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

Radiance factor — where it appears

What an instrument actually reports for a fluorescent sample: a ratio that depends on the lamp, and therefore not a property of the sample. The standards give its two components separate letters — reflected and luminescent — because only the first is a property of the surface alone.

Named by 11 essays across 5 fields — each of them below, with the objects they name alongside it.

A sample with two reflectance curves, and neither below one. The apparent reflectance of an optically brightened sample, measured under D65 and A. It exceeds 1 — the shaded band — which no reflector can do: more light leaves at these wavelengths than arrives at them, because the sample absorbs in the violet and re-emits in the blue. And the two curves differ, so the sample has no single reflectance to store. The effect drawn here is a floor: most of the excitation band lies below 380 nm, outside the range computed here.

Some paper is brighter than white

The reflectance model assumes light leaving at a wavelength arrived at that wavelength. A fluorescent sample breaks the assumption, has no reflectance curve at all, and is in almost every sheet of white paper sold.

light · Light The same twenty-four samples, measured two standard ways. How far apart a 45°/0° instrument and a sphere with its gloss port closed are, on samples running from three per cent reflectance to seventy. The whole of the difference is the interface reflection — four per cent of the light, returned without ever meeting a pigment, thrown away by one geometry and collected by the other. It is the same four points in every row, which is why the disagreement is a property of how dark the sample is rather than of what colour it is: ΔE00 8.7 on the darkest samples against 1.93 on the lightest.

An instrument has a geometry

Every reflectance here arrives through a model with a bandpass, a sampling interval and no position at all. Real instruments say where they were standing, and the two standard answers disagree by ΔE00 8.35 on a dark gloss sample — a difference that adds rather than multiplies, and that no adaptation removes.

matching · Gamut A sample with two reflectance curves, and neither below one. The apparent reflectance of an optically brightened sample, measured under D65 and A. It exceeds 1 — the shaded band — which no reflector can do: more light leaves at these wavelengths than arrives at them, because the sample absorbs in the violet and re-emits in the blue. And the two curves differ, so the sample has no single reflectance to store. The effect drawn here is a floor: most of the excitation band lies below 380 nm, outside the range computed here.

A surface that is not a multiplication

Every argument here about what light does to a surface begins by multiplying two spectra together. A surface with a brightener in it takes light at one wavelength and returns it at another, so it is a full operator rather than a diagonal one — and it does not have a reflectance at all.

scene · Scene A fluorescent sample is a matrix, and a reflectance is only its diagonal. The Donaldson matrix of a brightened sheet: how much light leaves at each wavelength for light arriving at each wavelength. A reflecting surface has entries on the diagonal and nowhere else, which is exactly the statement that light leaving at 440 nanometres arrived at 440. The block off the diagonal is the fluorophore — it takes light between about 305 and 420 nanometres and returns it between 400 and 500, wherever in that band it was absorbed, which is why the block is a rectangle rather than a smear along the diagonal. A spectrophotometer that reports a reflectance is reporting the diagonal and folding the block into it at whatever weight its own lamp happened to give.

A reflectance is a diagonal

A reflecting surface returns light at the wavelength it arrived at, so its whole description is one number per wavelength. A fluorescent one returns it somewhere else, so its description is a square matrix — and the curve every instrument reports is that matrix's diagonal with the rest of it folded in at whatever weight the lamp happened to give.

light · Light A radiance factor, split into the part that was reflected and the part that was not. The two components of what leaves a heavily brightened sheet under M₁ — D50 including its ultraviolet. The lower band is the reflected component, which is what a reflectance curve means and is everything a reflectance-based model can hold. The band above it is light emitted at wavelengths it did not arrive at, and its total is decided by how much ultraviolet the source had rather than by anything about the sheet's colour. The line at one is the boundary a reflecting surface cannot cross; the sum reaches 1.21 at 430 nanometres.

The eye weights where the light is not

A brightened sheet returns a quarter more light than arrives at 430 nanometres, and it is three tenths of one per cent brighter for it. The luminous efficiency function is 0.017 there against 1.0 in the middle of the band, so the whole effect lands in the blue-yellow axis — brighter than white is a colour claim wearing a brightness word.

matching · Cones What a sheet of glass takes out of the band a brightener eats. The transmittance of four glazings across the short-wave band, with the brightener's own absorption shaded underneath. The overlap between a curve and the shading is what the sheet behind that glass has to work with. Ordinary window glass stops below about 310 nanometres and leaves most of the band; laminated glass has a plastic interlayer that was put there to hold the sheet together in a crash and happens to absorb almost to 380; a filter sold to protect a print removes the band entirely. The curves are logistic edges at stated wavelengths rather than measurements of particular products.

The window is part of the light

A viewing condition here has always been a spectrum and a geometry. For anything fluorescent it needs a third thing — the transmittance of whatever the daylight came through — because ordinary window glass, a laminated windscreen and a museum filter remove three quite different parts of the band a brightener eats, and the sheet is a different colour behind each.

scene · Scene Six sheets, four standard measurement conditions, and every pair of them. How far apart two measurement conditions put the same sample. Darker is further. The top row has no brightener in it and every pair agrees to within a unit except the ones involving M₃, whose difference is cross-polarisation removing the interface reflection and is a change of geometry rather than of spectrum. Every row below it disagrees, and the M₁ against M₂ column reaches ΔE00 7.7 — several times any tolerance a printer would accept, on one sheet measured twice by two instruments that are both working correctly. The numbers under the columns are the means.

An instrument brings its own light

ISO 13655 names four measurement conditions and they are usually read as four degrees of care. They are not. They are four different quantities — on an unbrightened sheet all four agree to a rounding, and on a brightened one they are up to seven and a half units apart, with every instrument in calibration and every answer correct.

applied · Delivery What a proof on an unbrightened sheet cannot reach. The paper white of a heavily brightened stock beside the paper white of an unbrightened one, both under an ultraviolet-included instrument. They are ΔE00 9.8 apart and 10.3 of that is in the blue-yellow axis. A proofing system on the unbrightened sheet can print towards the brightened one only by adding ink, which makes the paper darker rather than bluer; it cannot add light at 435 nanometres because it has no brightener and its own lamp is the one in the room. This is why a soft proof and a hard proof of the same job disagree about the white, and why the disagreement is in one direction.

A proof cannot glow

A proof is a different sheet of paper pretending to be the production one, and the pretence works by adding ink until the two agree. It cannot work for a brightened stock, because the direction the proof has to travel is towards more blue at the same lightness and every ink a proofer owns moves it towards less light instead.

applied · Delivery Outside the set of colours a reflecting surface can be. How far each stock sits from the boundary of the object-colour solid, as a fraction of the bound. The line at zero is the boundary: a perfect diffuser sits exactly on it, and every reflectance ever made sits to its left. The pale marker is the sheet measured with the ultraviolet excluded and the dark one with it included. Two of the six cross the line — they are brighter, in a direction that can be written down, than any reflecting surface of their colour could be. This is a proof rather than a hull: for each sample a direction is found in which the largest value any reflectance can reach is computed exactly, and the sample exceeds it.

A white that is not a reflectance

The object-colour solid is the hardest boundary in colorimetry — the set of tristimulus values any reflecting surface can produce, with no assumption about pigments in it at all. A coated press stock under a measurement standard's own lamp sits 1.5 per cent outside it, and a heavily brightened one 4.0, and with the ultraviolet removed both come back inside.

limits · Gamut A whiteness measurement has a date on it. A brightener is consumed by the ultraviolet that makes it glow: the molecule that absorbs a photon occasionally does something other than re-emit it, and what it does is break. So the loading falls with accumulated dose and the sheet's whiteness falls with it, from W 123 to 88 — most of the way back to the unbrightened base. The fall is steepest at the start because the absorption saturates, so the first molecules lost are the ones that were doing the least work and the curve is convex from the beginning. The dose axis is in arbitrary units whose half-life is stated; what is not arbitrary is the shape.

The brightener is being used up

The molecule that absorbs an ultraviolet photon occasionally does something other than re-emit it, and what it does is break. So a sheet's whiteness has a half-life, the fall is steepest at the start, and a specification quoting a whiteness figure without a date is quoting a property of a sheet that no longer exists.

limits · Limits A radiance factor, split into the part that was reflected and the part that was not. The two components of what leaves a coated press stock under M₁ — D50 including its ultraviolet. The lower band is the reflected component, which is what a reflectance curve means and is everything a reflectance-based model can hold. The band above it is light emitted at wavelengths it did not arrive at, and its total is decided by how much ultraviolet the source had rather than by anything about the sheet's colour. The line at one is the boundary a reflecting surface cannot cross; the sum reaches 1.15 at 430 nanometres.

The ultraviolet is half the product

A fluorescent sample's departure from the reflectance model is exactly proportional to the ultraviolet the lamp carries — to twelve figures, over a range that includes zero. It is the only one of the round's four departures that really is a product of two magnitudes, and the reason is a rule about how molecules relax rather than anything about arithmetic.

light · Light

Named alongside it

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

Optical brightenersFluorescenceUltravioletAssertionThe Donaldson matrixIlluminantMeasurement conditionReflectanceSpecificationSpectrophotometryBispectralPaper white

All concepts