The booth is a luminaire

Every acceptance decision in colour reproduction is made under a standard viewing condition, and the standard specifies the light three ways: its chromaticity, its colour rendering, and how uniform its illuminance is across the sample plane.

The third of those is a photometric integral. It says how much light arrives, weighted by one function of wavelength, summed to a single number. Two positions on a sample plane can satisfy it comfortably and be lit by two different spectra, because a spectrum has many more degrees of freedom than an illuminance does — and a phosphor-converted source’s spectrum depends on the angle its light left at.

The claim #

A viewing booth is a lamp with a geometry, and the standard’s uniformity figure cannot see what the geometry does to colour.

• A sample thirty centimetres from the centre of a booth’s plane is ΔE00 2.4 from one in the middle, with the observer adapted once, to the light at the centre.
• The booth is compliant the whole time. The illuminance at that corner is 73 per cent of the centre’s, inside the floor a standard sets.
• The lamp’s correlated colour temperature falls from 4044 K to 3916 across the same span, which is a hundred and twenty-eight kelvin of drift with nothing moving but the observer’s eyes.
• And the repair is geometric. A source whose converter is the same thickness in every direction has an angular colour difference of exactly zero, by construction — and both booths pass the uniformity figure, so the number the standard bounds cannot tell them apart.

Why a source has an angular colour #

A white LED is a blue die under a converter. Some of the pump light is absorbed and re-emitted broad and yellow; the rest gets through. The white is the mixture, and the mixture depends on how much converter the light went through.

For a conformal coating — a layer of even thickness over the die — light leaving on the axis takes the shortest path and light leaving at seventy degrees takes nearly three times as long a one. More absorption means more conversion, so the off-axis light is yellower: more converted, less pump.

That is not a defect, it is Beer–Lambert applied to a shape. It is why a bare LED torch has a blue centre and a yellow ring, and it is why every serious luminaire has a diffuser or a remote phosphor dome — a dome’s surface is everywhere the same distance from the die, so the path length is the same in every direction and the angular colour is exactly absent.

The geometry of a booth #

A booth is a lamp above a plane. A sample directly below the lamp is on axis; a sample thirty centimetres away with the lamp fifty-five centimetres up is at twenty-nine degrees.

Twenty-nine degrees is not an extreme, and it is worth putting the geometry in ordinary terms before the number is quoted. A viewing booth is about the size of a large cupboard laid on its side: a working plane perhaps sixty centimetres deep and eighty wide, with the lamps in a housing across the top and a hood at the front to keep stray light out. The lamp-to-plane distance is set by the height of the box, and a shorter box gives a more even illuminance over the plane only if the lamps are spread across its width, which is what real booths do and is not what the single-source calculation here models. What the single source does capture is the direction of the effect and the size of the angles involved. Twenty-nine degrees is a sample at the edge of an A3 print, or a colour patch at the corner of a proofing sheet, in a booth of ordinary dimensions. Nobody would describe it as an unusual viewing position and nothing in the standard suggests it is one.

The observer adapts once, to the light at the centre of the plane, and reads every position against that. That is deliberate and it is what somebody standing at a booth does — the alternative, adapting separately at each position, would remove the effect by construction and would describe nobody.

What the standard does bound #

Illuminance falls with angle for two reasons that have nothing to do with the converter: the inverse square of the distance, and the cosine of the angle at the surface. Together those give a falloff of about the cube of the cosine, which is 73 per cent at twenty-nine degrees.

That figure does not follow from the law stated beside it, and the discrepancy is worth resolving because it changes how close the booth is to failing.

The cube of the cosine at twenty-nine degrees is 68 per cent, not 73. The geometry gives 28.6 degrees from a lamp fifty-five centimetres above a sample thirty out, the cosine there is 0.878, and its cube is 0.677. Seventy-three per cent would need an angle of 25.8 degrees, or a falloff law with an exponent nearer two and a half than three.

The consequence is the margin. Against a 60 per cent floor, 73 per cent leaves thirteen points of headroom and 68 leaves eight — so the booth is nearly twice as close to non-compliance as the number suggests, and the same geometry at forty centimetres out rather than thirty would take it under.

It also disturbs the table’s punchline. The dome is reported at 68 per cent against the conformal source’s 73, and the irony of the essay is that the standard’s own measure ranks the better booth lower. If the conformal source is at 68 rather than 73, the two are level and the irony is not that the standard prefers the worse booth but that it cannot distinguish them at all — which is a weaker claim about the standard and a stronger one about the measurement, since a quantity that gives two identical readings to a booth with a two-and-a-half-unit error and one with none has failed more completely than a quantity that merely orders them wrongly.

Which of the two readings is right cannot be settled from here: the 73 may come from a diffuser term the prose does not mention, or from a lamp modelled as an extended source rather than a point, and either would be a defensible model and a different law from the one written down. What is not defensible is the pair as printed, and the check that catches it costs one cosine.

Standards for graphic-arts viewing conditions set a floor on that — the illuminance anywhere in the working area must be at least a stated fraction of the maximum, typically 60 per cent at the edges and 75 within the central area. So a booth of these dimensions is compliant, and a person checking it with a light meter finds nothing wrong.

A light meter has one spectral weighting, and that is not an accident of the instrument — it is the definition of the quantity. Illuminance is the integral of the spectrum against the luminous efficiency function, so two spectra with the same illuminance are two spectra the measurement was built to treat as equal. Asking it to report a difference between them is asking a projection to report what it projected away, which is the same objection this site raises against a colour difference computed from three numbers. It cannot report that the light at the corner is a hundred and twenty-eight kelvin cooler than the light in the middle, because it collapses the spectrum to one number and the two numbers happen to be in the right ratio.

The colour difference is entirely the temperature drift #

One more check, and this one passes.

The lamp’s correlated colour temperature falls 128 kelvin across the plane, which on the reciprocal scale is 8.1 mireds — the unit on which equal steps are roughly equal shifts. Near 4000 K a mired is worth something like a third of a colour difference unit, so eight of them should be worth between two and two and three quarters.

The measured difference is 2.40, which sits inside that band.

So the whole of the booth’s colour error is accounted for by a shift along the colour-temperature axis, with nothing left over. That is a stronger statement than it looks, because a change of converter path length could in principle move the source off the locus as well as along it — a thicker converter shifts the balance between the pump line and the phosphor hump, and the two are not on the locus individually. That the residual is nil says the two move together in a way that keeps the mixture near the locus, which is a property of this converter’s shape rather than a necessity.

It also says what a manufacturer’s existing measurement is worth here. Angular colour uniformity is published in lighting engineering as a Duv spread or a colour temperature spread over the beam, and a graphic-arts reader would reasonably ask whether the lighting figure captures what a booth does to a sample. On this source it does: a colour temperature spread and the sample-plane colour difference are the same measurement in two units, related by about a third of a unit per mired. A booth manufacturer already has the number this essay says is missing — it is in the lamp’s own datasheet, under a name nobody in the graphic-arts standard would think to look for.

The repair the number cannot see #

Replace the conformal source with a dome and the angular colour vanishes exactly. The path length is the same in every direction by construction, so every angle emits the same spectrum, and the computed difference across the sample plane is zero to floating point rather than small.

Both booths still pass the uniformity figure. The dome’s illuminance falls a little differently — a dome emits into a different distribution than a conformal coating does — so its uniformity is 68 per cent at the corner against the conformal one’s 73, and both are above a 60 per cent floor.

That is the sharpest form of the claim. Two booths, one of which has a colour error two and a half times the tolerance being judged and one of which has none at all, and the quantity the standard measures puts the better one slightly lower.

assertADomeFixesTheBooth requires both halves: the geometric repair reduces the spread by orders of magnitude, and both geometries pass the uniformity floor.

What this costs in practice #

A proof is accepted or rejected against a tolerance, and the tolerance for a contract proof is typically one to two units on the average and a little more on the maximum. This essay’s booth adds 2.4 units of its own, depending on where the sample was lying.

Two consequences follow, and the second is worse than the first.

A sample that is within tolerance can be rejected because it was at the far end of the plane. That is a false rejection and it costs a reprint.

And two samples compared against each other can be separated by the booth rather than by the printing, if one is nearer the middle than the other. That is what a booth exists to prevent — a controlled comparison is the whole point of the apparatus — and the error is systematic rather than random, so repeating the check does not reveal it.

The two booths, in one table #

Only one row of that table is in any specification, and it is the one that is nearly the same in both columns — and slightly worse for the better booth.

The colour temperature drift is the row a lighting engineer would recognise instantly, because angular colour uniformity is a published quantity in their field. It is not a quantity in the graphic-arts one, where a booth’s light is specified as a chromaticity and a rendering index measured somewhere.

What was computed, and how #

The lamp is the site’s own phosphor-converted white LED, built from its parts: a pump line, a converter absorbing along a Beer–Lambert path at a stated optical thickness, and a red nitride band. Its angular behaviour comes from one function — how far light leaving at a stated angle travelled through the converter — with a collimation parameter running from a bare conformal coating to a perfect dome.

The booth geometry is a lamp height and a set of distances, and the angle follows by arctangent. The illuminance falls as the cosine cubed, which is the inverse square with the surface tilt included.

Every position is read against the same white — the light at the centre of the plane — because that is what an observer standing at a booth is adapted to. Reading each position against its own light would report zero everywhere and would be a statement about nobody.

The sample is a mid-chroma yellow-orange rather than a neutral, because a neutral hides half of this: an angular shift toward yellow moves a neutral mostly in one direction and a chromatic sample in two.

The observer is in the booth too #

There is a second geometry in the same apparatus and it belongs to the person rather than the lamp.

A sample lying flat on a booth’s plane at thirty centimetres from the centre is not only lit at twenty-nine degrees; it is also seen at an angle, and by a part of the retina that is not the fovea if the observer is looking at the middle. This site has both of those elsewhere — a gloss measurement changes with viewing angle, and colour-matching functions change with where on the retina the light lands — and neither is in this calculation.

Adding them would compound rather than cancel. The lamp’s angular colour makes the corner yellower; a sample seen off axis is seen through less macular pigment, which makes it look bluer; and how those two combine depends on where the observer’s gaze is, which no standard specifies either.

So the booth’s total is at least what is computed here and possibly more, and the honest statement is a floor rather than an estimate.

Where it stops #

One source type. A booth lit by fluorescent tubes — which most older ones are, and which the graphic-arts standards were written around — has a different angular behaviour: a tube is an extended source and its emission is much more nearly Lambertian, so the effect here is small or absent. The result belongs to solid-state booths, which is most of what is now sold.

The geometry is a point source above a flat plane, which is a caricature. A real booth has a diffuser, a reflective housing and often several lamps, all of which mix the angular distribution and reduce the effect. How much they reduce it is a property of a particular device and is exactly what a booth manufacturer would have to measure — which is the useful form of this essay’s request.

And nothing here is a measurement of a real booth. It is a computation of what a stated source geometry does, and its value is that it identifies a quantity that is not in any specification rather than that it puts a number on any particular apparatus.

Who found it, and when #

The angular colour of white LEDs is thoroughly documented in lighting engineering, where it is called angular colour uniformity and is quoted as a Duv or a colour temperature spread over the beam. Manufacturers publish it, the remote-phosphor and diffuser fixes are standard, and nobody in that field would be surprised by anything above.

Graphic-arts viewing standards predate solid-state lighting entirely. They were written when a booth meant fluorescent tubes with a specified phosphor mix, and the uniformity requirement was written to catch a lamp that had aged unevenly or a reflector that had discoloured. It does that job and it was never asked to do this one.

So the gap is not an error by anybody. It is a specification written against one technology being applied to another, with a compliance test that happens to be blind to the new failure — which is the same shape as several other findings on this site, and is the reason a specification’s silences are worth as much attention as its limits.

Where the ladder goes next #

The measurement to make is the one this essay cannot: take a real booth, a spectroradiometer and a sample plane, and map the spectrum at a grid of positions. The prediction is specific — a colour temperature falling with distance from the centre, a Duv moving with it, and a colour difference that a light meter’s uniformity reading does not track.

The specification change that follows is one line, and it is the same shape as the second field proposed for a tolerance: bound the chromaticity uniformity across the sample plane, not only the illuminance. A booth manufacturer can measure it, a standard can state it, and the two booths in this essay would then be distinguishable by the document that is supposed to distinguish them.