Telescopes and the Basics of Radio Astronomy

ICRAR/CASS Radio School R. D. Ekers 1 Oct 2018 Geraldton, WA Cygnus region - CGPS (small)

Radio Image of Ionised Hydrogen in Cyg X CGPS (Penticton)29 Sep 2008 R D Ekers 2 WHY?

. National Facilities  Easy for non-experts to use  don’t know what you are doing . Cross fertilization . Doing the best science . Value of radio astronomy

25 Sep 2017 R D Ekers 3 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

27 Sep 2018 R D Ekers 4 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?

29 Sep 2008 R D Ekers 5 HOW ?

. Don’t Panic! – Many entrance levels

29 Sep 2008 R D Ekers 6 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

29 Sep 2008 R D Ekers 7 References

─ David Wilner, ANITA lectures, Swinburne, 2015 2017, 3rd

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

29 Sep 2008 R D Ekers 8 Detecting Signals from Radio Telescopes

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Digitizer 01110010

computer 25 Sep 2017 R D Ekers 9 Planck’s Law Rayleigh-Jeans approximation

25 Sep 2017 R D Ekers 10 Radhakrishnan ”noise” ASPC 180 671, 1999 Noise in Radio and Optical

25 Sep 2017 R D Ekers 11 Resolving Power

. Angular resolution = wavelength/aperture

Light Radio Wavelength 0.00005cm 21cm

Aperture 10cm 10km

0.00005/10 rad 21/106 rad Resolution = 1” arc = 4” arc

29 Sep 2008 R D Ekers 12 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

29 Sep 2008 R D Ekers 13 Greenbank 300' Radio Telescope

29 Sep 2008 R D Ekers 14 Greenbank 300’ Radio Telescope

29 Sep 2008 R D Ekers 15 Notes on Units

25 Sep 2007 - David Wilner, ANITAR lectures, D Ekers Swinburne, 2015 16 Spatial Coherence

P1 P2 P1 & P2 spatially incoherent sources

At distant points Q1 & Q2 The field is partially coherent Q1 Q2 van Cittert-Zernike theorem The spatial coherence function is the Fourier Transform of the brightness distribution

29 Sep 2008 R D Ekers 17 Analogy with single dish

. Big mirror decomposition

23 Sep 2012 R D Ekers 18 19 20 Free space Guided ( Σ Vi )2

21 Free space Guided

(Σ Vi )2

22 Free space Guided

Delay

Phased array Σ 2 ( Vi ) 23 Free space Guided

Mechanical v Electronic steering

Delay

Phased array Σ 2 ( Vi ) 24 Free space Guided

Delay

Phased array Σ 2 ( Vi ) 25 Free space Guided

Delay

Phased array Σ 2 Σ 2 Σ × ( Vi ) = (Vi ) + (Vi Vj ) 26 Free space Guided

Ryle & Vonberg (1946) phase switch

Delay

Phased array (Σ Vi )2 = Σ (Vi )2 + Σ (Vi × Vj )  27 Correlation array 28 Phased Array θ

Split signal x2 x2 x2 x2 x2 x2 no S/N loss

∆t

Phased array (Σ Vi )2 (Σ Vi )2 Tied array Beam former I(θ) I 29 Synthesis Imaging

∆t correlator

∆ϕ= ∆ t/λ Fourier Transform van Cittert-Zernike theorem I(r) 30 Fourier Transform

31 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

23 Sep 2012 R D Ekers 32 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

29 Sep 2008 R D Ekers 33 Redundancy

1unit 5x (source same atmosphere different) 2units 4x 3units 3x 4units 2x 5units 1x n(n-1)/2 = 15

1 2 3 4 5 6 Non Redundant 1unit 1x 2units 1x 3units 1x 4units 1x 5units 0x 6units 1x 7units 1x etc

1 2 3 4 5 6 7 8 HERA Epoch of Reinization Array

. Maximally redundant array to decouple the sky from the instrumental errors

29 Sep 2018 R D Ekers 35 Basic Interferometer

29 Sep 2008 R D Ekers 37 Storing visibilities

A powerful tool to manipulate the coherence But will this be function and re- part of our image. pipeline future?

Not possible in most other domains Storage

27 Sep 2015 R D Ekers 38 Aperture Array or Focal Plane Array?

. Why have a dish at all? – Sample the whole wavefront – n elements needed: n ∝ Area/( λ/2)2 Computer – For 100m aperture and λ = 20cm, n=104 » Electronics costs too high!

29 Sep 2008 R D Ekers 39 Radio Telescope Imaging image v aperture plane

λ

Computer Active elements ~ A/λ2

Dishes act as concentrators Computer Reduces FoV Reduces active elements Cooling possible Increase FoV Increases active elements 29 Sep 2008 R D Ekers 40 Radio Telescopes

MWA aperture plane

Meerkat

image plane ASKAP29 Sep 201 R D Ekers 41 8 Fourier Transform and Resolution

. Large spacings – high resolution

. Small spacings – low resolution

29 Sep 2008 R D Ekers 42 Fourier Transform Properties from Kevin Cowtan's Book of Fourier

FT 

FT 

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

FT 

10% data omitted in rings Fourier Transform Properties

FT 

Amplitude of duck Phase of cat Fourier Transform Properties

FT 

Amplitude of cat Phase of duck In practice… 1. Use many antennas (VLA has 27) 2. Amplify signals 3. Sample and digitize 4. Send to central location 5. Perform cross-correlation 6. Earth rotation fills the “aperture” 7. Inverse Fourier Transform gets image 8. Correct for limited number of antennas 9. Correct for imperfections in the “telescope” e.g. calibration errors 10.Make a beautiful image…

•47 Terminology

RADIO OPTICAL Antenna, dish ⇔ Telescope, element Sidelobes ⇔ Diffraction pattern Near sidelobes ⇔ Airy rings Feed legs ⇔ Spider Aperture blockage ⇔ Vignetting Dirty beam ⇔ Point Spread Function (PSF) Primary beam ⇔ Field of View (single pixel receivers)

25 Sep 2017 R D Ekers 48 Terminology

RADIO OPTICAL Map ⇔ Image Source ⇔ Object Image plane ⇔ Image plane Aperture plane ⇔ Pupil plane UV plane ⇔ Fourier plan Aperture ⇔ Entrance pupil UV coverage ⇔ Modulation transfer function

22 Sep 2012 R D Ekers 49 Terminology

RADIO OPTICAL Dynamic range ⇔ Contrast Phased array ⇔ Beam combiner Correlator ⇔ no analog no analog ⇔ Correlator Receiver ⇔ Detector Taper ⇔ Apodise Self calibration ⇔ Wavefront sensing (Adaptive optics)

22 Sep 2012 R D Ekers 50