Telescopes and the Basics of Radio Astronomy

ICRAR/CASS Radio SchoolR. D. Ekers1 Oct 2018

Geraldton, WA

29 Sep 2008 R D Ekers 2

Cygnus region - CGPS (small)

Radio Image ofIonised Hydrogen in Cyg XCGPS (Penticton)

National FacilitiesEasy for non-experts to use don’t know what you are doing

Cross fertilization Doing the best science Value of radio astronomy

Indirect Imaging Applications

Interferometry– radio, optical, IR, space...

Fourier synthesis – measure Fourier components and make images– Earth rotation, SAR, X-ray crystallography, ….

Axial tomography (CAT)– NMR, Ultrasound, PET, X-ray tomography

Seismology Fourier filtering, pattern recognition Adaptive optics, speckle

Antikythera

Doing the best science

The telescope as an analytic tool– how to use it– integrity of results

Making discoveries– Most discoveries are driven by instrumental developments– recognising the unexpected phenomenon– discriminate against errors

Instrumental or Astronomical specialization?

Don’t Panic!– Many entrance levels

Basic concepts

Importance of analogies for physical insight Different ways to look at a synthesis telescope

– Engineers model» Telescope beam patterns…

– Physicist electromagnetic wave model» Sampling the spatial coherence function» Barry Clark Synthesis Imaging chapter1» Born & Wolf Physical Optics

– Quantum model» Radhakrishnan Synthesis Imaging last chapter

References

─ David Wilner, ANITA lectures, Swinburne, 2015

• Ekers & Wilson, Radio Telescopes, in Planets, Stars and Stellar Systems, Springer, 2013

Detecting Signals from Radio Telescopes

This image cannot currently be displayed.This image cannot currently be displayed.

computer

Digitizer01110010

Planck’s LawRayleigh-Jeans approximation

Noise in Radio and OpticalRadhakrishnan ”noise” ASPC 180 671, 1999

Resolving Power

Angular resolution = wavelength/aperture

Light Radio

Wavelength0.00005cm 21cm

Aperture 10cm 10km

Resolution0.00005/10 rad

= 1” arc21/106 rad

= 4” arc

Imaging at Radio Wavelengths

Bad news– Radio waves are big– Need large aperture or an interferometer

Good news– Radio frequencies are low– Interferometers are easy to build

Greenbank 300' Radio Telescope

Greenbank 300’ Radio Telescope

Notes on Units

25 Sep 2007 R D Ekers 16- David Wilner, ANITA lectures, Swinburne, 2015

Spatial Coherence

van Cittert-Zernike theoremThe spatial coherence function is the Fourier Transform

of the brightness distribution

P1 & P2spatially incoherent sources

At distant points Q1 & Q2The field is partially coherent

Analogy with single dish

Big mirror decomposition

( Σ Vi )2

Free space

Guided

(Σ Vi )2

Free space

Guided

23(Σ Vi )2Phased array

Free space

Guided

24(Σ Vi )2Phased array

Free space

Guided

Mechanical v

Electronic steering

25(Σ Vi )2

Free space

Guided

Phased array

26(Σ Vi )2 = Σ (Vi )2 + Σ (Vi × Vj )

Free space

Guided

Phased array

27(Σ Vi )2 = Σ (Vi )2 + Σ (Vi × Vj )

Free space

Guided

Phased array

Correlation array

Ryle & Vonberg (1946)

phase switch

PhasedArray

x2 x2 x2 x2 x2 x2

Split signalno S/N loss

Phased array (Σ Vi )2

(Σ Vi )2

Tied arrayBeam former

∆ϕ= ∆ t/λ

correlator

Fourier Transform

I(r)van Cittert-Zernike

theorem

Synthesis Imaging

Fourier Transform

Analogy with single dish

Big mirror decomposition Reverse the process to understand imaging with a

mirror– Eg understanding non-redundant masks– Adaptive optics

Single dishes and correlation interferometers– Darrel Emerson, NRAO– http://www.gb.nrao.edu/sd03/talks/whysd_r1.pdf

Filling the aperture

Aperture synthesis– measure correlations with multiple dishes– moving dishes sequentially– earth rotation synthesis– store all correlations for later use

Partially unfilled aperture– some spacings missing

Redundant spacings– some interferometer spacings occur twice

Non-redundant aperture

1 2 3 4 5 6

1unit 5x (source same atmosphere different)2units 4x3units 3x4units 2x5units 1x

15n(n-1)/2 =

Redundancy

1 2 3 4 5 6 7 8

1unit 1x2units 1x3units 1x4units 1x5units 0x6units 1x7units 1xetc

Non Redundant

HERAEpoch of Reinization Array

Maximally redundant array to decouple the sky from the instrumental errors

Basic Interferometer

Storing visibilities

Storage

A powerful tool to manipulate the coherence function and re-image.

Not possible in most other domains

But will this be part of our

pipeline future?

Aperture Arrayor Focal Plane Array?

Why have a dish at all?– Sample the whole wavefront– n elements needed: n ∝ Area/( λ/2)2

– For 100m aperture and λ = 20cm, n=104

» Electronics costs too high!

Computer

Radio Telescope Imagingimage v aperture plane

Computer

Dishes act as concentratorsReduces FoV

Reduces active elementsCooling possible

Increase FoV Increases active elements

Active elements~ A/λ2

29 Sep 2018

R D Ekers 41

Radio Telescopes

aperture plane

image plane

Meerkat

Fourier Transform and Resolution

Large spacings– high resolution

Small spacings– low resolution

Fourier Transform Propertiesfrom Kevin Cowtan's Book of Fourier

http://www.ysbl.york.ac.uk/~cowtan/fourier/fourier.html

Fourier Transform Properties

10% data omitted in rings

Amplitude of duckPhase of cat

Amplitude of catPhase of duck

In practice…1. Use many antennas (VLA has 27)2. Amplify signals3. Sample and digitize4. Send to central location5. Perform cross-correlation6. Earth rotation fills the “aperture”7. Inverse Fourier Transform gets image8. Correct for limited number of antennas9. Correct for imperfections in the

“telescope” e.g. calibration errors10.Make a beautiful image…

Terminology

RADIOAntenna, dish

Sidelobes

Near sidelobes

Feed legs

Aperture blockage

Dirty beamPrimary beam(single pixel receivers)

OPTICAL⇔ Telescope, element

⇔ Diffraction pattern

⇔ Airy rings

⇔ Spider

⇔ Vignetting

⇔ Point Spread Function (PSF)

⇔ Field of View

Terminology

Source

Image plane

Aperture plane

UV plane

Aperture

UV coverage

OPTICAL⇔ Image

⇔ Object

⇔ Image plane

⇔ Pupil plane

⇔ Fourier plan

⇔ Entrance pupil

⇔ Modulation transfer function

Terminology

RADIODynamic range

Phased array

Correlator

no analog

Receiver

Self calibration

OPTICAL ⇔ Contrast

⇔ Beam combiner

⇔ no analog

⇔ Correlator

⇔ Detector

⇔ Apodise

⇔ Wavefront sensing (Adaptive optics)

Telescopes and the Basics of Radio Astronomy · Basic concepts Importance of analogies for physical...

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