Keith GraingeCalibration requirementsAAVP 2010

Calibration and Imaging Calibration and Imaging RequirementsRequirements

Keith Grainge

(plus teams at ASTRON, Oxford, Cambridge)

Keith GraingeCalibration 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 ImagingLimits to Imaging

Keith GraingeCalibration requirementsAAVP 2010

AA Calibration 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

Keith GraingeCalibration 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

Keith GraingeCalibration requirementsAAVP 2010

Antenna alignmentAntenna alignment

• Usual argument is that alignment error cause negligable loss in beamformer– Depends on cos(Δθ)

– LOFAR uses 1o

• 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

Keith GraingeCalibration requirementsAAVP 2010

““Estimation noise”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

Keith GraingeCalibration requirementsAAVP 2010

Other Calibration IssuesOther 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

Keith GraingeCalibration requirementsAAVP 2010

Simulation Outline

Keith GraingeCalibration requirementsAAVP 2010

Sky and atmosphereSky 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

Keith GraingeCalibration requirementsAAVP 2010

Effects of CouplingEffects of Coupling

• AA elements very strongly coupled; use macro basis fns

• Issues: sparceness; configuration; channel bandwidth

• See Nima’s talk

Keith GraingeCalibration requirementsAAVP 2010

Beam Forming - Array FactorBeam 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

Keith GraingeCalibration requirementsAAVP 2010

OSKAROSKAR

• 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

Keith GraingeCalibration requirementsAAVP 2010

Station beam formation: OSKAR

Keith GraingeCalibration requirementsAAVP 2010

Interferometry

• Input from sky model, atmosphere and station beam work here.

• Initially concentrate on Phase I: 50 stations

Keith GraingeCalibration requirementsAAVP 2010

InterferometryInterferometry

• 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 Tsys(ν))

• Many “blocks” of code exist; link with Python wrapper

Keith GraingeCalibration requirementsAAVP 2010

SummarySummary

• 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?