# How does beam shape (elliptical vs circular/Gaussian) affect interferometry?

I want to understand the importance of beam quality to interferometer systems. This article says the following:

A very high (close to diffraction-limited) beam quality, associated with a high spatial coherence, is often required for interferometers, optical data recording, laser microscopy, and the like.

But how does beam shape (elliptical vs circular/Gaussian) affect interferometry?

## EDIT

I'm specifically asking how the beam shape (elliptical vs circular/Gaussian) affects interferometry; and, so, should I aim to make (using optical elements) the beam as circular/Gaussian as possible (assuming it starts out more elliptical, such as from a laser diode). The goal is to maximise the performance of the interferometer (within reason).

The beam shape is not as important in interferometry as the shape of the wavefront. However, the shape of the beam can affect the shape of the wave front. An elliptical Gaussian beam would have different beam divergence angles along the two orthogonal transverse direction. It means that the beam will pick up different curvatures in the wavefront along these two directions as it propagates. A beam that appears elliptical may also be astigmatic, which means that the wavefront curvatures are again different along the two transverse directions and may even be opposite.

For successful interferometry, one would have to determine the shape of the wavefront of a beam and then use optics to correct for that as far as possible to obtain a flat wavefront.

• Ahh, I see. So you'd say that the clear winner here thorlabs.com/images/TabImages/… (see slides 13/14) is to use a "spatial filter" (it has the lowest "RMS wavefront")? Jul 25, 2021 at 3:39
• Yes, that is one way to do it. Jul 26, 2021 at 5:01

Is the cross section of a TEM00 Gaussian beam always circular?

It is often defined like that, but one may use a generalized definition where you require Gaussians in x and y direction, but not necessarily with the same width.

An elliptical Gaussian Beam is very much like a circular one. It has a beam waist with a different diameter in the x and y directions. Instead of a circular contour in the plane of the waist, the E field is elliptical.

Using the divergence angle formula

$$\Theta = \frac{\lambda}{\pi w_0}$$

you can calculate two different far field divergence angles. The narrow waist diverges more than the narrow waist. In the far field, the beam is again elliptical instead of circular, but the long orientation has switched. In between, the beam has elliptical an contour with various eccentricities that pass through circular.

If you start with a high quality beam, you always have a high quality beam at any distance from the waist. The shape is all that changes from the circular case.

• But this doesn't really address my question. I'm specifically asking how the beam shape (elliptical vs circular/Gaussian) affects interferometry; and, so, should I aim to make (using optical elements) the beam as circular/Gaussian as possible (assuming it starts out more elliptical, such as from a laser diode). The goal is to maximise the performance of the interferometer (within reason). Jul 25, 2021 at 1:40