Correlator Field-of-View Shaping

Transcription

1 Correlator Field-of-View Shaping Colin Lonsdale Shep Doeleman Vincent Fish Divya Oberoi Lynn Matthews Roger Cappallo Dillon Foight MIT Haystack Observatory

2 Context SKA specifications extremely challenging High resolution, wide FoV, high D.R. How do you get a wide FoV? Small antennas (small d a ) large FoV For fixed area, N da -2, correlation da -4 Δf, Δt to avoid smearing means data rate da -6 Δf, Δt (baseline length) -1 exacerbates issue Wide FoV at high angular resolution is a problem Excessive data volumes and map sizes Sidelobe confusion demands source removal across FoV Source removal intractable with huge data volumes

3 SKA simulated sky (courtesy L. Matthews, using S 3 utility, Wilman et al.)

4 Fields of View High resolution small FoV Data rates: For VLBI resolution and SKA FOV, petabytes/sec needed Can reduce by station beamforming, or big dishes+fpas Increase the parameter n a Focal plane arrays on big dishes are equivalent In practice, high resolution requires restriction of FOV

5 Correlator FoV Different names: Time-average and bandwidth smearing Delay-rate beam Caused by coherence loss over time/frequency range Integration over (f, t) cell Maps to region of (u, v) plane Distant sources generate phase slope in (u, v) plane Problem: (f, t) to (u, v) mapping is strong function of baseline Correlator FoV is inherently inconsistent Array PSF becomes variable across field Can we control the correlator FoV?

6 It can work for VLBI... 8

7 Conventional correlation F/X correlator, fixed channel width and accum. period Strongly mismatched time/freq smearing across baselines Simulate in MAPS, using VLA-like configuration MAPS implements accurate model of correlator (f, t) integration:

8 Inconsistent Data on Distant Sources Visibilities distorted Differing primary beams Differential atmosphere/ ionosphere baseline-dependent decorrelation Sidelobes contaminate entire field Removal options Calibrate and subtract Fully decorrelate (how?)

9 Layers of attenuation Correlator attenuation Station beam rms Array beam rms Combined response rms Antenna pattern What matters is σ tot

10 Stations, or full correlation? For instantaneous, monochromatic case: This is independent of both N s and n a For attenuating distant sources, low station sidelobes are unimportant. There are tradeoffs to be made at intermediate distances Full cross correlation impractical/unnecessary at high angular resolution

11 Minimizing sidelobe confusion Design array to have very low PSF sidelobes B(r) Large number of stations in all resolution regimes Optimize for range of observing parameters Make A(r) a steeper function of r In practice, this means modifying C(r), the correlator attenuation function Setting B(r) constrains S(r), depends on antenna size Not much we can do about P(r) Subtract sources from the visibility data Computationally expensive Minimize how many, and how accurately

12 Correlator FOV Shaping: Smart (t, f) averaging Concept: Make use of Fourier relationship between measurement (u-v) plane and the sky plane Multiply the sky by a weighting (window) function convolve the u-v plane by Fourier transform of the window function, effectively tailoring the FOV Jinc/top hat function Applying single weighting function in (u, v) plane will impose same FOV on all baselines Do this for each visibility, during correlation, pre-calibration

13 u-v Plane Convolution in Correlator v u freq v time u

14 Why not convolve in postprocessing? Conventional (t,f) averaging in correlator destroys essential information Residual power from distant source persists Power condensed into single complex visibility number Convolving delta function only spreads power, doesn t decorrelate it Places sky window over sidelobe pattern Pattern unchanged within desired FoV For convolution to work, need (t, f) resolution for full FoV Implies original data volume problem Convolution must be done where these data rates and volumes naturally exist... inside correlator

15 Tailored correlation Select weighting function in (u,v) plane To implement chosen FoV Map to function in (f, t) space, per visibility. Apply weights to samples inside correlator, pre-calibration Match FoV for all visibilities Cleanly removes sensitivity to distant sources Including those too weak to find/subtract conventionally Also removes their sidelobes Reduces effective FoV Reduces data rate/volume accordingly Key Assumption Negligible calibration/spectral gradients across (f, t) domain

16 Decorrelation methods compared MERLIN 4-telescope 18cm data, 3C343 and 3C343.1 Original image Modest far-field miscalibration Time-frequency averaging Per-visibility Jinc function convolution Limited attenuation Attenuation factor >150 Severe sidelobe responses

17 Gaussian convolution Time/freq averaging - makes a mess Gaussian - factor of ~4 attenuation

18 u-v Plane Convolution in Correlator v Question: How many samples can you accumulate before a different weight is required? u freq v time u

19 New correlator elements Station bitstream Fourier transform Station bitstream Fourier transform Accumulate in bin Weight lookup Accumulate to output shaped visibility

20 Estimating computational cost It can be shown that the number of samples per accumulation period, n s that can be tolerated is given approximately by: Where n a is the number of antennas per beamformed station, f is the areal filling factor of the station on the ground, and n bin is the number of bins used to define the weighting function in one dimension. For D=350km, n bin =10, at 1.4 GHz, and n a =1, we find n s ~20

21 Limitations Baseline length range Long baselines need a lot of computation (fine f,t cells) Short baselines need a lot of (f, t) space Calibration parameters must be stable over this space Simple tests suggest 100:1 baseline length range Computational load related to square of this ratio Effects of data editing Non-contiguous time/frequency coverage RFI excision Scan boundaries, finite scan times The smaller the desired FOV, the more severe the effects Both these limitations are under study

22 The Problem of RFI: u-v plane Correlator v t 1 RFI f t 2 f 2 f 1 f 2 f 1 t 1 t 2 u t Each excised time/frequency interval on a given baseline will cause a particular gap in the u-v patch for that baseline convolution function in u-v plane no longer uniform among baselines different FOV shape for each visibility Simulations and MERLIN data being used to characterize RFI effects.

23 MERLIN RFI excision tests Performance metric - degree of 3C343.1 attenuation Experiment with Gaussian and Jinc convolution functions Observe degradation in suppression factor Try various types/amounts of data excision Comb of frequencies Regular dropouts in time Preferentially on short or long baselines Randomly in time and frequency Between 6% and 50% data flagging

24 Preliminary RFI Excision Results Jinc convolution No flagging: source suppression factor >150 Flagging: source suppression factor Character of flagging does not strongly affect result Gaussian convolution No flagging: partial suppression (by design) 4:1 Flagging: No significant change Conclusion Method robust for modest suppression Much more sensitive testing needed (6-station data)

25 Limits to pre-cal convolution v Calibration gradients across (t,f) domain, sky spectral effects, will limit convolution accuracy. Worst effects on shortest baselines. u freq u v time Effects can be empirically determined by simulation, MERLIN data

26 Summary High resolution at SKA sensitivity demands small FoV Reduce post-correlation data rates, computing loads Limit aggregate sidelobe confusion noise Correlator FoV shaping can do this Computationally affordable for useful parameters Suppresses distant sources at early processing stage, cleanly Reduces data volume Limitations Only useful/needed for higher resolution observations Maximum baseline length d.r. ~100 Compromised by sky spectrum, (t,f) variable calibration, RFI Modest sensitivity hit Ongoing work Explore limitations in detail with simulation and real data

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