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

Lambertian — where it appears

A surface that scatters light equally in every direction, so its appearance does not change with viewing angle. It is an idealisation nothing quite meets, and it is the assumption behind every form factor and every radiosity calculation.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

A spectrum after 2 bounces off the same surface. The lamp's spectrum at the top, then the same spectrum multiplied by a reflectance peaking at 530 nm once for each bounce. Interreflection is elementwise multiplication, so light that reaches the eye by the long way round carries ρ raised to the number of surfaces it met. Each row's swatch is drawn at fixed luminance so only the chromaticity changes, and the distance from the D65 white point, printed at the right, rises from 0.000 to 0.235. The spectrum narrows every time, which is why a room painted in one colour is more saturated in its corners than on its walls.

A bounce is a multiplication

Colorimetry multiplies an illuminant by a reflectance once and integrates. A surface in a room is lit by every other surface the lamp reached first, so the spectrum arriving at the eye has been multiplied several times — and the second multiplication is where the whole apparatus of matching starts to come apart.

scene · Scene The form-factor matrix of the box. F_ij is the fraction of everything leaving face i that arrives at face j. The diagonal is zero because a flat face sees none of itself; each row sums to exactly 1 because the cavity is closed; and A_i F_ij = A_j F_ji, which is reciprocity and is checked to 10⁻⁹. For a cube the opposite face takes 19.98% and each of the four adjacent faces 20.00%, and the near-equality of those two numbers is a coincidence of the cube rather than a rule.

A corner is not a wall

A form factor is the fraction of everything leaving one surface that arrives at another, and it is the only place geometry enters the colour of a room. It is also the one number here with a published closed form to check against — and the check turned out to converge at two different rates for two cases that look identical.

scene · Scene Five fields, by how much light arrives from each elevation. The radiance arriving at a surface from each direction in one vertical plane, for five ways of lighting it. The vertical axis is logarithmic, spanning the three decades between a sun and the sky around it. The number beside each name is the share of the light that would have to be moved to make the field uniform: zero for the overcast sky, 0.93 for a lamp on a stand. A uniform field is the condition under which a reading is the sample's own reflectance, and the only place it exists is inside an instrument.

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.

scene · Scene

Named alongside it

The objects these essays reach for when they reach for this one.

RadiosityColour bleedingForm factorInterreflectionQuadratureReciprocityReflectanceStandard observerAlbedoBidirectional reflectanceChromaticityGloss

All concepts