SKADS: Array Configuration Studies Implementation of Figures-of-Merit on Spatial-Dynamic-Range Progress made & Current status Dharam V. Lal & Andrei P. Lobanov (MPIFR, Bonn)

To quantify imaging performance of the SKA. HUGE task

 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 Some 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  [U 2 – U 1 ] / U 2 for a circular (u,v)-coverage where, U 2 and U 1 are the (u,v)-radii of two adjacent baselines. … 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 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 (u 1,u 2 ):  u/u = (u 2 – u 1 )/u 2 (u 2 > u 1 )  Uniform sensitivity is provided by  u/u = const Spatial 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 Factors

 Generate test array (X,Y) for logarithmic (equiangular) spiral array configuration  Project this array on Earth’s 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” Methodology

Preliminaries Observing direction, RA 00:00:00 Dec +90:00:00 A RUN of 12 hrs  An arbitrary choice of source model  Observing 1.4 GHz

Experiment 1  A station at origin  Three spiral arms  Five stations in each arm  Range of baseline from 20 – 100m to 20 – 5000m  [U2 – U1] / U2 “B max /B min ” vary “B max /B min ” “N” & constant “N”

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 2 (U,V) gap parameter  [U 2 – U 1 ] / U 2 “B max /B min ” i.e., fix “B max /B min ” “N” & vary “N”

Experiment 2 … dirty mapCLEAN map  Results (Use AIPS task IMAGR)  8k x 8k image size and each pixel being 3 arcsec  Figures-of-Merit

Experiment 2 …  Shortest spacings, a few 10s of metres  ~degree  Longest spacings (5000 m )  ~arcseconds

 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. Results

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.

Thanks!