Virtual image size/distance in an OAP mirror

[Skypuppet]

These seems like an easy question, but I have found nothing online:

Does the size and distance of the virtual image produced by an off-axis parabolic mirror vary as a function of the off-axis angle, or will it be the same as the parent parabola?

Specifically, I am trying to create a simple off-axis collimated display which produces a virtual image of a certain size and distance. Can I simply ray trace the virtual image produced by the parent parabola on-axis, and presume the size and distance will be the same when viewed off-axis? If not, then how do I ray trace or otherwise calculate the virtual image off-angle to determine its size and distance? (The object to be reflected is a flat screen display pointed in the direction of the off-axis angle.)

 

[pixel]

Can I simply ray trace the virtual image produced by the parent parabola on-axis, and presume the size and distance will be the same when viewed off-axis?

I think so. Isn't the image being "off-axis" just due to the fact that a piece of the parent parabola is being used?

 

[sophiecentaur]

I think so. Isn't the image being "off-axis" just due to the fact that a piece of the parent parabola is being used?

Yes - in principle. But Coma distortion is present to a greater and greater extent as the offset increases. This can be a matter of just a few degrees in an astronomical telescope.

 

[Charles Link]

The ray that is incident on the OAP when the slope of the paraboloid is 45 degrees, ($y=2f$), goes to the focal point with a distance of 2f from the mirror to the focal point. This compares with a distance of "f" for the central ray. (Using paraboloid equation $y^2=4 f x$.) The equations that work for the imaging of a thin lens will thereby not work for an OAP. The image distortion wil be tremendous, and I think that is why you couldn't find very much info on the topic. An OAP simply is not used for the application of forming images. It is ideal for focussing a collimated beam (with parallel rays), but basically useless for forming any kind of even low quality image. $\\$ Editing... For astronomical purposes, if you had two stars located very near each other, you could get two focused spots that are both of good quality, but any extended image is likely to have much distortion.

 

[Skypuppet]

Thanks for the responses--what an education. I think I have the answer I need. To be clear, this is a fairly crude display system. My eyeballs will be used to refine the system through trial and error, but I needed a rough starting point as to size and shape of OAP. I've experimented with holding up a tablet screen image up to a commercial grade heads-up OAP display, since this is roughly what I'm trying to emmulate, and it produced the effect I'm looking for. The difference is, I will be using a mirror OAP instead of a see-through beam splitter, since I only want the reflection. Similar to the system used in simulator visuals. Distortion--comatic or otherwise--wasn't enough to be an issue, at least to my eyeballs. I'll be interested to see what kind of OAP angle would make the system unusable.