How You See

Depth perception test

Put on red–cyan glasses (red over the left eye). Each square hides a shape that only both eyes together can see.

Random-dot stereograms in the style of Béla Julesz. Neither eye's image contains the shape; it appears only when the brain matches the two. This is a demonstration, not a clinical stereoacuity test.

How to take it

  1. Wear red–cyan anaglyph glasses with the red filter over the left eye. Use a bright screen in a dim room.
  2. Set your viewing distance and keep it. Look at the square of dots; after a few seconds a shape should seem to float in front of them.
  3. Name the shape. The plates get harder as the disparity shrinks. If you see no shape, say so: guessing makes the result meaningless.
  4. Use Left eye only and Right eye only to check that neither image contains the shape on its own.

How it works

Each plate is a random-dot stereogram of the kind Béla Julesz introduced in 1960[1]. Both eyes get the same random dots, displaced sideways: by one amount for the background and by a different amount inside a hidden shape. Neither image alone shows an edge, and because the background is displaced too, the colors give nothing away without glasses. Only by matching the two images can the brain find the region with a different disparity, and it sees that region nearer than the rest. The glasses route the cyan dots to the left eye and the red dots to the right; dots in both images are black.

The disparity of the shape relative to the background comes from the extra shift s between the two images inside the shape, seen from your viewing distance D: δ = arctan(s/D). With 3-pixel dots, the last plate's extra shift is 6 pixels, about 11 arcminutes at 50 cm if your screen uses the standard 96 pixels per inch.

What this test can and cannot tell you

It can show that your two eyes cooperate to give stereo depth. It cannot measure fine stereoacuity: most people detect disparities of 30 arcseconds[2], about twenty times finer than this screen's last plate. Screen color, glasses that do not match the screen, screen pixel size and an unknown viewing distance all affect the result, and one guess in four is right by chance. Clinical tests use controlled stimuli and are interpreted by professionals.

Not a diagnosis and not medical advice. If you could not see the shapes, the glasses or the screen may be the cause. If you are concerned about depth perception, a lazy eye or a squint, see an optometrist or ophthalmologist.

Sources

  1. B. Julesz (1960). Binocular depth perception of computer-generated patterns. Bell System Technical Journal 39(5), 1125–1162. doi:10.1002/j.1538-7305.1960.tb03954.x. paper
  2. B. E. Coutant and G. Westheimer (1993). Population distribution of stereoscopic ability. Ophthalmic and Physiological Optics 13(1), 3–7. doi:10.1111/j.1475-1313.1993.tb00419.x. paper