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The Human Eye

Intro

The human eye is an amazing thing. For decades now, we’ve been trying to emulate the human eye with camera technology, but we’re nowhere close to being even nearly as good. I recently received a Quora request to write about what the specifications of the human eye would be as a camera. Unfortunately, no one really read it, but I learned so much while researching that I thought I should share it here. I had to remove a lot of the actual math from my Quora answer, but I am going to put it here as a form of documentation.

Parameters

So, what are the important parameters to consider here?

  • Resolution: How much detail can the human eye perceive?

  • Focal Length: What is the focal length of the human eye, and how does it change?

  • Shutter Speed: How fast can the human eye perceive things?

  • Aperture: What is the range of f/stop values that the eye can achieve?

  • Dynamic Range: How much difference in light can the human eye see?

Resolution

imiIn order to figure out resolution, we must first talk about visual acuity. Visual acuity is the spatial resolution of the visual processing system, and measures the clarity of vision. This clarity of vision determines the human eye's ability to percieve details, a factor that should be taken into consideration when talking about resolution.

The first way we can talk about resolution is by simply adding the number of data points within the human eye. The human eye has two types of photoreceptors; rods and cones. Rods mostly deal with low light vision, and lack colour sensitivity. The cones are less sensitive to light than the rods, but they are able to detect colour. There are about 120 million rods in the average person's eye, and approximately 6-7 million cones. The colour information of the cones is combined with the light information from the rods. This is similar to the way that older black and white photographs would be taken with coloured filters, then projected with those same filters to make a full colour image. By adding the number of rods and cones together, we get a value of about 126-127 million data points in the eye. This would be equivalent to about 126.5 million pixels, or 126.5 megapixels.

However, this doesn't take into account visual acuity. Let's look at a worst case scenario; in 0.34 lux (an amount of light approximately equal to the light put out by the full moon on a clear night) the human eye has a visual acuity of 1.7. For reference, a visual acuity of 0.1 on the decimal scale would qualify as being legally blind, and a visual acuity of 1.6 would represent the limit of a normal range of vision right before ranging into the realm of visual impairment.

A visual acuity of 1.7 when taking a Snellen test (the test when you go to the eye doctor) represents a value of 0.59 arc-minutes per line. Two pixels per line pair are needed to see any object that isn't a point, so this returns a value of 0.259 arc-minutes per pixel. The number of pixels/data points that the human eye is able to see is calculated by taking this value, then figuring out the arc-minutes per degree. The number of degrees the human eye can see is respresented by our Field Of View (FOV), which is about 120 by 120 degrees.

This allows us to calculate the resolution from the following equation: Horizontal FOV x Vertical FOV x (arc-minutes/(arcminutes/line)) 2 . When the relevant values are substitued into the equation, it gives us 120 x 120 x (60/0.3) 2 .

The final output of the equation is 576,000,000 data points, which is approximately equal to 576 megapixels. However, we have to account for loss of FOV from hair, nose, overlap, eyelashes, etc. It's safe to say that the average person's eyes will have a resolution of about 360 megapixels. This value isn't exactly representative of the resolution of the human eye, since we rarely utilize all of the data points simultaneuously to give that incredible resolution.

Just how incredible is that resolution? Well, watch this video:

This video shows an initial image with a resolution of 560 megapixels, and zooms in on a 12 megapixel crop of this image. This would be the same as being able to utilize the full resolution of the eye to detect the minor details in any image.

Focal Length

This may not be the first thing you think about when you hear about the eye, but it is very important. This impacts the aperture of our eyes, and is one of the most hotly debated topics when considering how the human eye compares to a camera. It’s a commonly stated fun fact that the human eye is similar in focal length to a 50mm lens. However, that is quite untrue. The field of view of the human eye, including peripheral vision, is about 120 degrees. This would make it equivalent to about a 10mm lens on a full frame camera. However, this is different from the actual image focal length of the eye.

The image focal length of the eye is the distance from the back of the lens inside the eye to the retina. Now, the image focal length is what we need to consider here, rather than the object focal length, because the focal length of a camera lens only measures image focal length. This distance is measured using this equation:

so represents the distance from the eye to the object. si represents the distance from the back of the lens to the retina when the lens is pulled taught (approximately 24mm). n i represents the refractive index of the liquid inside the eye (approximately 1.33). fi represents the image focal length of the eye.

At infinity focus, the equation simplifies out to fi = si. When focusing at infinity focus, the lens is pulled taught because it doesn't need to distort the light rays to cause them to converge. As such, the focal length is equal to 24mm.

At close focus, the focal length differs on a person by person basis. Adults can only focus at about 25cm away from their eyes. By substituting the values into the equation (so = 250, ni = 1.33, and si = 24), we get the final result of fi = 22.4mm - However, this result is only for adults. Children's eyes can focus as close as 6.5 centimetres. When we work out the equation, this time substituting 65 for so, we get the final result of fi = 18.8mm.

To summarise, the focal length of the average adult’s eyes is about 22-24mm. The focal length of children’s eyes can be as large as 19-24mm. The field of view is approximately 120 degrees by 120 degrees including peripheral vision, which makes the human eye similar to a 10mm lens on a full frame camera body.

Aperture

Aperture is the opening inside the camera lens that allows in the light. The direct equivalent to this in the human eye would be our pupils. A wider aperture results in a brighter picture and the opposite is true for a narrow aperture, just like the dilation and constriction of our pupils. Aperture is ususally measured in 'f-stops', which help us figure out the aperture range of the human eye. F stops are measured by dividing the lens' focal length by a number, for example - f/1, f/1.4, f/2, f/2.8, etc. Since the diameter of the entrance pupil differs on a lens by lens basis, aperture is denoted by the divisor of the focal length. The equation to measure the aperture is:

N represents the aperture setting, L represents the focal length of the lens, and D represents the diameter of the opening that allows light into the lens.

According to a study carried out by the National Center for Biotechnology Information (a part of the US National Library of Medicine), adult's pupil size ranges from 2-4 mm when constricted, to 4-8mm when dilated. This gives us theoretical minimum and maximum widths of 2mm and 8mm respectively.

When these are substituted into the equation, the resultant f/stop range is f/2.75 to f/12. However, when children's ability to focus on close objects is taken into account, we can achieve a maximum aperture of f/2.35.

One important thing to note is that f/stop isn't directly proportional to the t/stop value. The light transmittence is rarely less than the f/stop, but is usually quite similar. This was just to establish details of the human eye in terms we can all understand.

Shutter Speed

The optic nerve in the eye is made up of axons which then turn into a bundle of nerves that form the optic nerve, which is then myelinated. Unmyelinated nerves fire anywhere from 0.5m/s to 15m/s. However, since the optic nerve is myelinated, it can theoretically travel at speeds of up to 150m/s. Additionally, the nerves in the eye are shown to be able to fire up to 300-1000 times per second. However, that is purely theoretical.

In practice, people are not able to perceive differences from one 1000th of a second and the next. People can typically see changes from one 1/150th of a second and the next. However, people can perceive an image that only exists for 1/220th of a second. The issue here is not the eye’s ability to see the images, but the ability to see any changes in between them. It’s similar to using a 1/1000th shutter speed while filming a video at a lower frame rate- The camera can have a much higher shutter speed, but the gaps in between each exposure aren’t filled with any data.

As such, people can really only comprehend images that exist for 1/220th of a second or longer. However, this varies on a person-by-person basis. It is also possible to train your perception- some E-sports gamers have trained their perception so that they can use 240Hz monitors to make sure they can see changes and react to them as fast as possible.

Dynamic Range

The dynamic range of the eye changes depending on scene (more on this later), which makes it hard to have any definitive value that represents it. However, it is somewhat easy for people to calculate the dynamic range of their own eye in a more practical sense.

Dynamic range is measured in stops, where each stop represents twice the amount of light of the previous stop, calculated like so: Light * 2 number of stops. A simple test of this can be looking at a bright object, then looking at a dark one. People often measure their dynamic range by looking at stars, because they vary wildly in stellar magnitude. You can compare the luminance of the faintest and brightest star you can see to find out the dynamic range.

Theorectically, the human eye is able to see a luminance range of 1014:1. When we put this value into the equation log2(100,000,000,000,000), the result is approximately 46.5 stops. This, therefore, is the theoretical dynamic range of the human eye. However, the human eye cannot percieve this data at all points in time.

The rods inside the eye have a dynamic range of about 20 stops. However, the rods are able to increase and decrease their sensitivity to light in order to view brighter or darker objects. The majority of this change can occur in as little as 4 seconds, but the full adaptation of the rods to the dark takes considerably longer (this is influenced by a myriad of factors including blood flow, retinal health, etc.).

However, the static dynamic range of the human eye is about 30 stops- this is the range that the human eye can see 100% of the time, and as such is the best way to measure the dynamic range of the human eye in a majority of circumstances.

Summary

This exercise was quite interesting, as it incorporates physics, biology, and photography into an exercise that’s easy to understand. The goal of many photographers is to make their photos look realistic, and document the scene as the eye would have scene it. However, the capability of the human eye is very different from that of any camera, so it is best to go for a more artistic choice.

Who knows? Maybe in a few decades we’ll be able to surpass the capabilities of the human eye with our own technology. Until then, we’ll be striving to achieve the same level of quality.

Ankit KumarComment