1. Basics of Interferometry
Satoki Matsushita
(松下 聡樹)
Academia Sinica,
Institute of Astronomy & Astrophyscis
(ASIAA)

2. High-Resolution vs Low-Resolution
Mitton & Ryle 1969, MNRAS, 146, 221
12” x 19”
Perley et al. 1984, ApJL, 285, L35
0.5” x 0.5”

3. Single-Dish Telescopes

4. Single-Dish vs Interferometer
Resolution goes high with higher frequency and bigger telescope:
Resolution ~ l/D
l: Wavelength
D: Diameter of telescope
If you need <1” resolution, you need to make 1 km diameter telescope
It is IMPOSSIBLE !
⇒ Interferometer !!
Telescope
Diameter
115　GHz
(2.6mm)
230 GHz
(1.3mm)
345 GHz
(0.8mm) 6m
108”
54”
36”
10m
65”
32”
22”
30m
11” 7”
100m 3” 2”
1000m
0.6”
0.3”
0.2”

5. Single-Dish ⇒ Interferometer

6. Single-Dish ⇒ Interferometer
It is impossible to make huge single-dish antennas.
⇒ Divide into small pieces.
Advantage: If you move antennas far away, you can obtain high spatial resolution image.
Disadvantage: Light collecting area will be smaller than single-dish antennas.

7. Interferometers

8. Young’s Experiment

9. Young’s Experiment

10. Young’s Experiment

11. Basics of Interferometry
E1 = E exp{2pin(t-t)} E2 = E exp{2pin(t)}
Phase information tells us position information.
Visibility (You can obtain this information from interferometer):
b・s = b・(s0+s)

12. Basics of Interferometry
Define coordinates:
For the observing source: s = (l,m)
E2 = E(l,m)2 = I(l,m)
: Intensity distribution of observing source. We want to obtain this information.
For the antenna baselines: b = (u,v)
: Fourier transformation relation between V(u,v) and I(l,m) !!

13. Basics of Interferometry
So, the intensity distribution of the observing source is :
This equation tells us that if you obtain as many uv data points as possible toward the source, i.e.,
observe the source with many baselines,
observe the source for long time,
you can obtain the source intensity distribution.

14. Basics of Interferometry
Fourier transformation relation between V(u,v) and I(l,m).
l,m indicate the spatial distribution.
u,v are therefore indicate the spatial frequency distribution.
For example, if you FT a time sequence plot, you can obtain a frequency distribution plot.
Longer the u,v distance, smaller the l,m distribution, i.e., higher the spatial resolution.

15. uv data ⇔ image data
image data
uv data ⇔ FT ⇔ FT

16. Further Readings
“Interferometry and Synthesis in Radio Astronomy” Second Edition Thompson, Moran, & Swenson (New York: Wiley-Interscience)
“Synthesis Imaging in Radio Astronomy II” ed. G.B. Taylor, C.L. Carilli, & R.A. Perley A.S.P. Conf. Ser. Vol (NRAO Summer School Textbook)