Colour Science & Perception
what the eye settles, and what it cannot
What light is

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.

Assumes Three ways to dim a lamp and What no adaptation can remove.

14 min read 7 figures Computed, not quotedThe instrument is the reader

An earlier essay established that “dimmed to a tenth” names three different colours. Switch a lamp on and off faster than the eye can follow and the spectrum is unchanged; drive it at less current and the die’s peak moves while the phosphor stays where it is; take power away from a filament and it cools, and follows the Planckian locus down.

That measurement is about the lamp. The lamp arrives at three different chromaticities, and a specification quoting one of them without saying which method produced it has said very little.

There is a second question underneath it, which is what a person standing in the room is left with, and it has a different answer.

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.
Fig. 1 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 on exactly zero at every depth. The other two do not, and the one that moves furthest in chromaticity is not the one that leaves the most.

The claim

One of the three dimming methods is free to an adapted observer, exactly and at any depth, and the ordering by what is left is not the ordering by how far the chromaticity moved.

  • Duty-cycle dimming leaves ΔE00 0 at every level tested, to 10⁻¹⁶, out of a change of 36.7 at a tenth. It scales the spectrum and nothing else, and a scaling is a gain in every basis there is.
  • Current dimming leaves 0.153 at a tenth and 0.345 at one per cent — small, and not zero, because the pump and the phosphor slide apart.
  • A filament leaves 3.63 at a tenth and 9.96 at one per cent, which is by far the largest of the three.
  • And it leaves the most while being the method whose chromaticity stays exactly on the Planckian locus — the one place a colour engineer would call well behaved.
  • The whole of the difference is spectral shape. A change of level is the census’s control row and comes out at zero by construction; everything reported here is what each method does besides changing the level.

Three methods, one arithmetic

Each method is compared with its own lamp at full output, not with a common one. That matters and the first draft got it wrong: measuring a dimmed filament against a full-output LED reports the difference between two lamps under a caption about dimming, and it put a five-unit residual on the method whose whole virtue is that it stays on the locus.

Corrected, the comparison is: take the lamp at full output as the reference context, take the same lamp dimmed as the changed context, and ask the question the census asks of every change of light — how far does it move a surface, and how much of that can a gain remove.

The same lamp, sampled across its beam. Five directions out of one device, each normalised to its own peak so the shape is what is being compared. The blue line falls and the converted band rises as the angle grows, because the converter is thicker along a slanted path — one absorber, one exponential, and the whole angular colour of a white LED. Nothing about the emitters differs between these curves; only the distance the light took through the layer above them.
Fig. 2 The lamp the three methods act on. A blue pump under a broad phosphor, which is what almost every white LED is, and which gives current dimming two things to move independently.
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.
Fig. 3 The three chromaticity paths, which is the earlier essay’s measurement. The filament’s path is the longest and stays exactly on the locus; the duty-cycle path is a point.

Why a duty cycle is exactly nothing

Switching a lamp on and off above the fusion frequency multiplies its spectrum by a number. Every band is scaled by the same factor, so every cone signal is scaled by the same factor, so the change is a scalar multiple of the identity — which is diagonal in every basis, and which the ratio of the whites removes exactly.

That is not an approximation and it does not degrade with depth. At eighty per cent, at ten per cent, at one per cent, the residual is arithmetic noise. The site’s gate asserts it: the change has to be large — ΔE00 36.7 at a tenth, for an observer who does not adapt — and what is left has to be under 10⁻⁹.

The white of one lamp dimmed to 10 per cent, by three methods. Each patch is that method's white at the same output, normalised to the same luminance so the comparison is of colour alone. The largest gap between them is ΔE00 26.2 — twenty times any tolerance a supplier is held to — and the instruction that produced all three was the same one. A specification that says how bright a lamp should be has said nothing about which of these it will get.
Fig. 4 The three methods at a tenth, as colour. What the duty-cycle patch differs from the full-output one by is a level, and a level is what adaptation is best at.

The cost is elsewhere and this site has measured it: switching a lamp gives it a waveform, and a waveform costs a stroboscopic artefact on anything that moves and a visible flicker to anybody whose retina is scanning across it. A duty-cycle dimmer buys spectral perfection with temporal structure, and the trade is real.

Why a filament is the worst of the three

A filament has no spectrum of its own to move. It is a blackbody at whatever temperature the power leaves it at, so taking power away lowers the temperature and the whole spectrum re-shapes according to Planck’s law.

That re-shaping is a large change of shape, not of level, and the census’s central result applies: what a gain can remove is the diagonal part, and a Planckian re-shaping is not diagonal in the CAT16 basis. At a tenth of full output the filament sits around two thousand kelvin, and 3.63 units survive an observer who has adapted completely.

The irony is worth stating because it inverts the professional intuition. A filament dimmer is the one a lighting designer trusts: the chromaticity stays exactly on the Planckian locus, the Duv is zero throughout, and the colour it arrives at is a colour that exists in nature. Every quality measure a lamp is sold on says it is the well-behaved method.

And it is the one that leaves the most behind, because staying on the locus is a statement about where the chromaticity is and not about how the spectrum got there. The essays on which lamp changes are free are about that distinction and nothing else.

How far each method leaves the Planckian locus. A colour temperature is a projection onto the locus and says nothing about the distance from it, which is the second number a lamp is sold by and the one that decides whether it looks pink or green. The filament sits at Duv zero at every level — exactly, to 3e-16, because a blackbody at any temperature is on the locus by definition. The two LED methods do not, and the one whose colour temperature barely moved is the one that moves furthest here.
Fig. 5 The Duv of each path — how far off the Planckian locus each method strays. The filament’s is exactly zero throughout, which is the measurement that makes it look best and predicts nothing about the residual.

Current dimming, which is nearly free and for a reason

Between the two sits current dimming, at 0.153 at a tenth. That is small — a fifth of what a change from D65 to D50 leaves — and it is small for a reason worth separating from the others.

Driving an LED at less current does two things. The die’s emission peak moves by the quoted nanometres per decade of current, and the junction cools, because it is dissipating less, so all three thermal slopes run backwards. Both effects are small at ordinary dimming depths, and both are changes of shape rather than level.

So current dimming is a genuine change of spectral shape and it is a small one. The residual grows steadily with depth — 0.012 at eighty per cent, 0.039 at a half, 0.153 at a tenth, 0.345 at one per cent — which is the signature of a shape change rather than of a level change, and is exactly what a scaling would not do.

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.
Fig. 6 The junction’s own contribution, which is the larger of current dimming’s two mechanisms. A lamp dimmed this way is not a smaller version of itself; it is a slightly different lamp.

What happens at the bottom of the range

The three methods separate most at the depths a dimmer is actually used at, which is worth following because a specification’s tolerance is usually stated at full output.

At eighty per cent — a barely perceptible trim — the three leave 0, 0.012 and 0.214. Nobody would notice any of them, and no measurement would flag any of them.

At half, the numbers are 0, 0.039 and 0.739. The filament has crossed into the range where a careful side-by-side comparison would show something.

At a tenth, 0, 0.153 and 3.63. The filament’s residual is now larger than what a change from daylight to tungsten leaves, which is the largest lamp change in the whole census — because a filament at a tenth is a change of that kind, arrived at by turning a knob.

And at one per cent, 0, 0.345 and 9.96. That last number is larger than any other change of light this site models, larger than two bounces off a coloured wall, larger than any lamp swap. A filament at one per cent is the most extreme change of light this site can produce, and it is produced by a domestic dimmer at the bottom of its travel.

The shape of the three curves is as informative as their values. The duty-cycle row is a flat line on zero. The current-dimming row rises smoothly and very nearly in proportion to the number of decades dimmed. The filament row rises steeply and accelerates as it goes, because Wien’s displacement moves the peak out of the visible band and the visible part of the spectrum becomes a tail — though not all the way to the bottom, as the next section measures.

The two curves have laws

Both of the methods that cost anything follow something simple enough to state, and their two laws differ in a way the four sample levels cannot show.

Current dimming is linear in decades. Fitted between neighbouring levels, the exponent relating its residual to the number of decades dimmed stays between 1.03 and 1.17 across the whole range from nine tenths down to one hundredth. So the cost is very nearly a fixed 0.15 ΔE00 per decade, and it is still that at the bottom. That is what a shape change accumulating steadily looks like, and it is a stronger statement than four printed values can make.

The filament accelerates, and then stops accelerating. Its exponent starts at 1.03 beside the LED’s, rises through 1.25 at four tenths and 1.44 at a fifth, peaks at 1.61 between a tenth and a twentieth — and then falls back, to 1.51 and finally to 1.13 across the last halving. The Planckian re-shaping does not accelerate all the way down. It accelerates while the peak is leaving the visible band and steadies once the peak has left, because a spectrum that is already a rising tail across the whole band changes shape more slowly as it cools further.

That corrects an intuition rather than a conclusion. The filament’s residual is still 9.96 units at one per cent; it simply reaches most of that by five per cent and grows slowly afterwards.

Where the filament crosses a tolerance

The curves give a number a specifier could use, which four sample levels do not.

A filament dimmer leaves more than one unit of ΔE00 below 41 per cent of full output, and more than two below 22 per cent. Above four tenths it sits inside a coating tolerance; below a fifth it is at twice one. Those are ordinary positions on a domestic dimmer — the range a room is actually taken through in an evening — and they bracket the point at which the method stops being invisible.

Current dimming reaches neither. Its worst value anywhere on the sweep is 0.345, at one per cent, which is a third of a unit at the very bottom of the travel, and a duty cycle sits at 10⁻¹³ throughout.

The ratio between the two moves as well, so quoting it once is quoting it at a level. The filament costs 18.6 times what current dimming costs at nine tenths, 19.0 at a half, 23.7 at a tenth and 29.1 at two per cent, before narrowing slightly to 28.9 at one. The two methods are closest where nobody would notice either of them, and furthest apart where a room is genuinely dim — which is the one place a dimmer is doing what it was bought for.

What this changes about a specification

A dimming specification records a level and, if it is careful, a chromaticity tolerance. Both are properties of the lamp.

What the numbers here say is that the two ordinary quality measures — how far the chromaticity moved, and whether it stayed on the locus — are both uninformative about what an occupant of the room will actually be left with. The method with the best Duv performance is the worst on this measure by a factor of twenty-four over current dimming, and the method with no chromaticity change at all is exactly zero.

That is not an argument for duty-cycle dimming, because its cost is temporal and this measurement says nothing about temporal costs. It is an argument that a lamp’s dimming behaviour needs two numbers and is sold with one.

The two numbers a lamp is sold with, and the third

A dimmable luminaire is specified with a level range and, on the better data sheets, a chromaticity tolerance across that range — usually expressed as a maximum departure from the Planckian locus, or as staying inside a stated ellipse. Both of those are properties of where the lamp is.

Neither predicts this essay’s quantity, and the filament makes the point twice over. Its Duv is exactly zero at every level, which is the best possible score on the second number; its chromaticity moves further than either other method, which is the worst possible score on a tolerance expressed as distance travelled; and what it leaves an adapted observer is 3.63 units at a tenth. The lamp with the best score on one number and the worst on the other is the same lamp, and the quantity that matters agrees with neither.

The third number is not difficult to compute. It is the residual after the ratio-of-whites gain, over a stated set of surfaces, at each level — one column of numbers a manufacturer could publish from the spectra they already measure to compute a rendering index.

What it would tell a specifier is the thing they actually want to know, which is whether the room changes colour as it dims. A duty-cycle dimmer is exactly free by construction and pays for it in modulation; a current dimmer is nearly free and pays for it in nothing; a filament is expensive and is the one people describe as warm and pleasant, which is a preference for the change rather than an absence of it.

That last point is worth conceding rather than arguing past. A filament dimming toward candlelight is doing something people like. The measurement says it is a large change that survives adaptation — not that it is unwelcome, only that it is not invisible, which is what a chromaticity tolerance would have implied.

Who found it, and when

The three methods are older than the LED. Filament dimming is Edison-era; duty-cycle switching arrived with thyristor dimmers in the 1960s and became universal with solid-state drivers; current dimming is specific to semiconductors and dates from the 1990s.

That each produces a different colour path is well known to lighting designers and is a routine consideration in specification. Which of them an adapted observer is left with does not seem to be a question the trade asks, and the reason is structural: the measurement everybody has is a chromaticity meter, and a chromaticity meter cannot answer it. The quantity needs a spectrum, a set of surfaces and an adaptation model.

What was computed, and how

Each method’s spectrum comes from this site’s luminaire model, which builds an LED from a die and a phosphor with stated thermal slopes and builds a filament from Planck’s law with a stated power exponent. Nothing is tabulated.

The comparison holds the level in rather than normalising it out, which is a deliberate departure from the rest of the census. Normalising a dimmed lamp back to a common luminance removes the very thing being measured and leaves a duty-cycle-dimmed lamp indistinguishable from the lamp at full output, which it is not. So the change column here includes the level and the residual does not, because a gain removes the level exactly.

The residual is the mean CIEDE2000 over a hundred and twenty-five surfaces after the ratio-of-whites gain in the CAT16 basis. The gate requires the duty-cycle row to be under 10⁻⁹ and the other two to be above 0.05, and requires the change to exceed ten units — so a version of the machinery that quietly stopped dimming anything would fail rather than reporting three perfect methods.

A lamp switched on, and what it is still doing minutes later. The junction warms from ambient to 73 °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 22 per cent and the colour moves ΔE00 2.2. Nine tenths of the way takes 245 seconds. The vertical mark is the eye's own slow adaptation constant, 60 seconds, for scale.
Fig. 7 The other thing a lamp does that adaptation cannot follow: warm up. It is the same kind of change as current dimming — the junction temperature moving and the spectrum re-shaping — arriving on a different clock.

Where it stops

The three lamps are constructed from stated coefficients, and the absolute residuals are properties of those coefficients. The ordering is not: a duty cycle is exactly a scaling for any lamp whatever, and a filament is a blackbody for any filament whatever, so the two ends of the ordering follow from the physics rather than from the model. Only current dimming’s position between them depends on the numbers.

The observer is assumed to adapt completely to the dimmed lamp, which is generous. At one per cent of full output the adapting luminance is low enough that the appearance model’s degree of adaptation would not be one, and the residuals would be larger.

And nothing here models the interaction between dimming and the room’s own settling. A lamp dimmed slowly is a moving target for an observer whose pools are still relaxing, and the room takes several minutes to settle even when the lamp is not being adjusted.

There is also a question about what the numbers mean at very low levels that this arithmetic quietly assumes away. At one per cent of a domestic lamp the room is at a few candelas per square metre, which is the top of the mesopic range, and the rods are contributing to what is seen. The census’s observer is photopic throughout, so the filament’s 9.96 at one per cent is a photopic observer’s number for a condition a photopic observer is not really in. The direction of the correction is not obvious and it is not computed here.

Where the ladder goes next

The two-number problem generalises. Every lamp control — dimming, tuning, mixing two channels of different colour temperature — is a change of light chosen by an engineer, and each can be put through the same question. Colour-tunable luminaires that mix a warm and a cool channel are the obvious next case, because mixing two lamps does not average their rendering and it is not obvious what mixing does to the residual either.

The other direction is the one the duty cycle points at. It is spectrally perfect and temporally structured, and this site has a camera whose shutter samples that structure. A dimmer that is invisible to a person is not invisible to a machine, and the method with the best score on this essay’s measure is the one with the worst score on that one.

Where this goes next

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. Every change of light this site models, and how much of it a gain removes. 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 the fraction left rather than by the size of the change, because the two orderings are different: the largest change here is removed almost entirely and the worst row is a change less than a third its size. What no adaptation can remove A change of light is exactly a 3×3 matrix on tristimulus values, and adaptation is a diagonal one. Putting every change of illumination this site models through that distinction sorts them by how much of themselves they leave behind, and the smallest residual in the census belongs to a filter inside the eye. 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.

Named alongside this one

Essays reaching for the same objects. Nobody chose these; they are what the index of named objects makes visible.

What links here

Every essay whose body links to this one.

The objects this essay names

Each one links to every other essay that touches it.

AdaptationAssertionChromatic adaptationCorrelated colour temperatureDuvFlickerLED emissionLuminancePlanckian locusSpecificationSpectral power distributionThermal radiation