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Wide-field imaging. Max Voronkov (filling up for Tim Cornwell) Software Scientist – ASKAP 1 st October 2010. General information. This presentation is heavily based on the original presentation by Tim Cornwell. Further info in the White book and Tim’s presentation. In this talk:. - PowerPoint PPT Presentation
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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
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