A simple VR headset

Figure 4.30: In VR headsets, the lens is placed so that the screen appears to be infinitely far away.

Now suppose we are constructing a VR headset by placing a screen very close to the eyes. Young adults would already be unable to bring it into focus it if were closer than 10cm. We want to bring it close so that it fills the view of the user. Therefore, the optical power is increased by using a convex lens, functioning in the same way as reading glasses. See Figure 4.30. This is also the process of magnification, from Section 4.2. The lens is usually placed at the distance of its focal depth. Using (4.6), this implies that $ s_2 = -f$, resulting in $ s_1 = \infty$. The screen appears as an enormous virtual image that is infinitely far away. Note, however, that a real image is nevertheless projected onto the retina. We do not perceive the world around us unless real images are formed on our retinas.

To account for people with vision problems, a focusing knob may be appear on the headset, which varies the distance between the lens and the screen. This adjusts the optical power so that the rays between the lens and the cornea are no longer parallel. They can be made to converge, which helps people with hyperopia. Alternatively, they can be made to diverge, which helps people with myopia. Thus, they can focus sharply on the screen without placing their eyeglasses in front of the lens. However, if each eye requires a different diopter, then a focusing knob would be required for each eye. Furthermore, if they have astigmatism, then it cannot be corrected. Placing eyeglasses inside of the headset may be the only remaining solution, but it may be uncomfortable and could reduce the field of view.

Many details have been skipped or dramatically simplified in this section. One important detail for a VR headset is each lens should be centered perfectly in front of the cornea. If the distance between the two lenses is permanently fixed, then this is impossible to achieve for everyone who uses the headset. The interpupillary distance, or IPD, is the distance between human eye centers. The average among humans is around $ 64$mm, but it varies greatly by race, gender, and age (in the case of children). To be able to center the lenses for everyone, the distance between lens centers should be adjustable from around $ 55$ to $ 75$mm. This is a common range for binoculars. Unfortunately, the situation is not even this simple because our eyes also rotate within their sockets, which changes the position and orientation of the cornea with respect to the lens. This amplifies optical aberration problems that were covered in Section 4.3. Eye movements will be covered in Section 5.3. Another important detail is the fidelity of our vision: What pixel density is needed for the screen that is placed in front of our eyes so that we do not notice the pixels? A similar question is how many dots-per-inch (DPI) are needed on a printed piece of paper so that we do not see the dots, even when viewed under a magnifying glass? We return to this question in Section 5.1.

Steven M LaValle 2020-01-06