Applying full polarization A-Projection to very-wide fields of view instruments: An imager for LOFAR Cyril Tasse

Transcription

1 Applying full polarization A-Projection to very-wide fields of view instruments: An imager for LOFAR Cyril Tasse ASTRON/Leiden: Joris van Zwieten, Bas van der Tol, Ger van Diepen NRAO: Sanjay Bhatnagar

2 Bas van der Tol Sanjay Me Ger van diepen missing :( Joris van Zwieten

3 Overview 1- LOFAR and the Measurement Equation 2- How do you get AW-Projection? Why? 3- Implementations / Optimisations for LOFAR 4- Simulations / Test / Perfomance 5- Conclusion Paper submitted: arxiv:

4 4-pol visibility for one baseline One off axis polarized source (IQUV=100, 40, 20, 10)

5 When Direction Dependent Effects (DDE) become a problem : Beam y x MHz MHz y x LOFAR stations are phased arrays - Beam is variable in frequency and time - Projection of the dipoles in the sky is non trivial - Beam can be station-dependent --> Strong effects on polarisation

6 When Direction Dependent Effects (DDE) become a problem : Ionosphere Incoming wavefront Outcoming wavefront PSF Ionosp here Big field of view : station, direction, time and frequency dependent Other direction dependent effects : - Projection of the dipoles on the sky - Faraday rotation + Effect on the polarisation

7 The Measurement Equation Direction independent Direction dependent Source coherency F Hamaker 1996 Linear transf. [Voltage antenna p] x [ Voltage antenna q]* Beam Geometrical delay +Correlator Ionosphere Van der Tol thesis Electric field F'

8 An imager for LOFAR Mesurement ( points) Calibration Numerical instrument ( A-Projection ): generalized adaptative optics - Primary beam - Dipole projection - Ionosphere - Faraday rotation Constrain: Operate on the data in postprocessing real time (< obs time) GOAL: Dynamiques range of 1: Unknown Sky Calibration

9 The Vec Operator If Columns of a Matrix And then

10 The Vec Operator applied to the ME Applying: To: DDE (4*4) Then: 3D FT With:

11 The direction-dependent Mueller matrix for a given baseline LOFAR LBA beam: Off-diagonal Mueller element as high as 10%

12 A-Projection Bhatnagar 08 DDE are in general smooth on the sky --> small support in the uv-domain Convolution theorem DDE (4*4) Convolution 2D FFT W term (scalar)

13 DeGridding for a given time, frequency, baseline FFT XXgrid XYgrid YXgrid YYgrid Sky domain IQUV XXgrid XYgrid YXgrid YYgrid

14 DeGridding for a given time, frequency, baseline FFT XXgrid XYgrid YXgrid YYgrid Sky domain IQUV Convolved XXgrid XYgrid YXgrid YYgrid

15 DeGridding for a given time, frequency, baseline FFT XXgrid XYgrid Sky domain IQUV YXgrid Convolved YYgrid XX XXgrid XYgrid YXgrid YYgrid

16 DeGridding for a given time, frequency, baseline FFT XXgrid XYgrid Sky domain IQUV YXgrid Convolved YYgrid XX, XY, YX, YY XXgrid XYgrid YXgrid YYgrid

17 Testing fullpol A-Projection One off axis polarized source (IQUV=100, 40, 20, 10) It works, but: - 16 operation instead of 4-16 convolution function instead of 1 - More memory access

18 Saparating the element beam from the station beam - Naive AW-Projection with beam: - DDE to convolution functions: Y BUT: X

19 Saparating the element beam from the station beam Baseline independent 16 terms slow Element beam (4*4) Baseline dependent 1 term, fast variation (ionosphere) Array factor*w term*ionosphere (scalar) Practical HowTo: 1- In a time/frequency interval: correct the 4-pol grids for the element beam 2- Degrid using a scalar time/freq/baseline dependent CF Advantage: - CF estimate per baseline: 1 CF instead of 16 - gridder: 1 memory acess instead of 16 - per visibility 4 gridding step instead of 16 Disadvantage: - Assumption may happen to be wrong for the long baselines and for Faraday rotation - Code is more complicated

20 Tests on simulated data 100 sources with flux density following NVSS 1.4 GHz source counts

21 Tests on simulated data Wterm + Scalar /diagonal beam 100 sources with flux density following NVSS 1.4 GHz source counts

22 Tests on simulated data Wterm + full beam Mueller matrix 100 sources with flux density following NVSS 1.4 GHz source counts

23 Tests on simulated data W-Proj only W-Proj + Array Factor Convergence of CLEAN W-Proj + Full Beam W-Proj + Full Beam + fuzzy corr

24 Tests on simulated data 100 sources with flux density following NVSS 1.4 GHz source counts

25 Computation ballance For CF estimate every 20 minutes With zero padding interpolation But: can be much worst Huge limitations for: - Wide FOV - Ionospheric corrections (until November 2012)

26 New implementation: hybrid w-stacking In the current (old) implementation w-term is annoying because: 1- For each baseline, we have to compute a big CF 2- We have to grid each individual baseline with that big CF BUT: The w-term is not in itself baseline dependent!!! We can rewrite the problem (degridding - predict) Old New 2- Conv with a element beam-term 3- Conv with a w-term (only step 4 is baseline dependent!) 4- Conv with a Aterm and dw-term 1- FFT of sky model

27 New implementation: w-stacking Gridding... Put selected visibilities of given baseliene on w-plane 0, with a kernel containing delta-w and scalar A-term W-plane 0

28 New implementation: w-stacking Gridding... loop over baselines, time and frequency bins W-plane 0

29 New implementation: w-stacking Gridding Convolve this plane with the w-term of the plane 0 W-plane 0 w-term

30 New implementation: w-stacking Gridding... Loop over w-planes... W-plane 1 W-plane 0 w-term

31 New implementation: w-stacking Gridding... Sum the grids of all wplanes + apply the element beam W-plane 1 W-plane 0 w-term

32 New implementation: w-stacking Advantage: - The delta-w/a-term CF is much smaller: the CF calculation time too - The W-term is applied to all baselines simultaneously --> we win a lot of computing time for the quickly varying / long baseline DDE - The CF always have the same support: easy scheduling for parallel gridding

33 Parallel gridding All convolution functions have the same support! - Before: one grid per thread and awimager limitted to small grids Thread 1 Thread 2 Thread 3 Thread 4

34 Parallel gridding All convolution functions have the same support! - Before: one grid per thread and awimager limitted to small grids - now: one grid only and all threads operate on it [movie] Thread 1 Thread 2 Thread 3 Thread 4

35 Performance Scaling: Typically, 2-3 hours for 11000x11000 pixel image, 12 hours, 12 subbands, 10 major cycles We can now apply quickly varying DDEs NB: At the moment, the parellelisation only uses multicores on single node.

36 Putting ionosphere in... Bas van der Tol Incoming wavefront Outcoming wavefront PSF The same idea: FT Convolution function

37 Putting ionosphere in the imager... A grid of sources with equal flux 2D phase screen on top Corrected for the center only

38 Putting ionosphere in the imager... A grid of sources with equal flux 2D phase screen on top The direction dependent ionospheric has been applied.

39 Putting ionosphere in the imager... Phased array beam + Ionosphere corrupted Simulated dataset with many point sources (LOFAR's beam+ionosphere)

40 Putting ionosphere in the imager... Phased array beam + Ionosphere corrected Simulated dataset with many point sources (LOFAR's beam+ionosphere)

41 Putting ionosphere in the imager... Simulated dataset with many point sources (LOFAR's beam+ionosphere)

42 Putting ionosphere in the imager... Simulated dataset with many point sources (LOFAR's beam+ionosphere)

43 Conclusion Several AW-Projection implementation for LOFAR DDE: Time, Frequency, Baseline dependent 1- Full naive implementation too slow 2- Separate the element beam much better (x16) - LOFAR's architecture related 3- Separate the w-term from the A-Term (x5-10) - Faster than real time - Many pixels: wide fields, high resolution - and for quickly varying DDE Next steps - Memory consumption still big in certain cases - Pythonisation of the imager (Bas, Joris, Alexey): - Easy platform to include compressed sensing - GPUs development - Parallelisation of the imager over the cluster - Multi-Term / Wide-Band cleaning - Open issues in the image plane (CLEAN doesn't use varying Direction Dependent PSFs) - Calibration of quickly varying DDE