SKADS: Array Configuration Studies Implementation of Figures-of-Merit on Spatial-Dynamic-Range

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SKADS Array Configuration StudiesImplementation
of Figures-of-Merit on Spatial-Dynamic-Range
Progress madeCurrent status Dharam V.
Lal Andrei P. Lobanov
(MPIFR, Bonn)
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HUGE task

• To quantify imaging performance of the SKA.

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Some Terminologies

• Figures-of-Merit
• Any parameter which is a measure of
  (u,v)-plane coverage
• e.g., SDR, RMS noise levels, synthesized beam
  size, etc.
• Spatial Dynamic Range
• The ratio of the largest adequately imaged
  structure and the synthesized beam

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Terminologies

• (u,v)-gap parameter OR ?u/u
• A measure of quality of the (u,v)-plane coverage
  characterising the relative size of holes in
  the Fourier plane
• ? U2 U1 / U2
• for a circular (u,v)-coverage
• where, U2 and U1 are the (u,v)-radii of two
  adjacent baselines.

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Figures of Merit

• Commonly used resolution, beam shape, sidelobe
  level, dynamic range, etc
• Additional spatial dynamic range, pixel
  fidelity

Resolution
Spatial dynamic range
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Spatial Dynamic Range

• Spatial dynamic range (SDR) the ratio
  between largest and smallest adequately
  imaged scales it measures, effectively,
  brightness sensitivity of an array on all
  scales.
• SDR reflects a number of aspects of array
  design, including the type of primary
  receiving element (antenna), signal
  processing, and distribution of
  antennas/stations.
• Array configuration SDR can be expressed as a
  function of a gap, Du/u, between
  adjacent baselines (u1,u2) Du/u (u2
  u1)/u2 (u2 gt u1)
• Uniform sensitivity is provided by Du/u
  const

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SDR Factors

• Integration time

• FoV
• Channel bandwidth
• UV-coverage

Analytical estimate SDR of SKA will not be
limited by the uv-coverage if Du/u ? 0.1 on all
scales
The goal is to derive more specific requirements
from numerical testing.
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Methodology

• Generate test array (X,Y) for logarithmic
  (equiangular) spiral array configuration
• Project this array on Earths surface and
  determine (Lat, Lon, Z)
• Choose an appropriate input source model
• RUN glish scripts in aips to obtain
  visibilities
• Import these visibilities into AIPS and perform
  the mapping using IMAGR task.
• Determine the figures of merit

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Preliminaries

• An arbitrary choice of source model
• Observing ?
• 1.4 GHz

Observing direction, RA 000000 Dec
900000 A RUN of 12 hrs
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Experiment 1

• A station at origin
• Three spiral arms
• Five stations in each
• arm
• Range of baseline
• from 20 100m
• to 20 5000m

vary Bmax/Bmin constant N

• U2 U1 / U2

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Experiment 1

• Input group of source components
• six Gaussian components,
• typical size 1 arcsec
• Results from Dirty Map
• (Use AIPS task IMAGR)
• 4k x 4k image size
• each pixel 2 arcsec
• Figures-of-Merit

VLA D? ? A
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Experiment 2
(U,V) gap parameter ? U2 U1 / U2
i.e., fix Bmax/Bmin vary N
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Experiment 2

• Results (Use AIPS task IMAGR)
• 8k x 8k image size and each pixel being 3 arcsec
• Figures-of-Merit

dirty map
CLEAN map
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Experiment 2

• Shortest spacings, a few 10s of metres ? degree
• Longest spacings (5000m) ? arcseconds

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Results

• The behaviour of figures of merit and hence the
  SDR does not seem to have a simple dependence on
  ?u/u.
• Close to small (u,v)-gap parameter values, the
  (nearly) linear relationship does not hold good.
• We show that uv-gap parameter can be used to
  relate the (u,v)-coverage to the characteristics
  of the map.

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Results

• These empirical solutions can be implemented
  into any proposed configuration.
• We plan to use the SDR FoM to quantify imaging
  performance of
• KAT / MEERKAT, ASKAP, SKA Phase I
• Limitations of CLEAN deconvolution algorithm
• Need new algorithms and parallelisation.

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Thanks!