Wide-field imaging

Max Voronkov (filling up for Tim Cornwell)Software Scientist – ASKAP

1st October 2010

This presentation is heavily based on the original presentation by Tim Cornwell

General information

Further info in the White book and Tim’s presentation

This talk is about algorithms….

But I will not give recipes.

€

i = j = −1In this talk:

Instantaneous FOV

Instantaneous FOV

Dynamic range concept

Dynamic range concept

Structure of an imaging algorithm

Non-coplanar baselines

• Two-dimensional Fourier transform is only an approximation

V (u,v,w)=I (l,m)

1−l2 −m2⋅e

j2π. ul + vm+w( 1−l2 −m2 −1)( )∫ dl.dm

Points far from the phase center are defocused Effect is important if Not a problem at all if w=0

Baseline component towards source Equation for celestial sphere

λB ≥ D Strange requirement

Standard 2D reduction

Non-coplanar baselines

Point sources away from the phase center are distorted

Bad for long baselines, large field of view, and long wavelengths

Fix: use faceted or w projection deconvolution

Faceted approaches

• Approximate integral by summation of 2D Fourier transforms

V (u,v,w)= ej2π . ulk+vmk+w 1−lk

2 −mk2 −1⎛

⎝⎜⎞⎠⎟

⎛⎝⎜

⎞⎠⎟ Ik(l,m)ej2π . u(l−lk )+v(m−mk )( )∫ dl.dm

k∑

Can do in image plane or Fourier plane Fourier plane is better since it minimizes facet edge

problems Number of facets ~

3λBD2

Faceted approach

Origin of non-coplanar baselines effect

If we had measured on planeAB then the visibility would be the 2D Fourier transform of the

sky brightness

Since we measured on AB’,we have to propagate back to plane AB, requiring the use ofFresnel diffraction theory since

the antennas are in eachothers near field

%G(u,v,w)≈ejπw(u2 +v2 )

Fresnel scale

Baseline length 4 1 0.21 0.06350 37 19 9 5

1000 63 32 14 83500 118 59 27 14

10000 200 100 46 2435000 374 187 86 46

100000 632 316 145 77350000 1183 592 271 145

Wavelength

λB• Fresnel scale = size of region of influence• If Fresnel scale > antenna diameter, measurements must be

distorted

Roughly the size of convolution function in pixels

W-projection

The convolution function

Image plane phase screen Fourier plane convolution function

ej2πw 1−l2 −m2 −1( ) ≈e jπ w(u

2 +v2 )

W projected image

DR limitations

Sources outside the field of view

• Sidelobes from sources outside the antenna primary beam fall into the field of view

• Can deconvolve if the convolution equation is obeyed

• BUT probably not….• Due to….

• Non-symmetry of primary beam

• Non-isoplanatism• Likely to be a limitation for

wideband telescopes• Can probably correct

• Some problems doing so

Rotating primary beam

• Primary beam is not rotationally symmetric

• e.g. antenna feed legs

• As it rotates on the sky, sources low in the primary beam are modulated in amplitude

• Can be 100% modulation

ASKAP 3-axis antenna mount

• 3-axis mount allows us to keep beam pattern fixed on the sky

Mosaic example

This was just a tip of an iceberg

• Bandwidth and Time-average smearing• Reobserve with a better spectral or time resolution

• Ionosphere (non-isoplanatism)• For small baselines can fit Zernike polynomial phase delay screen

• Pointing errors• Wide bandwidth effects• Polarization of the primary beam• Second order effects which may/will be significant for SKA

• e.g. see my presentation from the last synthesis school• http://www.narrabri.atnf.csiro.au/people/vor010/presentations/MVoronkovSynthSchool2008.pdf

• Mosaicing issues• errors of the primary beam

• Wide bandwidth

• Joint vs. individual deconvolution

Contact UsPhone: 1300 363 400 or +61 3 9545 2176

Email: enquiries@csiro.au Web: www.csiro.au

Thank you

Australia Telescope National FacilityMax VoronkovSoftware Scientist (ASKAP)

Phone: 02 9372 4427Email: maxim.voronkov@csiro.auWeb: http://www.narrabri.atnf.csiro.au/~vor010