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!