Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.atnf.csiro.au/whats_on/workshops/synthesis2001/material/basics_rpn.pdf Дата изменения: Tue Jan 15 06:15:18 2002 Дата индексирования: Wed Dec 26 12:15:32 2007 Кодировка: Поисковые слова: arp 220

The Australia Telescope National Facility

The Australia Telescope

Ray Norris CSIRO ATNF

Why is it a "National Facility"?
· Funded by the federal government (through CSIRO) · Provides radio-astronomical facilities to Australian (+international) astronomers. · Ranks #2 in the world
­ (in terms of publications, etc.)

Who uses the AT?
China

200 180 160 140 120 100 80 60 40 20 0

Japan

Aust

Ireland India Spain Canada Russia Netherlands

Proposals

O/S

Taiwan Europe Sweden France Italy UK

· Cost ~$15M p.a. · Employs ~150 people,
­ of whom ~15 are astronomers, ­ all of whom have support duties.

ATNF
91 92 93 94 95 96

Germany USA

0

20

40

60

80

100

Year

Number of proposals

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The AT Compact Array
· · · · Formally opened in 1988 Started routine operation in 1990 6 antennas * 22 m diameter on E-W track frequency range 1.3 -10 GHz (wavelength range 21 - 3 cm) · angular scales ~ 1 arcsec to 30 arcmin · currently being upgraded to 3mm

Why are radiotelescopes so big?

Radio telescopes and optical telescopes can see different things
Radio telescopes mainly see things like highenergy electrons Optical telescopes mainly see things like stars

Radio-telescopes show us things which are hidden at optical wavelengths

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An Xray telescope

How telescopes work

An optical Cassegrain telescope

An optical refracting telescope

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What does the lens do (version 1)?
CCD array

What does the lens do (version 2)?
CCD array

Lens delays some rays more than others

So that rays from different directions end up in step at different places

Electric field Distribution

FOURIER TRANSFORM

Image

The Fourier Transform
Comte Jean Baptiste Joseph Fourier 1768-1830

All waveform are formed from a sum of sine waves
In general, any function can be composed "synthesised" - from a number of sines and cosines of different periods and amplitudes.

Relates:
· time distribution of a wave - frequency distribution · amplitude of a wavefront - image producing it · many other pairs of quantities

Image courtesy Dave McConnell

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y

A Violin String
The open D string of a violin has the following waveform in the time domain:
A m p l i t u d e

Sawtooth Wave

x

f(t) = 1sin(t) +

sin(2t) +
1

sin(3t) +

sin(4t)

Frequency

Fourier Transforms

Fourier Transforms

f(t) t
The wave is a function of time
FOURIER TRANSFORM

f(t) t
The Inverse Fourier Transform is a function of time

g(f) f
The Fourier Transform is a function of frequency

Ў

The Fourier Transform gives this frequency domain representation

Amplitude

The amplitude and frequency of the twelve sine waves (the fundamental plus 11 overtones) which make up the vibration of the D-string are easily read from the graph.

1st sine wave

This is called a Fourier Spectrum

2nd sine wave 4th sine wave


1
2



2

3
x Frequency

4

INVERSE FOURIER TRANSFORM

g(f) f
The Fourier Spectrum is a function of frequency

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A p a ra b o l i c d i s h c a n a l s o b e viewed in this way · The shape of the dish delays different rays s o t h e y ar e i n s t ep at o n e p l a c e (t h e fo c u s ) · The image formed at the focus is the Fourier transform of the wavefront
focus focus

Back to telescopes

So how can we synthesise a really large telescope?
· View 1: we capture the rays at different palces, and then delay them b y the right amount, bring them together to form an image · View 2: we measure the electric field in various places, and then calculate the Fourier transform of that distribution

Problem 1: we can't actually measure the electric field fast enough. Instead we measure the cross-correlations between the signals at each element

A synthesised radio telescope

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A two-element Interferometer


wa vef ron t

Direction to source

Need to measure the crosscorrelation over as many spacings as possible
Direction to source

Bsi n


T2

B
T1 Correlator Computer disk

For n antennas, we get n(n+1)/2 spacings

Using the Earth's Rotation

Problem 2
· We can't fill the aperture with millions of small radio telescopes. · Solution: let the Earth's rotation help us

baseline telescopes Earth

T1 T2

top view

Source Source

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The u-v Plane
· As seen from the source, each baseline traces out an ellipse with one telescope at the centre of the ellipse:
v
T2 T1

Example 1: ATCA at declination = -85 degrees

u

The projected baseline can be specified using u-v coordinates, where · u gives the east-west component of the baseline; and · v gives the north-south component of the baseline.
/2

The projected baseline is given by B sin = (u2 + v2)1

Example 2: declination = -40 degrees Example 3: declination = -10 degrees
Gap



100 k = 6 km at 6 cm

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VLBI - The Highest Resolution Instrument

The effect of increasing coverage in the u-v plane

The process of synthesis observing
· Observe the source for some hours, letting the Earth rotate the baseline · Correlate the signals between telescopes, and store the results of those multiplications on disk · At the end of the observation, assign the results of the multiplications to the correct position on the u-v disk · Fourier Transform the uv plane to produce an image

So is that all?
· If we were able to cover all the u-v plane with spacings, we could in principle get a perfect image · In practice there are gaps, and so we have to use algorithms such as CLEAN and Maximum Entropy to try to guess the missing information · This process is called deconvolution

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Cleaning dirty images
· A process was designed by HЖgbom in the early 1970s to clean dirty images.
· Estimate value and position of peak · Subtract off the `dirty beam' due to a point source of this flux · repeat until only the noise is left on the image. · Add back the flux, convolving each point source with an ideal "clean beam" · The result is the `cleaned image'.

So is that all?
Other problems include · calibration errors
­ use calibrator sources

· b ad d at a
­ edit the data

· "twinkling" in the atmosphere or ionosphere
­ use techniques such as "Selfcal" and phase referencing

Ha ob ppy ser vin

g!

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