Colour Science & Perception
what the eye settles, and what it cannot
Generator

The reflectance of one surface, against the direction the light arrives from

Three surfaces of the same body reflectance, 0.50, with the fraction each returns plotted against the angle of the incoming light. A Lambertian surface would be a horizontal line. The smoothest of the three runs from 0.540 near the normal to 0.780 at grazing, because Fresnel's term rises towards ninety degrees. The short dashes mark the bihemispherical albedo — the single number a radiosity calculation uses for the surface — which lies inside the range and equals no particular one of the readings. There is a number only where the curve is flat.
The reflectance of one surface, against the direction the light arrives from. Three surfaces of the same body reflectance, 0.50, with the fraction each returns plotted against the angle of the incoming light. A Lambertian surface would be a horizontal line. The smoothest of the three runs from 0.540 near the normal to 0.780 at grazing, because Fresnel's term rises towards ninety degrees. The short dashes mark the bihemispherical albedo — the single number a radiosity calculation uses for the surface — which lies inside the range and equals no particular one of the readings. There is a number only where the curve is flat.

Drawn at its defaults, in the directions the number was averaged over. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 4 essays

the blast radius of changing it

What a scene does

Paint is not a filter

Stacking two filters multiplies their transmittances. Stirring two pigments together does not multiply their reflectances, because a mixture is one scattering layer rather than two in series — light meets whichever particle is nearest. Treating the two as the same operation is a 15-unit error, and which way it errs turns out to depend on whether the comparison holds the amount of pigment fixed.

 Where the model breaks

The model has six arguments

Every colour computed here is an integral of a reflectance against a light against three curves, and a reflectance is one number per wavelength. A real surface's response is a function of six arguments — the wavelength, direction and place light arrives with, and the three it leaves with — so the model keeps one of them, takes a diagonal, integrates two away and assumes two more equal.

 What a scene does

A room is not a sphere

An integrating sphere reads a surface's own reflectance exactly, and the exactness is a theorem rather than good engineering — under a hemisphere of constant radiance, reciprocity makes the reading the sample's directional-hemispherical reflectance whatever the surface is. Every room fails that condition, and a viewing booth and a window get the sign of the error wrong in opposite directions.

 What a scene does

A mixture in the variable nobody named

Kubelka–Munk works because absorption and scattering add over a mixture and reflectance does not. What adds is the absorption of the pigment layer, and what an instrument reports is that layer seen through an interface — related by a Möbius function rather than by a constant. Mixing in the reported variable instead of the internal one costs between three and eight ΔE₀₀, and no source this collection quotes says which variable its curves are in.

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