# Quantitative Comparison of VR Headset Fields of View

Although I’ve taken many through-the-lens pictures of several common VR headsets with a calibrated wide-angle camera, until recently I was still struggling how to compare the resulting fields of view (FoV) quantitatively, how to put them in context, and how to visualize them appropriately. When trying to answer questions like “which VR headset has a bigger FoV?” or “by how much is headset A’s FoV bigger than headset B’s?” or “how does headset C’s FoV compare to the field of vision of the naked human eye?”, the basic question is: how does one even measure field of view, in a way that is fair and allows comparison across a wide range of possible sizes. Does one report a single angle, and how does one measure it? Across the “diagonal” of the field of view? What if the field of view is not a rectangle? Does one report a pair of angles, say horizontal⨉vertical? Again, what if the field of view is not a rectangle?

Then, if FoV is measured either as a single angle or a pair of angles, how does one compare different FoVs fairly? If one headset has 100° FoV, and another has 110°, does the latter show 10% more of a virtual 3D environment? What if one has 100°⨉100° and another has 110°⨉110°, does the latter show 21% more?

To find a reasonable answer, let’s go back to the basics: what does FoV actually measure? The general idea is that FoV measures how much of a virtual 3D environment a user can see at any given instant, meaning, without moving their head. A larger FoV value should mean that a user can see more, and, ideally, an FoV value that is twice as large should mean that a user can see twice as much.

Now, what does it mean that “something can be seen?” We can see something if light from that something reaches our eye, enters the eye through the cornea, pupil, and lens, and finally hits the retina. In principle, light travels towards our eyes from all possible directions, but only some of those directions end up on the retina due to various obstructions (we can’t see behind our heads, for example). So a reasonable measure of field of view (for one eye) would be the total number of different 3D directions from which light reaches that eye’s retina. The problem is that there is an infinite number of different directions from which light can arrive, so simple counting does not work.

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# Field of View and Resolution of the PlayStation VR Headset

It has been a very long time since I did the original optical measurement of then-current VR headsets. I have owned a PlayStation VR headset (PSVR from now on) for almost a year now, and I finally got around to measuring its optical properties in the same way. I also developed a new camera calibration algorithm (that’s a topic for another post), meaning I am even more confident in my measurements now than I was then.

One approach to measuring the optical properties of a VR headset, which includes measuring its field of view, its resolution in pixels/°, and its lens distortion correction profile, is to take a series of pictures of the headset’s screen(s) through its lenses using a calibrated wide-angle camera. In this context, a calibrated camera is one where each image pixel’s horizontal and vertical angles away from the optical axis are precisely known.

If one then displays a test pattern that lets one identify a particular pixel on the screen, one can measure the viewer-relative angular position of that pixel in the camera image, which is all the information needed to generate the projection matrices and lens distortion correction formulas that are essential to high-quality VR rendering.

Without further ado, here is a series of 7 images taken with the camera lens at increasing distances from the headset’s right lens (Figures 1-7, and yes, I forgot to clean my PSVR’s lens). The camera was carefully positioned and aligned such that it was sliding back along the lens’s optical axis, and looking straight ahead. The first image was captured with an eye relief value of 0mm, meaning that the camera lens was touching the headset’s lens. The rest of the images were captured with increasing eye relief values, or lens-lens distances, of 5mm, 10mm, 15mm, 20mm, 25mm, and 30mm: Continue reading

# The Display Resolution of Head-mounted Displays, Revisited

I wrote an article earlier this year in which I looked closely at the physical display resolution of VR headsets, measured in pixels/degree, and how that resolution changes across the field of view of a headset due to non-linear effects from tangent-space rendering and lens distortion. Unfortunately, back then I only did the analysis for the HTC Vive. In the meantime I got access to an Oculus Rift, and was able to extract the necessary raw data from it — after spending some significant effort, more on that later.

With these new results, it is time for a follow-up post where I re-create the HTC Vive graphs from the previous article with a new method that makes them easier to read, and where I compare display properties between the two main PC-based headsets. Without further ado, here are the goods.

# HTC Vive

The first two figures, 1 and 2, show display resolution in pixels/°, on one horizontal and one vertical cross-section through the lens center of my Vive’s right display.

Figure 1: Display resolution in pixels/° along a horizontal line through the right display’s lens center of an HTC Vive.

Figure 2: Display resolution in pixels/° along a vertical line through the right display’s lens center of an HTC Vive.

# Projection and Distortion in Wide-FoV HMDs

There is an on-going, but already highly successful, Kickstarter campaign for a new VR head-mounted display with a wide (200°) field of view (FoV): Pimax 8k. As I have not personally tried this headset — only its little brother, Pimax 4k, at the 2017 SVVR Expo — I cannot discuss and evaluate all the campaign’s promises. Instead, I want to focus on one particular issue that’s causing a bit of confusion and controversy at the moment.

Early reviewers of Pimax 8k prototypes noticed geometric distortion, such as virtual objects not appearing in the correct places and shifting under head movement, and the campaign responded by claiming that these distortions “could be fixed by improved software or algorithms” (paraphrased). The ensuing speculation about the causes of, and potential fixes for, this distortion has mostly been based on wrong assumptions and misunderstandings of how geometric projection for wide-FoV VR headsets is supposed to work. Adding fuel to the fire, the campaign released a frame showing “what is actually rendered to the screen” (see Figure 1), causing further confusion. The problem is that the frame looks obviously distorted, but that this obvious distortion is not what the reviewers were complaining about. On the contrary, this is what a frame rendered to a high-FoV VR headset should look like. At least, if one ignores lenses and lens distortion, which is what I will continue to do for now.

Figure 1: Frame as rendered to one of the Pimax 8k’s screens, according to the Kickstarter campaign. (Probably not 100% true, as this appears to be a frame submitted to SteamVR’s compositor, which subsequently applies lens distortion correction.)

# Optical Properties of Current VR HMDs

With the first commercial version of the Oculus Rift (Rift CV1) now trickling out of warehouses, and Rift DK2, HTC Vive DK1, and Vive Pre already being in developers’ hands, it’s time for a more detailed comparison between these head-mounted displays (HMDs). In this article, I will look at these HMDs’ lenses and optics in the most objective way I can, using a calibrated fish-eye camera (see Figures 1, 2, and 3).

Figure 1: Picture from a fisheye camera, showing a checkerboard calibration target displayed on a 30″ LCD monitor.

Figure 2: Same picture as Figure 1, after rectification. The purple lines were drawn into the picture by hand to show the picture’s linearity after rectification.

Figure 3: Rectified picture from Figure 2, re-projected into stereographic projection to simplify measuring angles. Concentric purple circles indicate 5-degree increments away from the projection center point.

# HoloLens and Field of View in Augmented Reality

Since Microsoft’s Build 2015 conference, and increasingly since Microsoft’s showing at E3, everybody (including me) has been talking about HoloLens, and its limited field of view (FoV) has been a contentious topic. The main points being argued (fought) about are:

1. What exactly is the HoloLens’ FoV?
2. Why is it as big (or small) as it is, and will it improve for the released product?
3. How does the size of the FoV affect the HoloLens’ usability and effectiveness?
4. Were Microsoft’s released videos and live footage of stage demos misleading?
5. How can one visualize the HoloLens’ FoV in order to give people who have not tried it an idea what it’s like?

# Measuring Field of View

Initially, there was little agreement among those who experienced HoloLens regarding its field of view. That’s probably due to two reasons: one, it’s actually quite difficult to measure the FoV of a headmounted display; and two, nobody was allowed to bring any tools or devices into the demonstration rooms. In principle, to measure see-through FoV, one has to hold some object, say a ruler, at a known distance from one’s eyes, and then mark down where the apparent left and right edges of the display area fall on the object. Knowing the distance X between the left/right markers and the distance Y between the eyes and the object, FoV is calculated via simple trigonometry: FoV = 2×tan-1(X / (Y×2)) (see Figure 1).

Figure 1: Calculating field of view by measuring the horizontal extent of the apparent screen area at a known distance from the eyes. (In this diagram, FoV is 2×tan-1(6″ / (6″×2)) = 53.13°.)

# On the road for VR: Silicon Valley Virtual Reality Conference & Expo

Yesterday, I attended the second annual Silicon Valley Virtual Reality Conference & Expo in San Jose’s convention center. This year’s event was more than three times bigger than last year’s, with around 1,400 attendees and a large number of exhibitors.

Unfortunately, I did not have as much time as I would have liked to visit and try all the exhibits. There was a printing problem at the registration desk in the morning, and as a result the keynote and first panel were pushed back by 45 minutes, overlapping the expo time; additionally, I had to spend some time preparing for and participating in my own panel on “VR Input” from 3pm-4pm.

The panel was great: we had Richard Marks from Sony (Playstation Move, Project Morpheus), Danny Woodall from Sixense (STEM), Yasser Malaika from Valve (HTC Vive, Lighthouse), Tristan Dai from Noitom (Perception Neuron), and Jason Jerald as moderator. There was lively discussion of questions posed by Jason and the audience. Here’s a recording of the entire panel:

One correction: when I said I had been following Tactical Haptics‘ progress for 2.5 years, I meant to say 1.5 years, since the first SVVR meet-up I attended. Brainfart. Continue reading

# On the road for VR: Microsoft HoloLens at Build 2015, San Francisco

I have briefly mentioned HoloLens, Microsoft’s upcoming see-through Augmented Reality headset, in a previous post, but today I got the chance to try it for myself at Microsoft’s “Build 2015” developers’ conference. Before we get into the nitty-gritty, a disclosure: Microsoft invited me to attend Build 2015, meaning they waived my registration fee, and they gave me, like all other attendees, a free HP Spectre x360 notebook (from which I’m typing right now because my vintage 2008 MacBook Pro finally kicked the bucket). On the downside, I had to take Amtrak and Bart to downtown San Francisco twice, because I wasn’t able to get a one-on-one demo slot on the first day, and got today’s 10am slot after some finagling and calling in of favors. I guess that makes us even. 😛

So, on to the big question: is HoloLens real? Given Microsoft’s track record with product announcements (see 2009’s Project Natal trailer and especially the infamous Milo “demo”), there was some well-deserved skepticism regarding the HoloLens teaser released in January, and even the on-stage demo that was part of the Build 2015 keynote:

The short answer is: yes, it’s real, but… Continue reading

# On the road for VR: Oculus Connect, Hollywood

After some initial uncertainty, and accidentally raising a stink on reddit, I did manage to attend Oculus Connect last weekend after all. I guess this is what a birthday bash looks like when the feted is backed by Facebook and gets to invite 1200 of his closest friends… and yours truly! It was nice to run into old acquaintances, meet new VR geeks, and it is still an extremely weird feeling to be approached by people who introduce themselves as “fans.” There were talks and panels, but I skipped most of those to take in demos and mingle instead; after all, I can watch a talk on YouTube from home just fine. Oh, and there was also new mobile VR hardware to check out, and a big surprise. Let’s talk VR hardware. Continue reading

# An Eye-tracked Oculus Rift

I have talked many times about the importance of eye tracking for head-mounted displays, but so far, eye tracking has been limited to the very high end of the HMD spectrum. Not anymore. SensoMotoric Instruments, a company with around 20 years of experience in vision-based eye tracking hardware and software, unveiled a prototype integrating the camera-based eye tracker from their existing eye tracking glasses with an off-the-shelf Oculus Rift DK1 HMD (see Figure 1). Fortunately for me, SMI were showing their eye-tracked Rift at the 2014 Augmented World Expo, and offered to bring it up to my lab to let me have a look at it.

Figure 1: SMI’s after-market modified Oculus Rift with one 3D eye tracking camera per eye. The current tracking cameras need square cut-outs at the bottom edge of each lens to provide an unobstructed view of the user’s eyes; future versions will not require such extensive modifications.