# In astronomical interferometry, what values do the points in the uv-plane have?

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.

(image from lecture notes from nrado.edu)

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?

• different but related question: Math behind a uv plot in interferometry?
– uhoh
Jan 28, 2021 at 15:28

I was struggeling to understand 2080's question, so I looked up the given reference which might be worth re-quoting:

With this additional information in hand, the question (initially) seemed to be mainly about the interpretation of 2D discrete Fourier trafo, 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? is that the units used in the u-v-plane are wavelength, e.g. in meters.

### References

• 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
Feb 9, 2021 at 9:09
• @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? Feb 9, 2021 at 9:19
• See my edited question
– 2080
Feb 9, 2021 at 9:48