VLBI long and wide International LOFAR and efficient wide-field mapping Olaf Wucknitz wucknitz@astro.uni-bonn.de ICRAR, Curtin University of Technology, 22nd October 2010 AIfA The far side of Bonn If we can t be free, at least we can be cheap (Frank Zappa) O. Wucknitz 2010 1 VLBI long and wide LOFAR International LOFAR baselines LOFAR long baseline issues, fringe-fitting first long-baseline fringes first long-baseline images The Sun! Efficient wide-field mapping for VLBI what is wide-field VLBI? why is it difficult? standard solutions more efficient methods: FWFM limits of FWFM LOw Frequency ARray low frequencies LBA: 30(10) 80 MHz HBA: 110 250 MHz 40 stations in Netherlands additional stations in Germany, France, England, Sweden, Poland, Finland!, Italy?, Spain?... wide field of view, several beams good survey speed full synthesis imaging at low frequencies with high resolution O. Wucknitz 2010 2 O. Wucknitz 2010 3 LOFAR is VLBI LOFAR resolution independent clocks at the stations Rubidium + GPS data sent directly to correlator in Groningen (e-vlbi) no mixers, signal sampled directly (16 bit) Nyquist / undersampled for conversion no phase offset between clock (sampling) and LO no automatic gain control, no normalisation of correlations amplitude calibration does not need T sys, but only gain fringe-spacing θ = λ/l resolution λ/m freq/mhz 1 km 30 km 300 km 1000 km 30 10 1. 7 3. 4 21 6. 2 10 30 34 1. 1 6. 9 2. 1 3.8 80 13 26 2. 6 0. 77 2.5 120 8. 6 17 1. 7 0. 52 1.9 160 6. 4 13 1. 3 0. 39 1.4 220 4. 7 9. 4 0. 94 0. 28 O. Wucknitz 2010 4 O. Wucknitz 2010 5 International LOFAR stations LOFAR core: the superterp O. Wucknitz 2010 6 O. Wucknitz 2010 7
German LOFAR stations LBA at Effelsberg O. Wucknitz 2010 8 O. Wucknitz 2010 9 LBA + HBA at Effelsberg LBA details at Unterweilenbach O. Wucknitz 2010 10 O. Wucknitz 2010 11 HBA + LBA in Tautenburg Not connected yet: Potsdam O. Wucknitz 2010 12 O. Wucknitz 2010 13 VLBI methods for LOFAR Very Long Baseline Interferometry meaning of long depends on circumstances (λ) unstable phases, short coherence times weak signal: have to average in time and frequency solve for delays τ = 1 φ 2π ν solve for rates r = 1 φ 2π t = ν τ t non-dispersive τ = τ 0 dispersive ( ν0 ) 2 τ = τ 0 ν O. Wucknitz 2010 14 Fringe-fitting for LOFAR either for single subbands (BW 200 khz, τ 5 µsec) or coherent multi-band (BW 48 MHz, τ 0.02 µsec) beware of multiple peaks in delay/rate produce 2-d delay/rate spectra simultaneously fit for four parameters (per baseline) dispersive/nondispersive delays/rates no residual phase needed? O. Wucknitz 2010 15
Very first long baseline fringes (NL-Ef, Aug 2009) Are the fringes real? Yes! 3C196, one subband, LBA Coherently averaged over time intervals, then FFTed in frequency, then incoherently averaged over 1 h. O. Wucknitz 2010 16 O. Wucknitz 2010 17 Fringes in delay/rate space (single subband) Phases and dispersive delays 5 subbands continuous mod phase [full turns] 0-5 -10 30 40 50 60 70 80 freq [MHz] O. Wucknitz 2010 18 O. Wucknitz 2010 19 Multi-band: more sensitivity and higher resolution delay Fringes to Tautenburg and Unterweilenbach (Jan 2010) O. Wucknitz 2010 20 O. Wucknitz 2010 21 Interfering sources (observations of 3C48) Delay/rate map of field around 3C196 VLSS (74 MHz): A 19Jy B 6 Jy C 17 Jy 3C196 140 Jy O. Wucknitz 2010 22 O. Wucknitz 2010 23
Results of fringe analysis LBA long-baseline map: some details long baseline fringes found clock offsets in some stations confusion in LBA polarisation labels strong 8 MHz ripple 63 MHz LBA resonance strong differential Faraday rotation fringe-rate/delay map produced time for imaging! 3C196, LBA, 31 / 160 subbands, 44 59 / 30 80 MHz (ripple!) bandwidth 6 MHz / 48 MHz D2010 16704 6 h on 12/13 Feb 2010 5 NL + 3 DE stations (Effelsberg, Unterweilenbach, Tautenburg) corrected for 1 µsec and 17 µsec constant delays RR and LL from XX/XY/YX/YY using geometric model (self-)calibrated and imaged LL/RR in difmap MFS with/without spectral index correction O. Wucknitz 2010 24 O. Wucknitz 2010 25 UV coverage with long and short baselines MTRLI (MERLIN) observations of 3C196 at 408 MHz [ Lonsdale & Morison (1980) ] O. Wucknitz 2010 26 O. Wucknitz 2010 27 LOFAR maps of 3C196 (LBA: 30-80 MHz) Same with circular beams NL only, 35 22 beam NL+DE, 1. 5 0. 9 beam NL only, 30 beam NL+DE, 1. 5 beam O. Wucknitz 2010 28 O. Wucknitz 2010 29 LOFAR LBA vs. MERLIN 408 MHz First interferometric Solar observations [ Wucknitz + Lonsdale & Morison (1980) ] initiated by J. Anderson, F. Breitling, G. Mann, A. Polatidis, C. Vocks, O. Wucknitz (alphabetical order) 8 ten-minute scans on 9th June 2010, 9:48 15:50 UT 4 with LBA and HBA each phase/pointing centre near Sun and calibrator sources LBA difficult, other sources dominating: 3C123, CygA, CasA,... situation unclear HBA much clearer signal, Sun dominating on short baselines self-calibration possible because of compact component only short baselines used! O. Wucknitz 2010 30 O. Wucknitz 2010 31
The very first map Dynamic spectra of the Sun Significant variability as function of time and frequency! O. Wucknitz 2010 32 O. Wucknitz 2010 33 Variability: 30 sec in 1 sec steps (8 subbands) Summary LOFAR long baseline LOFAR works! but no pipeline yet all own software + AIPS + difmap fringe analysis revealed a number of technical problems (mostly solved now) Sun can be observed and resolved with LOFAR! to do full fringe-fitting and calibration not independent of polarisation calibration (differential Faraday rotation) Sun as function of time and frequency O. Wucknitz 2010 34 O. Wucknitz 2010 35 Wide-field VLBI: What s so special? Why is it difficult? resolution (6 cm global) θ λ L 1mas other limiting factors bandwidth smearing N ν ν f.o.v. limit (primary beam) Θ λ D 8 number of pixels N 2 = ( ) 2 L (500000) 2 D wide-field VLBI means very, very many pixels not necessarily many degrees time-averaging smearing N 1d 2π t e.g. ν = 1.6GHz, D = 25m, L = 10000km ν 4kHz = 64MHz 16000 14 % loss t 0.03s 6 % loss correlator limitations and huge correlated data sets O. Wucknitz 2010 36 O. Wucknitz 2010 37 Current solutions An example: the Lenc et al. field postage-stamps: only map small regions of interest need to know sources in advance individual correlator passes per region (no smearing) need n correlations for n regions DiFX can now do it in one run (for reasonable n) all regions from one wide-field correlation post-correlation computing time n data set size hybrid approaches all too demanding for full primary beams VLBA (92/49 cm) + JB + phased WSRT, 14 h in Nov. 2005 Emil Lenc, Olaf Wucknitz, Mike Garrett, James Anderson field around lens B0218+357 4 4 MHz, dual polarisation, 2-bit sampling correlation at JIVE: 3 passes narrow field: all bands, 4 pols, 32 channels, 1 sec wide field: one band, LL, 512 channels, 0.25 sec (80 GB) wide field: one band, RR, 512 channels, 0.25sec, shifted O. Wucknitz 2010 38 O. Wucknitz 2010 39
The target: B0218+357 (VLA+Pt 2 cm) The telescopes natural weighting uniform weighting O. Wucknitz 2010 40 O. Wucknitz 2010 41 Diversion: maps of B0218+357 Emil Lenc s postage stamps 43 mas 34 mas 50 mas 50 mas 70 mas 70 mas primary beam VLBA 2. 6 circles at 15, 30, 1, 1. 5, 2, 3 uv range, tapering exclusion of WB + JB crosses: WENSS red: compact, above limit blue: resolved or below limit [ Lenc et al. (2008) ] boxes: VLBI detections (10%) O. Wucknitz 2010 42 O. Wucknitz 2010 43 Gallery Mission accomplished? total area imaged 0.5% of 2 radius ring 2.2% of VLBA primary beam 6 weeks processing time [ Lenc et al. (2008) ] total field would need 6 years! reasons to map complete field? possible transient found! future: blind surveys O. Wucknitz 2010 44 O. Wucknitz 2010 45 Going logarithmic FWFM schematic learn from other fields tree-codes (e.g. n-body simulations) Fast Fourier Transform (FFT) FT example: N elements direct: N 2 FFT: N logn try hierarchical down-averaging (Fast Wide Field Mapping, FWFM) shift and average for 4 sub-fields (diameter /2) treat each sub-field in the same way O. Wucknitz 2010 46 O. Wucknitz 2010 47
What s the benefit? Large-scale test field size: N N pixels (max. 400000) number of facets of size n n: (N/n) 2 standard direct method number of facets data-set size total N 4 /n 2 FWFM number of averaging steps data-set size 4 total 4N 2 log 2 (N/n) extreme case: N = 400000, n = 1000 gain factor 4500 N = 256k, n = 2k (64Gpix), 2 2 theoretical gain factor 585 direct mapping with (UVFIX/SPLAT+)IMAGR: 16384 31 min 1 year FWFM 7 steps: 2.0+8.0+7.0+2.6+1.4+1.9+3.1 h IMAGR: 16384 3 sec 40 hours ( factor 220, could even Clean) O. Wucknitz 2010 48 O. Wucknitz 2010 49 UVFIX+SPLAT+IMAGR with reduced resolution FWFM+IMAGR with reduced resolution O. Wucknitz 2010 50 O. Wucknitz 2010 51 shifting Problems and limits of FWFM exact definition of uvw essential (aberration etc) UVFIX not consistent, nor with correlators want to shift with full delays (DiFX: John Morgan) uncertainty principle in uv plane for one correlation cannot do ν 0 and t 0 at the same time ν t 1 N 2 ν 1d 2π (few 106 ) 2 field c 1d L 2πν 10 2π D L ν 1d few m no faceting Alternative approach: w-projection one huge, fine grid for FFT special gridding convolution function to correct for w-term very efficient for moderate field-sizes disadvantages convolution function gets wide for large fields have to do FFT of TB field no faceting, no position dependent calibration have to redo gridding after new calibration O. Wucknitz 2010 52 O. Wucknitz 2010 53 The next project 92/49 cm VLBA observations of Pic-A PI: Emil Lenc uncorrelated data stored for piggyback wide-field project correlate with DiFX in Bonn planning to try different strategies full primary beam (blind survey) full-resolution correlated data 15TB dedicated computer cluster (with GPUs) O. Wucknitz 2010 54 Another current project L-band observations of M31 (Argo, Morgan, Wucknitz, Lenc, Middelberg, Tingay,... ) VLBA (BA97) and EVN (EM 82), not global correlate and image in different ways at different places NRAO + Bonn (MPIfR) with normal resolution ICRAR with multiple phase centres Bonn (AIfA) with high resolution for FWFM goal science case test, compare and improve different strategies combine advantages of methods O. Wucknitz 2010 55
Transport of large long-baseline experiments for you Summary wide-field VLBI full wide-field VLBI is possible, even at 90 cm! highly efficient FWFM method ungridded averaging, faceted calibration possible 15 TB in 5 min 400 Gb/s 5 days 250 Mb/s with higher bandwidth still possible but demanding small clusters can do it in progress! to do extrapolate to LOFAR and SKA compare with w-projection and hybrid methods write the paper O. Wucknitz 2010 56 O. Wucknitz 2010 57 Additional material The International LOFAR Telescope (ILT) International LOFAR stations Station layout Multi-band delay fitting (details) Short baseline map of 3C196 Expectations: 3C196 at 5 GHz Very first LBA long-baseline imaging attempts First HBA long-baseline imaging attempt 10 min movie of the Sun relation FWFM FFT O. Wucknitz 2010 58 http://www.astron.nl/~heald/lofarstatusmap.html O. Wucknitz 2010 59 Station layout: international (originally all) Station layout: NL remote O. Wucknitz 2010 60 O. Wucknitz 2010 61 Station layout: NL core do not fit phases directly Delay fitting only know phase modulo 2π data are noisy equivalent (but better!): maximise the corrected signal measured and original visibility V(ν) = e 2πiντ(ν) V 0 (ν) hope that V 0 (ν) = const and correct for delay find maximum of dν e 2πiντ(ν) V(ν) 2 this is Fourier transform if τ = const O. Wucknitz 2010 62 O. Wucknitz 2010 63
Multi-band delay fitting delay almost constant within subbands apply FFT for all subbands combine the results incoherently combine the results coherently f i (τ i ) = i dν e 2πi(ν ν i)τ i V(ν) ( F[τ] = e 2πiν iτ(ν i ) f i τ(νi ) ) i with coarse FFT on fine grid, interpolation τ arbitrary function of frequency (non-/dispersive) Include fringe rates have to integrate in time to increase S/N take into account rates (time-derivatives) do not use phase rates but delay rates r = τ dispersive/non-dispersive t f i (τ i,r i ) = dν e 2πi(ν ν i)τ i dt e 2πi(t t 0)r i V(ν,t) i ( F[τ,r] = e 2πiν iτ(ν i ) f i τ(νi ),r(ν i ) ) i all phase rates are frequency-dependent O. Wucknitz 2010 64 O. Wucknitz 2010 65 VLSS vs. LOFAR map of field around 3C196 3C196 on long baselines: expectations Cambridge 5km at 5 GHz [ Pooley & Henbest (1974) ] O. Wucknitz 2010 66 O. Wucknitz 2010 67 Very first long baseline maps of 3C196 HBA observations of 3C196: some details 3C196, HBA, 120 / 244 subbands, 131 155 MHz bandwidth 24 MHz L2010 07608 12 h, 22nd May 2010 7 NL + 2 DE stations (Effelsberg, Tautenburg) corrected for 8 µsec in superterp,... (self-)calibrated and imaged YY in difmap phase jumps, rates, inconsistent delays (in freq) low S/N in German stations most of the time imaging very tough, details not reliable yet O. Wucknitz 2010 68 O. Wucknitz 2010 69 HBA observations: uv coverage, dirty beam LBA + HBA images of 3C196 beam size 1. 0 0. 5 O. Wucknitz 2010 70 O. Wucknitz 2010 71
LBA + HBA images of 3C196 with contours Variability: 10 min in 10 sec steps (1 subband) O. Wucknitz 2010 72 O. Wucknitz 2010 73 Relation to Fast Fourier Transform n 1 f j = e 2πi jk/n F k k=0 = even k n/2 1 = k=0 n/2 1 = k=0 + odd k e 2πi jk/(n/2) ( F 2k +e 2πi j/n F 2k+1 ) }{{} averaging of visibilities e 2πi jk/(n/2) { (F2k + F 2k+1 ) for one half (F 2k F 2k+1 ) for the other half FFT corresponds to shifting and averaging O. Wucknitz 2010 74