# What resolution does the human eye see in?

Visual acuity is defined as 1/a where a is the response in x/arc-minute. The problem is that various researchers have defined x to be different things. However, when the different definitions are normalized to the same thing, the results agree. Here is the problem:

Usually a grating test pattern is used, so x is defined as cycles in the pattern. Different researchers have used a line, a line pair, and a full cycle as the definition of x. Thus, they report seemingly different values for the visual acuity and resolution. It is easy to recompute the acuity to a common standard, when the study defines what was used.

So when we define x to be a line pair, as is normally done in modern optics, the 1/a value is 1.7 under good lighting conditions. This was first determined by Konig (1897 [yes that's 1897] in 'Die Abhangigkeit der Sehscharfe von der Beleuchtungsintensitat,' S. B. Akad. Wiss. Berlin, 559-575. Also in: Hecht (1931, 'The Retinal Processes Concerned with Visual Acuity and Color Vision,' Bulletin No. 4 of the Howe Laboratory of Ophthalmology, Harvard Medical School, Cambridge, Mass.) A summary plot of numerous subjects of visual acuity as a function of brightness appears Pirenne (1967, "Vision and the Eye," Chapman and Hall, London, page 132).

The acuity = 1.7 when the light level is greater than about 0.1 Lambert. A Lambert is a unit of luminance equal to 1/pi candela per square centimeter. A candela is one sixtieth the intensity of one square centimeter of a blackbody at the solidification temperature of platinum. A point source of one candela intensity radiates one lumen into a solid angle of one steradian according to the photonics dictionary http://www.photonics.com/dictionary.

The acuity of 1.7 corresponds to 0.59 arc minute PER LINE PAIR. I can find no other research that contradicts this in any way.

Thus, one needs two pixels per line pair, and that means pixel spacing of 0.3 arc-minute!

Blackwell (1946) derived the eye's resolution, which he called the critical visual angle as a function of brightness and contrast. In bright light (e.g. typical office light to full sunlight), the critical visual angle is 0.7 arc-minute (see Clark, 1990, for additional analysis of the Blackwell data). The number above, 0.7 arc-minute, corresponds to the resolution of a spot as non-point source. Again you need two pixels to say it is not a point, thus the pixels must be 0.35 arc-minute (or smaller) at the limit of visual acuity, in close agreement with the line pairs. Line pairs are easier to detect than spots, so this too is consistent, but is closer than I thought it would be.

In modern studies, like Curcio et al. (1990), acuity is measured in cycles per degree. Curcio et al. derived 77 cycles per degree, or 0.78 arc-minute/cycle. Again, you need an minimum of 2 pixels to define a cycle, so the pixel spacing is 0.78/2 = 0.39 arc-minute, close to the above numbers.

## Visual Acuity and Resolving Detail on Prints

How many pixels are needed to match the resolution of the human eye? Each pixel must appear no larger than 0.3 arc-minute. Consider a 20 x 13.3-inch print viewed at 20 inches. The Print subtends an angle of 53 x 35.3 degrees, thus requiring 53*60/.3 = 10600 x 35*60/.3 = 7000 pixels, for a total of ~74 megapixels to show detail at the limits of human visual acuity.

The 10600 pixels over 20 inches corresponds to 530 pixels per inch, which would indeed appear very sharp. Note in a recent printer test I showed a 600 ppi print had more detail than a 300 ppi print on an HP1220C printer (1200x2400 print dots). I've conducted some blind tests where a viewer had to sort 4 photos (150, 300, 600 and 600 ppi prints). The two 600 ppi were printed at 1200x1200 and 1200x2400 dpi. So far all have gotten the correct order of highest to lowest ppi (includes people up to age 50). See: http://www.clarkvision.com/articles/printer-ppi

## How many megapixels equivalent does the eye have?

The eye is not a single frame snapshot camera. It is more like a video stream. The eye moves rapidly in small angular amounts and continually updates the image in one's brain to "paint" the detail. We also have two eyes, and our brains combine the signals to increase the resolution further. We also typically move our eyes around the scene to gather more information. Because of these factors, the eye plus brain assembles a higher resolution image than possible with the number of photoreceptors in the retina. So the megapixel equivalent numbers below refer to the spatial detail in an image that would be required to show what the human eye could see when you view a scene.

Based on the above data for the resolution of the human eye, let's try a "small" example first. Consider a view in front of you that is 90 degrees by 90 degrees, like looking through an open window at a scene. The number of pixels would be 90 degrees * 60 arc-minutes/degree * 1/0.3 * 90 * 60 * 1/0.3 = 324,000,000 pixels (324 megapixels).

At any one moment, you actually do not perceive that many pixels, but your eye moves around the scene to see all the detail you want. But the human eye really sees a larger field of view, close to 180 degrees. Let's be conservative and use 120 degrees for the field of view. Then we would see 120 * 120 * 60 * 60 / (0.3 * 0.3) = 576 megapixels.

The full angle of human vision would require even more megapixels. This kind of image detail requires A large format camera to record.

## The Sensitivity of the Human Eye (ISO Equivalent)

At low light levels, the human eye integrates up to about 15 seconds (Blackwell, J. Opt. Society America, v 36, p624-643, 1946). The ISO changes with light level by increasing rhodopsin in the retina. This process takes a half hour our so to complete, and that assumes you haven't been exposed to bright sunlight during the day. Assuming you wear sunglasses and dark adapt well, You can see pretty faint stars away from a city. Based on that a reasonable estimate of the dark adapted eye can be done.

In a test exposure I did with a Canon 10D and 5-inch aperture lens, the DSLR can record magnitude 14 stars in 12 seconds at ISO 400. You can see magnitude 14 stars in a few seconds with the same aperture lens. (Clark, R.N., Visual Astronomy of the Deep Sky, Cambridge U. Press and Sky Publishing, 355 pages, Cambridge, 1990.)

So I would estimate the dark adapted eye to be about ISO 800.

Note that at ISO 800 on a 10D, the gain is 2.7 electrons/pixel (reference: http://clarkvision.com/articles/digital.signal.to.noise) which would be similar to the eye being able to see a couple of photons for a detection.

During the day, the eye is much less sensitive, over 600 times less (Middleton, Vision Through the Atmosphere, U. Toronto Press, Toronto, 1958), which would put the ISO equivalent at about 1.

## The Dynamic Range of the Eye

The Human eye is able to function in bright sunlight and view faint starlight, a range of more than 100 million to one. The Blackwell (1946) data covered a brightness range of 10 million and did not include intensities brighter than about the full Moon. The full range of adaptability is on the order of a billion to 1. But this is like saying a camera can function over a similar range by adjusting the ISO gain, aperture and exposure time.

In any one view, the eye eye can see over a 10,000 range in contrast detection, but it depends on the scene brightness, with the range decreasing with lower contrast targets. The eye is a contrast detector, not an absolute detector like the sensor in a digital camera, thus the distinction. (See Figure 2.6 in Clark, 1990; Blackwell, 1946, and references therein). The range of the human eye is greater than any film or consumer digital camera.

Here is a simple experiment you can do. Go out with a star chart on a clear night with a full moon. Wait a few minutes for your eyes to adjust. Now find the faintest stars you can detect when the you can see the full moon in your field of view. Try and limit the moon and stars to within about 45 degrees of straight up (the zenith). If you have clear skies away from city lights, you will probably be able to see magnitude 3 stars. The full moon has a stellar magnitude of -12.5. If you can see magnitude 2.5 stars, the magnitude range you are seeing is 15. Every 5 magnitudes is a factor of 100, so 15 is 100 * 100 * 100 = 1,000,000. Thus, the dynamic range in this relatively low light condition is about 1 million to one, (20 stops) perhaps higher!

Another test is to use a telescope to see the brightest star in the nighttime sky, Sirius A and is close companion, Sirius B. The distance from Sirius A to Sirius B varies in its orbit but varies from about 3 to 12 arc-seconds, so is always close, even in large telescopes. Yet with good (low flare) optics and a clear atmosphere, both can be seen. Sirius A has a brightness of -1.47 stellar magnitudes and Sirius B 8.44 magnitudes, for a brightness range of 10.28 magnitudes or a brightness range of 12,900, or 13.7 stops. Detecting faint stars near a bright star may be limited by lens/telescope flare. But at larger distances than Sirius A and B, fainter stars can be detected in the same view as bright stars, thus the dynamic range is more than 13.7 stops. Use a star chart (like stellarium) and a telescope and see what faint stars you can see around Sirius.

My own testing I conducted an experiment where a bright cloud was seen outside a window, and details in a dark room were measured using a light meter and were found to be 14 stops fainter. Multiple people could see detail both in the cloud and in the dark room in the same view.

## The Focal Length of the Eye

What is the focal length of the eye? I did a google search and found many "answers" ranging from 17mm to 50mm (50 is totally absurd). For the correct answer, is Reference: Light, Color and Vision, Hunt et al., Chapman and Hall, Ltd, London, 1968, page 49 for "standard European adult":

Object focal length of the eye = 16.7 mm
Image focal length of the eye = 22.3 mm

The object focal length is for rays coming OUT OF THE EYE. But for an image on the retina, the image focal length is what one wants. E.g. see: l11.pdf.

So this explains the commonly cited ~17mm focal length, but the correct value is ~22 mm focal length.

This then makes more sense for the f/ratio: with an aperture of 7 mm, the f/ratio = 22.3/7 = 3.2.

Of course these values vary, with cited values from 22 to 24 mm, same with the aperture. The maximum aperture also decreases with age.

The f/stop maximum in the astronomical community is spec'd at f/3.5 for a dark adapted human eye. With a maximum aperture of 7mm, this implies about a 25mm focal length. Astronomical telescope minimum magnification is commonly cited as an f/3.5 light cone, meaning if you look through a faster system, the eye's f/3.5 optics can't gather all the light.