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!