Hi Eugen,

Unless I’m mistaken, I believe this should be the anticipated behavior of such a system? I took a look at the paper you referenced, and I wonder if the key phrase is “the aberrations for a paraboloid observing off axis are dominated by the Seidel aberrations Astm3 and Coma3”. There is a reference to a paper A simple active corrector for liquid mirror telescopes observing at large zenith angles, and I think this reinforces looking at an off-axis field point rather than it being an off-axis section:

What do you think? Thanks!

I agree with Angel. With the object at infinity and an on axis field, every ray through the pupil is parallel to the axis of the parabolic mirror and will be sent to the focus. The ray fan and OPD fan should both be flat.

Kind regards,

David

Dear Angel, David,

thanks for your reply!

I fully agree with your explanation, especially concerning the behaviour of the OPD-plot. In a ray-optical model, all rays converging towards the mirrors focal point travel the same optical path and the OPD with respect to an ideal spherical wave is of course zeros, no matter if we have a symmetrical parabolic mirror or an off-axis parabolic. 

But maybe this article  explains my point a little bit more clear:

OSA | Diffraction patterns formed by an off-axis paraboloid surface (osapublishing.org)

As I understand, this is the underlying geometry:

The off axis parabolic case is parameterized by the angle φ. There is no field angle of the incident collimated beam with respect to the optical axis. The authors give then the formula for the surface as:

For φ=0° the formula reduces to the parabolic equation. The authors state that the first term gives astigmatism and the second coma for φ>0. They insert the equation for φ > 0° into the phase of the electromagnetic wave and do a propagation with Fresnel-Kirchhoff integral. The diffraction pattern at focus for off axis parabolics then differs from the on axis case. So maybe this effect is rather due to diffraction and can not be described using classical ray tracing?

Best,

Eugen 

Maybe this discussion is one for the paper authors? The behavior of a parabolic surface with a source at its focus is well known. BTW, the drawing you give is for an on-axis parabola: maybe you should decenter the parabola to see the behavior described in the paper.

Hi all,

I know it has been some time since this post was updated, but Eugen, based on the other paper you referenced, I think I see what you mean, and I agree -- I think this might strictly be a diffraction-based effect. I didn’t have a chance to dig very deeply into the paper you referenced, but I did try to mock up a file using two configurations (axial parabolic mirror vs OAP mirror), and I overlaid the cross-section of a Huygens PSF plot for the two configurations for easier comparison:
 

I think we can see more clearly see the spreading of the PSF similar to what is shown in paper you linked if we use a Logarithmic scale for the data:

Is this kind of effect what you were after? I am not too sure if I had set up the example properly, as I am not sure the scale of different PSFs you were expecting to see. I’ve shared the file here in any case for reference.

Let me know what your thoughts are here!

Dear Angel,

thank you so much for your response, this helps me a lot in understanding this effect. The difference in the PSF you plotted is very subtle, but I think there might be cases like beam coupling where this might be relevant.

Best regards,

Eugen