Understanding imaging limits due to approximations in ALMA primary - PowerPoint PPT Presentation

Understanding imaging limits due to approximations in ALMA primary beam models Urvashi Rau Kara Kundert Sanjay Bhatnagar NRAO, Socorro Intern from NRAO, Socorro U.Michigan / U.C.Berkeley ALMA Future Science Development Program Workshop 24-25 August 2016, Charlottesville, VA

Outline Problem : ALMA antenna aperture illuminations vary a lot within an observation - DA,DV,PM, illumination ofgsets, Pointing, Parallactic angle rotation Imaging algorithms can account for this via A-Projection but at a very high computing cost. => Need to understand when approximations can be used. Simulations : Use measured aperture illumination functions to simulate data and perform only standard Stokes I imaging. [ Similar to a study for CARMA by S.Corder 2009] Results : DR < 1000 : Only dish sizes matter (7m/12m). DR > 1000 : Pointing ofgsets (uncorrected, 2-4arcsec) DR > 5000 : Illumination ofgsets, variations between antennas, corrected pointing ofgsets (<0.5arcsec) DR > 10000 : Parallactic angle rotation, DA/DV combination ALMA Future Science Development Program Workshop, 24,25 Aug 2016 2

Wide-Field Imaging – Primary Beams The Sky is multiplied by a PB, before being sampled by each baseline PSF ( l ,m,t ) ∗ [ P ij ( l ,m,t ) sky ( l ,m ) ] obs ( l ,m )= ∑ ij ,t I ij I ⋅ I Primary Beam for baseline ij P ij ∗ = FT [ A i ∗ A j ∗ ] = FT [ A ij ] P ij = V i .V j b max D Aperture Illumination for antennas The antenna fjeld of view : A i , A j i and j : D = antenna diameter λ/ D A ij = Baseline aperture Illumination ALMA Future Science Development Program Workshop, 24,25 Aug 2016 3

Primary beam variations - Difgerent antenna structures – 3 types for 12m and 1 for 7m - Illumination ofgsets – all antennas - Pointing errors and parallactic angle rotation – all antennas/times ALMA DA - aperture DV - aperture PM - aperture uncorrected pointing DA - power DV - power PM - power EVLA – parallactic angle rotation Measured beams from S.Corder & D.Gunawan ALMA Future Science Development Program Workshop, 24,25 Aug 2016 4

Primary Beam – Effect on images (VLA simulated example) (1) Multiplicative gain pattern PBCOR : Divide out an average PB (2) Artifacts around bright sources PSF ( t ) ∗ [ δ P ( t ) obs = ∑ t I sky ] δ I ⋅ I A-PROJECTION : Partial UV-domain correction before combining visibilities CASA gridder=’mosaic’ : Accounts for difgerent antenna sizes (7m,12m) by default and allows specifjcation of separate models for each antenna. [No parallactic angle rotation or squint corrections] CASA gridder=’awproject’ : Rotationally asymmetric beams with parallactic angle rotation and squint correction (i.e. uses complex conjugates to undo systematic phase structures). Full Mueller support is in progress [Uses ray-traced models for EVLA and assumes identical antennas. Not ready for ALMA yet.] ( Mosaics : Additional phase gradient on the baseline aperture functions ) ALMA Future Science Development Program Workshop, 24,25 Aug 2016 14

Primary Beam Correction : A-Projection Bhatnagar et al, 2008 Apply PB correction in the UV-domain before visibilities are combined. sky ] psf ∗ [ P ij . I sky ] obs = S ij . [ A ij ∗ V obs = I ij I ij V ij T A ij − 1 ≈ A ij For each visibility, apply T ∗ A ij A ij T A ij (1) Use as the convolution function during gridding FT [ ∑ ij A ij T ∗ A ij ] (2) Divide out from the image (in stages). – Conjugate transpose during imaging corrects for phase structures in the baseline aperture functions. e.g. : pointing ofgsets such as beam squint. ALMA Future Science Development Program Workshop, 24,25 Aug 2016 15

Computational Cost of full A-Projection – Number of convolution kernels to be computed : N = Na(Na - 1)/2 * Nt * Nf (for Na antennas, Nt steps in PA, Nf channels) - Each kernel has [ support x oversampling ] pixels on a side. Support : approximately 7 - 20 (for a f-o-v that avoids aliasing) Oversampling : 20 – 100 ( to account for sub-uv-pixel shifts ) - Combining with W-Projection : Multiply N by N_wplanes N_support can be >100 pixels - Full polarization : multiply N by 16 to get the full Mueller matrix - Combine A-proj, W-proj, anti-aliasing func => 3 convolutions per kernel. => Need viable approximations ! Stokes I : Mosaicft : ALMA-specifjc AWProject : EVLA-specifjc. But, for high dynamic range and full-pol imaging, both need components from each other and computing costs escalate quickly. ALMA Future Science Development Program Workshop, 24,25 Aug 2016 16

Simulations to test what features we really need Data : Each antenna has a : - (complex) aperture illumination function - pointing ofgset as a phase gradient - parallactic angle rotation (numerical) For each timestep and antenna pair, - PB = product of complex antenna voltage patterns - Predict visibilities for real(PB) x sky Imaging : Standard imaging and deconvolution with post-deconvolution (average) PB-correction Variants : Stage 1 : toy beam models Stage 2 : measured beams ( Simulations done at 100 GHz ) Kundert, Rau, Bhatnagar, Bergin (in prep), 2016 ALMA Future Science Development Program Workshop, 24,25 Aug 2016 17

Understanding imaging limits due to approximations in ALMA primary - PowerPoint PPT Presentation

Understanding imaging limits due to approximations in ALMA primary beam models Urvashi Rau Kara Kundert Sanjay Bhatnagar NRAO, Socorro Intern from NRAO, Socorro U.Michigan / U.C.Berkeley ALMA Future Science Development Program Workshop

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