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First, when I say infinite focus, I am using the term from photography, perhaps incorrectly. Secondly, I believe am not talking about convergence, but about focus. If I am not mistaken, with stereoscopic displays, only the convergence is manipulated, but if the monitor is 4 feet away, your eyes remain focused at 4 feet.

With head mounted displays, the display is extremely close to your eyes. It is very difficult to focus on your hand if it is only a couple inches from your face, and makes your eyes hurt a great deal. Somehow head mounted displays overcome this. I've always thought it was just through the use of a projection off of a reflective surface, just to add a few more inches to the distance from the image source to your eyes. I.e. the bulky part above your forehead projecting forward, and then reflecting off of the mirrors in front of your eyes. So I believed that head mounted displays would still involve you focusing on something at a fixed distance, that simulated focusing on something 5" or so from your eyes.

Now I read about this HMD Oculus Rift, which claims that you are always focused on the "distance" which I assume is the same as infinity focus in photography. I wonder how they achieve this. I feel like I have a pretty good handle on how focusing works, and why something appears blurry when not in focus, i.e. when the light from some point that enters our pupil, but is not converging on a single point on our retina. It just boggles my mind though, how something so close to your face would simulate having to focus on the distance. I understand how it would be able to simulate this for convergence, but not for focus.

The real reason I find this interesting, is thinking about multifocal displays. I.e. something that can dynamically display some regions in different depths of field:

But baby steps: An HMD on the other hand is relatively simpler in that it deals with a single focal plane, and I'm really curious: How is an HMD able to make it appear that the focal plane is far in the distance?

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In the same way as a telescope eyepiece, they create a virtual image at infinity.

enter image description here

In the HUD the objective lens focus the image from a display (on the left in the diagram) and the lens at the front of the HUD reimages it at infinity.

In order to get a large aperture in a small thickness and with low weight they typically use fresnel or holographic lenses.

As you said, the big advantage of the HUD isn't that the user doesn't have to look down at their instrument panel - but that they don't have to wait for their eyes to refocus. It's even more important for military pilots using helmet mounted image intensifiers (night sights) which are focussed for viewing at infinity.

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I don't claim that this is how it's done, but this is one way in which it could be done.

Placing an object a distance $s$ away from a converging lens with focal length $F$ where $s<F$ produces a "virtual image" of that object on the same side of the lens as the original object at distance \begin{equation} D=\frac{s F}{F-s} \end{equation} with magnification \begin{equation} M=-\frac{D}{s} \end{equation} (where the '$-$' sign indicates that the image is upside-down). In this way, a very small display very close to the lens can be made to appear to be a much larger display much further from the lens. A second, diverging lens can be used to make the rays approximately parallel on their path to the eye, so that they appear to be coming from roughly infinity. If the tiny, real display is inverted (that is, upside-down and flipped left-to-right), then another lens is not needed to correct the image to be upright for the eye.

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