Basics of InterferometryBasics of Interferometry

Satoki MatsushitaSatoki Matsushita(( 松下 聡樹松下 聡樹 ))

Academia Sinica,Academia Sinica, Institute of Astronomy & AstrophyscisInstitute of Astronomy & Astrophyscis

(ASIAA)(ASIAA)

Mitton & Ryle 1969, MNRAS, 146, 221Mitton & Ryle 1969, MNRAS, 146, 221

12” x 19”12” x 19”

High-Resolution vs Low-ResolutionHigh-Resolution vs Low-Resolution

Perley et al. 1984, ApJL, 285, L35Perley et al. 1984, ApJL, 285, L350.5” x 0.5”0.5” x 0.5”

Single-Dish TelescopesSingle-Dish Telescopes

Single-Dish vs InterferometerSingle-Dish vs Interferometer Resolution goes high Resolution goes high

with higher frequency with higher frequency and bigger telescope:and bigger telescope:• Resolution ~ Resolution ~ /D/D

: Wavelength: WavelengthD: Diameter of telescopeD: Diameter of telescope

If you need <1” If you need <1” resolution, you need resolution, you need to make 1 km to make 1 km diameter telescopediameter telescope• It is IMPOSSIBLE !It is IMPOSSIBLE !

⇒ ⇒ Interferometer !!Interferometer !!

TelescopTelescopee

DiameterDiameter

115115　　GHzGHz

(2.6mm)(2.6mm)

230 GHz230 GHz

(1.3mm)(1.3mm)345 GHz345 GHz

(0.8mm)(0.8mm)

6m6m 108”108” 54”54” 36”36”

10m10m 65”65” 32”32” 22”22”

30m30m 22”22” 11”11” 7”7”

100m100m 7”7” 3”3” 2”2”

1000m1000m 0.6”0.6” 0.3”0.3” 0.2”0.2”

Single-Dish Interferometer⇒Single-Dish Interferometer⇒

Single-Dish Interferometer⇒Single-Dish Interferometer⇒ It is impossible to make It is impossible to make

huge single-dish antennas.huge single-dish antennas.

⇒ ⇒ Divide into small pieces.Divide into small pieces.• Advantage:Advantage: If If

you move antennas far away, you move antennas far away, you can obtain high spatial you can obtain high spatial resolution image.resolution image.

• Disadvantage: Disadvantage: Light collecting area Light collecting area

will be smaller than single-will be smaller than single-dish antennas.dish antennas.

InterferometersInterferometers

Young’s ExperimentYoung’s Experiment

Young’s ExperimentYoung’s Experiment

Young’s ExperimentYoung’s Experiment

Basics of InterferometryBasics of Interferometry EE1 1 = E exp{2= E exp{2ii(t-(t-)})} E E2 2 = =

E exp{2E exp{2ii(t)}(t)}• Phase information tells us position Phase information tells us position

information.information.

Visibility (You can obtain this Visibility (You can obtain this information from interferometer):information from interferometer):

bb・・ s = bs = b ・・ (s(s00++))

dSc)πiνb(-

dSc)πiνb(-

c)sπiνb(-

dS cs)πiνb(-

πiνt)dS (-

}/2exp{E

}/2exp{

}/2exp{E

}/2exp{E

source) over the (integrate

2expE

EE V

2

02

2

2

*21

Basics of InterferometryBasics of Interferometry

Define coordinates:Define coordinates:• For the observing source: For the observing source: = (l,m) = (l,m)

EE22 = E(l,m) = E(l,m)22 = I(l,m) = I(l,m) : Intensity distribution of observing source.: Intensity distribution of observing source. We We

want to obtain this information.want to obtain this information.• For the antenna baselines: b = (u,v)For the antenna baselines: b = (u,v)

: : Fourier transformation relation Fourier transformation relation between V(u,v) and I(l,m) !!between V(u,v) and I(l,m) !!

mv)/c}dldm(lui{-

)/c}dS bi{(-

2expm)I(l,

2expE v)V(u, 2

Basics of InterferometryBasics of Interferometry

So, the intensity distribution of the observing source is :So, the intensity distribution of the observing source is :

This equation tells us that if you obtain as many uv data This equation tells us that if you obtain as many uv data points as possible toward the source, i.e.,points as possible toward the source, i.e.,• observe the source with many baselines,observe the source with many baselines,• observe the source for long time,observe the source for long time,

you can obtain the source intensity distribution.you can obtain the source intensity distribution.

mv)/c}dudv(lui{ 2expv)V(u, m)I(l,

Basics of InterferometryBasics of Interferometry

Fourier transformation relation Fourier transformation relation between V(u,v) and I(l,m).between V(u,v) and I(l,m).

• l,ml,m indicate the spatial distribution. indicate the spatial distribution.• u,vu,v are therefore indicate the spatial frequency are therefore indicate the spatial frequency

distribution.distribution. For example, if you FT a time sequence plot, you caFor example, if you FT a time sequence plot, you ca

n obtain a frequency distribution plot.n obtain a frequency distribution plot.• Longer the u,v distance, smaller the l,m distribLonger the u,v distance, smaller the l,m distrib

ution, i.e., higher the spatial resolution.ution, i.e., higher the spatial resolution.

uv data ⇔ image datauv data ⇔ image data

uv datauv data image dataimage data

⇔⇔FTFT

⇔⇔FTFT

Further ReadingsFurther Readings

““Interferometry and Synthesis in Interferometry and Synthesis in Radio Radio AstronomyAstronomy” ” Second EditionSecond Edition Thompson, MoraThompson, Moran, & Swenson n, & Swenson (New York: Wiley-Int(New York: Wiley-Interscience)erscience)

““Synthesis Imaging in Radio Synthesis Imaging in Radio Astronomy IAstronomy III” ” ed. G.B. Taylor, C.L. Caed. G.B. Taylor, C.L. Carilli, & R.A. Perley rilli, & R.A. Perley A.S.P. Conf. Ser. Vol. 180A.S.P. Conf. Ser. Vol. 180

(NRAO Summer School Textb (NRAO Summer School Textbook)ook)