The eye stops at the lens

The two standard observers are tabulated from 360 nanometres. Below that there is no table, and the absence has been read for ninety years as a statement about the eye’s sensitivity.

It is a statement about the eye’s transmittance, which is a different organ, and it belongs beside the other things the filters inside the eye do to a stimulus before any receptor is reached.

The claim #

The short-wave edge of human colour vision is a filter in front of the receptors rather than a property of the receptors, and every consequence of that follows from the fact that filters can be different from person to person, can change with time, and can be taken out.

• The photopigments absorb well below 360 nanometres. Rhodopsin and the three cone opsins all have a second absorption peak in the near ultraviolet, and it is not small.
• The cornea is opaque below about 295 nanometres and the crystalline lens takes nearly everything between 300 and 400. At a lens of thirty-two years this collection’s model passes 10 per cent at 360 nanometres and 1.6 per cent at 320.
• It moves by a factor of twenty across a working life. Of the band a brightener absorbs in, a twenty-year-old’s retina receives 18.4 per cent and a seventy-year-old’s 0.9.
• An eye without a lens sees it. Aphakic observers — cataract patients, before ultraviolet-absorbing implants became standard — report a whitish violet from wavelengths nobody else has a name for, and the transmittance model says why: with the lens gone the limit is the cornea’s, at 297.
• So the observer’s table has an edge for an optical reason and the illuminant’s table does not. The daylight basis runs to 300 because the light does; the colour-matching functions stop at 360 because the eye does not let it in. Two different kinds of edge, in the same integral, and this collection had been treating them as one.

What is actually absorbing #

The eye’s optics are three filters in series and only one of them is famous.

The cornea absorbs below about 295 nanometres almost completely — proteins and nucleic acids absorb hard in the ultraviolet-C, which is the same chemistry that makes short-wave ultraviolet dangerous to everything else made of protein. Nothing shorter than that reaches anything in the eye, in anybody, which is one of the few statements about whose eyes an observer is that holds for all of them.

The crystalline lens is the interesting one. It is built of crystallin proteins laid down in layers and never replaced, and it accumulates yellow chromophores throughout life — tryptophan derivatives, principally — which absorb in a broad band rising steeply towards the short wavelengths. That is the yellowing every eye does, and its effect at 450 nanometres is the largest single optical difference between two people. Its effect at 350 is not a difference at all: everybody’s lens is nearly opaque there, and what varies is how nearly.

The macular pigment sits in front of the fovea and absorbs around 460 nanometres, which is why the two standard observers are two observers rather than one. It has nothing to do with the ultraviolet edge, and it is in the model here only because leaving it out would make the visible half of the curve wrong.

Why the tables stop where they do #

The colour-matching experiment is a matching experiment: a bipartite field, a test light on one side, three primaries on the other, and an observer turning knobs. Below 360 nanometres two things go wrong at once and only the second is about the eye.

The test light gets very dim. Not because the source is weak but because the lens is eating it, so the experimenter has to raise the radiance to keep the field visible — and the radiance needed rises faster than the source can supply it. At 340 nanometres a young observer needs about twenty times the radiant power for the same visual effect they needed at 400.

And the match stops meaning anything about a standard observer, because at that radiance the answer is dominated by whose lens is in the way. Two observers with the same cone fundamentals and lenses ten years apart disagree by a factor a matching experiment cannot average away — the spread between people is the measurement.

So the CIE stopped at 360, and the stop is a statement that a standard observer cannot be defined there rather than that there is nothing to define. The distinction matters because a table with no entries and a table of zeros behave identically in an integral and mean opposite things — the same trap as quoting a standard observer as though it were a person. A zero says the response is nothing. An absence says the quantity was never a property of a standard eye in the first place.

The eye without a lens #

The clearest evidence that the limit is optical comes from people who have had the filter removed.

Cataract surgery replaces the crystalline lens. For most of the twentieth century it removed it and put nothing back — the aphakic eye, corrected with thick spectacles — and for a period after intraocular implants arrived the implants were plain polymer with no ultraviolet absorber in them. Both leave an eye whose short-wave limit is the cornea’s.

Aphakic observers see further into the short wavelengths, and they say so consistently: light that is invisible to a phakic eye appears as a desaturated violet or blue-white. The colour is what the model predicts. Below 400 nanometres the S cones dominate by a wide margin but the L and M cones are not zero — their pigments have secondary absorption peaks there — so the signal is S-heavy and not S-only, and an S-heavy but not S-exclusive stimulus is a whitish violet rather than a saturated one.

This collection’s model puts the aphakic transmittance at 100 per cent of the excitation band a brightener works in, against 8.5 per cent for a thirty-two-year-old eye. That is a twelve-fold difference in what arrives, produced entirely by removing one piece of tissue, with the receptors untouched.

Why an eye would give that up #

The obvious question is why evolution put a filter in front of a working receptor, and it has an unusually clean answer with two halves.

Ultraviolet is destructive to the retina and the retina is not replaced. Photoreceptor outer segments are renewed, but the retinal pigment epithelium behind them accumulates damage for a lifetime, and short-wave light drives that accumulation faster than anything else in the visible range. A lens that yellows is a lens that is progressively better at protecting the tissue behind it, which is at least a coherent story about why the yellowing is not repaired.

And ultraviolet cannot be focused with the rest. The eye’s refractive index rises steeply towards short wavelengths — this is longitudinal chromatic aberration, and it is about two dioptres across the visible band alone. Extending the range to 320 nanometres would add roughly another two dioptres of defocus at the short end. Light that far out of focus does not carry an image; it carries a veiling haze over the whole field, reducing contrast everywhere.

So an eye that transmitted the ultraviolet would be trading a damaged retina and a lower-contrast image for a stimulus it cannot localise. Some animals make the other trade — many insects, and birds with a fourth cone class — and they have optics and retinas built for it.

What it means for a sheet of paper #

The whole arrangement makes a brightener possible, and this is the sentence worth carrying out of the essay.

A brightener works in a band its user cannot see, and cannot see because of a filter rather than because of a receptor. The excitation band sits at 320 to 400 nanometres, where an ordinary eye passes a few per cent; the emission band sits at 400 to 500, where the same eye passes most of what arrives. So the chemistry takes light out of a window the observer has closed and puts it back through one that is open.

Nothing about that is deliberate on the chemist’s part, but the constraint is real and narrow. Move the excitation band twenty nanometres longer and the sheet starts absorbing violet light the observer can see, and reads dirty. Move it shorter and there is less daylight to work with, and none at all behind a window.

The age effect has a consequence people notice without diagnosing. A seventy-year-old’s retina receives about a twentieth of the excitation band a twenty-year-old’s does. What that changes is not the sheet’s glow, which is a property of the sheet and the light: it changes how much of the illuminating ultraviolet the observer’s own retina receives directly, which is a small correction. The glow itself is at 435 nanometres, and there both observers’ lenses are largely transparent — the older one about eighteen per cent less so.

So the two effects go in opposite directions and neither is large. Age changes what a person makes of a brightened sheet far less than the lamp does, which is worth stating because it is the opposite of what the lens-yellowing literature would lead one to expect and it falls straight out of where the two bands sit.

What was computed, and how #

The ocular media model is this collection’s own, extended below 380 nanometres. The lens density is a level rising by 0.02 per year past twenty, applied to an exponential in wavelength with a 68-nanometre scale; the macular pigment is a Gaussian at 460; the cornea is a logistic edge at 297 with a 3.5-nanometre width.

The visible half is not recomputed. It is the same expression the rest of this collection uses, and the extension is checked against it band by band on all eighty-one shared wavelengths — worst difference 9 × 10⁻¹², which is floating-point noise. Two copies of a formula is the arrangement this collection keeps writing gates against, and the only defence against it is to check rather than to intend.

The short-wave continuation is an extrapolation and is declared as one. The exponential was fitted where the measurements are; running it to 300 nanometres produces the right shape and a transmittance at 320 that is a property of the fit rather than of any measured eye. What survives that caveat is every comparison — between ages, between an eye and an aphakic one, between the excitation band and the emission band — because all of them use the same continuation on both sides.

Two assertions. That almost nothing at 360 nanometres reaches a retina behind a lens, and that an eye without one is transparent there. The pair is the claim: not that the number is small, but that removing one component makes it large, which is what makes the limit optical rather than neural.

The model reproduces its own two transmittances #

The lens model is stated in words — a density of 0.5 rising by 0.02 a year past twenty, on an exponential in wavelength with a 68-nanometre scale, referred to 380 — and the two transmittances quoted for it fall straight out.

At thirty-two years the density level is 0.5 + 0.24 = 0.74. At 360 nanometres the exponential factor is exp(20/68) = 1.343, giving a density of 0.994 and a transmittance of 10.15 per cent. At 320 the factor is exp(60/68) = 2.421, giving 1.792 and 1.62 per cent. The essay’s 10 and 1.6 are those numbers rounded, and the ratio of the two densities, 1.796, is exp(40/68) = 1.801 to three parts in a thousand.

So the 68-nanometre scale is recoverable from the two figures alone, which is the check worth having on a model quoted in prose: a reader can confirm the shape without the source.

The factor of twenty is a band average of a much wider range #

The age effect is quoted as a single factor and the model makes it a function of wavelength.

Between twenty and seventy the density level rises by exactly 1.0, so the transmittance ratio at wavelength λ is 10 raised to exp((380 − λ)/68). That is 10 at 380 nanometres, 22 at 360 and 63 at 340 — a sixfold spread across the excitation band itself.

The quoted 18.4 per cent against 0.9, a factor of 20.4, is therefore a weighted average over the band, and the weighting is doing something the single number hides: the long end of the excitation band dominates the survivor’s share, because it is where an old eye still passes anything. An older observer’s remaining ultraviolet is not a scaled-down version of a young one’s — it is the long-wave sliver of it, shifted towards 400 nanometres, and the shift is larger than the level change at any one wavelength.

That matters for the section’s own conclusion. The claim that age changes what a person makes of a brightened sheet far less than the lamp does is right about the magnitude, and there is a second reason it is right about the kind: the surviving band is the part nearest the visible, which is the part a window’s glazing also passes. So the ageing eye and the glazing select the same sliver, and their effects are not independent.

Two numbers checked against physics outside the model #

Two of the essay’s supporting figures come from outside its own machinery and both hold.

The chromatic defocus. On the standard reduced-eye formula for the eye’s chromatic difference of refraction, the span from 400 to 700 nanometres is 2.10 dioptres — about two dioptres across the visible band alone — and extending to 320 adds a further 2.57. Roughly another two is right and slightly conservative, and the steepening is the point: the second two dioptres are bought over eighty nanometres where the first two took three hundred.

The daylight at the short end. D65 at 350 nanometres is 44.9 per cent of its value at 560, on the wide grid this collection now computes daylight over. The caption’s 45 per cent is exact, and it is the number that makes the whole argument non-trivial — an eye that opened its filter would find a great deal of light waiting.

One figure does not check quite as cleanly. The luminous efficiency function at the emission wavelength is given as 0.018, and the tabulated value at 435 nanometres is 0.01684; the reciprocal is 59 rather than the fiftieth the caption implies, and 0.018 is nearer the value at 437. Nothing turns on it — the argument needs the weighting to be small and it is a sixtieth — but the sharper figure is the one the neighbouring essay uses, and the two should agree.

Where the model stops #

The photopigments’ secondary peaks are asserted and not modelled. The claim that the cone opsins absorb in the near ultraviolet is well established — the beta band of a rhodopsin-family pigment is a standard feature of the template — but this collection’s pigment template covers the alpha band only, so nothing here computes what an aphakic observer’s colour-matching functions actually are.

The aphakic case is an idealisation. A real aphakic eye has no accommodation, considerable spherical aberration from the correcting lens, and in the intraocular-implant case a polymer with its own short-wave edge. The model removes the crystalline lens and changes nothing else.

And there is no photochemical damage term. The protective argument above is a reason, not a computation; nothing here puts a number to what an ultraviolet-transparent eye would cost its owner over fifty years.

Who found it, and when #

That the ocular media rather than the receptors set the short-wave limit was established through the 1950s and 1960s; Wald’s work on the aphakic eye is the standard reference and the observation that aphakes see ultraviolet is older than that. Monet’s cataract surgery in 1923 is the case usually cited outside the literature, and the blue period that followed it is at least consistent with a lens removed.

The lens’s own absorption spectrum has been measured many times, on donor eyes, and its age dependence is one of the better-characterised facts about the eye. The CIE’s decision to tabulate from 360 predates most of that work; the 1931 functions were extrapolated at both ends from data that did not reach them.

What is new here is only the arithmetic in the direction these essays needed: how much of a brightener’s excitation band a retina receives, at three ages and with the lens removed, computed on the same grid the illuminants are now computed on.

The generalisation #

The pattern is a limit attributed to the wrong component because only the composite was measurable.

An observer is a filter and a receptor in series and the experiment measures the product. Every property of the product gets attributed to whichever component the experimenter’s discipline is about — which for colorimetry has always been the receptor, because that is where the three-ness comes from and three-ness is the subject.

The way out is the same in every such case and it is not cleverness. It is finding a preparation where the components come apart: an eye without a lens, a lens without an eye, an animal with different optics. What separates the components is never a better measurement of the composite.

Where the ladder goes next #

If the eye’s edge is optical and the illuminant’s is not, the next question is what the weighting does inside the range where both exist. A brightener emits at 435 nanometres, where the luminous efficiency function is 0.018 — so the eye weights the glow at a fiftieth of what it weights the middle of the band, and a sheet returning a quarter more light than arrives gains under one per cent of luminance.

The other direction is the sheet rather than the eye. If the excitation depends on the glazing more than on the observer, then where the sheet is is part of what colour it is, and no viewing condition this collection has modelled has had to carry a window.