A finish adds colour only to a daylight meter

A tenth of the return arriving white established the mechanism: nine per cent of what leaves a satin wall is a Fresnel reflection at the interface, which never entered the pigment and carries none of its colour. A gloss finish takes colour out of the whole room kept a ledger of every flux between a room’s faces and found the finish removing about a tenth of the reflected light’s chroma. A gloss room looks less colourful than it measures read the same room through an appearance model.

All three were computed under daylight, and the Fresnel return is white in the lamp’s spectrum rather than white in any absolute sense. So the obvious next question is what happens to the tenth under a lamp that is not daylight — and the answer depends, before anything else, on which white the room’s colour is measured against.

This essay first appeared with the wrong one. Its table ran from −6 to +42 per cent, it reported rooms that gain colour when their walls are made glossy, and it said the chroma had been measured against each lamp’s own white. It had been measured against daylight’s white in every room. What follows is the same thirty-six rooms measured both ways, and the reason the two answers differ is worth more than either of them.

About a tenth, in every room #

Measured against the white of the lamp that lights it, a satin finish takes between 7.7 and 12.9 per cent of the chroma out of every one of thirty-six rooms. No room gains. At no wall colour do the six lamps disagree by as much as three points.

• Against daylight’s white the same rooms run from −6.0 to 41.7 per cent, and one of them — a blue-green wall under a 3000 K lamp — reads as more colourful glossy than matt.
• The difference is entirely the lamp’s own colour. A daylight-referenced instrument counts the lamp’s departure from daylight as part of the room.
• What the finish does is geometric and the same everywhere. On the daylight instrument’s own plane every room moves within 9.2 degrees of straight towards the lamp’s white, by between 7.6 and 12.9 per cent of the way.
• That pull predicts every daylight reading to within 1.7 points, including the room that reads as a gain. The spread carries no information about the rooms.
• And every room is brighter glossy, by 18 to 20 per cent at the glossiest finish, under every lamp alike.

Two instruments, one room #

A colour is a departure from a white, so every chroma is a statement about two lights: the one being measured and the one it is measured against. CIELAB makes this explicit — its first step divides the stimulus by a reference white, channel by channel — and an instrument reporting CIELAB has to be told which white to use.

In a room lit by daylight the choice makes no difference, because the lamp is daylight. In a room lit by a 3000 K lamp there are two defensible readings and they are different measurements. Against the lamp’s own white, a surface that returns the lamp’s spectrum unchanged is neutral, which is what a person who has adapted to the room would also say of it. Against daylight’s white, the same surface has a chroma of 62, because the lamp itself does.

This is the table the essay first published. Down the daylight column the numbers are the ones the earlier essays had, from 8.3 per cent on the green wall to 11.9 on the red one, and in every other column they wander. The warm LED on a blue wall reads 41.7; the 3000 K lamp on a blue-green wall reads −6.0, the one shaded cell. Along the blue row the six lamps span forty points and along the green row four.

Read as a finding about gloss, that table says the lamp decides what a finish costs and can even reverse it. Read as a finding about instruments, it says something narrower and more useful, and the second table is the test between the two readings.

Every number in the daylight column is unchanged, which is the check that the two tables describe the same rooms: under daylight the two whites are one white, and the readings agree to rounding. Every other column has collapsed onto it. The blue row that spanned forty points now spans half of one. The red row, the widest, spans 2.1 points, from 10.9 under the 3000 K lamp to 12.9 under both LEDs. There is no negative cell.

So the rooms were never behaving differently. The finish takes about a tenth of the colour out of a room whatever the room is lit by, and how much of a tenth is decided by the wall — a green, yellow or orange wall loses eight or nine per cent, a blue or blue-green one ten or eleven, a deep red one eleven to thirteen — and hardly at all by the lamp.

The gloss pulls towards the lamp #

The daylight reading is not noise, and it is worth understanding rather than discarding, because it is what a colorimeter left on its default reference reports in a shop, a kitchen or a studio lit by anything but daylight.

The interface term of a satin wall carries the lamp’s spectrum exactly. Adding a little of it to a room’s reflected light moves the room’s colour towards the lamp’s colour — and on a daylight instrument the lamp’s colour is not at the centre of the plane.

Every arrow points at the diamond. Over the thirty rooms lit by something other than daylight, the move points within 9.2 degrees of the lamp’s white, at a median of 3.6, and covers between 7.6 and 12.9 per cent of the distance to it. Those shares are the same numbers as the lamp-referenced losses, which is what they should be: a room pulled a tenth of the way towards its lamp’s white has lost a tenth of its colour relative to that white.

What a daylight instrument then reports depends only on where the room started relative to the two whites. The hero picture above draws the 3000 K lamp’s six rooms. The lamp’s white sits at a chroma of 62, up and to the right of the cross, and five of the six rooms are further from the cross than a tenth of the way to the diamond carries them — so they read smaller losses than the lamp-referenced tenth, between one and five per cent. The blue-green room is the exception: at a daylight chroma of 32 it is nearer the cross than the lamp’s white is, on roughly the same side, and a pull towards the diamond carries it away from the cross. The instrument reads a gain of six per cent.

The warm LED’s blue room is the opposite case, and it is the table’s largest number for the same reason. Against the LED’s own white that room is vividly blue, at a chroma of 90. Against daylight’s white it is almost grey, at 17, because the LED’s yellow cast and the wall’s blue nearly cancel on a plane referenced to something else. The finish pulls it a tenth of the way towards a white that lies on the far side of the cross, the reading falls from 17 to 10, and the instrument reports 41.7 per cent of the room’s colour gone.

The daylight reading, predicted #

That account makes a prediction precise enough to test room by room. Take each matt room’s position on the daylight plane, move it the lamp-referenced share of the way to the lamp’s white, and read off the chroma. If the account is complete, that number is the daylight reading.

Every room lies on the diagonal to within 1.7 points, including the room that reads as a gain and the room that reads as losing two fifths. The residual is CIELAB’s own curvature — a straight move in tristimulus terms is not quite straight on a plane built from cube roots — and it is small against a spread of forty-eight points.

So the daylight table carries exactly two pieces of information: the lamp-referenced tenth, and where the lamp’s white sits. Neither is news about gloss. The spread that made the first version of this essay was a map of the six lamps’ colours, drawn on a plane that does not know it is looking at them.

What the lamp does change, which is little #

With the white right, the lamp’s remaining influence is small enough to measure directly on one room.

At the glossiest finish the green room loses between 8.4 and 9.8 per cent — 9.1 under daylight, 9.8 under the 3000 K lamp, 8.4 under the triphosphor tube. The curves rise together as the walls are made glossier, in the ordering the daylight measurement found, and the gap between them is smaller than the step between two adjacent finishes.

The residual has a cause, and it is not the one the first version gave. A lamp changes how much of its own light the wall returns. A green wall returns half of a triphosphor tube’s light, because the tube concentrates its power in a green phosphor band the wall reflects, and 35 per cent of a 3000 K lamp’s, whose power sits mostly in the red. The wall that returns more loses less — the tube’s room 8.4 per cent, the 3000 K room 9.8 — and across the six lamps the losses follow the wall’s luminance factor at a rank correlation of −0.94, on the green wall and again on the red one. That is a second-order effect of a point or two, not a sign change and not a factor of nine.

What decides the tenth is how much light the wall returns, and not how colourful the wall is. The first version said a weak colour loses a larger share of itself, and drew that from the daylight table, where the lamp’s cast and the room’s own colour are mixed together. It does not survive the correct white: two walls whose rooms are equally colourful can lose shares nearly six times apart, and a dark wall pays for a finish measures the rule across seventy-two paints.

The other half of the ledger #

One quantity was never in doubt, and it is what the colour half is a trade against.

Every room is brighter glossy, under every lamp: by 14.8 to 16.5 per cent at a satin finish and 18.2 to 20.2 at the glossiest. A lobe takes colour out of a bounce is where the two halves of the trade were first separated. A wall that reflects nine per cent at its surface still returns whatever its pigment gives back of the rest, and the arithmetic favours the interface because the pigment absorbs.

The six brightness curves nearly coincide, and they coincide for the same reason the lamp-referenced colour curves do. The interface’s share is a property of the interface — the refractive index and the angles — and it is the same share of whatever light arrives. Its colour is the lamp’s, and a measurement referenced to the lamp’s own white is precisely the measurement that removes the lamp’s colour from the question.

Which reading a person needs #

Both readings are correct statements about the room and they answer different questions, which is the practical content of the correction.

A specifier choosing a finish needs the lamp-referenced reading. A person in a room lit by a 3000 K lamp adapts to it within a minute or two — a gain has a time constant prices how long — and judges the walls against the room’s own light, not against daylight. For that person the finish costs a satin room about a tenth of its colour whatever the lamp is, and the paint that looks right on a card under the same lamp loses the same tenth on the wall. An appearance model does not agree that the tenth is the whole story, and a gloss room looks less colourful than it measures is where that disagreement is priced — but it disagrees about the size of the tenth, not about which white to start from.

An instrument set to daylight answers a different question: how far the room’s light is from daylight. That is the right question for a colour-critical booth, where the lamp is supposed to be daylight and any cast is an error to be reported. It is the wrong question for a room lit by a lamp chosen on purpose, and its answers there — a finish adding colour here, taking two fifths there — are a report on the lamp, delivered through the walls.

And a comparison of rooms under different lamps has to name its white. Two reports of “chroma lost to a finish”, one from a kitchen and one from a gallery, can disagree by forty points about the same paint without either instrument being faulty. The white is a third argument to every chroma, and a viewing condition is an argument makes the general case: a reading that leaves it out has assumed one.

How the thirty-six rooms were computed #

The room is the unit cube the directional work uses throughout: a lamp in the ceiling, two opposite walls painted with a Gaussian reflectance band of width 25 nanometres and peak 0.85 on a base of 0.03, the other faces a neutral 0.5, every face carrying a microfacet lobe of the stated roughness, solved directionally in eighty-one bands. Only the lamp’s spectrum and the wall’s band centre change between cells.

The quantity is the ledger’s: the chroma of the room’s total reflected flux, with the lamp’s own emission removed from the ceiling first, so that what is measured is light reflected at least once, normalised to its own luminance. The loss is one minus the glossy room’s chroma over the matt room’s. It is computed twice, with CIELAB’s reference white set to the tristimulus values of the lamp’s own spectrum and to those of D65.

The six lamps are three smooth ones — D65, a 3000 K Planckian radiator and 4000 K daylight — and three with structure: a neutral white LED, a warm white LED and a triphosphor tube, each built from a stated emission model rather than tabulated. The pull is measured on the daylight-referenced ab plane, as the angle between each room’s move and the direction to the lamp’s white, and the move’s length as a share of that distance.

What this leaves out #

Every room is solved at a roughness of 0.15 or above, where the solver still resolves the lobe; the boundary belongs to the quadrature is what it would cost to go further. A high-gloss finish is outside the method, and the pull would be larger there.

The lamp-referenced reading divides by the lamp’s white in XYZ, which is CIELAB’s own normalisation and not a good chromatic adaptation transform. It is the right choice for asking what the finish did, because it is exactly the division that makes the lamp’s own light neutral; it is not a prediction of what a viewer sees, and the appearance reading of the same thirty-six rooms is a separate computation with a different answer.

And the walls are a Gaussian band in a room whose other faces are grey. A room of several colours pulls its average light away from the lamp’s white, which gives an adapted viewer a third white to judge by, and none of the whites here is that one.

Still open: what a viewer adapted to each room sees #

The lamp-referenced reading removes the lamp’s colour and nothing else. A person standing in one of these rooms adapts to the room’s own average light, which a coloured pair of walls tints away from the lamp, and the earlier appearance measurement under daylight found that an adapted viewer loses more colour to a finish than the light does, not less.

So the question the correction leaves is whether that holds in all thirty-six rooms, and whether it is the lamp or the wall that decides how much more. The computation is the daylight one repeated: read each face through CIECAM16 with the adopted white set to each room’s own average light, matt and glossy, under each lamp. What an adapted viewer loses is set by the wall runs it, and the answer is not the tenth.

A white is an argument, not a setting #

The habit is about a quantity that looks like a property of one thing and is a relation between two.

Chroma, saturation, a colour difference against a neutral, an “added cast”: each is computed against a reference white, and each is reported as though it belonged to the stimulus alone. Under the light the reference was written for, nothing is lost by the shorthand. Under any other, the reported number is partly a measurement of the reference.

The move is to compute the quantity twice — against the white the question is about and against the white the instrument assumed — before believing anything that differs between conditions. When the two agree the condition matters; when one of them is flat, the variation lived in the white. Here the check takes one extra division and removes a forty-point spread and a sign change.

The failure mode is a surprising variation discovered under several lights and explained by the physics of the thing measured. The explanation is usually available — a weak colour does lose more to dilution, in some regime — and it is usually wrong, because the variation was the lights all along and the thing measured was holding still.