In the dark, a single cell in your eye can register a single grain of light. And even in perfect darkness, your eye is never quite in the dark.
Chapter 6 · Eye
The Last Instrument
A patch of your own retina in the dark. Why is one photon not enough to see, and what changes when you decide to see more readily? Then, a last look at the diatom.
Look first
Five hundred rods, in the dark
This is a model of a small patch of retina, a little to the side of where you look: five hundred rods, each a cell that can register a single photon. You have been in the dark for half an hour, so they are as sensitive as they will ever be.
No light is arriving. Watch the patch in glimpses of a fifth of a second each.
computed
Each lit rod has produced an event indistinguishable from the response to a photon. In total darkness, the patch averages 0.6 of them per glimpse.
Commit to a prediction
Why not one?
Chapter 5 ended with a puzzle. A single rod registers a single photon. Yet in 1942 Hecht, Shlaer and Pirenne found that a person reports a flash only when something like five to eight rods have each absorbed one.
Why does seeing need several?
You just watched it. In complete darkness the rods produce events that look exactly like the response to a photon: a rhodopsin molecule, jostled by the warmth of the body, changes shape on its own. For any one molecule this happens about once in fifty thousand years at room temperature. But a rod holds about a hundred million of them, and a patch holds hundreds of rods. In primate rods the rate comes to about 0.006 events per rod per second. Across this patch, in one glimpse, that is 0.6.
Now suppose the visual system reported a flash on any single event. It would see a flash in 45% of glimpses of total darkness. Waiting for two events brings that down to 12%; three, to 2%; six, to almost never.
Why the other guesses made sense
Losses are real; noise is the reason
If you chose A, you were right that most photons are lost. Of those that reach the eye, only a few percent produce a rod signal: some are reflected, half are absorbed on the way through the eye, most pass between or through the rods. That is why a flash of ninety photons at the cornea gives only a handful of events. But losses alone would not demand several events. One, if it could be trusted, would do.
If you chose B, the opposite turns out to be true: the retina has a pathway specialised for carrying single-photon signals, and thousands of rods converge on one output cell. The signal gets through. The problem is that so does the dark.
If you chose D, you were closer than it seems. The final step is a decision. Part of it is already made in the retina: the first connection after the rods discards much of their small, continuous electrical noise before anything is counted. The rest belongs to the observer.
The mechanism, in ordinary language
In each glimpse the visual system receives a count of events from a patch of retina. Some come from the flash, if there was one. Some come from the dark. The count does not say which is which. So it says “flash” when the count reaches some level, and that level is a trade. Set it low, and you catch faint flashes but also see flashes that never happened. Set it high, and you are rarely fooled but miss the faint ones.
Here, exactly, is where the physics stops. Everything up to the count is light, optics and chemistry, and it can be calculated. The level at which you say “yes” is not set by the light at all.
The bench
Run the experiment
Flash the patch, or show it nothing, and let the model observer decide. The curve shows how often a flash of each strength is seen; the dashed line shows how often nothing is seen as a flash.
How often a flash is seen
Reading the curve
Hecht and his colleagues read the number of events from the steepness of this curve, not its position: the more events needed, the steeper it rises. The light’s own Poisson scatter sets its shape.
Things to try
- Set the criterion to 1. Run 200 blanks. How many times does the observer see a flash that was never there?
- Set the dark events to zero. What criterion would you choose now?
- Raise the share of photons that make rod signals, as a better eye might. Where does the curve move?
What you can now say
At the limit of vision, the eye counts events and the visual system decides. Rods also fire in the dark, so a report of “seen” needs more events than the dark is likely to make. Where that line is drawn is a choice, not a property of the light.
So the physical account runs, without a break, from the lamp to a number of events in a patch of retina in a fraction of a second. After that comes a criterion. Change the criterion and the same light, the same eye, gives a different answer.
For the determined reader: the model, a worked case, and its limits
The quantities
| Symbol | Meaning | Unit |
|---|---|---|
| I | mean number of photons in the flash, at the cornea | photons |
| a | share of them that produce a rod signal | none |
| L | mean number of dark events in the pooled rods during one glimpse | events |
| k | events needed before the observer says “seen” | events |
The model
P(seen | I) = P( Poisson(aI + L) ≥ k ) P(seen | nothing) = P( Poisson(L) ≥ k )
Hecht, Shlaer and Pirenne measured the energy at the cornea for threshold vision: 54 to 148 quanta. Correcting for 4% reflection at the cornea, almost exactly 50% absorption in the eye’s media, and at least 80% of the rest passing through the retina unabsorbed, they found that at most 5 to 14 are absorbed by rods, spread over about 500 rods. From the steepness of the frequency-of-seeing curve they estimated 5 to 8 critical events.
A worked case
a = 0.06, L = 0.6 (500 rods × 0.006 s−1 × 0.2 s), k = 6. A flash of 90 photons gives 5.4 + 0.6 = 6.0 events on average. P(Poisson(6.0) ≥ 6) = 0.55. The 50% point falls at 85 photons, close to the average of about 90 in Hecht’s experiments; a and k were chosen to match it, so this shows the numbers are consistent, not that the model is confirmed. On blank trials, P(Poisson(0.6) ≥ 6) = 0.00004.
What changes on screen. Raise a and the whole curve slides to weaker flashes without changing shape. Raise k and it slides to stronger flashes and grows steeper. Raise L and blank trials are seen more often unless k rises with it.
Where the model stops
It counts all pooled events equally and adds them over one fixed glimpse; the real retina weights them in space and time, and its first synapse discards much of the rods’ small continuous noise before counting starts. It treats the criterion as a sharp count; real observers use something softer, and can be asked to rate their confidence instead of saying yes or no. When they are, as Barbara Sakitt did in 1972, they reveal reliable information at flash strengths three or more times below the classical threshold. In 2016 Tinsley and colleagues delivered single photons from a quantum light source and found observers right 51.6% of the time against a chance level of 50%, with an uncertainty of 1%: possible evidence that a single photon can sometimes reach awareness, at the edge of statistical reliability.
The dispute
Noise in the light, or noise in the eye?
Hecht, Shlaer and Pirenne’s 1942 argument was elegant. Their flashes were so weak that the number of photons absorbed varied from flash to flash by pure chance, in a Poisson spread. They argued that this spread in the light itself, not any unreliability of the eye, accounted for why the same flash was sometimes seen and sometimes not. Differences between observers they put down to each adopting a different criterion for how strong a sensation had to be before saying yes.
In 1956 Horace Barlow changed the question. If the retina produces events of its own in the dark, then seeing at threshold is not just counting photons; it is telling a signal from noise, and the criterion must sit above the noise. He could not yet measure that noise directly. Two decades later, electrodes on single rods could: in darkness, rods produce spontaneous events with the same size and time course as the response to a photon, at about 0.006 per second in primate rods. The eye in total darkness sees a faint light of its own, sometimes called dark light.
Both pictures survived, refined. The light’s own graininess shapes the curve, as Hecht said. The dark sets where the criterion must sit, as Barlow said. And the criterion is the observer’s: when experimenters let observers rate their confidence, the information was there at far weaker flashes than a confident “yes” required.
A case you have not seen
Say yes more readily
Same eye, same dark, same flashes of 60 photons, the same blank trials mixed in. The only change is in the instruction. Before, the observer said “seen” only when sure: about six events. Now they are told to say “seen” whenever there might have been something: two events.
What happens?
| Criterion | Flashes of 60 seen | Blanks “seen” |
|---|
The light is unchanged, and so is every event in the retina. What changed is the line drawn through them. Lower the line and more real flashes clear it, and so do more of the dark’s random clusters. You cannot have one without the other, because in any single glimpse the count does not say where its events came from.
If you chose B, you treated “seeing” as something the flash does, which caution can only hide. The model says seeing is something the observer does with a count, and the count from the dark gets the same treatment.
Back to the front door
How much of what you are looking at is the diatom?
Here is the image the exhibition opened with. You can now answer its question one link at a time.
Source. The lamp’s light reached the specimen through a condenser opened to 0.75, so it kept step across only about 0.45 µm, a little less than one stria spacing. The image sits between Abbe’s case and Helmholtz’s, neither pure. Chapter 3.
Specimen. The striae are drawn as dimming the light. Real silica mostly delays it, and nothing in this image tells you whether its stripes are ridges or holes. Chapter 2, and chapter 4 for what polarised light could add.
Instrument. With an objective of 1.25 and that condenser, the finest spacing that can appear is about 0.28 µm, so the half-micrometre striae come through at their true spacing. The softness of every edge, and the faint ripples beside them, belong to the lens. Chapter 1, chapter 2.
Detector. A real camera would have counted the light, and every pixel would carry a scatter of about the square root of its count. This image, computed, has none, which is one way to tell it is not a photograph. Chapter 5.
Eye. In ordinary light the counting limits of this chapter are far away, and the stripes are simply clear. At the faintest levels, whether you see them at all is a decision against the dark. This chapter.
So: the spacing of the striae, and the outline, are the diatom’s. Their darkness is the model’s. Their softness and the ripples are the lens’s. And the fact that you see a diatom at all, rather than a pattern of light, is yours.
Where the explanation stops
After the count
Every link in this exhibition had an equation. The lamp’s coherence, the specimen’s beams and its slow and fast directions, the lens’s cutoff, the detector’s scatter, the eye’s count and its criterion. Each has been checked here, against independent calculations and against the historical record.
None of them says what it is like to see the diatom. The calculation takes the light all the way to a decision. What happens after that, the seeing itself, is outside every equation here, and is the question this exhibition was built to reach.
End of the first room
Added to your notebook
At the limit of vision, the eye counts events and the visual system decides. Where the line is drawn is a choice, not a property of the light.
How much of what you were looking at was the diatom?
Everything in this room used light your eyes can see: one narrow band. The second room asks what lies on either side of it, and how anyone found out.