<p>How did they determine the angular diameter, please? How to predict the baseline length with the first lobe?
Thank you.</p>
<p><a href="https://www.chara.gsu.edu/public/basics-of-interferometry" rel="nofollow noreferrer">https://www.chara.gsu.edu/public/basics-of-interferometry</a></p>
<p><a href="https://i.sstatic.net/OiqLk.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/OiqLk.png" alt="enter image description here" /></a></p>
<p>If they are theoretical curves, my question is what formula is used. There needs to be some relation to how to compute the length of baseline for the particular angular diameter <span class="math-container">$\theta$</span>.</p>

CC BY-SA 4.0
2024-01-08T19:46:13.523Z
Putting the diagramme and the question into *slightly* more context would be really helpful. Did you consider it being theoretical curves?
planetmaker
CC BY-SA 4.0
2024-01-09T07:33:39.700Z
If they are theoretical curves, my question is what formula is used. There needs to be some relation to how to compute the length of baseline for the particular angular diameter $\theta$.
Elena Greg
CC BY-SA 4.0
2024-01-09T08:01:04.763Z
Did you look at the extensive explanation material the site links? Why or how wasn't that helpful?
planetmaker
CC BY-SA 4.0
2024-01-09T10:28:57.927Z
I quickly went through it and did not find it.
Elena Greg
CC BY-SA 4.0
2024-01-10T12:04:52.180Z
Stellar interferometry is a cool way to measure the diameters of stars when we can't directly image them. cf. [What equipment and techniques were used to study Betelgeuse's diameter in 1920?](https://astronomy.stackexchange.com/q/36363/7982) I can't give you a formula, but I'll be it can be derived for a uniform disk and two slits.  If the start was a point, the visibility would be flat at 1.0 (perfect constructive and destructive interference) but the finite diameter has a "smearing" effect that makes the max/min ratio drop because the angle from one part of the star is producing a maximum
uhoh
CC BY-SA 4.0
2024-01-10T12:06:50.267Z
while the angle from another part of the star is producing a minimum. This effect gets worse as the optical path difference increases, either by letting the star drift, or by increasing the baseline. You have to write an expression for the amplitude of the fringes for a point source, then integrate over the disk of the star to get this curve. Maybe it's an easy integral and results in an analytic expression, maybe not. Sorry I can't be more helpful, but I'll bet within a half-day you have a very nice answer.
uhoh
CC BY-SA 4.0
2024-01-10T12:09:25.480Z
Oh, see "Box 2" on page 652 in [Measuring the Sizes of Stars; Fringe Benefits of Interferometry by Rajaram Nityananda](https://www.ias.ac.in/article/fulltext/reso/022/07/0645-0657) *I think* there's your equation, with the integral over the disk. ([archived](https://web.archive.org/web/20211026214505/https://www.ias.ac.in/article/fulltext/reso/022/07/0645-0657))
uhoh
CC BY-SA 4.0
2024-01-13T08:11:35.127Z
What do you mean by "compute the length of the baseline"? You measure it. Then the visibility varies as a function of angular diameter, as shown.
ProfRob
CC BY-SA 4.0
2024-01-15T07:50:35.030Z
I mean that I have a prediction of the angular diameter of a star and I would like to know how long should be the baseline to see the first lobe (to choose an appropriate interferometer). Basically, I am asking about the relation between visibility, baseline, angular diameter, and wavelength.
Elena Greg
CC BY-SA 4.0
2024-01-15T08:20:17.047Z
Is it $b = \frac{1.22 \lambda }{ \Theta}$?
Elena Greg
CC BY-SA 4.0
2024-01-15T08:27:49.557Z
What about to compute where the visibility is 0.5 instead of 0?
Elena Greg
<interferometry>
Angular diameter and length of baseline
Elena Greg
# Angular diameter and length of baseline

(Asked by: username_0 on 2024-01-08)

How did they determine the angular diameter, please? How to predict the baseline length with the first lobe?
Thank you.

<https://www.chara.gsu.edu/public/basics-of-interferometry>

[![enter image description here](https://i.sstatic.net/OiqLk.png)](https://i.sstatic.net/OiqLk.png)

If they are theoretical curves, my question is what formula is used. There needs to be some relation to how to compute the length of baseline for the particular angular diameter $\theta$.

**Tags:** interferometry

> **Comments:**
> **username_1**: Putting the diagramme and the question into *slightly* more context would be really helpful. Did you consider it being theoretical curves?  
> **username_0**: If they are theoretical curves, my question is what formula is used. There needs to be some relation to how to compute the length of baseline for the particular angular diameter $\theta$.  
> **username_1**: Did you look at the extensive explanation material the site links? Why or how wasn't that helpful?  
> **username_0**: I quickly went through it and did not find it.  
> **username_2**: Stellar interferometry is a cool way to measure the diameters of stars when we can't directly image them. cf. [What equipment and techniques were used to study Betelgeuse's diameter in 1920?](https://astronomy.stackexchange.com/q/36363/7982) I can't give you a formula, but I'll be it can be derived for a uniform disk and two slits.  If the start was a point, the visibility would be flat at 1.0 (perfect constructive and destructive interference) but the finite diameter has a "smearing" effect that makes the max/min ratio drop because the angle from one part of the star is producing a maximum  
> **username_2**: while the angle from another part of the star is producing a minimum. This effect gets worse as the optical path difference increases, either by letting the star drift, or by increasing the baseline. You have to write an expression for the amplitude of the fringes for a point source, then integrate over the disk of the star to get this curve. Maybe it's an easy integral and results in an analytic expression, maybe not. Sorry I can't be more helpful, but I'll bet within a half-day you have a very nice answer.  
> **username_2**: Oh, see "Box 2" on page 652 in [Measuring the Sizes of Stars; Fringe Benefits of Interferometry by Rajaram Nityananda](https://www.ias.ac.in/article/fulltext/reso/022/07/0645-0657) *I think* there's your equation, with the integral over the disk. ([archived](https://web.archive.org/web/20211026214505/https://www.ias.ac.in/article/fulltext/reso/022/07/0645-0657))  
> **username_3**: What do you mean by "compute the length of the baseline"? You measure it. Then the visibility varies as a function of angular diameter, as shown.  
> **username_0**: I mean that I have a prediction of the angular diameter of a star and I would like to know how long should be the baseline to see the first lobe (to choose an appropriate interferometer). Basically, I am asking about the relation between visibility, baseline, angular diameter, and wavelength.  
> **username_0**: Is it $b = \frac{1.22 \lambda }{ \Theta}$?  
> **username_0**: What about to compute where the visibility is 0.5 instead of 0?  

---

## 0 answers

