Tag Archives: Lens distortion

The Display Resolution of Head-mounted Displays, Revisited

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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.

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The Display Resolution of Head-mounted Displays

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What is the real, physical, display resolution of my VR headset?

I have written a long article about the optical properties of (then-)current head-mounted displays, one about projection and distortion in wide-FoV HMDs, and another one about measuring the effective resolution of head-mounted displays, but in neither one of those have I looked into the actual display resolution, in terms of hard pixels, of those headsets. So it’s about time.

The short answer is, of course, that it depends on your model of headset. But if you happen to have an HTC Vive, then have a look at the graphs in Figures 1 and 2 (the other headsets behave in the same way, but the actual numbers differ). Those figures show display resolution, in pixels/°, along two lines (horizontal and vertical, respectively) going through the center of the right lens of my own Vive. The red, green, and blue curves show resolution for the red, green, and blue primary colors, respectively, determined this time not by my own measurements, but by analyzing the display calibration data that is measured for each individual headset at the factory and then stored in its firmware.

Figure 1: Resolution in pixels/° along a horizontal line through my Vive’s right lens center, for each of its 1080 horizontal pixels, for the three primary colors (red, green, and blue).

Figure 2: Resolution in pixels/° along a vertical line through my Vive’s right lens center, for each of its 1200 vertical pixels, for the three primary colors (red, green, and blue).

At this point you might be wondering why those graphs look so strange, but for that you’ll have to read the long answer. Before going into that, I want to throw out a single number: at the exact center of my Vive’s right lens (at pixel 492, 602), the resolution for the green color channel is 11.42 pixels/°, in both the horizontal and vertical directions. If you wanted to quote a single resolution number for a headset, that’s the one I would go with, because it’s what you get when you look at something directly ahead and far away. However, as Figures 1 and 2 clearly show, no single number can tell the whole story.

And now for the long answer. Buckle in, Trigonometry and Calculus ahead. Continue reading →

Optical Properties of Current VR HMDs

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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 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 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.

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.

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