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

Every essay — page 13

Page 13 of 40, continuing through the fields in the same order.

What light is What the eye does Matching and measuring Difference and uniformity What the brain does What a scene does What a camera does Where the model breaks What it takes to deliver it

SeriesObserversNamed objectsRefutationsSearch

What the eye does

Three cone types project an infinite-dimensional spectrum onto three numbers. Everything colour science can and cannot do follows from that one collapse.

The arguments a standard observer does not have. Seven choices inside a set of colour-matching functions, each with the shape it takes and what it is worth in ΔE₀₀ on a red pigment under a 6500 K radiator. Six are measurements: a field size, an age, a macular density, a cone optical density, three peak wavelengths and a rod contribution. The seventh is not — a change of basis is a change of curves and not a change of observer, and its entry is exactly zero because the space an experiment measures is what an observer is. Printing that zero beside the others is the clearest statement of what the other six are measurements of.

Three curves for one space

Rotate a set of colour-matching functions by an arbitrary invertible matrix, undo the rotation at the end, and the computed colour is identical to eight parts in a thousand million million. An observer is a three-dimensional subspace, not a set of curves, and the literature keeps reopening a question that is a theorem.

5 figures What choosing a space to divide the white out in is worth. Three pairs of routes to the same colour, over forty-two surfaces: dividing the white out in tristimulus values, in a published cone space, and in the observer's own cones. The first two agree to 0.59 ΔE₀₀ at the median. Either of them differs from the observer's own cones by more than fifteen. That is why the two exact conditions in this round are exact only in the eye's own coordinates: the identity belongs to the receptors, and every published arithmetic works in a basis somebody else chose.

The identity is in the eye's own coordinates

Two conditions in this round are exact — a gain on each cone is not a different observer, and three curves for one space are one observer. Imposed in a published cone space rather than the eye's own they leave 13.0 and 8.11 ΔE₀₀ standing. The identities belong to the physiology and every arithmetic in use works somewhere else.

5 figures Every departure under every light. Six departures across six lights, each cell the difference between two observers in ΔE₀₀, drawn as a bar whose length is the number. The rows are not multiples of one another: the lens is worst under tungsten and the pigment peaks are worst under a three-emitter LED, because a departure is a pairing and which light is being paired with decides it. The laser projector's row is empty, and that is not a fact about lasers — on this collection's five-nanometre grid a three-line spectrum is a one-line spectrum, and a single wavelength is a stimulus every observer agrees about exactly.

The lens is worst under tungsten

An ageing lens costs 4.38 ΔE₀₀ under a tungsten lamp and 2.20 under a fluorescent tube. The pigment peaks cost 2.84 under a three-emitter LED and 1.87 under the same tube. Six departures across six lights do not form a single ordering, which is what a pairing looks like and what a dominant term would not.

5 figures Each departure over forty-two surfaces rather than one. The same six departures measured over a family of forty-two analytic reflectances — an absorption band of stated centre, width and depth — with the smallest, the median, the ninety-fifth percentile and the largest marked. Every one of them spans more than a factor of three, and the ranking between them is not stable across the family: what decides a departure's size is which sample it is asked about, because a departure is a pairing and the sample is one of the two factors. Quoting any single number for what an observer's age is worth is quoting a choice of example.

The ranking is not stable

On a red pigment under daylight the six observer departures run from 2.38 down to 1.20 ΔE₀₀. Over forty-two surfaces two of them change places, the top two separate, and every one spans between a factor of ten and a factor of thirty-five. A chart of six bars is a chart of one example.

6 figures The three cone absorptances at two settings of the field size. Solid and dashed are the same construction at the two ends of the CIE's own second observer. The curves are built from one pigment template through its ocular media, which is the same model its population of two hundred eyes is drawn from. The largest difference between the two sets is 16.0 per cent of the peak, and where it sits along the wavelength axis is what decides which stimuli the two observers disagree about — a departure concentrated in the blue is invisible on a sample with no blue in it.

A field size is two changes

The CIE publishes two standard observers and the difference between them is usually described as a field size. What actually differs is a macular pigment the light no longer passes through and a cone outer segment the light no longer travels the length of — two changes, in two places, with different signs and different sample dependence.

7 figures The three cone absorptances at two settings of the age of the lens. Solid and dashed are the same construction at the two ends of twenty years old against seventy. The curves are built from one pigment template through its ocular media, which is the same model its population of two hundred eyes is drawn from. The largest difference between the two sets is 25.5 per cent of the peak, and where it sits along the wavelength axis is what decides which stimuli the two observers disagree about — a departure concentrated in the blue is invisible on a sample with no blue in it.

The observer has no age

Five of the six arguments in this round are spreads — a population differs about them and the mean is a reasonable summary. The lens is not. Everybody's lens yellows in the same direction at about the same rate, so a standard observer with no age is not an average over a population; it is a snapshot of one moment in every reader's life.

6 figures The three cone absorptances at two settings of the rods. Solid and dashed are the same construction at the two ends of a tenth of the cone response, which is a dim room. The curves are built from one pigment template through its ocular media, which is the same model its population of two hundred eyes is drawn from. The largest difference between the two sets is 9.1 per cent of the peak, and where it sits along the wavelength axis is what decides which stimuli the two observers disagree about — a departure concentrated in the blue is invisible on a sample with no blue in it.

The rods are a fourth curve

Colorimetry has three numbers and a rod signal is a fourth. It cannot be absorbed by a gain, it cannot be removed by a white point, and adding a tenth of one to a three-curve observer costs 1.60 ΔE₀₀ — the narrowest distribution of the six departures, because an addition behaves quite differently from a filter.

5 figures The three cone absorptances at two settings of the macular pigment. Solid and dashed are the same construction at the two ends of two standard deviations of the reported spread. The curves are built from one pigment template through its ocular media, which is the same model its population of two hundred eyes is drawn from. The largest difference between the two sets is 31.5 per cent of the peak, and where it sits along the wavelength axis is what decides which stimuli the two observers disagree about — a departure concentrated in the blue is invisible on a sample with no blue in it.

The macular is a band, not a filter

The lens absorbs everything below 500 nanometres with a long tail; the macular pigment absorbs forty nanometres either side of 460 and nothing else. The two have similar sizes and completely different distributions, and the reason is that one is broad and one is narrow — which is what decides whether a sample is affected at all.

5 figures The three cone absorptances at two settings of the pigment peaks. Solid and dashed are the same construction at the two ends of two standard deviations, and the L/M polymorphism on top. The curves are built from one pigment template through its ocular media, which is the same model its population of two hundred eyes is drawn from. The largest difference between the two sets is 8.9 per cent of the peak, and where it sits along the wavelength axis is what decides which stimuli the two observers disagree about — a departure concentrated in the blue is invisible on a sample with no blue in it.

The peaks move the flanks

Shifting a cone's peak wavelength by three nanometres changes its sensitivity at its own maximum by almost nothing and on its flanks by several per cent, because a maximum is flat and a flank is steep. Every display primary sits on a flank, which is why a pigment polymorphism is worth 3.60 ΔE₀₀ under a laser projector.

6 figures The conditions under which an observer's departure is exactly zero. A departure of the observer is the pairing of something belonging to the observer with something belonging to the stimulus, so emptying either factor empties the product. The axis is logarithmic in what is left when the condition is imposed. Six rows empty the stimulus's factor — a perfectly neutral sample is the same colour for every observer, at any age and any field size — and two empty the observer's, since a gain on each cone and a change of basis are both absorbed exactly. All eight are identities rather than small numbers. The last two are the same two conditions imposed in a published cone space rather than in the observer's own, and they are worth eight and thirteen units: the identity is about the eye, and the arithmetic everybody uses is in somebody else's coordinates.

Two observers and one metamer

An observer departure is invisible on a single sample compared with nothing. It becomes a disagreement the moment two spectra are being asked to match, because a match is an identity between three integrals and a different observer takes different integrals. Everything in this round is a statement about pairs wearing a single sample's clothes.

5 figures 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.

6 figures 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.

5 figures