Focusing of a 2D Parabolic Mirror

[DonLumpo]

Summary: How to explain the focusing properties of a 2D parabolic mirror based on third-order aberration theory?

Hello everyone,

I am currently studying with full-wave simulations the focusing properties of a 2D parabolic mirror, i.e. the scattered fields resulting from plane wave incidence at oblique angles.

What I observe for shallow reflectors is that the maxima of the scattered field generally lie on a curve that bends towards the reflector for increasing angles of incidence, just as the tangential focal surface shown in the attached figure.

What I learned for the 3D case (paraboloid mirror) is the following:
- As every optical system, the mirror has associated with it a sort of basic field curvature, called the Petzval curvature. When there is no astigmatism, the sagittal and tangential image surfaces coincide with each other and lie on the Petzval surface

- The sagittal focal surface from third-order Seidel aberration theory is the focal plane, and the tangential focal surface lies between the focal plane and the mirror

- As in any optical system, the tangential surface is three times as far from the Petzval surface as the sagittal surface

Now my question is, how can the focusing contour that I observe for the 2D case (obviously astigmatism is not defined in 2D) be explained with this/third-order aberration theory?

Many thanks

 

[anorlunda]

I'm curious. Why did you choose Electrical Engineering for your optics question?

 

[Andy Resnick]

Summary: How to explain the focusing properties of a 2D parabolic mirror based on third-order aberration theory?
<snip>

I am currently studying with full-wave simulations the focusing properties of a 2D parabolic mirror, i.e. the scattered fields resulting from plane wave incidence at oblique angles.

I'm not entirely sure what you are asking- for one thing, you seem to be mixing ray (third-order aberrations) and wave optics models. Are you asking how aberration coefficients are computed in general? Are you asking how parabolas are handled in wave optics? Are you asking for detailed computations of aberration coefficients for a parabolic mirror?

The largest off-axis aberration of parabolic reflectors is usually coma, not field curvature:

https://www.telescope-optics.net/Newtonian_off_axis_aberrations.htm

 

[vanhees71]

I'm curious. Why did you choose Electrical Engineering for your optics question?

Hm, it's not a bad choice given that optics is entirely a subject of (quantum) electrodynamics and its applications, I'd call "electrical engineering". Well nowadays one talks about "photonics" in analogy to "electronics". Whether you consider photonics also as part of electrical engineering is just a matter of choice. I'm not sure whether the standard electrical-engineering curriculum today also already contains some photonics ;-)).