SKADS: Array Configuration StudiesSKADS: Array Configuration StudiesImplementation of Figures-of-Merit Implementation of Figures-of-Merit
on Spatial-Dynamic-Rangeon Spatial-Dynamic-RangeProgress madeProgress made
&&Current statusCurrent status
Dharam V. Lal & Andrei P. Dharam V. Lal & Andrei P. LobanovLobanov
(MPIFR, (MPIFR, Bonn)Bonn)
To quantify imaging performance of To quantify imaging performance of the SKA.the SKA.
HUGEHUGE task task
Figures-of-MeritFigures-of-MeritAny parameter which is a measure of Any parameter which is a measure of
(u,v)-plane coverage;(u,v)-plane coverage;
e.g., SDR, RMS noise levels, e.g., SDR, RMS noise levels, synthesized beam size, etc.synthesized beam size, etc.
Spatial Dynamic RangeSpatial Dynamic RangeThe ratio of the largest adequately imaged The ratio of the largest adequately imaged
structure and the synthesized beamstructure and the synthesized beam
Some TerminologiesSome Terminologies
(u,v)-gap parameter OR (u,v)-gap parameter OR u/uu/u
A measure of quality of the (u,v)-plane A measure of quality of the (u,v)-plane coverage characterising the relative size coverage characterising the relative size of “holes” in the Fourier planeof “holes” in the Fourier plane
[U[U22 – U – U11] / U] / U22
for a circular (u,v)-coveragefor a circular (u,v)-coveragewhere, Uwhere, U22 and U and U11 are the (u,v)-radii of two are the (u,v)-radii of two
adjacent baselines.adjacent baselines.
… … Terminologies …Terminologies …
Commonly used:– resolution, beam shape, sidelobe level, dynamic range, etc…
Additional: – spatial dynamic range, pixel fidelity
Resolution
Spatial dynamic range
VLBISKA
Pixel fidelity
Figures of MeritFigures of Merit
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“, u/u, between adjacent baselines (u1,u2):
u/u = (u2 – u1)/u2 (u2 > u1)
Uniform sensitivity is provided by u/u = const
Spatial Dynamic RangeSpatial Dynamic Range
FoV:
Channel bandwidth
UV-coverage
Integration time:
Analytical estimate: SDR of SKA will not be limited by the
uv-coverage if u/u 0.1 on all scales
The goal is to derive more specific requirements from numerical testing.
SDR FactorsSDR Factors
Generate test array (X,Y) for logarithmic Generate test array (X,Y) for logarithmic (equiangular) spiral array configuration(equiangular) spiral array configuration
Project this array on Earth’s surface and Project this array on Earth’s surface and determine (Lat, Lon, Z)determine (Lat, Lon, Z)
Choose an appropriate input source modelChoose an appropriate input source model RUN glish scripts in aipsRUN glish scripts in aips++++ to obtain to obtain
visibilitiesvisibilities Import these visibilities into AIPS and Import these visibilities into AIPS and
perform the mapping using IMAGR task.perform the mapping using IMAGR task. Determine the “figures of merit”Determine the “figures of merit”
MethodologyMethodology
PreliminariesPreliminaries
Observing direction, RA 00:00:00Dec +90:00:00
A RUN of 12 hrs
An arbitrary choice of source model Observing
1.4 GHz
Experiment 1Experiment 1
A station at origin Three spiral arms Five stations in each
arm Range of baseline
from 20 – 100mto 20 – 5000m
[U2 – U1] / U2[U2 – U1] / U2 vary “B“Bmaxmax/B/Bminmin”” & constant “N”“N”
Experiment 1 …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
Experiment 2Experiment 2
(U,V) gap parameter(U,V) gap parameter
[U[U22 – U – U11] / U] / U22
i.e., fix “B“Bmaxmax/B/Bminmin”” & vary “N”“N”
Experiment 2 …Experiment 2 …
dirty map CLEAN map
Results (Use AIPS task IMAGR) 8k x 8k image size and each pixel being 3 arcsec
Figures-of-Merit
Experiment 2 …Experiment 2 … Shortest spacings, a few 10s of metres ~degree Longest spacings (5000m) ~arcseconds
The behaviour of figures of merit and The behaviour of figures of merit and hence the SDR does not seem to have a hence the SDR does not seem to have a simple dependence on simple dependence on u/u.u/u.
Close to small (u,v)-gap parameter Close to small (u,v)-gap parameter values, the (nearly) linear relationship values, the (nearly) linear relationship does not hold good.does not hold good.
We show that uv-gap parameter can be We show that uv-gap parameter can be used to relate the (u,v)-coverage to the used to relate the (u,v)-coverage to the characteristics of the map.characteristics of the map.
ResultsResults
Results …Results …
These empirical solutions can be These empirical solutions can be implemented into any proposed implemented into any proposed configuration.configuration.
We plan to use the SDR FoM to quantify We plan to use the SDR FoM to quantify imaging performance of:imaging performance of: KAT / MEERKAT, ASKAP, SKA – Phase IKAT / MEERKAT, ASKAP, SKA – Phase I
Limitations of CLEAN deconvolution Limitations of CLEAN deconvolution algorithmalgorithm Need new algorithms and parallelisation.Need new algorithms and parallelisation.
Thanks!Thanks!