How much of a whiteness figure is the sheet, and how much is the lamp
Drawn at its defaults, in the band below 380 nanometres. It takes no options at all, so every essay calling it gets this exact drawing.
Called by 13 essays
the blast radius of changing it
Two sheets that match until the window
Ordinary metamerism is two reflectances that agree under one light and not another, and it can always be undone by putting the first light back. A dyed sheet and a brightened one have the same reflectance everywhere an eye can see, agree exactly under any lamp with no ultraviolet, and separate by ten units under daylight — and no change of light puts them back together.
What a scene doesThe 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.
What it takes to deliver itA 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.
Difference and uniformityWhiteness is mostly the lamp
The CIE whiteness formula ranks white samples the way people do, which is what it was built for and is not in question. What is in question is what it is a measurement of — take the ultraviolet out of the instrument and 82 per cent of the scale collapses, because the part that separates a premium sheet from an ordinary one was contributed by the lamp.
Where the model breaksA 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.
Where the model breaksThe 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.
What the brain doesA brighter white still looks white
Colorimetry says a brightened sheet is nine units of b* from neutral, which sounds like a visible blue. An appearance model with the observer adapted to the room says it carries eleven units of chroma at a hue of 295 degrees — genuinely blue-violet — and that the number falls by nearly half between a bright room and a dark one. What it cannot say is why anybody calls the result white.
Where the model breaksThe limits assume a pigment that switches instantly
The hardest boundary in colorimetry is reached by reflectances that jump between nought and one at a wavelength, and no material does that. Constrain the jump to take twenty nanometres — a sharp dye — and the median direction of the object-colour solid loses under half a per cent of its reach. Constrain it to eighty, an ordinary pigment, and the median loses five per cent, the tenth percentile nearly a quarter, and seven directions in ten lose more than one. The cost is in a corner only for chemistry sharper than paint.
Where the model breaksThree lines spare a slow pigment
A pigment that cannot switch faster than forty nanometres loses more than a per cent of its reach in 183 of the object-colour solid's 305 directions under daylight. Under an LED whose light sits in three narrow lines, it loses that much in 62. Between the lines almost nothing is measured, so a slow reflectance can do its changing there — until its transitions are as wide as the lines are far apart, at which point the lamp stops helping and the count jumps to daylight's.
Where the model breaksA limit written in energy charges the reds
A slope limit on reflectance is usually written in nanometres and applied the same way across the spectrum. An absorption band's width is closer to a fixed spread of photon energy, which is nearly twice as many nanometres at 700 as at 500. Written that way, a limit that is forty nanometres at 550 is kinder to the object-colour solid overall — 489 of 913 directions lose a per cent rather than 544 — and it charges the reds more. Which directions pay is decided by one thing: whether their optimal edges fall above or below the reference wavelength.
Where the model breaksA fourth emitter spends the gap it fills
A three-emitter LED lets a pigment that takes forty nanometres to switch reach most of its ideal solid, because the lamp is dark where the pigment is slow. Adding a fourth emitter to render better takes that darkness back — but only if it is put in the middle of a gap. At 490 nanometres it costs 172 of the solid's 312 directions against the three-emitter lamp's 62, and renders two points worse. At 540 it costs three directions and renders two and a half points better.
Where the model breaksThe gap has to be dark, not the line narrow
A lamp whose light sits in three narrow emitters lets a blunt pigment reach most of its ideal solid, and the reason was given as the spacing of the lines. Broadening those emitters without moving them says otherwise. At 1.3 times their nominal width the lamp still looks like a line spectrum, its closest spacing has not changed at all, and half the rescue is gone — because the darkest point of the narrow gap has risen from one per cent of the lamp's peak to seven.
Where the model breaksA sharp edge is bought with depth
A slope limit on reflectance was introduced as the weakest honest statement of a pigment's bluntness, with a band-shape limit named as the stronger version to be written later. Written, it is not stronger. Three absorption bands none narrower than forty nanometres reach further than a forty-nanometre slope limit in 94 of 154 directions of the object-colour solid, because a band's width and the width of the reflectance edge it draws are different quantities — and what converts one into the other is how much colorant is in the film.