A blown highlight turns

A photosite is a well. It collects electrons until it is full, and then it stops. Nothing about that is subtle and nothing about it is gradual — a full well reports the same number however much more light arrives.

What is less obvious is that the three channels fill at different times, and the interval between them is where a colour turns into a different colour.

The claim #

An exposure that clips nothing changes no hue at all — the shift is exactly zero, asserted rather than described. Once one channel saturates, the recorded hue rotates, and by the time two have saturated it can be sixty-seven degrees from where it started.

The first half is what makes the second half an argument. If exposure moved the hue a little at every level, the shift would be a gradual property of the pipeline and hard to attribute. It does not: the shift is identically zero for every unclipped exposure and then large, so the cause is unambiguous.

Why the hue turns #

Raising the exposure multiplies all three channels by the same factor, and multiplying a triple by a scalar does not change its ratios — so hue and saturation are unchanged and only lightness moves. That is the unclipped case and it is exactly flat.

Clipping breaks the scalar. Once the largest channel hits the ceiling it stops rising while the others continue, so the ratios start moving, and they move towards equality. A saturated red at $(0.95, 0.28, 0.12)$ pushed up two stops becomes $(1.00, 1.00, 0.48)$ — red and green both at the ceiling, blue still climbing — which is a yellow.

The hue therefore travels along a specific path: towards the hue of whichever channels are still rising, and finally to white when all three are full. A red goes through orange to yellow to white. A deep blue goes through cyan. A magenta splits and goes towards whichever of its two components was smaller.

That path is the reason a blown sunset is not simply a white patch with a coloured edge. It is a sequence of hues arranged by how far past the ceiling each part of the scene went, and the sequence is an artefact of the sensor rather than a feature of the sky.

What the ceiling actually is #

Three things set it, and they are usually conflated.

The full-well capacity is the physical limit: how many electrons the potential well can hold. Beyond it, additional charge either recombines or spills into neighbouring sites, which is blooming.

The analogue-to-digital converter’s range is the numerical limit, and on most sensors it is reached slightly before the well fills, so the recorded ceiling is a number rather than a physical saturation.

And the white balance moves it per channel. White balance multipliers are applied to the raw values, and a channel multiplied by 2.1 reaches the output ceiling at half the raw level that a channel multiplied by 1.0 does. So the order in which channels clip depends on the estimated illuminant, which means a guess about the scene partly determines which hue a highlight turns towards.

That is an uncomfortable coupling and it is real: under tungsten, where the blue multiplier is large, blue clips first in the output even though it was the smallest raw signal.

Which hues turn, and by how much #

Sixty-seven degrees is one stimulus’s answer, and the answer depends strongly on which stimulus.

Sweeping saturated colours round the hue circle and taking each one’s largest rotation under clipping: red 13.0°, orange 46.4°, yellow 2.3°, chartreuse 25.6°, green 3.9°, spring green 48.6°, cyan 0.7°, azure 88.9°, blue 7.9°, violet 16.8°, magenta 1.0°, rose 36.2°. The largest anywhere on the sweep is 107.2°, at a blue-violet just off the blue primary.

That pattern is not noise; it is the structure of the clip. A stimulus sitting on a primary or a secondary barely turns at all. Red is 0.95, 0.06, 0.06 — two channels equal, so they reach the ceiling together and the ratios hold. Yellow is 0.95, 0.95, 0.06 — again two equal, again nothing to separate. Cyan turns by seven tenths of a degree, which is arithmetic noise.

The hues between the axes are where the rotation lives, because they have three distinct channels, the channels reach the ceiling one at a time, and each arrival is a separate turn. Azure at 0.06, 0.47, 0.95 is the worst of the twelve at 88.9°, and the true worst sits a little further towards blue.

There is a practical reading in that a photographer would recognise. The colours that survive over-exposure with their hue intact are the ones nearest a display primary. The ones that go somewhere else are the intermediate hues — skin, sunsets, foliage, a sky near the horizon — which is exactly the set anybody would have wanted to keep.

It also means the two examples above are not equivalent. The red the claim is stated on turns 67.1°; the blue drawn beside it turns 92.6°, half as far again, on the same axes over the same twelve stops.

What the white balance is worth #

The coupling to the illuminant estimate is real, and it is modest.

Putting one raw triple through three balances — a daylight gain of unity on all three channels, a tungsten one of 1.00, 1.05 and 2.10, and a shade one of 1.55, 1.00 and 0.75 — gives largest rotations of 67.1°, 71.2° and 63.7°. A spread of 7.5 degrees, from a decision taken before the pixel is written and recorded nowhere afterwards.

So the estimate changes the size of the turn by about a ninth, and does not change where it ends: all three arrive at the same place, because all three arrive at white. The guess about the light decides how far a highlight travels rather than where it goes.

Highlight recovery is a reconstruction #

Converters offer to recover blown highlights, and it is worth being exact about what they do, because the operation is often read as undoing a loss.

When one channel is clipped and two are not, there is information left: the two survivors constrain what the third would have been, given an assumption about the surface. If the highlight is a specular reflection, the assumption is that it was the colour of the illuminant, and the missing channel can be filled from the other two and the estimated white point. If it is a bright diffuse surface, the assumption is that the hue is locally continuous with the unclipped pixels around it.

Both are reasonable and both are inventions. The recovered value was not measured, and the recovery’s success is a statement about the assumption rather than about the file.

When two channels are clipped the constraint is much weaker and the result is close to a guess. When all three are clipped there is nothing whatever to work with, and every converter renders white.

The honest description is that highlight recovery converts a hue error into a plausible hue, which is usually preferable and is not a return to the measurement.

The interaction nobody wants #

The estimator the previous rung was about needs unclipped specular highlights, and specular highlights are the first thing in any frame to clip.

That is not a coincidence but the same fact twice. A specular reflection returns a large fraction of the source’s radiance in a small solid angle, so it is typically several stops brighter than anything diffuse in the scene — which is exactly what makes it a good sample of the illuminant and exactly what makes it saturate.

So the best physical white-balance method requires an exposure that protects the highlights, and protecting the highlights costs several stops of signal everywhere else, which costs noise, which the previous essay measured the price of.

Why the number is sixty-seven degrees and not three hundred #

The size of the rotation is worth unpacking, because it depends on the stimulus in a way that predicts which photographs will show it.

A hue rotation needs two things: a channel that clips early, and a channel that keeps rising for a long time afterwards. Both come from the ratios in the original stimulus. A stimulus with three nearly equal channels — anything near neutral — clips all three within a fraction of a stop and rotates by almost nothing on the way to white. A stimulus with one channel far above the others has a long interval between the first ceiling and the last, and rotates a great deal.

So the rotation is largest for the most saturated stimuli, which is the same conclusion this field has reached from three other directions: the matrix is worst on saturated surfaces, metamerism is worst on spectrally narrow ones, and the infrared collapse is worst on the ones with the most chroma to lose.

Two more stimuli complete the circuit of the hue circle, and between the five of them the direction of the turn is never the same twice.

The practical list follows directly. Stage lighting, neon and LED signage, sunsets, brake lights, flowers photographed in direct sun, and anything specular on a coloured object — every one is a saturated stimulus with a long clipping interval, and every one is a photograph people complain about.

The exposure decision this forces #

The consequence for anybody taking a photograph is a rule that is well known and rarely derived.

Expose so that nothing important clips, and accept that everything else is darker and therefore noisier. This is the practice usually called exposing to the right in its optimistic form and protecting the highlights in its cautious one, and the two differ in how much margin to leave.

The reason it is a rule at all is the asymmetry between the two ends of the range. A shadow that is too dark has been measured badly — the signal is there, buried in noise, and lifting it in processing recovers a noisy version of something real. A highlight that is clipped has not been measured at all, and no processing recovers what was never recorded.

Noise is recoverable and clipping is not, so the sensible margin is asymmetric.

That rule interacts badly with the one from the previous rung, which wants the specular highlights unclipped for the estimator, and specular highlights are several stops above everything else. Protecting them costs the whole scene several stops of signal — which is why nobody does it, and why the best physical white-balance method is not the one in the camera.

Where the model stops #

The ceiling is modelled as a hard limit and real wells are not quite. Response falls away slightly before saturation rather than stopping abruptly, and some sensors are deliberately given a soft knee. The shape near the ceiling is a manufacturer’s choice, and it changes how gradual the hue shift is without changing its direction or its endpoint.

Blooming is not modelled at all. Charge spilling from a full well into its neighbours spreads the artefact spatially, so a blown highlight is often larger in the file than it was in the scene, with a coloured halo that is the spill arriving in differently filtered sites.

And this is entirely about the ceiling. The floor has its own colour failure — three channels with different pedestals and different read noise produce a chromatic cast in the deepest shadows — and it is a smaller effect that behaves quite differently, because it is additive rather than a clip.

A violet is the hue where the two clipping channels are the two the eye is least sensitive to, which makes it the case a photographer would least expect.

The generalisation #

The transferable claim is about saturating measurements and what happens to derived quantities when only some of the inputs saturate.

A ratio, a difference or an angle computed from several sensors is well-behaved as long as they are all in range, and misbehaves the moment one of them stops responding — and it misbehaves in a way that has none of the character of a measurement error. There is no noise, no scatter, no growing uncertainty. The derived quantity moves smoothly and confidently along a path determined by which input clipped first.

The three properties that make this dangerous are worth naming together. The failure is silent, because a saturated reading is a valid number. It is systematic, so it does not average away. And it is smooth, so it produces plausible trends rather than obvious garbage.

The general protection is not a better sensor but a flag: record which inputs were at their limit, and propagate that flag through every derived quantity. Almost every scientific instrument does this and almost no consumer one does — a raw file records the ceiling implicitly, as a value that happens to be at maximum, and every stage downstream has to infer the flag rather than read it.

That is a small design decision with a large consequence, and it is the same shape as several others this collection has recorded. A generator that substitutes a default for an unrecognised argument rather than throwing, and a fallback that draws a different answer when it does not know the right one, both fail the same way — a value meaning this is unknown is represented as a value meaning something else.

The eye has a ceiling too, and it behaves differently #

A comparison worth making, because it explains why the artefact looks so unnatural.

Human vision has an upper limit as well — a luminance above which the response saturates and everything looks equally bright, which is why a photograph of the sun and the sun itself both appear as a featureless white disc. But the visual system reaches its limit in a way that is nothing like a well filling.

Adaptation moves the range rather than extending it. The eye operates over about three log units at any one adaptation state and shifts that window across ten or more as conditions change, so the ceiling is not fixed relative to the scene; it is fixed relative to whatever the eye has adapted to. A camera’s ceiling is fixed relative to the exposure, and the exposure is chosen once for the whole frame.

And the response is compressive well before the limit, so the approach to saturation is gradual and does not change hue in the way a hard clip does. Brightness is inferred from edges rather than read off an absolute level, which makes the whole question of a ceiling much less sharp than it is for a sensor.

So the reason a blown highlight looks wrong is not that it is bright. It is that it is bright in a way nothing in visual experience is: uniformly flat, sharply bounded, and — the part this essay is about — the wrong colour on the way in.

Who noticed, and when #

Photographic emulsions do not clip. Density rises, the characteristic curve rolls off through a shoulder, and it approaches a maximum asymptotically over several stops — so film’s highlight behaviour is a gradual desaturation rather than a rotation, and colour negative film in particular has an extraordinarily long shoulder. That difference is most of what people mean when they describe film’s rendering of bright light as more forgiving, and it is a real physical difference rather than a matter of taste.

Electronic sensors clip abruptly, and the consequence was recognised immediately in broadcast video, where the “knee” — a deliberate compression applied before the ceiling — has been a standard camera control since the nineteen-eighties for exactly this reason.

Highlight reconstruction from partially clipped data appears in the raw-conversion literature from the early two-thousands and is now standard in every converter. The best of the current methods use the unclipped channels plus a strong prior about scene statistics, which is the same escalation demosaicing went through: a better prior applied to recover measurements that were never made.

What the figure asserts, and why it needs to #

The measurement here rests on a comparison that could easily have been made against the wrong thing, and the choice is worth stating because it decides what the number means.

The hue shift is measured against the same stimulus rendered without clipping at the same exposure — that is, against what the sensor would have recorded if its ceiling were higher. It is not measured against the base exposure, which would confound the clipping with the ordinary lightness change, and it is not measured against a normalised version, which would remove the effect being looked for.

The assertion that makes the comparison trustworthy is the negative one: every exposure at which no channel clips must show a shift below $10^{-6}$ degrees. If the reference were wrong, or the hue calculation drifted, or the exposure model introduced a nonlinearity, that would fail — because there is no reason for a wrong comparison to come out exactly zero over half the range.

A flat line at zero is a much stronger check than a large number is a finding, and it is the same argument the control sensor makes elsewhere in this field. A quantity asserted to be exactly nothing under conditions where it should be nothing is where a measurement earns the right to report something.

Where the ladder goes next #

Downward, this rung sits on raw is not a picture, which lists the decisions this one is about, and on how bright is white, which is where the top of a range first became a subject here.

Upward, the grid this site cannot see turns from the camera to the collection describing it, and a photograph is not a measurement closes the field with this failure among its exhibits.