Flexible displays & the Rift

I keep seeing posts on the Oculus forums along the lines of this

I think the next major step in head mounted displays will be flexable OLED panels as displayed here: http://www.oled-info.com/lg-display-starts-6-flexible-oled-mass-production-products-expected-2014

no... no... NO...

Flexible display panels are a solution in desperate need of a problem. Maybe they'll be handy for making more durable electronics at some point, but certainly not until all the rest of your cellphone is also flexible. Even then, the screen is going to be extremely fragile and vulnerable to damage unless it's covered by a hard surface such as glass, so it's basically a non-starter.

Curved TVs were all the rage at the last CES, but Ars Technica has a good deconstruction on why it's total bullshit.  Short version:  all the marketing from the various vendors says different things about why curved TVs are awesome.  If three people tell you tell you three different reasons why something is useful, you can bet that none of them are exactly the truth, and perhaps all three have some ulterior motive.  In the case of TV manufacturers, the ulterior motive is pretty clear (hint: it's "Buy a new TV").

Curved display panels would be a disaster for HMDs.  First off, they're not going to curve like Geordi's visor.  The curvature has to be centered on the lens axis that use radially symmetrical lenses (like the Rift). So that means that there's going to need to be a kink in the middle, like so:

While OLED panels can currently bend, I don't believe there are any that can fold.  So you'd have to have two separate screen panels, each separately curved; which instantly doubles the cost of making the display.  Unless curved OLEDs are miraculously cheaper than today's display, this would push the price of a Rift a lot closer to the $500 mark.  Badness.

Even more damning is the need for radial symmetry.  The radial symmetry in the lenses means that you get radial symmetry in the display, to maintain a constant distance between the lens and the panel for a given theta (angle between the lens axis and the direction you're looking). This doesn't work with a flexible panel if you bend it, because the flexible panel only bends along one axis. Suddenly the distance between the panel and the lens changes depending on whether you're looking up or to the left. Look 30 degrees to the left and the panel surface is closer because of the curvature. Look 30 degrees up and the panel is the same distance as it was on an flat panel.  Which means that we're still stuck with all the complexity of the distortion shader.  We were supposed to be free of that complexity!  OLEDs!  You were the chosen one!

The only way to solve that would be to make a panel which can bend in two dimensions, like a contact lens.  But that's not a flexible screen any more--that's custom-molded plastics and circuitry, ie., super-expensive again.  There's no way to flex a single sheet (a surface with local curvature zero, for the more mathematically inclined among the audience) into a cup.  One (entertainingly named) way to visualize the problem is via the Hairy Ball Theorem.  The latter says that if you have a sphere that is covered with hair, there is no way to arrange the hair so that it lies flat everywhere.  Somewhere you're going to have a cowlick.

Finally, curving the display doesn't actually gain you anything. The limiting factor to the field of view is the lens, not the display. Sure, the display being slightly bigger might take some work off the lens, and possibly simplify the shader code, but ultimately the greatest angle you're going to be able to see is determined by how far off the lens axis you can look and still be looking through the lens itself. No amount of screen curvature is going to change that.