May I treat the light from a star as a light beam?

• I
• Haorong Wu
In summary, the conversation discusses the approximation of treating starlight as a point source and a line when studying wavefront evolution, and the desire to extend this approximation to a light beam. The speaker suggests considering a plane perpendicular to a specific direction and only accounting for photons propagating along that direction. The conversation also touches on the use of Gaussian beams in modeling light and the need for further clarification on the specific measurements being studied.

Haorong Wu

TL;DR Summary
Is the approximation that the starlight in a long distance forms a light beam usable?
Hi. I am studying the wavefront evolution of light from a star. In the papers I have read, the star is often treated as a point source and the light is approximated as a line (geodesics), but this approximation is not very useful when I study the wavefront evolution, so I want to extend the approximation to a light beam. Here are my reasons:

I am considering a plane that is perpendicular to some direction ##\hat n_k## and is far away from the star. Then I think only photons propagating along that direction ##\hat n_k## can reach the area I am interested in, so the light can be approximated as a beam that has the same radius as the star has.

Is this approximation correct? Thanks.

Haorong Wu said:
so the light can be approximated as a beam that has the same radius as the star has.
What do you mean? The star has an absolutely tiny angular diameter. Much less than its image on the sensor.
If you mean to treat the beam of light as having a diameter that's the same as the physical diameter of the star, well no, you can't do that. That wouldn't make any sense in terms of optics.

Haorong Wu said:
In the papers I have read, the star is often treated as a point source and the light is approximated as a line (geodesics), but this approximation is not very useful when I study the wavefront evolution, so I want to extend the approximation to a light beam.
I don't see why you couldn't. I was under the assumption that this was exactly how light was treated normally. A 'beam' of light passing through the atmosphere and entering the aperture of the telescope. Treat the beam as being made up of rays of light or as wave fronts depending on which one is appropriate for what you're doing.

To elaborate, when talking about the 'shape' of the incoming light we can do a few things.

First, we need to decide if we're talking about light from a single point or light from a region of interest (like all the light from the surface of a star). For light coming from a single point we usually treat it as an expanding cone whose base is the diameter of the aperture of the optical system and whose point starts are the point of emission/reflection. When the distance to the target is so large that the cone's side angles are extremely close to 90 degrees we often just treat the light as a 'beam' instead of a cone and say that all the rays are parallel to each other.

For light from a region of interest, we have a different shape. Instead of a pointed cone, we have a cone with its top 'chopped off'. The base is the diameter of the target region and the 'top' is the diameter of the aperture of the optical system. All the light cones from each point that reach the optical system are contained within the shape.

For objects like stars that are at extreme distances and also have extremely small angular diameters, we can treat the light from both individual points and from the entire region as if it comes from a point source. That is, the light rays from any single point on the target can be treated as if they parallel to each other and parallel to light rays from other points on the target.

As for how wave optics treats point-like sources, I can't say much. I was under the impression that you treat the whole thing as a single wave front coming from a single point.

Haorong Wu said:
TL;DR Summary: Is the approximation that the starlight in a long distance forms a light beam usable?

Hi. I am studying the wavefront evolution of light from a star. In the papers I have read, the star is often treated as a point source and the light is approximated as a line (geodesics), but this approximation is not very useful when I study the wavefront evolution, so I want to extend the approximation to a light beam. Here are my reasons:

I am considering a plane that is perpendicular to some direction ##\hat n_k## and is far away from the star. Then I think only photons propagating along that direction ##\hat n_k## can reach the area I am interested in, so the light can be approximated as a beam that has the same radius as the star has.

Is this approximation correct? Thanks.
I do not know what you are asking. You may treat the star as an isotropic point source very far away. The light will arrive as essentially a plane wave. What part of the "wavefront evolution" concerns you? In short what are you measuring?.

Haorong Wu said:
TL;DR Summary: Is the approximation that the starlight in a long distance forms a light beam usable?

Hi. I am studying the wavefront evolution of light from a star. In the papers I have read, the star is often treated as a point source and the light is approximated as a line (geodesics), but this approximation is not very useful when I study the wavefront evolution, so I want to extend the approximation to a light beam. Here are my reasons:

I am considering a plane that is perpendicular to some direction ##\hat n_k## and is far away from the star. Then I think only photons propagating along that direction ##\hat n_k## can reach the area I am interested in, so the light can be approximated as a beam that has the same radius as the star has.

Is this approximation correct? Thanks.
This seems very similar to the question that you asked a year ago:

Haorong Wu said:
I am aware that a laser could be modeled as a Gaussian beam, e.g., $$E=E_0\frac{w_0}{w_z}\exp (\frac {-r^2}{w^2_z}) \exp (-i(kz+k \frac {r^2}{2R(z)}-\psi(z))).$$

Now I want to study the propagation of light emitted from stars. But I am not sure how to model it, especially by some kind of functions.

I am particularly interested in the situation where the light has traveled a great deal of distance. Since it then can be treated as parallel beam, I argue that they can be model as a Gaussian beam with the waist radius equal to the radius of the star, given a certain frequency. Does this make sense?

What key words should I search in google scholar?

Thanks!

Haorong Wu said:
TL;DR Summary: Is the approximation that the starlight in a long distance forms a light beam usable?

Is this approximation correct? Thanks.
What you will measure on earth is a plane wave with no transverse structure. If it is Gaussian (which is not likely) with the halfwidth size of a star will it really matter ?

@Drakkith @hutchphd @berkeman Thanks for your help.

I study the phase distribution on the wavefront of light. It has been reported that light emitted from an accretion disk surrounding a rotating black hole can carry a phase distribution on the wavefront (here and here).

What about I divide the surface of a star into small elements each of which will emit a light ray to a detector after passing near a Kerr black hole? Since each ray experiences a different metric, they will carry different phases when they are detected. And that is what I am looking for. Is this method physically wrong?

Unfortunately this is well beyond my area of expertise, so I will probably not be able to help you. Best of luck to you though.

Haorong Wu said:
What about I divide the surface of a star into small elements each of which will emit a light ray to a detector after passing near a Kerr black hole? Since each ray experiences a different metric, they will carry different phases when they are detected. And that is what I am looking for. Is this method physically wrong?
The light received from the star does, of course, comprise the addition of random contributions from every point of the surface. It is the sum of many noise sources, which creates a single, more intense, noise source. You might, however, be interested to read on Wiki about the Hanbury-Brown effect, which allows the diameter of the closer stars to be found using an interferometer based on noise correlation.

sophiecentaur, vanhees71, berkeman and 1 other person
tech99 said:
The light received from the star does, of course, comprise the addition of random contributions from every point of the surface. It is the sum of many noise sources, which creates a single, more intense, noise source. You might, however, be interested to read on Wiki about the Hanbury-Brown effect, which allows the diameter of the closer stars to be found using an interferometer based on noise correlation.
Thanks! I will dig into it.

Concerning the propagation of the light from the star to us you can well apply geometrical optics, i.e., the leading-order eikonal approximation of the Maxwell equations (see Sommerfeld, Lectures on Theoretical Physics vol. 4 (Optics)).

However, if it comes to the optics using a telescope you have to use wave optics to evaluate the resolution of your devices (diffraction limit etc.). Another application of wave optics is Hanbury-Brown-Twiss interferometry (HBT), which can be used to measure the diameter of a star. Wikipedia discusses it in terms of quantum theory, but it's well applicable also in classical electrodynamics:

https://en.wikipedia.org/wiki/Hanbury_Brown_and_Twiss_effect

Haorong Wu said:
TL;DR Summary: Is the approximation that the starlight in a long distance forms a light beam usable?

Then I think only photons propagating along that direction n^k can reach the area I am interested in, so the light can be approximated as a beam that has the same radius as the star has.
It is not appropriate to consider photons anywhere else than the beginning and end of the optical path. The concept of photons propagating an a particular direction is meaningless because there's a finite chance that a photon resulting from a charge interaction on one point of the star could turn up anywhere on a sphere with Earth on the surface. Just stick to the wave treatment which can be taken to a depth of your choice (see some of the above comments).
The notion of a star being equivalent to a hole in a black background would have to involve something about the position of an actual source, in behind so that a frustum (beam) would be formed. I wonder about the suitability of that approach as opposed to initially assuming an isotropic source.
Haorong Wu said:
What about I divide the surface of a star into small elements each of which will emit a light ray to a detector after passing near a Kerr black hole?
That's the same approach as can be used in lens analysis - optical path lengths determining how any image would be formed. The behaviour of 'rays' passing through a medium with varying refractive index could be treated in a similar way. But wouldn't the size of the source be very small, compared with the size of the refracting region?