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Introduction to Imaging
Mark Wieringa - ATNF Fourier Basics Image plane and uv-plane Imaging decisions Image estimation Image errors

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Fourier Basics
f(x) Large f(ax Real F(s) Small F(s/a) Hermitian
(F(s)=F(-s)*) g

)

Multiply f Shift f(x+a) Add f+g Rotate

Convolve F*G Phase Gradient Add(F+G) Rotate

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Image Plane and UV plane

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UV plane features
! ! !

Dense rings
­ Baselines ­ track in uv plane

Low level in between rings
­ Gaps in coverage, missing information

Hole in center
­ No information on low 'spatial frequencies', i.e., no info on large scale structure

!

Outer boundary
­ No info on small scale structure ­ resolution limit

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Image plane
PSF or `dirty beam' Partially Cleaned Image

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Imaging Decisions
!

Field of view (FOV)
­ Based on primary beam size, mosaicing(multiple fields) » 20cm ­ 33' beam, 3mm ­ 30'' beam ­ may need to image larger field to remove sidelobes from distant sources

!

Resolution/tapering, cell size (>2 pixels/beam)
­ Many observations do NOT want maximum resolution because sensitivity to extended structure is low » Many short baseline configurations: EW352, H75 ­ may elect not to include long baselines (e.g., deselect CA06 ) » Only adds high frequency ripple to image with mostly short baselines

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Imaging Decisions(2)
!

Weighting scheme
­ Uniform (min. sidelobe level) ­ Natural (min noise level) ­ Robust (optimal combination of above two)

Uniform
Beam: 7x5" Sens.: 1.45

Robust=0.5
8x6.5'' 1.16

Robust=1.0
9.6x7.5'' 1.06

Natural
12x8'' 1.0

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Imaging Decisions (3)
!

Continuum vs Spectral line imaging
­ Continuum
» combine channels (ATCA continuum obs. has 32x 4MHz channels) » possibly combine multiple center frequencies (MFS) · E.g. for max. sensitivity at 6cm use 4800 & 5824 MHz each with 32 channels over 128 MHz.

­ Line
» Check velocity frame, doppler correction » Specify spectral resolution & velocity range » Remove continuum emission !

Polarization
­ Choice of Stokes I,Q,U,V

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Some details
!

Imaging uses FFT ­ works on sampled data
­ Need to grid the uv data (choice of gridding methods)
» Specify gridding convolution function » Suppresses aliasing

! !

Tapering (gaussian taper applied to vis weights)
­ Another form of weighting to influence beam size

Non-coplanar baselines (e.g.VLA at low freq)
­ Small field approx fails, do e.g., facet imaging + joint deconvolution

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Image estimation
Imaging is estimating the sky brightness distribution from incomplete information ­ The imaging process can be generalized into a minimization process ­ minimize discrepancy between model of sky and the visibility data » Some effects are easy to correct in image plane · e.g. Primary beam » Others are easily corrected in visibility data · eg. atm. Gain, phase calibration ­ But when e.g. Primary beam varies with time or phase varies with position in the sky an iterative approach is needed.
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Improving the Image
!

We need to:
­ Fill in the gaps in the uv-coverage (deconvolution) ­ Correct the instrumental responses (calibration)

» Filter response (bandpass correction) » Polarization response (leakage terms)
­ Measure and Correct the atmospheric & instrumental responses that vary rapidly

» Mainly atmospheric path length (phase errors) and attenuation (gain vs. elevation)
(latter two require calibration observations of known sources)

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Deconvolution
! ! !

Need to make assumptions to get a realistic estimate Different algorithms make different assumptions, e.g., CLEAN ­
­ Sky is mostly empty, with occasional peaks ­ Works well for field with point sources, poor for extended emission

!

MEM
­ Sky is uniform ­ Works well for very extended sources, poor for point sources

!

Many variations on each basic scheme available
­ e.g., multi-scale clean, sdi clean

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Common errors in Image plane
Problems remaining after deconvolution ! (grating) rings uv tracks
­ Improve by calibrating slowly varying gain&phase
!

Radial spokes short times
­ Improve by calibrating fast varying gain & phase

!

'Fuzzy' sources outer tracks bad
­ decorrelation/bad phase errors (common at high frequency)

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Example miriad imaging
!

Use task invert with following parameters:
­ ­ ­ ­ ­ ­ vis, line, select to specify the data included imsize, cell, options(mfs) to specify image (or cube) sup, robust, fwhm, options(systemp) to specify weighting Produces dirty image and beam Use clean and restor to deconvolve the image Use xmtv, kview to look at the image

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Example aips++ imaging
!

Use imager tool:
­ setdata() to select the data to use in the image ­ setimage() to specify the image parameters and how to combine the data (mfs or spectral cube) ­ weight() to apply a weighting scheme ­ makeimage() to make a 'dirty image' or ­ clean() to make a deconvolved image ­ Use the viewer to look at the image

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VRI
!

VRI, the virtual radio interferometer
­ http://www.narrabri.atnf.csiro.au/astronomy/vri.html ­ Lets you experiment with Fourier transforms and ATCA configurations

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