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

Temporal sensitivity — where it appears

How much a modulation has to change before it is seen, as a function of how fast it changes and which colour direction carries it. The luminance and chromatic channels give out about four times apart in frequency, which is why a flicker can be invisible and its colour still be moving.

Named by 10 essays across 5 fields — each of them below, with the objects they name alongside it.

Temporal sensitivity, and where each channel gives out. Modulation frequency in hertz against relative sensitivity. The luminance channel is band-pass, peaking at 8 hertz and running out at 60; an isoluminant modulation is low-pass and runs out at 15, which is 4.0 times sooner. Both cutoffs are at the same criterion of 5 per cent of that channel's own peak, so the ratio between them is a ratio between two measurements rather than between two conventions.

The eye has a shutter

An isoluminant flicker fuses at fifteen hertz and a luminance one at sixty, so a light whose colour changes forty times a second is a steady light of a colour it never emits. And the frequency at which flicker stops being visible is not a property of the eye — it moves twelve and a half hertz for every decade of light.

eye · Cones A 100 hertz drive, and whether anybody sees it. 3 cycles of a 100 hertz drive at 100 per cent modulation. The number beside each is how far above the threshold for seen flicker its loudest harmonic sits: above one and a stationary observer sees the flutter, below it and only something moving does. Fusion is at 60 Hz at 100 cd/m², and moves 12.5 Hz for every decade of light.

A lamp has a waveform

A lamp modulating a thousand times a second is a hundred times past the frequency at which flicker fuses, and it is plainly visible — as a dotted trail, during any glance across the room. The reason is not a new measurement; it is the spatial contrast sensitivity function, arriving from an unfamiliar direction.

light · Light The eye's own drift, and what it does to every spatial frequency. A pattern of f cycles per degree, drifting across the retina at 0.5 degrees a second, arrives at each receptor at f × 0.5 hertz. The curve is the temporal sensitivity at that rate, against the pattern's spatial frequency. Every frequency the eye can resolve stays above a quarter of the temporal peak, and the band of drift speeds for which that holds is 0.02–0.71 degrees a second — with the measured drift inside it. Faster and the finest detail is carried past 60 hertz, where there is no sensitivity at all.

The eye is never still

A perfectly stabilised retinal image disappears within seconds. What keeps the world there is a drift of about half a degree a second between the microsaccades — fast enough to keep the finest detail modulating and slow enough not to carry it past fusion, in a band whose upper edge is at 0.71 degrees a second.

brain · Appearance The drift window, asked about each channel in turn. Every spatial frequency a channel can resolve, drifting at v degrees a second, arrives at f × v hertz; the bar is the range of v over which all of them stay above a quarter of that channel's temporal peak. The luminance band is closed at both ends — 0.018 to 0.71 degrees a second — because its temporal sensitivity has a dip at zero to fall into. The chromatic bands have no slow edge at all, because chromatic temporal sensitivity is low-pass: a stationary chromatic pattern sits at the top of its own sensitivity. The mark is the measured drift, and it is inside all three.

The drift is a luminance mechanism

The eye's own drift was shown to sit inside a band of speeds that keeps every spatial frequency modulating, and the band was quoted as though it were about vision. Asked about colour, it has no slow edge at all — a stationary chromatic pattern needs no eye movement whatever. And a stabilised chromatic pattern is the first thing to fade.

eye · Cones Dimmed to a fiftieth, three ways. Switching a lamp on and off faster than anyone can see scales the spectrum and changes nothing else, so its colour temperature is a horizontal line and its chromaticity moves by 7.3e-14 ΔE00 — exactly, to floating point. Reducing the drive current moves the die's peak and cools the junction, which moves the mixture: ΔE00 3.5 across the range. A filament has no spectrum of its own to move; it is a blackbody at whatever temperature the power leaves it at, and it falls 1672 K. Three methods, one instruction, three colours.

Three ways to dim a lamp

"Dimmed to ten per cent" names three different colours. Switching the lamp on and off faster than anybody can see changes the chromaticity by nothing at all — exactly, to floating point. Reducing the current moves it a few units. Reducing the power to a filament moves it eighteen hundred kelvin down the Planckian locus, and stays on the locus exactly the whole way.

light · Light Where a pooled gain gives out, against where the eye does. The falling curve is how much of a pattern of each spatial frequency a local adaptation pool of 0.5° can see — and therefore how much of it a settled eye can cancel. It is half gone by 0.37 cycles per degree, which is a feature about 2.7° across. The three marks are the acuity limits of the luminance channel and the two chromatic ones. Every one of them is more than an order of magnitude finer than the pool, which is why a stabilised eye loses the fill of a picture and keeps its outline rather than losing the picture.

What a still eye stops seeing

A stabilised image is said to vanish, and nothing in a temporal filter predicts it — sensitivity at zero frequency is a quarter of the peak, not nothing. Give the adaptation gain a size and the answer falls out — fading is a high-pass filter that switches on over a minute, it takes the fill and leaves the outline, and a patch has to be about two degrees across before it goes at all.

eye · Cones The same flicker, written across the frame. A rolling shutter exposes each row of the sensor at a different moment, so a lamp that flickers above fusion is recorded as bands. There are 1.7 of them here — the readout time times the lamp's frequency, which is a camera setting and not a property of the light — spanning 2.37 stops. Held at matched luminance the lightest band and the darkest are still ΔE00 5.40 apart in colour, because the two drive currents are two spectra and the shutter caught one of each.

The shutter samples the lamp

A lamp switched between two drive currents at a hundred hertz is one steady colour to a person and two spectra to a camera. A thousandth-of-a-second exposure catches whichever phase the shutter opened at — two and a third stops of exposure and five units of colour, decided by nothing but timing — and a rolling shutter writes the difference across the frame as bands.

imaging · Capture A stabilised grating fades at a rate that depends on which way its bars run. What is left of a 0.3 cycle-per-degree grating, in multiples of its own threshold, as a function of its orientation, at four moments after the image was stabilised on the retina. The first curve is flat to floating point: at the instant the pattern arrives, orientation does not matter, because the filter that carries it has no orientation preference at this frequency. The anisotropy arrives with the fading, reaching ×2.09 after five minutes, and a pool with no axis predicts none of it.

A fading pool has a shape

Giving the local adaptation pool two axes instead of one costs a single parameter and produces a prediction the circular version cannot make — a stabilised grating fades at a rate that depends on which way its bars run. The obvious objection is the oblique effect, and the two act in bands that do not overlap.

eye · Cones What is left of one colour difference when the two colours alternate. 23 pairs built at exactly ΔE₀₀ 1.000, alternated at a rate, with each part of the difference scaled by its own temporal channel and the formula then applied unchanged. At rest every pair is the flat line at one. By 7 hertz the median is 1.11 and the pairs run from 0.57 to 3.04 — a factor of 5.3 between pairs the formula calls identical. By sixty hertz the largest of them is 0.15.

A difference has no rate

A colour difference formula answers for two patches that are both there and stay. Alternate the same two colours and the difference is not scaled but taken apart: the colour half is gone by fifteen hertz and the lightness half is four times louder at eight, so twenty-three pairs the formula calls identical run over a factor of six at the rate the eye is best at, and are worth nothing at all above sixty.

difference · Metric The confusion matrix, and which corner the common lamps are in. Twelve fixtures sorted two ways. Down the page is what their spectra are; across is what flicker says. The two corners on the diagonal are 7 fixtures the classifier gets right. The 3 missed are structured lamps that do not flicker — a white LED and a warm LED on constant drivers, and a three-emitter fixture — and those are the lamps most modern interiors are lit by. The 2 false alarms are smooth lamps that do flicker: a halogen lamp on mains and a tinted radiator, both of which a photograph of a room is quite likely to contain.

Flicker sorts lamps the wrong way

A camera cannot see a spectral line in its own white, so the essay on the two-matrix profile named the classifiers a device might have instead, and the first of them was flicker. Flicker is measurable, and it measures the wrong thing. It sorts lamps by how their power is delivered while the matrix needs them sorted by how their spectrum is shaped, and the two are independent: a white LED on a constant driver is perfectly steady and strongly structured, and it is what most indoor photographs are lit by.

imaging · Capture

Named alongside it

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

Contrast sensitivityFlickerSpatial frequencyAdaptationOpponent processingThresholdCritical fusion frequencyEccentricityLuminanceSpectral power distributionAfterimageAssertion

All concepts