# I Virtual image size/distance in an OAP mirror

1. Feb 10, 2017

### 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.)

2. Feb 10, 2017

### pixel

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?

3. Feb 10, 2017

### sophiecentaur

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.

4. Feb 10, 2017

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.