# Focusing of a 2D Parabolic Mirror

• DonLumpo
In summary, the conversation discusses the focusing properties of a 2D parabolic mirror and the use of third-order aberration theory to explain these properties. The speaker also mentions the role of astigmatism and how it affects the focusing contour observed in the 2D case. They then ask for further clarification on how aberration coefficients are computed and the role of electrical engineering in the study of optics.
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

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

DonLumpo said:
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

anorlunda said:
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 ;-)).

## 1. What is the purpose of a 2D parabolic mirror?

A 2D parabolic mirror is used to focus light or other electromagnetic radiation to a single point, creating a highly concentrated beam. This is useful in various applications such as telescopes, solar energy collectors, and laser technology.

## 2. How does a 2D parabolic mirror work?

A 2D parabolic mirror works by reflecting light rays that are parallel to its axis towards a single focal point. The shape of the parabolic mirror causes the light rays to converge at the focal point, creating a concentrated beam of light.

## 3. What factors affect the focusing ability of a 2D parabolic mirror?

The focusing ability of a 2D parabolic mirror is affected by its curvature, size, and surface quality. A larger mirror with a higher curvature will have a shorter focal length and thus a stronger focusing ability. A smooth and perfectly curved surface is also crucial for accurate focusing.

## 4. Can a 2D parabolic mirror focus light from all directions?

No, a 2D parabolic mirror can only focus light that is parallel to its axis. Light coming from different angles will not be accurately focused, resulting in a less concentrated beam.

## 5. How is the focal length of a 2D parabolic mirror calculated?

The focal length of a 2D parabolic mirror can be calculated using the formula f = R/2, where f is the focal length and R is the radius of curvature of the mirror. The radius of curvature is the distance from the center of the mirror to its edge.

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