly quantifying colour.