Colour Science & Perception
what the eye settles, and what it cannot
Concept

Rods — where it appears

The retina's low-light receptors: one class with one pigment peaking near 507 nanometres, so on their own they signal light but not colour. In a dim room their signal reaches the cone pathways as a fourth curve summed into a three-number match.

Named by 9 essays across one field — each of them below, with the objects they name alongside it.

The same two surfaces, weighed by each system. A long-wavelength and a short-wavelength surface under D65, with their relative luminance under the photopic curve and under the scotopic one. Under daylight vision the red surface is 1.33 times the blue; under rod vision it is 0.15 times, a reversal by a factor of 9.0. The swatches are the photopic appearance, which is the only one a display can produce: rod vision has no colour, and drawing a guess at it would be an invention.

The eye that has no colour

Rods outnumber cones twenty to one, work alone below a hundredth of a candela, and are absent from the centre of gaze. Between dusk and a lit room both systems run at once, and neither standard curve describes what is happening.

eye · Cones What the rods cost a match, by where their signal enters and under which lamp. For five lights, the median colour difference over forty-two surfaces between the reference observer and the same observer with a rod signal a tenth of each cone's peak added — into all three cone channels, into the long- and middle-wavelength channels only, or into the short-wavelength channel only. Under daylight the first two are 1.03 and 0.90: whether the rods reach the S pathway hardly matters. Under a phosphor white LED they are 1.24 and 0.45, a factor of 2.75, and the S-only route alone costs 0.96.

The rods' route is priced by the lamp

A rod signal in a dim room disturbs a colour match, and how much depends on which of the cone pathways it reaches — a weight the physiology leaves uncertain, especially for the blue–yellow pathway. Under daylight the uncertainty is nearly free: a rod signal that skips the S pathway costs 0.90 at the median surface against 1.03 for one that enters all three. Under a phosphor white LED it is worth a factor of 2.75, 0.45 against 1.24. What decides it is one number per lamp: how large the rod signal is compared with each cone class's own catch of the light.

eye · Cones Which two lamps to stand a mesopic match between. Every pair of the five lights, by how far a match made under one and set under the other moves as the rod signal's weight into the S channel goes from nothing to equal — the median over forty-two surfaces, which is the signal an experiment has to resolve. The best pair is daylight against phosphor LED at 0.58 ΔE₀₀; the worst is tungsten against fluorescent tube at 0.09, a factor of 6. The count at the right is how many settings it takes to resolve the weight to a tenth at half a colour difference of scatter per setting.

The reference lamp must not move

To measure an uncertain weight, use the condition in which the answer depends on it most. That is right about half of an asymmetric colour match and exactly wrong about the other half: a match measures a difference of two displacements, and a reference field that also moves with the weight cancels the signal the test field carries. Daylight is the least sensitive of five lamps and belongs in every one of the three best pairs — 75 settings against a phosphor LED, 2,804 against the pair of lamps the principle as stated would have chosen.

eye · Cones Two ways to ask how much rod signal an older eye has. The rod signal's catch of each lamp divided by the S cones' own catch, against the observer's age, for five lamps — drawn twice. The upper curves take the rod signal at a fixed absolute size, and every one of them roughly doubles from twenty to seventy-five: an older lens cuts the blue before the S cones see it and the rods, peaking further into the green, lose much less. The lower curves take the rod signal at a tenth of each cone's own peak absorptance, which is the model's own definition, and they barely move at all. Nothing about the retina differs between the two; only the normalisation does.

A rod signal has no natural size

An older lens absorbs where the S cones are sensitive, so it should make the uncertain rod-to-S-cone weight cheaper. Measured, the rod signal's catch of a phosphor LED as a share of the S cones' own catch more than doubles from twenty to seventy-five — and the share the model actually uses falls by a fifth. The two differ by the S cone's peak absorptance, which the lens takes 60 per cent of, and which entered the model as a normalisation rather than as a claim.

eye · Cones How far a mesopic match moves as the S weight opens: two rooms against one field. For every pair of the five lamps, the median over forty-two surfaces of how far a match moves as the rod signal's weight into the S channel goes from nothing to equal: pale for the two-room match, each half adapted to its own lamp; dark for a bipartite field whose two halves share one adaptation. The field's signal is larger for every pair, by ×1.5 to ×7.7.

One field keeps what two rooms divide out

An asymmetric match can measure how strongly the rods feed the blue-yellow pathway, but set with the observer adapted to each lamp in turn it needs seventy-five settings on the best pair of lamps and hours of waiting between them. Putting the two lamps on the two halves of one field was proposed as the quick version, at the cost of a weaker signal. The signal is not weaker. Under one shared adaptation it is three times stronger for daylight against a white LED, and the best pair needs six settings. The adaptation that makes the slow version slow is also what was dividing the rods' contribution out of each half.

eye · Cones What a weight fitted under the wrong reading does across ages. If the retina's rod signal has a fixed absolute size and the weight is fitted with the model's scaled reading, the fitted weight is the true one times the ratio of the two readings' signals: ×0.80 at twenty, ×1 at thirty-two, ×1.62 at seventy-five. The other way about, the reciprocal. A cohort of observers sharing one weight would show it as a trend with age.

Age can size the rod signal, if the lens is known

A rod signal leaking into the colour pathways has no natural size in the model: read as a fraction of each cone's own peak it shrinks as the lens yellows, read as a fixed amount it grows relative to the cones, and the two readings differ by a factor of two over a lifetime. An asymmetric match on observers of different ages can tell them apart, because they predict opposite trends: one says a weight fitted at seventy-five will look sixty per cent larger than at thirty-two, the other says it will not move. A handful of observers per age would show it. But a lens mistaken by ten years looks like forty per cent of the weight, and a tenth of an optical density of macular pigment as much again, so the experiment is only as good as what it knows of each eye's lens and macula.

eye · Cones What each pair of lamps pays to fit the lens and the macula as well. For each pair of lamps, the standard error of the rod signal's S weight fitted from one session — with the observer's lens and macula known (top bar), with the lens fitted too (middle) and with both fitted (bottom). Daylight against the LED is the best pair with everything known, ±0.026, and pays most of its advantage for the macula; tungsten against the LED pays almost nothing for either.

The matches carry their own lens

A lens mistaken by ten years moves a colour match as far as half the rod signal being measured, and a tenth of an optical density of macular pigment as far again, so an experiment on the rod signal looked as if it needed a densitometer for every observer. It does not. Across a family of surfaces the three move the matches in different patterns, and one session of forty-two settings fits all three together — the lens to within a year and a quarter, better than a densitometer was asked for. The price is the weight's precision, and a second pair of lamps nearly removes it.

eye · Cones Where a lens edge 10 nanometres off goes in a one-session fit. A sixty-year-old observer whose lens edge sits 10 nanometres longer (upper bars) or shorter (lower bars) than the model's, fitted by the model from one daylight-against-LED session: the shift in each fitted parameter, in that parameter's standard errors. The macula takes the most, 2.4 of its standard errors; the weight moves by 0.59 of its own, 0.035 in absolute terms, against a prediction of under a tenth for an edge ten nanometres off.

A lens of the wrong shape lands in the macula

One session of colour matches can fit an observer's rod signal, lens and macular pigment together — but it fits a lens of the model's shape, one exponential in wavelength scaled by age, and a real lens need not be that shape. Give a sixty-year-old a lens with the right density at 400 nm and its edge ten nanometres off, and the fit puts the error mostly in the macula, moves the rod signal's weight by six tenths of its standard error — six times the predicted tenth — and leaves a misfit the session cannot see. A second lamp pair makes it worse: 3.5 standard errors. Fitting the edge as a fourth number removes the bias, costs the weight three to fourteen per cent, and finds the edge.

eye · Cones Where one session puts a band in the lens, by the band's wavelength. A band of a tenth of an optical density in a sixty-year-old's lens, centred from 410 to 460 nm, fitted from one daylight-against-LED session by the model with weight, lens age, macula and the lens edge free: each parameter's shift in its own standard errors. Near 410 to 430 nm the band is read as lens; from 440 it is read as macula; the edge takes little of it anywhere; and the rod weight moves at every centre, by 0.37 to 1.39 of its standard errors.

A band in the lens reads as age or as macula

A lens whose absorption edge is steeper or shallower than the model's biases a matching session's fit, and fitting the edge's position repairs it. An ageing lens also grows bands: yellow pigments that add a shoulder of absorption just past 400 nanometres. The edge parameter takes none of one. A tenth of an optical density centred at 410 to 430 nm is read as four to six years of extra lens age; centred at 440 to 460, as three to ten hundredths of macular pigment. Either way the rod signal's fitted weight moves, by up to 1.4 of its standard errors in one session and 1.8 in two, and the session's misfit stays within its noise. The lens model has to carry the band, or the experiment has to state what it does not know.

eye · Cones

Named alongside it

The objects these essays reach for when they reach for this one.

Measurement uncertaintyCone fundamentalsIndividual variationLens yellowingMesopicObserver variabilityCorresponding coloursIdentifiabilityModelling assumptionStandard errorWhite LEDDegrees of freedom

All concepts