Christmas Day’s full moon made me decide to make my first post of the New Year about a resolution—specifically, the resolution of the human eye. (See what I did, there?)
We’re so used to images of the full moon like the one above, it’s difficult to remember that, until the invention of the telescope in the 17th century, people had a very limited idea of what it actually looked like.
Here’s a 16th-century sketch of the moon by Leonardo da Vinci:
A very careful observer and excellent draftsman, using the naked eye, was apparently able to record very little surface detail.
Lest you think Leonardo was having a bad day, or perhaps just wasn’t that interested in the detail, here’s the best effort of the astronomer William Gilbert:
Pretty rubbish, eh? Although Leonardo and Gilbert both captured some of the larger dark shapes on the lunar disc, neither was able to produce much in the way of detail.
What was the problem? The size of the moon was the problem. Although it can occasionally seem huge in the sky, especially when rising or setting, it’s actually surprisingly small, in angular terms. It averages about 31 minutes of arc in diameter—just over half a degree. For comparison, your thumb at the end of your outstretched arm covers about a degree of the sky. So it’s easy to blot out the whole lunar disc with a finger at arm’s length.
Now, the average human eye can resolve detail down to one minute of arc. The row of letters on your optician’s Snellen chart that corresponds to normal 6/6 vision (or 20/20 if you’re in the USA) is five minutes of arc high, with the black lines and narrow white spaces subtending one minute at your eye.
Part of that resolution limit is due to something called diffraction limitation—when your pupil is small, light rays are scattered by the edge of the iris and end up converging to form a small disc, rather than a point, on the retina. When your pupil is large, diffraction limitation is less of an issue, but imperfections in the optics of your eye, especially around the edge of the lens, become a problem. So most people end up with one minute of arc being their best resolution.
Even if the optics of your eye were perfect, you’d hit another resolution problem, which is the density of photoreceptor cells in the retina. Even at their densest, in the central fovea, there are only a couple of hundred thousand per square millimetre, packed so tight that each is just two microns across—translating to a resolution of about 0.4 minutes of arc. So that’s as good a resolution as you’re going to get even with an excellent human eye.
(And that is why, although that Ultra HD 4K television screen may look jaw-droppingly marvellous when you’re peering at it from a metre away in the shop, it’s probably going to be a disappointment when you get it home—for most sizes of TV, at the usual viewing distances, those 4K pixels are smaller than your ability to resolve. If your eyes are already at their resolution limit with HD, Ultra HD is going to look exactly the same. See if you can get a salesperson to admit that.)
Anyway, back to the moon. In terms of visual resolution, it’s just 31 pixels across, like some rubbish little 32×32 icon from a prehistoric version of Windows. That’s why Leonardo and Gilbert produced the surprisingly poor sketch maps they did. What we actually see of the moon with the naked eye is nothing like the image at the top of this post, but more like this *:
To be visible to the naked eye, at one-minute resolution, a lunar feature has to be about 110 km across. So Leonardo and Gilbert were easily able to pick out the distribution of lunar “seas” (dark lava plains) that give the “Man in the Moon” his face, but neither of them was able to record a single lunar crater. However, now that we know where to look, we can often pick out the bright patches of ejecta surrounding the craters Kepler, Aristarchus and Copernicus, superimposed as they are on dark lava plains. Tycho produces a bright splash in the south, discernible even against the paler rocks of the lunar highlands. The 110-kilometre crater Plato makes a dark-floored contrast with the surrounding pale highland terrain, but it’s right at the dubious edge of visibility for most people.
Now here’s the moon at half-minute resolution, right down at the limit imposed by the density of photoreceptors in our eyes:There’s a great deal more detail—the dark-floored notch of Plato is now pretty evident, and the bright patch around Tycho now contains a central, circular crater.
Are there people who see this well? There are. When the planet Venus is at its closest to Earth it shows as a tiny crescent, one minute of arc across, which can easily be discerned with a small telescope but which most of us see as a simple point of light. Some people claim to be able to discern the crescent shape, however, and many of them can make a sketch of its orientation which convincingly matches the telescopic view.
* I took the original image, and downsized it so that the moon was 31 pixels across. Then I enlarged it, to produce an image of the correct resolution, but it was full of blocky artefacts around the edge of the moon. So I took the original again, and applied Gaussian blur until it smoothly degraded the resolution to match my blocky 31-pixel version.