1. Keith Grainge Calibration requirementsAAVP 2010 Calibration and Imaging Requirements Keith Grainge (plus teams at ASTRON, Oxford, Cambridge)

2. Keith Grainge Calibration requirementsAAVP 2010 What limits the final map sensitivity? –Thermal noise (A/T; integration time) –Confusion noise (source counts; maximum baseline) –Inadequate dynamic range Related question of image fidelity –configuration and uv-plane coverage Key question: how accurate must calibration be such that it is not limiting performance? Limits to Imaging

3. Keith Grainge Calibration requirementsAAVP 2010 AA Calibration Aim is overall model for calibration of entire AA system –Investigate calibration requirements at all sub-system levels –Provide feedback and comment on specs Eventually will be limited by non-linear effects of systematics –Need to consider interaction of various errors Scope: Phase I is intial priority Also take forward Phase II considerations Approach: –Use existing experience, results from pathfinders –Combination of simulation and theory tested with measurement –Once simulations validated, extrapolate to SKA

4. Keith Grainge Calibration requirementsAAVP 2010 Antenna Placement Accuracy of placement affects beam-forming quality Also determines extent can exploit features such as regularity / redundancy LOFAR uses λ/40 –Based on experience and seems reasonable... –Should attempt to justify this Equivalent to 10 degrees – too much? Can we relax this - installation issues

5. Keith Grainge Calibration requirementsAAVP 2010 Antenna alignment Usual argument is that alignment error cause negligable loss in beamformer –Depends on cos(Δθ) –LOFAR uses 1 o However, polarisation errors depend on sin(Δθ) Also, standard polarimetric performance (co-, cross- pol) is not meaningful for AAs –Reconstructability of polarimetric properties of incoming field Are element level polarimetric corrections required? –Apply during beamforming –Only one point in FoV correct –A LOFAR study exists

6. Keith Grainge Calibration requirementsAAVP 2010 “Estimation noise” Winjholds and van der Veen (2008) Self-calibration will be required to reach desired dynamic range Estimation of calibration parameters extracts information from the data –Effective noise in the image increases with number of calibration parameters –Imposes a stability requirement Do the astronomical sources provide sufficient SNR to estimate the parameters? –May need dedicated calibration hardware

7. Keith Grainge Calibration requirementsAAVP 2010 Other Calibration Issues What is allowable gain/phase error in analogue chain –Encompasses all electronic and temperature effects Minimum system level for various calibration issues –Element? Tile? Station? –Purely astronomical calibration or artificial source required? Beam formation –Element coupling effects –Bandpass changes; filter performance (aliasing) –Sample bit count through processing chain Further issues in documents from: Faulkner; Wijnboer and Nijboer

8. Keith Grainge Calibration requirementsAAVP 2010 Simulation Outline

9. Keith Grainge Calibration requirementsAAVP 2010 Sky and atmosphere Initially concentrate on total intensity Construct sky model through linear superposition of: –Poisson sources from source count within inner area of PB –Spherical Harmonic representation of galaxy –Bright sources in far sidelobes –Consider effects of sources coming above horizon Simple ionospheric model –Function of time, geometry and frequency –Antenna based phase screen

10. Keith Grainge Calibration requirementsAAVP 2010 Effects of Coupling AA elements very strongly coupled; use macro basis fns Issues: sparceness; configuration; channel bandwidth See Nima’s talk

11. Keith Grainge Calibration requirementsAAVP 2010 Beam Forming - Array Factor Station beam from Array factor and mean embedded element pattern (Razavi-Ghods, Lera Acedo) Array factor: configuration; convolutional gridding; FFT Interpolation for different directions and frequencies

12. Keith Grainge Calibration requirementsAAVP 2010 OSKAR Oxford OeRC: Salvini, Mort and Dulwich A tool to investigate: –Hierarchical beam forming issues –Processing design structure –Digitisation issues –Weights during beam formation Has capability of simulating station time stream data Adapted to import embedded element patterns

13. Keith Grainge Calibration requirementsAAVP 2010 Station beam formation: OSKAR

14. Keith Grainge Calibration requirementsAAVP 2010 Interferometry Input from sky model, atmosphere and station beam work here. Initially concentrate on Phase I: 50 stations

15. Keith Grainge Calibration requirementsAAVP 2010 Interferometry Wide field considerations important –Formulate problem in wavelets basis (McEwen and Scaife 2009) Primary beam issues –Each station has different randomised element configuration –Station beams change as track source across sky –Every baseline has its own PB at each time step –Apply atmospheric effects to station beam Add random noise to visibility (model for T sys (ν)) Many “blocks” of code exist; link with Python wrapper

16. Keith Grainge Calibration requirementsAAVP 2010 Summary Calibration critical to realise potential sensitivity Guide AA design decisions at station and system level Will specific calibration hardware be required? Address issues with pathfinders and simulation tested against measurements Is overall calibration problem computationally tractable?