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

Every essay — page 20

Page 20 of 54, 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

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What light is

A spectrum is a function, not a colour. Illuminants, reflectance, blackbody radiation computed from Planck's law, and what has already been discarded before the eye is reached.

The colour of a beam, against the angle it leaves at. A conformal converter — an even layer laid straight onto the die — makes light leaving at θ cross 1/cos θ times as much of it, so it is more completely converted and the beam is warmer at its edge. From the axis to 75° the correlated colour temperature falls by 556 K and the whole difference is ΔE00 16.4. The flat line is the same emitters under a dome, whose path length is the same in every direction by construction: no angular colour at all, exactly, which is what a remote converter is sold for.

A lamp has a direction

A white LED is a blue die under a converter, and light leaving at an angle has travelled further through the converter than light leaving straight up. So the mixture is different in every direction, the beam is bluer in the middle than at its edge, and the number on the box is one direction's worth of a device that has no single colour.

7 figures 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.

7 figures A lamp switched on, and what it is still doing minutes later. The junction warms from ambient to 80 °C with a time constant of 150 seconds, and three quoted slopes act as it does: the die's peak moves, the die loses efficiency, and the converter loses quantum yield. The output falls 25 per cent and the colour moves ΔE00 2.6. Nine tenths of the way takes 405 seconds. The vertical mark is the eye's own slow adaptation constant, 60 seconds, for scale.

A lamp switched on is not the lamp measured

A luminaire takes about seven minutes to reach nine tenths of its working temperature, loses a quarter of its output on the way, and moves ΔE00 2.6 while it does. That is slower than every clock in the eye — so for the first minutes after a switch is thrown, both ends of the measurement are moving, and every appearance claim here has assumed one of them was still.

7 figures A surface in a room, from the moment the light goes on. How far a blue surface is from the colour it will settle at, second by second, for an observer who walked in from the snow as the lamp was switched on. It starts ΔE00 27 away, is still 6.1 away after a minute — the point at which the eye is conventionally said to have adapted — and does not fall under a unit until 295 seconds.

The room settles after the eye does

Four clocks run in a room and only three of them are in the observer. The slowest is the lamp, which takes four hundred seconds to reach nine tenths of its colour change — so a minute after the light goes on, when the eye is conventionally said to have settled, most of what is left is the lamp, and three quarters of that could not be adapted away by an observer of any speed.

8 figures A colour rendering index, computed for everybody instead of for one observer. Each bar spans what 120 eyes make of one lamp: the same reflectances, the same reference illuminant, the same arithmetic, different colour-matching functions. The mark is the standard observer's own answer, which is the number printed on the box. One lamp's spread is 3.8 points wide while the whole range the standard observer puts these lamps in is 1.8 — so a ranking quoted to a tenth of a point is a statement about one set of tables. Two of the marks fall outside the population's range entirely.

The index is one observer's opinion

A colour rendering index is printed to a tenth of a point and computed for a single set of colour-matching functions that no standard names as a choice. Scored by two hundred eyes instead, one lamp's spread is wider than the whole range the standard observer puts five lamps in — and two lamps the standard separates by four tenths of a point come out the other way round for every member of the population.

5 figures The same census, sorted by where the change of light came from. Each row is a change of illumination. The pale bar is how far it moves an ordinary surface for an observer who does not adapt; the solid bar at its left end is what is left after the observer has applied the one gain adaptation gives them, which is the ratio of the two whites in the CAT16 basis and is not fitted to anything. Sorted by where the change came from. The two kinds of light that existed before electricity sit at the top and leave the smallest share of themselves behind; the discharge lamps are worse, and the worst of them is d65 to a triphosphor tube at 33 per cent.

Which lamp changes are free

The changes of light that existed before electricity commute with one another to a couple of parts in a thousand, so one set of axes handles all of them. The lights the lighting industry invented do not, and the worst pair in the census is seventy-six times further from commuting than the best.

7 figures Three ways to dim a lamp, and only one of them is free. What an adapted observer is left with, as the same lamp is taken down to one per cent by each of the three methods. Duty-cycle dimming lies exactly on zero at every depth: it scales the spectrum, a scaling is a gain in every basis, and adaptation removes all of it. Current dimming moves the pump and the phosphor apart and leaves 0.15 at a tenth. A filament follows the Planckian locus, which is the largest chromaticity change of the three and leaves 3.63 — the ordering by chromaticity and the ordering by what a person sees are not the same ordering.

Only one dimmer is invisible

An earlier essay separated the three ways to dim a lamp by the chromaticity each arrives at. Asked instead what an adapted observer is left with, the ordering is different and one method comes out at exactly zero — a duty cycle is a scaling, a scaling is a gain in every basis, and adaptation removes all of it at every depth.

7 figures Six functions of wavelength, and the six different places they stop. Every table this collection integrates against, drawn over the range the body that published it defined it on. The scale is logarithmic so that the ultraviolet and the near infrared both fit. The bottom row is the range used here before the infrared band was added, and it is the intersection of the two rows that matter for an eye looking at a reflector — which is the right answer only while everything in the integral is being multiplied together. The daylight basis runs 80 nanometres further down than that intersection, and it was published that way because the ultraviolet in daylight is what makes a brightened sheet of paper glow. The analytic row is drawn to the edge of the plot because it has no edge: Planck's law is a formula and is exact at every wavelength, which is why illuminant A needs no table at all.

The tables do not stop together

This collection integrates from 380 to 780 nanometres, and decided once, in writing, that the range could not honestly be widened. The argument was correct at the long end and wrong at the short one — the CIE publishes the daylight basis from 300 nanometres, and publishes it from there for exactly the reason it matters.

6 figures A fluorescent sample is a matrix, and a reflectance is only its diagonal. The Donaldson matrix of a brightened sheet: how much light leaves at each wavelength for light arriving at each wavelength. A reflecting surface has entries on the diagonal and nowhere else, which is exactly the statement that light leaving at 440 nanometres arrived at 440. The block off the diagonal is the fluorophore — it takes light between about 305 and 420 nanometres and returns it between 400 and 500, wherever in that band it was absorbed, which is why the block is a rectangle rather than a smear along the diagonal. A spectrophotometer that reports a reflectance is reporting the diagonal and folding the block into it at whatever weight its own lamp happened to give.

A reflectance is a diagonal

A reflecting surface returns light at the wavelength it arrived at, so its whole description is one number per wavelength. A fluorescent one returns it somewhere else, so its description is a square matrix — and the curve every instrument reports is that matrix's diagonal with the rest of it folded in at whatever weight the lamp happened to give.

8 figures An instrument, as the only thing it really is. The 3 filters a bank of that size puts across the visible range, each drawn against wavelength. Everything the instrument can report about a spectrum is 3 numbers — the integral of the light against each of these — so the set of spectra it cannot tell apart is everything orthogonal to all 3 of them, which is 78 dimensions of the 81 this site works in. Three of these is a colorimeter in spirit; the eye is three of them too.

Three numbers cannot see a line

An instrument that returns three filtered readings of a spectrum determines a three-dimensional projection of it and is exactly blind to the other seventy-eight. On daylight that costs almost nothing; on a fluorescent tube, three quarters of the lamp lies in the part no reading reaches, and adding filters recovers it slowly.

8 figures The colour is right long before the spectrum is. The colour error of the projection, against the number of readings. At twelve readings the fluorescent tube's colour is right to 0.48 ΔE00 while 66% of its spectrum is still unmeasured. That is the trap in one line: a reconstruction good enough to pass any colorimetric check will predict a match under a second illuminant that does not happen, because the part it got wrong is exactly the part a different lamp weights differently.

The colour is right first

A reconstruction of a lamp from twelve filtered readings gets its colour right to half a unit while two thirds of its spectrum is still unmeasured. That combination is not a partial success — it is the exact condition under which a spectral prediction made from the reconstruction will be confidently wrong.

8 figures Every change of light in the census, under three bases. Fourteen changes of illumination, each drawn three times: the residual left by a gain in the basis built from the dichromat confusion points, in CAT16, and in the basis that minimises the average. The ordering between the three is the same on nearly every row, and — the part an average hides — the worst row is the same row for every basis nobody fitted, which is two bounces off the same wall. The difficulty belongs to the change rather than to the choice of axes — except for the fitted winner, whose worst row is D65 to a triphosphor tube instead. What a fit buys is not a uniform improvement; it is the abandonment of the one change everybody else is beaten by.

Which changes of light pay for it

A fitted adaptation basis beats the receptors by 0.68 units on average, and an average is a poor description of what it does. On six of fourteen changes of light it is worse, and the whole of its advantage comes from four — a tungsten lamp and three coloured walls.

9 figures