Spectral Power Distributions and Why RGB Is Not Enough

A spectrum becomes useful when you can pass it through the whole chain: source SPD, surface reflectance, observer or sensor response, sampling resolution, and illuminant change. This workbench lets those pieces interact as one system instead of as isolated definitions.

A spectral power distribution (SPD) is a curve. The horizontal axis is wavelength, usually 380 to 780 nanometers in steps of 5 or 10. The vertical axis is radiant power per unit wavelength - how much energy the light carries at each wavelength. That single curve is the physically complete description of a beam of light. Everything else - intensity, color, color temperature, CRI - is derived from it.

There are two practical forms. Continuous SPDs describe sources whose emission varies smoothly with wavelength - sunlight, incandescent bulbs, blackbody radiators of any kind. Discrete SPDs are sharp peaks at specific wavelengths - gas-discharge lamps, lasers, sodium-vapor street lights. Mixed SPDs have both, like fluorescent tubes (phosphor continuum with mercury peaks) or "white" LEDs (blue pump peak plus a broad phosphor hump).

Three types of features show up in almost every real SPD: a broad continuum from thermal sources or phosphors; narrow peaks from gas discharges or laser pumps; and a baseline that may dip toward zero outside the visible band. Reading an SPD comes down to identifying these features and reasoning about what they will do to a particular cone, observer, or camera.

To measure or specify color across labs, the CIE published reference light sources - standard illuminants - as named SPDs. Pick one as your reference, multiply it by your sample's reflectance, integrate against the standard observer, and you get the tristimulus values that uniquely identify the color under that illuminant. Different illuminants will produce different tristimulus values for the same surface, which is the whole reason illuminant choice matters.

The path from physical SPD to a numerical color goes through one operation: integration against the standard observer's color matching functions (x̄(λ), ȳ(λ), z̄(λ)). Each tristimulus value X, Y, Z is a weighted sum of the SPD over wavelength.

That is the formal moment color science becomes a number. Before this integration, a spectrum lives in a function space of effectively infinite dimensions. After it - whether by cones in a living eye or by computation against the CMFs - it lives in three. Two SPDs that integrate to the same XYZ triplet are, by definition, colorimetrically identical, even if their underlying physics is completely different.

Three numbers can describe what the human eye perceives, but they cannot describe the physical light that produces that perception. There are infinitely many SPDs that compress to the same RGB - or to the same XYZ - because cones and color matching functions both collapse the spectrum by integration.

That collapse is not a bug; it is the price of efficiency. Three cones cannot store an 81-point spectrum. They report integrated responses, a lossy compression that works most of the time because human vision is the destination. The problems show up whenever the destination changes - a different observer, a different illuminant, a different sensor, a different recipient material.

Two stimuli with different SPDs but identical tristimulus values are called metamers. Under one illuminant and one observer, they look the same. Under a different illuminant - or a different observer with slightly different cone sensitivities - they often look different. This is the source of an entire category of practical problems in printing, paint matching, textile dyeing, and display calibration.

Two light sources can have the same color temperature - and therefore look the same color when the bulbs are turned on - yet make objects in a room look very different. The color rendering index (CRI, also called R_a) is a 0-100 score summarizing how faithfully a light source reproduces a standard set of reference colors compared to a reference of the same correlated color temperature. CRI 100 is perfect (matches the reference exactly); CRI 80 is the rough threshold for residential use; CRI 90+ is considered "excellent."

CRI has well-documented limitations. It uses only eight desaturated patches (R1-R8), can be gamed by sources that score well on R_a while failing on the four saturated samples (R9-R12, especially R9 deep red). The newer IES TM-30-15 standard uses 99 evaluation samples plus separate Fidelity (R_f) and Gamut (R_g) scores to give a more nuanced picture.

A handful of source archetypes account for almost every light you will ever see. Each has a distinctive SPD signature.

In many everyday situations, RGB is enough. The screen you are reading lives on three primaries and most viewers will never notice. But there are specific workflows where the full spectrum is non-negotiable.

Six questions on SPDs, illuminants, and the limits of three-number color. Wrong answers come with brief explanations.