Instinctively, I would suggest a radial grating-type structure, but I don't know if that would work for you.

Without knowing the application, it's hard to say what you really need. Can you explain why you need a material when geometry might fit at least some of your needs. Specifically a short length of pipe or cardboard tube with an interior diameter of at least 2.5 inches would seem to meet most of your needs.

The pipe would have to be about 4 1/3 inches long to suit your needs, because
tan(30 degrees) = sqrt(1/3) = 2.5/4.33 (roughly)

Guiding Light's idea might be similar, I don't know where you'ld find his gratings for sale.

Using my trigonometry method, you can scale down and use thinner plastic straws cut to the same ratio and cluster them in a hexagonal lattice. If they are white and diffusely reflecting you will get very close to your desired effect for any radius. Maybe Guiding Light's gratings are similar to that. Also, Plastic (or paper) drinking straws are cheap.

Sounds like I need to clarify a bit.

I need a surface that will reflect a projected image if the image is at an angle of greater than 30 degrees to perpendicular, but will let the image pass through if it is within 30 degrees.

In other words, if I project an image from a steep enough angle, the surface will reflect the light like a white wall, but if a projected image is from within the 30 degrees then the image will pass through.

The surface would need to look like as blank, flat, and white of a surface as possible when white light is projected at a steep angle to it.

It for a full, visible spectrum miniture movie screen idea I have, where the projected image should be allowed to pass through the screen if projected from the right angle. The viewers should not be able to tell the difference between the pass-through-surface and a white screen if the image is projected from a steep enough angle.

The reason the cardboard tubes won't work is that the image projected from a steep angle wouldn't appear correctly to someone looking at the screen.

I hope that helps... I wish the solution was as simple as straws Let me know if there are any more clarifications needed.

A grating may not work so well in this application since it has its own dispersion. Maybe something based on total internal reflection would work better.

try holographically fabricated light shaping diffusers. they can design the diffuser based on hour requirements.