AbilityBenchRandom-dot stereogram, three ways to view it
Stereopsis test with the arcseconds worked out in front of you
A square hidden in a field of random dots sits at a different depth from its surround, and you say whether it is at the top, right, bottom or left. Neither half of the pair contains it on its own, so only two cooperating eyes can find it. The page will not start until you have matched a bank card against the screen and typed how far away you sit — without those two numbers a shift in pixels cannot become an angle.
- Free fusion or red-cyan
- Arcseconds from your own screen
- Refuses to score a failed fusion
A field of random dots hides a square that sits at a different depth from the rest — top, right, bottom or left. It is invisible to one eye, and invisible to two eyes that are not cooperating: each half of the pair is a plain random field with nothing in it. Before any of that can be turned into an angle, this page needs two measurements it cannot take itself.
The floor, before you start
At 60 cm from a screen with 3.79 device pixels per millimeter, the smallest shift that can be drawn is one pixel, and one pixel subtends 91 arcseconds. That is the finest disparity this page can present to you — coarser than the 20 to 40 arcseconds a polarized plate test resolves in a consulting room. Sitting further back makes the angle smaller and the dots harder to see; both effects are real and neither is under this page’s control.
Those 4 run at 5 pixels of shift — 454 arcseconds here, which is coarse enough that anybody who has fused the pair will see the square immediately. They decide whether there is a measurement to make, and they are not part of it.
From one pixel to an angle
| Pixel width | From a card matched against the glass. Bank cards, driving licenses and travel passes are all 85.6 mm wide under ISO/IEC 7810, which turns a wallet into a ruler |
|---|---|
| Viewing distance | Typed, in centimeters — measured, not estimated. It divides straight into every angle, so a distance guessed a fifth short makes the result a fifth finer than it was |
| The conversion | 206265 × pixel width ÷ viewing distance = arcseconds |
| A worked case | At 96 CSS pixels per inch, a pixel ratio of 1 and 60 cm, one pixel of shift is about 91 arcseconds; at a pixel ratio of 2 it is about 45 |
| As depth | Viewing distance × pixel width ÷ pupil separation. At 60 cm and ≈ 63 mm — the average adult figure in Dodgson (2004), Variation and extrema of human interpupillary distance, SPIE Stereoscopic Displays and Virtual Reality Systems XI — one pixel stands for about 2.5 mm in front of the glass |
One device pixel is the smallest shift a screen can draw, so it is also the floor of the measurement. A visitor who resolves it has been told about the panel rather than about their eyes, and the result says so instead of printing a threshold. A denser display lowers that floor without shrinking anything; sitting further away lowers it too, but shrinks every dot at the same rate, until the test starts measuring acuity instead of depth. No stereoacuity grade or prevalence figure appears anywhere here, for the reason the site’s reference module gives in its own words: “Clinical stereoacuity is measured in arcseconds with polarized or vectographic plates at a fixed distance. A browser cannot control viewing distance, screen size or pixel pitch, and a red-cyan anaglyph adds crosstalk and color loss that shift the threshold on its own. Prevalence figures for reduced stereopsis also vary widely with the criterion used and this file has no citation it would stake the page on.”
When the dots will not cooperate
Why does the page sometimes refuse to give me a number?
Because a ladder fed guesses still settles somewhere, and the arithmetic will happily turn that into arcseconds. With four positions a visitor who never fuses the pair is still right a quarter of the time. So four coarse stereograms at five pixels come first — unmissable to fused eyes, invisible without fusion — and three of four are needed to go on. After the ladder, an exact binomial test runs on the whole run: if accuracy is not separable from chance, or the ladder spent its time against the one-pixel floor, the page says which and prints no threshold.
Cross-eyed and parallel gave me opposite depth. Which is right?
Both. Crossing your eyes swaps which half-image each eye receives, so a shift that reads as nearer one way reads as further the other. That is why this page asks where the square is rather than whether it sticks out: its position does not change with the technique, and a front-or-behind answer key would depend on something the page cannot see. The renderer also swaps the two fields for the crossed route so the geometry it reports is the geometry you saw.
Do I need red-cyan glasses, and which eye gets the red?
You do not need them — both free-fusion routes are complete tests — and the red lens goes over the left eye. Glasses on backwards swap the fields and flip the depth, the same way crossing does. Skip this route if telling red from green is hard for you, since the filters work by removing exactly those wavelengths, and expect a coarser threshold through glasses because colored filters leak a little of the other eye's image.
I could not fuse it at all. Does that mean I have no stereopsis?
It means the pair was not fused, and free fusion is a skill most people fail at before they learn it. Try the other direction, try the glasses, try another day — a few minutes with a fingertip held in front of the screen is the usual difference. If all three routes keep failing, that is worth an appointment rather than another run: an eye examination checks this with plates and a cover test, not with dots on a web page.
Why random dots, and why the panels are sized from your eyes
A random-dot stereogram, the construction introduced in Julesz (1971), Foundations of Cyclopean Perception, University of Chicago Press, contains no shape in either half, so there is nothing for one eye, a camera or a pattern-matching visitor to find. The square exists only in the comparison between the two fields, which is what lets this page tell a failed fusion apart from a coarse threshold. The disparity the system can use is finer than the spacing of the receptors that detect it, the property described in Westheimer (1979), Cooperative neural processes involved in stereoscopic acuity, Experimental Brain Research — which is why a screen’s pixel, not your eye, is usually the limit here.
The two half-images are sized so their centers sit no further apart than your pupils, defaulting to the ≈ 63 mm average and editable. Parallel fusion asks each eye to look straight ahead at its own half; once the centers are wider than your eyes it would need divergence, which people cannot do — the usual reason a stereogram works on a phone and not on a large monitor. If fusion never comes, the depth perception test measures the depth cues that need only one eye, in ratios that need no calibration.
This is a measurement exercise, not a clinical assessment. It reports what you did on this page against a stated reference and nothing more — it cannot establish stereoblindness, amblyopia, a squint or any other reason two eyes might not cooperate. Only a qualified professional, working with more than a browser, can make that judgment.