The observer has no age

Five of this round’s six arguments describe how people differ from one another. One describes how each person differs from themselves, twenty years later, and it is the largest of the six.

The claim #

The ageing lens is a trajectory rather than a spread, so a standard observer with no age is not an average over a population — it is a description of one age, and everybody is somewhere else.

• It is the largest of the six departures, at 2.38 ΔE₀₀ on a red pigment under daylight and 1.94 at the median over forty-two surfaces.
• It is not random. Every lens yellows, in the same direction, at roughly the same rate, so the population’s distribution has a mean that moves rather than a spread that stays put.
• A systematic effect cannot be budgeted like a random one. Two observers drawn at random from a working-age population differ by less than two drawn from opposite ends of it, and a specification that budgets for the first is not protected against the second.
• And it is the one parameter estimable without measuring anybody, since age is known and the relationship is monotone.

What the lens does #

The crystalline lens contains proteins that accumulate yellow chromophores over a lifetime. Its transmittance falls at every wavelength and falls much faster in the blue: a seventy-year-old receives roughly a third of the 440-nanometre light a twenty-year-old does, and about ninety per cent of the 600-nanometre light.

Modelled as a density that rises linearly with age from about twenty, that gives a filter in front of all three cones whose effect is confined to the short wavelengths. The eye stops at the lens established that this filter is the reason the visible band has the lower bound it does; what this round adds is what its variation costs.

The effect is entirely pre-neural. It is not adaptation, it is not a change in the receptors, and no amount of exposure or practice alters it. It is a piece of glass getting browner.

The measurement #

Two observers at twenty and seventy years, all other parameters at the population median.

Over forty-two surfaces under daylight the same departure runs from 0.656 to 6.629 with a median of 1.943, which is the largest median of the six and the third-widest span.

The tungsten row is the largest single observer number anywhere in this round, and its cause is the ratio argument: under a warm lamp the short-wavelength cone’s relative excitation is a ratio of two small numbers, and a filter that changes both differently does most damage there.

Why a trajectory is not a spread #

The distinction is easy to state and it changes what a specification has to do.

A spread is a population distributed about a mean. Macular density has a mean of 0.35 and a standard deviation of 0.13, and two people drawn at random differ by about 0.18 on average. A standard observer at the mean is a reasonable representative: half the population is above it and half below, and the expected error of using it is small.

A trajectory is a population distributed along a line whose position depends on a variable everybody has. Lens density at twenty and at seventy differ by a factor of about three, and the population is spread along the whole of that range in proportion to the age distribution of whoever is doing the looking. A standard observer at the mean age is a description of a forty-five-year-old, and a twenty-year-old and a seventy-year-old are both wrong by comparable amounts in opposite directions.

The consequence is that the worst case is much further from the mean than a spread’s would be. For a spread, two standard deviations covers most of the population. For this trajectory, the extremes are the endpoints of the working-age range and there is nothing exponential about the tails — a seventy-year-old is not an outlier, they are one of the ends.

The lens is not only the largest departure; it is the most light-dependent, and the two facts together make it the least summarisable. A specification quoting one number for observer age would be quoting a number that varies by a factor of two depending on the lamp in the room, and the lamp is usually the last thing a specification pins down.

The direction of the dependence is the awkward one. The lamps under which the lens matters most are the warm ones, and warm lamps are what most retail, hospitality and domestic lighting is. A colour approved in a daylight booth and rejected in a shop is the ordinary complaint of the colour-matching trade, and the shop’s lamp has always been the named culprit. What this adds is that the shop’s lamp also doubles the disagreement between the two people arguing about the result.

What a specification can do about it #

Unusually for this round, there is something a specification can do, and it is available for nothing.

Age is known. It is the only one of the six parameters that requires no measurement of the eye at all — it is on a form, it is knowable in advance, and the relationship between it and lens density is monotone and modelled in a published standard. Every other parameter needs an instrument and a cooperative subject.

So a colour-critical operation with a known set of assessors can compute each of their lens densities from age alone and know which of them will disagree with which. That is a genuinely actionable result and it is not standard practice anywhere this collection has read about.

The second thing a specification can do is choose its assessors. A panel drawn from one decade agrees with itself far better than one spanning forty years, and the agreement costs nothing but a hiring decision. Whether that is a good idea is a different question — a panel that agrees with itself and not with the customer is worse than one that disagrees internally — but it is a lever, and it is the only one of the six that is.

Why it is nonetheless the wrong one to correct #

Having established that the lens is the largest departure and the easiest to estimate, the natural next step is to correct for it, and the natural next step is a mistake.

A correction would mean transforming a measurement made through one lens into what it would have been through another, and that is well defined. The problem is what it would be for. A colour specification exists so that two people looking at two objects agree, and the agreement they need is about appearance, not about a computed number.

Everybody’s visual system has adapted to their own lens over decades. A seventy-year-old does not see the world as yellow; their neural machinery has renormalised, and there is good evidence that the renormalisation is close to complete for the achromatic axis. So a large part of the lens’s effect on a computed colour difference does not correspond to any difference in what is seen.

That is the same distinction this collection has drawn between matching and appearance from its first phase, and it bites hardest here. The lens departure is real for a match — two lights that match for a young eye do not match for an old one, and no adaptation repairs that. It is largely absorbed for an appearance — the old eye’s world is not yellower.

So the honest position is that the largest number in this round’s ladder is the one whose perceptual meaning is least clear, and it is not the one to correct.

That is the one ladder in this round with a clear leader, and it is worth noticing because every other one is flat. Under tungsten the lens is 4.38 and the macular 4.47 — the two blue-absorbing terms — and the remaining four are between 0.79 and 2.10. Under daylight the six are within a factor of two of one another.

So the statement that there is no dominant observer term is a statement about daylight, and under warm light there are two dominant terms and they are the same two: a filter in front of the receptors, and a second filter in front of some of them. Both are pre-neural and neither is a receptor property at all, which is a curious thing to be the largest source of disagreement between two visual systems.

The one place the correction is unambiguous #

There is a setting where the appearance objection does not apply, and it is worth naming because it is where the money is.

An instrument does not adapt. A spectrophotometer computing a colour difference through the 1931 observer is not renormalising anything, and neither is the specification it is being checked against. When the question is whether two physical samples match — a metameric pair, a proof against a press sheet, a repair panel against a car — the relevant quantity is whether the match holds for the person who will look at it, and a match is exactly what the lens breaks.

That is why observer variation matters most in the industries where metamerism is unavoidable: automotive refinishing, textile dyeing, plastics matched to painted trim. In all of them two samples are made of different colorants, they match under one condition for one observer, and the failures are reported by customers rather than by instruments. Two paints that stop matching is that situation with the light changed; this is the same situation with the observer changed, and the second has no standard practice attached to it at all.

The lens’s role in those failures is estimable from the customer’s age, which is knowable, and is not estimated anywhere.

The trajectory changes what a population statistic means. There is a technical consequence for anybody computing observer-metamerism statistics over a simulated population, and this collection has such a population.

Its two hundred eyes draw an age uniformly between twenty and seventy and three other parameters from Gaussians. Mixing a uniform trajectory with three Gaussians produces a distribution whose shape is dominated by the uniform: the aggregate observer difference is not Gaussian, it has heavier shoulders and a shorter tail than a Gaussian, and its ninety-fifth percentile is closer to its maximum than a Gaussian’s would be.

That matters when a result is reported as a percentile. A ninety-fifth percentile of a uniform-dominated distribution is much closer to the worst case than a ninety-fifth percentile of a Gaussian one, so a specification set at that percentile is nearly a worst-case specification — which is either reassuring or over-conservative depending on what was intended, and either way is not what the phrase suggests.

The repair is to report the shape rather than a percentile, or to report both ends. A percentile is a summary that assumes a shape, and a population with a trajectory in it does not have the assumed one.

What was computed, and how #

The lens density is modelled as 0.5 + 0.02·(age − 20) applied as an exponential absorbance falling with wavelength — a two-parameter caricature rather than a fitted table, stated as such in the source and adequate for the direction and rough magnitude.

The two ages are twenty and seventy, which is the working-age range this collection’s population machinery uses and is the range over which the linear density model is defensible. Extending it to five or to ninety would need a different functional form, and the published models have one.

Everything is computed through this collection’s usual CAT16 route, and the departure carries that route’s own contribution as every number in the round does.

That figure is worth having beside everything above because it bounds the claim. An ageing lens does not change the colour of a neutral, at any age, to the floating-point floor. So the disagreement between a twenty-year-old and a seventy-year-old is confined entirely to chromatic stimuli and is proportional to how chromatic they are — which is the reason a room does not look yellow to its older occupants even though every saturated object in it is being reported differently.

It also explains why the effect took so long to be taken seriously in industry. The samples that go wrong are saturated ones under warm light, and the samples that get checked are neutrals under a daylight booth.

Where the model stops #

The linear-in-age density is the crudest of the published models. Van Norren and Vos give a two-component form with a slowly-rising baseline and a faster component that accelerates after about sixty, and the CIE’s 2006 observer uses something similar. Against that, the caricature here understates the oldest end.

The lens is not the only thing that ages. Pupil diameter falls, which changes retinal illuminance and therefore the operating point of every nonlinearity downstream; the macular pigment’s density changes with diet and, in some studies, with age; and the receptors themselves are lost slowly. None of that is in the model.

And the appearance argument above is asserted from the literature rather than computed. Nothing in this collection can measure whether an old eye’s renormalisation is complete, and the corresponding-colour data that might bear on it are the data this collection has recorded the absence of for six rounds.

One last observation is worth recording because it changes what the largest number in this round means. Of the six departures, the lens is the only one whose direction is the same for everybody: an older eye’s short-wavelength response is always lower, never higher. The other five are two-sided — a person’s macular density can be above or below the mean, their peaks longer or shorter.

That makes the lens the only departure that produces a systematic bias in a population rather than a spread. A group of assessors with a mean age of fifty has a mean lens density above the young reference, so their consensus is displaced rather than merely scattered — and a consensus is exactly what a colour-matching panel is for. A panel’s average is not the standard observer’s answer, and the offset between them is computable from the panel’s average age and is not computed anywhere.

The generalisation #

The habit is about the difference between variation across a population and variation along a variable everybody has.

A mean is a good summary of the first and a poor one of the second, and the two are easy to confuse because both present as a distribution of measured values. The test is whether the variation correlates with something known: if it does, the distribution is a trajectory seen edge-on, and the known variable should be a parameter rather than a source of noise.

The payoff for recognising one is large, because a trajectory is predictable. A spread has to be budgeted for; a trajectory can be computed from its argument, and the argument is often free.

The failure mode is to treat a systematic effect as random because the summary statistics look the same. A standard deviation computed across ages is a real number that describes nothing, and using it as an error bar over-covers the middle of the population and under-covers both ends.

Who found it, and when #

The lens’s yellowing has been measurable since the 1950s and its effect on colour matching was documented by Ruddock and others in the 1960s. Van Norren and Vos published the standard density-against-age model in 1974 and revised it later; the CIE’s 2006 fundamental observer takes age as an explicit argument on the strength of that work.

The observation that a standard observer is therefore a snapshot rather than an average appears to be nowhere in the standards, and the reason is probably that a standard is a contract rather than a description. The 1931 observer is not a claim about anybody’s eyes, and the next essay is about what it is instead.

Where the ladder goes next #

The rods are the departure that is not a filter and not a shift. They add a fourth curve to a three-curve system, and nothing in colorimetry has a slot for a fourth anything.