<p>I was struggeling to understand 2080's question, so I looked up the given reference which might be worth re-quoting:</p>
<p><a href="https://i.sstatic.net/DT6yU.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/DT6yU.png" alt="enter image description here" /></a></p>
<p>With this additional information in hand, the question (initially) seemed to be mainly about the  interpretation of 2D <a href="https://en.wikipedia.org/wiki/Discrete_Fourier_transform" rel="nofollow noreferrer">discrete Fourier trafo</a>, using the terms of astronomy.</p>
<p>If that interpretation was correct, I suggest e.g. <a href="http://bigwww.epfl.ch/demo/ip/demos/FFT/" rel="nofollow noreferrer">http://bigwww.epfl.ch/demo/ip/demos/FFT/</a> which offers an intutive and interactive approach to Fourier transformation in general.</p>
<p><strong>Edit:</strong> The question has been edited, and the main issue seems to be <em>How do I get these values <span class="math-container">$V(u,v)$</span> from the signals <span class="math-container">$T(x,y)$</span> of my telescopes?</em> I write &quot;seems&quot; since I am not 100% certain that <span class="math-container">$T(x,y)$</span> are indeed the signals of the telescope.</p>
<p>What I know from <a href="https://astronomy.stackexchange.com/questions/26413/math-behind-a-uv-plot-in-interferometry">Math behind a uv plot in interferometry?</a> is that the units used in the u-v-plane are wavelength, e.g. in meters.</p>
<h3>References</h3>
<ul>
<li>Lecture by Jason Hessels on <a href="https://www.astron.nl/astrowiki/lib/exe/fetch.php?media=ra_uva:ra_uva_lecture6.pdf" rel="nofollow noreferrer">Radio Astronomy: The Techniques of Radio Interferometry I: Basics</a> overs an introduction I found quite accessible.</li>
</ul>

CC BY-SA 4.0
2021-02-09T09:09:32.983Z
I know how to apply a fourier transform, but I do not know where the amplitude/phase information in each of the uv-dots comes from/how it is computed
2080
CC BY-SA 4.0
2021-02-09T09:19:56.140Z
@2080 I am still not fully understanding mathematically your issue, so let's try to break it down: (a) You have the functional form or the values of $T(x,y)$ given in real space, correct? (b) In the $uv$-plane, you have $V(u,v)$ fully determined by Fourier transformation. So at each point $(u,v)$ on the uv-plane, there is a (single) value $V(u,v)$. Is your question about that?
B--rian
CC BY-SA 4.0
2021-02-09T09:48:48.410Z
See my edited question
2080
CC BY-SA 4.0
2021-02-09T09:01:38.210Z
2021-02-12T10:34:18.093Z
2021-02-12T10:34:18.093Z
B--rian
<p>As I understand it, the image of an interferometer is the inverse fourier transform of the information in the uv plane. For each baseline (vector between any two telescopes in the array), representing a certain wavelength along its orientation, there is a point in the uv plane.</p>
<p><a href="https://i.sstatic.net/ubAoR.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ubAoR.png" alt="enter image description here" /></a></p>
<p>(image from <a href="https://science.nrao.edu/facilities/alma/naasc-workshops/nrao-cd-spf1/BasicsInterf.pdf" rel="nofollow noreferrer">lecture notes from nrado.edu</a>)</p>
<p>But what value does each of these data points have? I'd expect them to contain amplitude and phase information, but which exactly?</p>
<p>How do I get these values from the signals of my telescopes? Say, I already computed the phase shifts between the signals, what values do I put in the uv plane?</p>

CC BY-SA 4.0
2021-01-28T15:28:50.250Z
different but related question: [Math behind a uv plot in interferometry?](https://astronomy.stackexchange.com/q/26413)
uhoh
CC BY-SA 4.0
2021-02-07T20:04:45.653Z
@TheBigJoe1489 This is just a note to save [your link](http://articles.adsabs.harvard.edu//full/1989ASPC....6...11T/0000011.000.html) in case your link-only-answer gets deleted.
B--rian
<radio-astronomy><mathematics><interferometry>
In astronomical interferometry, what values do the points in the uv-plane have?
2080
# In astronomical interferometry, what values do the points in the uv-plane have?

(Asked by: username_0 on 2021-01-28)

As I understand it, the image of an interferometer is the inverse fourier transform of the information in the uv plane. For each baseline (vector between any two telescopes in the array), representing a certain wavelength along its orientation, there is a point in the uv plane.

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

(image from [lecture notes from nrado.edu](https://science.nrao.edu/facilities/alma/naasc-workshops/nrao-cd-spf1/BasicsInterf.pdf))

But what value does each of these data points have? I'd expect them to contain amplitude and phase information, but which exactly?

How do I get these values from the signals of my telescopes? Say, I already computed the phase shifts between the signals, what values do I put in the uv plane?

**Tags:** radio-astronomy, mathematics, interferometry

> **Comments:**
> **username_1**: different but related question: [Math behind a uv plot in interferometry?](https://astronomy.stackexchange.com/q/26413)  
> **username_2**: @TheBigJoe1489 This is just a note to save [your link](http://articles.adsabs.harvard.edu//full/1989ASPC....6...11T/0000011.000.html) in case your link-only-answer gets deleted.  

---

## 1 answers

### Answer by username_2 on 2021-02-09. Score: 1

I was struggeling to understand username_0's question, so I looked up the given reference which might be worth re-quoting:

[![enter image description here](https://i.sstatic.net/DT6yU.png)](https://i.sstatic.net/DT6yU.png)

With this additional information in hand, the question (initially) seemed to be mainly about the interpretation of 2D [discrete Fourier trafo](https://en.wikipedia.org/wiki/Discrete_Fourier_transform), using the terms of astronomy.

If that interpretation was correct, I suggest e.g. <http://bigwww.epfl.ch/demo/ip/demos/FFT/> which offers an intutive and interactive approach to Fourier transformation in general.

**Edit:** The question has been edited, and the main issue seems to be *How do I get these values $V(u,v)$ from the signals $T(x,y)$ of my telescopes?* I write "seems" since I am not 100% certain that $T(x,y)$ are indeed the signals of the telescope.

What I know from [Math behind a uv plot in interferometry?](https://astronomy.stackexchange.com/questions/26413/math-behind-a-uv-plot-in-interferometry) is that the units used in the u-v-plane are wavelength, e.g. in meters.

### References

* Lecture by Jason Hessels on [Radio Astronomy: The Techniques of Radio Interferometry I: Basics](https://www.astron.nl/astrowiki/lib/exe/fetch.php?media=ra_uva:ra_uva_lecture6.pdf) overs an introduction I found quite accessible.

> **Comments:**
> **username_0**: I know how to apply a fourier transform, but I do not know where the amplitude/phase information in each of the uv-dots comes from/how it is computed  
> **username_2**: @username_0 I am still not fully understanding mathematically your issue, so let's try to break it down: (a) You have the functional form or the values of $T(x,y)$ given in real space, correct? (b) In the $uv$-plane, you have $V(u,v)$ fully determined by Fourier transformation. So at each point $(u,v)$ on the uv-plane, there is a (single) value $V(u,v)$. Is your question about that?  
> **username_0**: See my edited question  

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