Definition of View Angle of Human Eye ?

[genxium]

Definition of "View Angle of Human Eye"?

I've been told (since high school I think) that "view angle" in a 2-dimensional plane is approximately (distance to the object/object's length).

The assumption is that I'm viewing an object $AB$ of length $L$, basically a segment in a 2-dimensional plane; $AB$ stands at a distance $d_v$ away from my eyes, like shown in the figure below. To make everything simple, $AB$ is perpendicular to the horizon and my eye is looking straight along the horizon.

Is the view angle for my eyes $\frac{d_v}{L}$ ?

The problems which are confusing me are:

1. If I put a convex lens between $AB$ and my eyes, how would it change my eyes' view angle of the object?

2. Based on problem 1, if my eyes is replaced by a silver-halide grained film, like an old camera, what is the definition of view angle now? Would it be related to the size of the film and size of the silver-halide grains (To my understanding this affects how clear a photo is captured)?

3. Back to discussion of human eyes (no external lens or film),is view angle affected by the focal length of my lens(in the eyes)?

Any help will be appreciated :)

 

[Andy Resnick]

The field of view of a single human eyeball is approximately 160 degrees; the field of view is truncated by your nose and also depends on the size of your retina. The field of view of the fovea is only a few degrees; saccadic and tracking movements create a larger field of view.

Putting an auxilliary lens in front of your eye will indeed change the field of view- for example, look through binoculars.

Replacing the retina with film or a CCD is (conceptually!) straightforward, what matters is the area of the detector. The standard is a 50mm focal length lens and a 35mm format image- the field of view is the same as an unaided eye. The ratio of the detector size compared to 35mm format (and similarly, the ratio of lens focal length compared to 50mm) is how much the field of view changes. Cameras with tiny sensors (cell phones) use lenses with tiny focal lengths; medium and large-format view cameras use lenses with large focal lengths.

None of this has to do with how 'clear' the image is- that's an entirely different issue.

The focal length of your lens does change, depending on the object distance. This is to ensure the image is properly focused onto the retina- myopic and hypermetropic eyes put the image at the wrong location. I'm not sure of the field of view is altered in any substantive way, given the existence of saccadic movements.

Does this help?

 

[Drakkith]

1. View angle decreases because you have increased the magnification of the optical system. Adding the convex lens causes the optical system to have a greater focal length, which corresponds to an increase in magnification.

2. Since neither your retina nor a camera's film/sensor is part of the optical system that focuses the light, the view angle will remain unchanged. The size of the film/sensor determines how much of the maximum view angle can actually be seen, while the size of the film grains, or the pixels, determines the resolution of the image. Small grains and pixels mean a greater resolution, at least until you reach the point that diffraction limits any further increase in resolution.

3. I'm not sure. Since the focal length of the lens is changing you would think so, but in practice I didn't see a difference in field of view when focusing on objects near by versus far away. Perhaps it has something to do with the focal point always being the same distance from the beginning of the optical system of the eye? (The cornea)

 

[genxium]

Thank you so much for the quick replies!

@Andy Resnick, I'd say I don't understand the numbers quite well :(

"The ratio of the detector size compared to 35mm format (and similarly, the ratio of lens focal length compared to 50mm) is how much the field of view changes." -- do you mean that for naked human eye, the focal length of ineye-lens and the size of retina both contribute to the eye's view angle?

"the field of view of a single human eyeball is approximately 160 degrees" -- In fact I want to ask how this "160 degrees" is calculated and by what parameters people determine this view angle. In other words, there should be a formula like

$160^o = f(length_1, length_2, length_3,...,constant \, number \; 1, constant \, number \;2,...)$

where $length_i$ may be distance, aperture size, film or retina size and $constant \, number \; j$ may be refractive indexes. I have no idea what the function $f()$ is or even what the parameter list should contain.

@Drakkith, I think I made a stupid mistake on my problem 2, for that an eye contains iris+lens+retina thus it's not comparable to a single film. I do agree on your answers to problems 1 & 3 however I'm still confused by some basic concepts mentioned above.

 

[Andy Resnick]

<snip>

"The ratio of the detector size compared to 35mm format (and similarly, the ratio of lens focal length compared to 50mm) is how much the field of view changes." -- do you mean that for naked human eye, the focal length of ineye-lens and the size of retina both contribute to the eye's view angle?

"the field of view of a single human eyeball is approximately 160 degrees" -- In fact I want to ask how this "160 degrees" is calculated and by what parameters people determine this view angle. In other words, there should be a formula like

$160^o = f(length_1, length_2, length_3,...,constant \, number \; 1, constant \, number \;2,...)$

where $length_i$ may be distance, aperture size, film or retina size and $constant \, number \; j$ may be refractive indexes. I have no idea what the function $f()$ is or even what the parameter list should contain.

<snip>

The field of view of any imaging system does indeed depend both on the focal length and the detector size. There are a lot of online calculators you can play around with, for example:

http://www.scotthusseyphotography.com/calculator.html

The field of view is easily measured- you can do this yourself, with your own eyes. The field of view for human vision is rarely calculated due to inherent variations in human anatomy and the presence of eye movements.

 

[genxium]

Thank you so much @Andy Resnick! The link you provided is extremely helpful :)

My problem is solved now ^_^

 

[Andy Resnick]

Final note- I wanted to post this relevant link:

http://imgs.xkcd.com/comics/visual_field.png