Visual Acuity ↔ Hyperacuity
What to do & see
The neighbouring interactive demo shows on its left 2 lines atop each other with a slight horizontal offset, that's the “vernier figure”. Right of it you see a “Landolt C” (the circle with a gap). Judge which way the top vernier line is offset from the bottom one, to the left or right? And do you recognise the direction of the gap?
Now click the correct button, for the vernier, on the left: which way is the top vernier line misaligned? For the Landolt C, on the right, where is the gap?
If you hit the correct button, the offset = gap size (number at the top) will decrease. The vernier and the Landolt C are redrawn with random directions. Keep on clicking (at least 10×) to make the vernier aligned or the the Landolt C very small.
Suggestion: start with the Landolt C on the right until you’re at your limit. Then continue with the vernier lines. Note that you can still correctly judge their offset, while the Landolt C on the right is just a fly blob. Do you agree that the vernier lines can still be judged when the gap of the Landolt C can no longer be recognised? For me, at reading distance, vernier resolution is ≈0.05 pixel, while I cannot recognize the Landolt C below ≈0.5 pixel gap size (the absolute limit depends on the distance, on your eyes and your visual display unit).
↑ a sliding caliper ↑
↓ its vernier scale ↓
Visual Acuity. A characteristic of our vision sense is visual acuity. In simple terms this is related to the smallest visible feature you can discern. A good test is to find the gap in the “Landolt C”. The neighbouring figure shows on its right a circle which has a gap at one of 8 orientations (top, top left, etc.). The smallest size of a Landolt C where the gap direction is recognized half of the time is a good measure of acuity. Normal spatial resolution is around 1 minute of arc, which roughly corresponds to the size of a pixel on your display at 0.5 m distance, and also to the size of a single cone in the centre of the retina in your eye. “Decimal acuity” (as used in many European countries) is 1/(resolved visual angle in arc minutes). Decimal acuity of 1.0 corresponds to a Snellen fraction of 20/20 or 6/6. Visual acuity corresponds to “recognition of shape”.
Hyperacuity. Vernier acuity is also called hyperacuity, because its resolution is 5-10× higher than that of visual acuity. Hyperacuity is the secret behind the precision of a sliding caliper. Hyperacuity corresponds to “recognition of relative position”.
The interactive demo uses anti-aliasing tricks to achieve sub-pixel resolution. The threshold algorithm is rather trivial: correct response reduces size by 20%, incorrect responses double the size. The “Freiburg Visual Acuity Test” uses a better algorithm, of course ;-).
Pierre Vernier, 1584–1638, military engineer in Franche-Comté
Westheimer G (1981) Visual hyperacuity. Prog Sensory Physiol 1:1–37
Bach M (1996) The “Freiburg Visual Acuity Test” – Automatic measurement of visual acuity. Optometry and Vision Science 73:49–53
Bach M (2005) The Freiburg Acuity Test (on-line demo + download)
Wikipedia Vernier An excellent explanation of the ingenious vernier scale on a sliding caliper.