Ways of achieving parallel rays of light?

The commonly available 'privacy screen' does this by blocking light beyond a certain angle off perpendicular. Typically the narrower the cutoff angle, the more expensive, but these work well for privacy.

They don't actually collimate light into an absolutely parallel beam, but in reality you wouldn't want this, as it would make the device quite unusable (you would only see a small area of the screen at any time), so what they actually do is allow between 15 and 30 degrees either side of 90 degrees, and heavily attenuate any light outside these angles.

All such methods are constrained by optical laws that ultimately are limited by the second law of thermodynamics.

If you have a light source of dimension H (one dimensional) in a medium of refractive index N, and it emits a beam over a range of angles from +U to -U (one dimensional), then the quantity NHSinU is invariant. In two dimensions, then (NHsinU)^2 is invariant. By invariant, we mean, under all geometrical optical transformations; reflection, refraction etc. This is true both for imaging optics, and non-imaging optics.

So if you try to reduce the beam angle (U), then the beam diameter must increase, assuming N is unchanged. So if you are talking about a single pixel on your screen, being made visible over only a small angle (in any direction), you can ONLY do this by throwing the rest of the light away.