A sensor has no lens

Six arguments a standard observer does not admit to having, and a camera has none of them. That is worth stating as a positive fact about sensors rather than as an absence, because it decides what a camera can and cannot stand in for.

The claim #

A camera is the only observer in this round with none of the six arguments, which makes it perfectly reproducible and disqualifies it as a model of any human observer.

• No lens ageing. A sensor’s cover glass and microlenses do not yellow on any timescale that matters, so the largest departure in the round is absent.
• No macular pigment, no cone optical density, no peak variation, no rods. Every one of the six is a property of a retina and a sensor has none of them.
• So two cameras of the same model agree with each other far better than two people do, which is why a camera profile is a stable object and a personalised observer is not.
• And the agreement is with each other rather than with anybody. A camera fails the Luther condition, so its sensitivities are not a linear transform of any human observer’s, and its stability does not make it representative.

What a sensor’s spectral sensitivity is made of #

A colour filter array’s transmittances are dyed polymer layers deposited photolithographically, and the silicon underneath has its own quantum efficiency. The product of the two is the sensor’s sensitivity, and both factors are fixed at manufacture.

Nothing in that chain has an analogue of the six arguments. There is no absorbing medium in front that changes over a working life; there is no self-screening, because the dye layer’s thickness is fixed rather than being a path length through a variable-length outer segment; and there is no polymorphism, because every sensor of a model is made from the same mask.

A camera is a fourth observer in the structural sense — three sensitivities collapsing a spectrum onto three numbers — and it is a fourth observer of a different kind. It is a manufactured one, and manufacture is a process that produces near-identical copies where biology produces a distribution.

The reproducibility, and what it is worth #

The consequence is that a camera profile is a stable object in a way no human characterisation could be.

Two bodies of the same model, profiled independently, agree to a fraction of a colour difference — the differences are manufacturing tolerance on the dye thicknesses and are small. The same profile applies to a body made three years later. Nothing drifts on a timescale anybody cares about except the infrared filter’s transmission with temperature, which is a small effect.

That stability is why colour management works at all in imaging. A profile is computed once, shipped, and applied to millions of exposures, and none of the terms this round measures enters anywhere.

The stability is with respect to the sensor and not with respect to any viewer, which is the whole point of the essay. A camera reproduces itself perfectly and reproduces nobody.

Why the absence is not an advantage #

There is a tempting reading of all this — that a camera is a better observer, because it is stable — and it is wrong in a specific way.

Stability and representativeness are different properties. A camera’s sensitivities are stable and are not a linear transform of any human observer’s, so its numbers can be mapped onto a standard observer’s only approximately, and the approximation depends on the spectra involved.

That is exactly the Luther condition failing, and this collection has measured what it costs: about 0.19 ΔE₀₀ on the patches a profile is fitted to and 1.65 on colours the chart does not contain.

So a camera has a departure of its own, it is of the same order as the human ones, and it has a completely different structure. It does not vanish on a neutral, it does not scale with the sample’s deviation from the light, and it does not respond to any of the conditions this round established. A camera’s departure is a fit residual and a viewer’s is a pairing, and the two do not combine into anything simple.

A camera is six times more faithful, to a table. Setting a profile’s residual beside the six makes the point quantitative. A nine-parameter matrix fitted on a chart reproduces its targets to about 0.19 ΔE₀₀; the smallest of the six human departures is 1.20 on the same kind of sample.

So a camera is roughly six times more faithful to the standard observer than any two people are to each other, and it is faithful to a table rather than to a person. Improving it further — better basis functions, root-polynomial forms, more patches — improves agreement with the table and moves nothing towards the viewer.

That is not an argument against the improvement. A pipeline needs a reproducible reference and the table is it. It is an argument about which number a photographer should compare against a complaint, and it is not the profile’s residual.

It also says where a colour-critical imaging chain’s remaining risk lives. The sensor is stable, the profile is precise, the display is calibrated — and the person looking carries two to three colour differences of spread that nothing in the chain measures or reports.

What a sensor does drift with #

The absence of the six does not mean a sensor’s response is constant, and the things that do move are worth listing because they are what an imaging pipeline actually manages.

Temperature. The infrared cut filter’s edge shifts slightly and the silicon’s quantum efficiency changes, both small and both real.

Exposure. A sensor’s response is linear over its working range and is not at the extremes, and a blown highlight turns as one channel clips before the others.

Unit-to-unit variation. Dye thickness tolerances produce small differences between bodies, which is why some manufacturers ship per-body profiles for critical work.

And the lens. A camera lens has its own transmission spectrum, which multiplies the sensor’s sensitivities, so a body-and-lens combination is strictly a different observer from the same body with a different lens.

That last is the closest thing a camera has to one of the six, and it is a good analogy for exactly one of them: a lens’s transmission is a filter in front of the receptors, which is what an ageing crystalline lens is. The difference is that a camera’s can be swapped and characterised and a person’s cannot.

There is a fourth absence worth adding to the list and it belongs to adaptation rather than to the receptors. A camera’s response to a change of illumination is a fixed set of sensitivities followed by a gain per channel — white balance in a basis of its own choosing — and it is exactly a von Kries transform applied in the sensor’s cone space.

A viewer’s response is that plus everything the round measures: the departures rise or fall with the light, differently for each of the six, in the table above.

So a camera adapts perfectly in a basis it defines, and a viewer adapts imperfectly in one nobody has settled. The camera satisfies the identity this round could only prove in the eye’s own coordinates, because a sensor’s coordinates are its own by construction and nobody is trying to fit them to behaviour.

That is an unexpected place to find the round’s cleanest condition satisfied, and it is a genuine advantage of a manufactured observer over a modelled one.

What it means for using a camera as a proxy #

The practical question is whether a camera can stand in for a viewer, and the round’s structure gives a sharp answer.

For a comparison against a numerical standard, yes, within the profile’s residual, because the standard is itself computed through a table and the camera is being fitted to reproduce that table. Both sides are contracts and the camera can be made to satisfy one.

For a prediction of what a person will see, no, and the failure has two independent parts: the profile’s residual against the standard observer, and the standard observer’s departure from the person. The second is the larger and is what this round measures.

And for a measurement of how much a population will disagree, no in a stronger sense. A camera has no population. It cannot exhibit observer metamerism because it is one observer, and photographing a metameric pair records the camera’s verdict on it rather than a distribution of verdicts.

That third is worth stating because it is a use cameras are put to. A photograph of two samples that a person says do not match is evidence that the camera does not match them, which is a different claim about a different observer.

The one condition a camera does satisfy #

There is one and it is instructive.

A flat sample is the same colour for a camera too. The derivation never used anything about the sensitivities: a stimulus that is a scalar multiple of the white produces relative excitations of (ρ, ρ, ρ) for any three curves, human or silicon.

So a camera photographing a grey card, white-balanced on the same light, records a perfect neutral, exactly, whatever its sensitivities are. That is why white balancing works as well as it does and why the highlight is such a good estimator of the illuminant: both exploit an identity that holds for any observer.

And it explains the shape of a camera’s failures. A camera is exact on neutrals and inaccurate on saturated colours, which is the same distribution the human departures have, for the same algebraic reason and with a completely different mechanism underneath.

Two different departures with the same condition is a reminder that a condition constrains where a departure can live without saying what it is.

The fine-grid table is the fair comparison for a sensor, because a camera does not have this collection’s tabulation problem either — its raw values come from a physical integration over its filters, which is a slit in the sense the tabulation audit means.

So a camera escapes both of the round’s computational terms and carries a fit residual instead, which is a third kind of departure with a third mechanism.

The rod term is the one absence with no sensor analogue whatever. A camera has exactly three sensitivities at every light level, so it does not become a four-channel device in the dark; what it does instead is get noisier, which is a different failure with a different remedy.

What was computed, and how #

Nothing about sensors is computed in this round. The profile residuals quoted are this collection’s own from its camera work, and the claim that a sensor has none of the six arguments is a statement about what a colour filter array is rather than a measurement.

The observer departures are the round’s, over forty-two analytic surfaces, and are quoted for comparison rather than as anything a camera exhibits.

The neutral identity’s applicability to a camera follows from its derivation, which never uses the sensitivities’ shape — the same reason it applies to a dichromat, a tetrachromat and any future observer.

A sensor could be designed for something it is not. The absence of the six has a design consequence nobody exploits, and it is worth stating because it is the reverse of the usual complaint.

A sensor’s sensitivities are chosen at manufacture from a wide space of achievable dye transmittances. The usual criteria are quantum efficiency, the conditioning of the matrix that maps them to XYZ, and cost. A primary is chosen for four things and a filter set is chosen for about the same number.

None of the criteria is agreement with a population. A filter set could be chosen to minimise, over a modelled population of observers, the disagreement between what the camera says and what a viewer sees — a different objective from minimising the residual against the 1931 tables, and one that would produce different filters.

Whether it would produce better photographs is genuinely unclear, and that is the honest state of it. The 1931 tables are what every downstream piece of the chain expects, so a camera optimised against a population and mapped through a table designed for a different observer might well be worse in the pipeline it has to live in.

A component optimised against a criterion nothing downstream shares is a component that fights its own chain, which is an argument for changing the chain and not for changing the component alone.

Where the model stops #

A real sensor does have small analogues of two of the six. Its dye layers have a thickness with a manufacturing tolerance, which is a faint echo of cone optical density, and its microlenses and cover glass have a transmission that is a fixed filter. Neither varies over a working life and neither varies between units by anything like the human spreads.

Nothing here measures a camera’s own departure structure, which would need the round’s method applied to a set of sensors — perfectly possible and not done, because this collection has one sensor model in its machinery.

And the essay treats a camera as a colorimetric device. A great deal of what a camera does to colour happens after the sensor, in demosaicing, tone mapping and rendering intent, and none of that is an observer question.

One last comparison closes the round’s treatment of observers. There are now four kinds in this collection: the tabulated standard, which is a contract; the analytic construction, which is a model with seven arguments; the population, which is two hundred draws from that model; and the sensor, which is a manufactured object with none of the arguments and a spectral sensitivity nobody chose for its resemblance to anything.

Each is right for a different question. The contract is what a specification is written against. The construction is what an audit needs. The population is what a manufacturer’s acceptance rate depends on. And the sensor is what actually records the photograph.

Confusing them is the commonest error in this subject and it has a specific form each time: treating whichever observer is at hand as the one the question is about. This round’s whole content is the size of the gaps between them.

The generalisation #

The habit is about the difference between reproducible and representative.

An instrument that agrees with itself is easy to build and is what engineering optimises for, because reproducibility is measurable and improvable. Agreement with the thing being modelled is neither, and the two are frequently confused because both present as low variance.

The test is to ask what the variance is between. A sensor’s variance between units is tiny; its variance against a population of human observers is not defined, because it is not a member. Low variance within a class says nothing about distance to another class.

The failure mode is to treat a stable instrument as an authority. A stable wrong answer is more persuasive than an unstable right one, and the persuasiveness comes from exactly the property that has nothing to do with correctness.

A brief note on why this essay sits in the imaging field rather than in the one about eyes. Everything in it is about what a camera lacks, which is a statement about the eye as much as about the sensor — and the reason it belongs here is that its consequences are all for imaging practice: which profile residual to believe, whether a photograph can settle a match, and what a sensor could be designed for.

The corresponding statement from the other side has already been made: the standard observer is an average over seventeen people and no camera is one of them either.

Who found it, and when #

Luther stated the condition for a camera to be a colorimeter in 1927 and it has been known to fail for every practical sensor since. The literature on camera characterisation is largely about how badly and what to do about it.

That a sensor lacks the physiological variation a population has is too obvious to have been discovered, and its consequence — that a camera cannot exhibit observer metamerism and therefore cannot be used to measure it — appears not to be stated, presumably because nobody attempts the measurement that way.

Where the ladder goes next #

The round is finished. Its three audits, its ten conditions and its eleven outstanding items are recorded, and the next object is on the other side of the tristimulus values — where nothing this round established applies, because nothing there is linear.