Optical Parameters of VR

I come across a very good article today on Sensics blog, which explains clearly and intuitively on some important terms about optical parameters of VR goggles. It’s so helpful that I decide to save a copy here, adding some words and high definition graphs (most copied from vr-lens-lab.com), in case someone who need it same as me can find it easier.

Field of View: typically measured in degrees, the field of view defines what is the horizontal, vertical and diagonal extent that can be viewed at any given point. This is often specified as a monocular (single eye) field of view, but it is also customary to specify the binocular field of view and thus the binocular overlap.

Monocular FOV describes the field of view for one of our eyes. For a healthy eye, the horizontal monocular FOV is between 170°-175° and consists of the angle from the pupil towards the nose, the nasal FOV which is usually 60°-65° and is smaller for people with bigger noses, and the view from our pupil toward the side of our head, the temporal FOV, which is wider, usually 100°-110°.

Binocular FOV is the combination of the two monocular fields of view in most humans. When combined they provide humans with a viewable area of 200°-220°. Where the two monocular fields of view overlap there is the stereoscopic binocular field of view, about 114°, where we are able to perceive things in 3D.

Wider FOV means better immersion.

FOV is related to another parameter Focal Length, by the formula: field of view = 2 atan ( dimension  / 2 focal length ).

I don’t quite understand the formula, math is always my nightmare. However, I figure out a simple rule is the longer focal length, the smaller FOV. Most Chinese VR headsets use 42mm lens, the focal length is 68mm, so we can get the FOV is 34.4° only! That why the field of view is very narrow, and we can see obvious black curtain around view. Google Cardboard 2015 and Daydream View offer FOV of 80°, Oculus and HTC 110°, Samsung Gear VR II 101°.

Eye relief: typically measured in millimeters, the eye relief indicates the distance between the eye and the closest optical element as seen in the illustration below.

Regular eyeglasses have an eye relief of about 12mm.

Advantages of larger eye relief:

• If the optics are too close to the eye, they generate discomfort such as when the eyelashes touch the optics.
• If the eye relief is large enough, the system might be able to accommodate people wearing glasses without the need to provide a focusing mechanism to compensate for not having glasses

Disadvantages of larger eye relief:

• The total depth of the optical system (distance from eye to screen) becomes larger and the overall system potentially more cumbersome.
• The minimal diameter first optical element is dictated by a combination of the desired field of view and eye relief. Keeping same FOB, larger eye relief requires the lens with a larger diameter, but this comes with its own set of challenges. Larger lenses need to be thicker in the middle which makes them heavier. This problem can be overcome by using Fresnel lenses but the second problem that remains regardless what kind of lens is used is that larger lenses introduce more optical aberrations.

Eye box (Pupil diameter): often specified in millimeters, the eye box determines how much the eye can move up/down/left/right from the optimal position without significant degradation in the image quality. Some optical systems such as rifle scopes have very narrow eye box because they want to ‘force’ the eye to be in the optimal position. Other optical systems, such as HMDs used in soldier training, might desire larger eye boxes to allow the trainee to see a good image even as the HMD moves on the head while the trainee is running. The image quality at the optimal position is most always best, but if the eye box is too narrow, the user will not obtain a good image without tedious adjustments.

For instance, the diagram below shows the simulation results of an optical design at the nominal eye position (left) and at 4 mm away from the optimal position:

Distortion: optical distortion is one type of imperfection in an optical design. Distortion causes straight lines not being seen as straight lines when viewed through the optics. These distortions can usually be classified as either barrel distortions or pincushion distortions:

	Barrel distortion In barrel distortion, image magnification decreases with distance from the optical axis. The apparent effect is that of an image which has been mapped around a sphere (or barrel). Fisheye lenses, which take hemispherical views, utilize this type of distortion as a way to map an infinitely wide object plane into a finite image area. In a zoom lens barrel distortion appears in the middle of the lens’s focal length range and is worst at the wide-angle end of the range.[2]
	Pincushion distortion In pincushion distortion, image magnification increases with the distance from the optical axis. The visible effect is that lines that do not go through the centre of the image are bowed inwards, towards the centre of the image, like a pincushion.
	Mustache distortion A mixture of both types, sometimes referred to as mustache distortion (moustache distortion) or complex distortion, is less common but not rare. It starts out as barrel distortion close to the image center and gradually turns into pincushion distortion towards the image periphery, making horizontal lines in the top half of the frame look like a handlebar mustache.

Source: Wikipidia

Distortion is reported in percentage units. If a pixel is placed at a distance of 100 pixels (or mm or degrees or inches or whichever unit you prefer) and appears as if it at a distance of 110, the distortion at that particular point is (110-100)/100 = 10%.

During the process of optical design, distortion graphs are commonly viewed during the iterations of the design. For instance, consider the distortion graph below:

Distortion graph. Source: SPIE

In a perfect lens, the “x” marks should reside right on the intersection of the grid lines. In this particular lens, that is quite far from being the case.

Chromatic aberration: Just like white light breaks into various colors when passing through a prism, an optical system might behave differently for different wavelengths/colors. This could cause color breakup. It is useful to explore how much the system is ‘color corrected’ so as to minimize this color breakup. The image below shows a nice picture at the center of the optical system but fairly significant color breakup at the edges.

Ok, it comes to an end. I may supplement more later, if I find it necessary. Contact me at gary@adcardboard.com.