Gloss changes the measurement

What the instrument reports makes the case that a spectrophotometer’s reading is a property of the arrangement as much as of the sample — the bandpass, the aperture, the calibration standard. This essay is the sharpest instance of that, and it is sharp because the two available answers differ by more than any tolerance and each of them is right.

Measure a glossy sample twice, once with the specular component included and once with it excluded, and the instrument returns two different colours.

The claim #

A measurement of a glossy surface is a measurement of the surface and of how the instrument arranged itself around it, and the two conventions in common use answer genuinely different questions.

This is not a calibration problem. Two instruments both working perfectly, both traceable, both agreeing on a matte tile, will disagree on a glossy one — and neither is faulty.

The two questions #

The split is the dichromatic model, which is the second rung of this ladder. Light leaving a dielectric is a sum of two components with different histories: the body component, which entered the material, scattered off pigment and came back carrying $\rho(\lambda)$; and the interface component, which never entered, and carries the illuminant with only Fresnel’s slight dispersion on it — a 5.5% variation across the visible band, against the pigment’s factor of twenty-five.

Now the two conventions:

Specular included (SCI). The instrument collects everything leaving the sample, interface component and all. It is measuring the material — what the colorant is, independent of how the surface was finished. Two samples of the same pigment, one polished and one abraded, read nearly the same.

Specular excluded (SCE). The instrument uses a gloss trap to discard the interface component and collect only the body term. It is measuring the appearance — what the surface looks like to somebody not standing in the highlight.

Both are useful and they are useful for different jobs. A formulator wants SCI, because the question is whether the pigment loading is right and the surface finish is a separate variable. A person approving a finished panel wants SCE, because the question is what it looks like.

Why the difference is large #

The interface component is spectrally flat and adds a constant to the reflectance at every wavelength. Adding a constant to a reflectance does not shift the colour uniformly — it desaturates, because it raises the low bands proportionally much more than the high ones.

For a dielectric at normal incidence the added term is around 4%, which sounds negligible and is not. A saturated pigment reflecting 0.03 in its absorption band goes to 0.07 — more than doubling — while the same 0.04 added to a peak of 0.75 is a 5% rise. The ratio between peak and trough falls from 25 to about 11, and the sample reads substantially less saturated.

So the SCI reading is lighter and less colourful than the SCE reading, always, and the gap grows with how saturated the pigment is. On a deep saturated colour the difference between the two conventions is comfortably larger than the tolerance the sample would be accepted against.

That is the practical hazard: two laboratories can measure the same panel, both correctly, and reach opposite verdicts on whether it passes, purely from an instrument setting that the specification may not have named.

A worked disagreement #

It is worth putting numbers on the two readings, because the size decides whether this is a footnote or a hazard.

Take a saturated pigment reflecting 0.03 in its absorption band and 0.75 at its peak — an ordinary strong colorant. Under a dielectric binder of index 1.5, the interface term at normal incidence averages 0.0424 across the band, and it is nearly flat: it varies by 5.5% between 400 nm and 700 nm, against the pigment’s factor of twenty-five.

Specular excluded reports 0.03 and 0.75.

Specular included reports about 0.072 and 0.792.

The peak has risen by 6%. The trough has risen by 140%. So the peak-to-trough ratio has collapsed from 25 to 11, and the sample reads far less saturated — while its lightness has barely moved, because the lightness was set by the peak.

That asymmetry is why the effect is easy to underestimate from the size of the added term. Four percent of the illuminant is a small amount of light and a very large fraction of what a saturated pigment returns where it absorbs. The instrument setting is therefore most consequential exactly where the colour is strongest, which is exactly where tolerances are tightest.

The difference in the unit a specification uses #

Two reflectance curves are not a verdict, and the disagreement between the conventions is worth having in the unit a contract is written in.

For the worked pigment — 0.03 in the trough, 0.75 at the peak, under D65 — specular included and specular excluded are 2.22 ΔE00 apart. That is above any tolerance a saturated colour would be accepted against, and the shape of it is not what the two reflectance curves suggest.

Sweeping the pigment from saturated to nearly neutral by holding the peak and raising the trough, the disagreement runs 2.22, 2.14, 1.98, 1.78, 1.57, 1.48 and 1.41 as the chroma falls from 76 to 6. It does grow with saturation, and only by 57 per cent across the whole range — and it never falls below a unit. The two conventions disagree by more than a tolerance on every sample, a grey included.

The decomposition says why. The lightness difference across that same sweep is +2.36, +2.34, +2.31, +2.24, +2.15, +2.14, +2.12 — essentially constant, because a flat four per cent added to any reflectance raises its luminance by about the same amount whatever the pigment underneath is doing. The chroma difference is the part that depends on saturation: −6.01 units on the strong pigment and −0.29 on the near-neutral one.

So the observation above, that the lightness has barely moved, is the wrong way round once it is read in the units the verdict is given in. In reflectance the peak barely moves and the trough more than doubles. In lightness and chroma the lightness moves by a constant two units and the chroma by an amount that varies. And because a difference formula discounts a chroma difference by how chromatic the sample already is, that constant lightness term is the larger contributor to the 2.22 on the saturated pigment — where the reflectance curves make the chroma collapse look like the whole story.

Which changes what a specification is protecting against. Naming the convention guards against a chroma disagreement that is large only on saturated samples, and against a lightness disagreement of about two units that is present on everything. The second is the one that turns up on a grey nobody was worried about.

Four attributes, one measured #

There is a wider point here, and the CIE’s own vocabulary makes it.

Visual appearance is conventionally divided into four attributes: colour, gloss, translucency and texture. Almost every instrument in routine use measures the first, most specifications quote the first, and the other three are handled by separate instruments, separate standards, and often separate departments.

The trouble is that they are not independent. Gloss changes the measured colour, as above. Translucency makes the measured colour depend on the sample’s thickness, which is why plastics standards specify a plaque thickness. Texture changes the effective geometry point by point, so a measurement over an aperture is an average over a distribution of local geometries.

Colour is the attribute that got standardised first and hardest, and it absorbed the others’ effects as measurement conditions rather than as attributes. Which is why the standards for measuring it are so specific about geometry — 45°/0°, 0°/45°, d/8° with the specular included or excluded — and why those geometries are the place all the other attributes leak in.

Two more readings of the same object say that neither the lamp nor the paint is what the geometry is reporting.

Why measuring harder does not help #

A natural response is that both numbers are available, so the sample can simply be characterised by both — measure SCI and SCE, report the pair, and the ambiguity is gone.

That works, and it is what careful laboratories do. It does not remove the underlying problem, for two reasons.

The pair is still two points on a continuum. SCI and SCE are the endpoints of how much interface component the geometry catches, and a real viewing situation catches some intermediate amount depending on where the observer and the light are. Neither endpoint describes a person looking at a panel at an ordinary angle, and the difference between them is a range within which the answer lies rather than two candidate answers.

And the specification downstream takes one number. A tolerance is quoted as a $\Delta E$ limit against a standard, and a tolerance is already a shape rather than a number in three dimensions before this is considered. Adding a geometry axis to it is not a matter of quoting two values; it is a change to what the acceptance criterion means, and the standards have not made it.

So the honest position is that measuring both is better practice and does not close the gap. The gap is in the specification’s vocabulary rather than in the instrument’s capability, which is the same conclusion this field reaches about metameric matches in corners and about scenes with two illuminants — three times over, from three unrelated directions, the missing field is a geometry.

The case where separation is impossible #

For an ordinary dielectric the two components can at least be separated in principle, because one is flat and one is not. There are two classes of sample where even that fails.

Metals, where there is no body component at all. What a metal reflects is specular and strongly wavelength-dependent, so excluding the specular component excludes the colour. Gold measured SCE is nearly black, which is a correct measurement of nothing anybody wanted.

Goniochromatic finishes, where the reflectance itself depends on the angle. A single-geometry instrument returns one point on a curve and gives no indication that a curve exists. Multi-angle instruments were built for this, and they were built because single-angle ones had been giving confident wrong answers about metallic and pearlescent automotive paint for years.

In both cases the honest statement is that the sample’s colour is not a scalar and no single-geometry measurement can be made to report one. The instrument is not failing; the specification asked for something that does not exist.

What was computed, and how #

The two components are computed separately from stated physics. The body term is an illuminant times a stated reflectance; the interface term is Fresnel’s unpolarised expression evaluated on a Cauchy dispersion, at a stated angle. Neither is fitted.

The near-neutrality of the interface term is a result, not an assumption. The refractive index is allowed to disperse — 1.5309 at 400 nm to 1.5132 at 700 nm — which is what makes the interface component 1.06 units of $\Delta E_{00}$ from the lamp rather than zero. Fixing the index would have made the answer flat by construction and proved nothing.

The assertion is comparative and two-sided. The generator requires the interface term to be within 2 units of the lamp and the body term to be more than 15 away. Checking only the first would pass on a neutral sample, where both components are near the lamp and the figure demonstrates nothing.

The angle is named in every caption, because the interface term’s magnitude depends on it — 0.0424 averaged across the band at normal incidence, 0.0726 at 55°, 0.3908 at 80°.

What the pictures cannot show #

Gloss is a spatial and directional phenomenon and these are flat patches. What makes a surface look glossy is a sharp, bright, view-dependent highlight, and a swatch has no view direction. The figures report the spectra correctly and convey nothing of the appearance the argument is about.

The body component of a saturated pigment is usually outside the display’s gamut and is hatched rather than clipped — marking, not the nearest available lie. So the reader sees the least saturated version of exactly the samples where the SCI/SCE gap is largest.

Nothing here is about how gloss looks. Perceived gloss depends on the sharpness of the highlight, the contrast against the body colour, and the structure of what is being reflected, and none of that is computed. This is colorimetry of the two components, and the line between measurement and appearance is one this site keeps deliberately.

A blue pigment at a middling angle is the case where the two components are furthest apart in colour, and it is the one a gloss meter is least able to report.

Where the model stops #

One smooth interface. Real gloss is microfacet structure, so the interface term is spread over a range of angles rather than mirror-sharp, and light reflecting off one microfacet onto another has met the interface twice.

No polarisation. Specular reflection is strongly polarised near Brewster’s angle. The unpolarised average is used throughout, and a real instrument’s optics may not be polarisation-neutral.

No internal reflection at the interface. Light inside the material reaching the surface from below is partly reflected back down, which is what the Saunderson correction accounts for in Kubelka–Munk practice. It is a real term and it is absent here.

No sphere geometry. SCI and SCE in practice are properties of an integrating sphere with or without a gloss trap, and the sphere itself has an interreflection gain that amplifies its own coating’s spectrum. Nothing here models the instrument as a cavity, which it is — and a sphere at 0.98 reflectance has a gain of 50, so its coating’s residual absorption bands are multiplied by that before they reach the detector. Sphere coatings are specified for spectral flatness rather than reflectance alone for exactly this reason.

And the sample is uniform. A textured surface presents a distribution of local angles inside the measuring aperture, so what the instrument reports is an average over geometries rather than a measurement at one — which is the third of the four appearance attributes leaking into the first, by the same route as the second.

The split into a body and an interface component is a statement about the light, so it should not move when the observer scoring it does.

The generalisation #

When a measurement has a convention, the convention is part of the result, and a number quoted without it is incomplete rather than approximate.

SCI and SCE are the clean case because both are standardised, both are named, and the gap between them is large enough that nobody can pretend it is noise. The general form is worse, because most conventions are not named — they are defaults, buried in an instrument’s configuration or a library’s parameters, and inherited by everybody who did not think to ask.

The diagnostic question is: what would have to be true for two correct measurements to disagree? If the answer is “nothing”, the quantity is well-defined. If there is an answer — a geometry, a bandwidth, an integration time, an aperture — then that answer is part of the specification whether or not it appears in it, and its absence from the document does not make it absent from the measurement.

This is the same failure as a metameric match certified on a flat chart and installed in a corner, and as a white point specified for a scene that has two. In all three the specification has no field for the thing that decided the answer, and in all three the missing field is a geometry.

Who found it, and when #

The two-component account of what leaves a dielectric is old as physics and recent as a measurement convention. Fresnel’s coefficients date from 1823; Shafer’s dichromatic reflection model, which framed the split as something a machine could exploit, is from 1985.

The instrument conventions came in between and came from industry. Integrating-sphere spectrophotometers with gloss traps were in use by the mid-twentieth century, and the SCI/SCE distinction was standardised because manufacturers and customers kept disagreeing about samples in ways that turned out to be traceable to which instrument had been used. The standards did not discover a phenomenon; they codified an argument.

The four appearance attributes were set out by Hunter, whose 1937 work on gloss measurement and later book on the measurement of appearance are the origin of treating the four as a set. His argument was precisely that colour had been standardised in isolation and that the other three were being handled as nuisance variables — which is still substantially the case, nearly ninety years later, and is visible in the fact that every reader knows what a colour tolerance is and few could state a gloss one.

Where the ladder goes next #

This is the top of the field as it stands, and the ladder’s own gaps are the honest place to end. Nothing here models the instrument as a cavity, nothing models microfacet gloss, and nothing separates the four appearance attributes rather than noting that they interact.

Below, the field’s base rung remains the whole of it: a bounce is a multiplication, and every essay above it — a broken metameric match, a shadow with its own illuminant, a renderer that loses accuracy per bounce, a bound no pigment can pass — is a consequence of doing that more than once, or of a specification written as though it had been done exactly once.