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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?
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