ALMA Future Sc. Program Development Workshop Aug. 2016, Charlottesville Wide-fjeld Wide-band Full-polarization Imaging: Impact of Direction Dependent PB efgects S. Bhatnagar, U. Rau, P . Jagannathan, K. Kundart S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 1/20
What is wide-fjeld? “True” sky S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 2/20
What do we call wide-band? When fractional signal bandwidth used for imaging > ~20% ● Plus source spectral index >= -1.0 ● Plus target dynamic range > 1000 ● Spectral efgects for higher source spectral index will become ● signifjcant at lower bandwidth ratios I α Empirical Dynamic range : ● 100 Spectral line imaging, by defjnition, does not require wide-band imaging ● algorithms − 0.7 S ( ν)∝( ν/ ν o ) S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 3/20
Wide-band Wide-fjeld Imaging Wide band data to image beyond the ~50% point of the PB at a ● reference frequency Bandwidth ratio > ~20% ● FoV > ~HPBW @ reference frequency ● Variable PB: ● ● Long integration (rotation), Mosaicking (pointings at difgerent PA), in-beam polarization is large (AA) PB Frequency dependence PB “Spectral Index” (blue curve) S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 4/20
Wide-band Wide-fjeld Imaging Characterization of the (WB) A-Projection + MT-MFS ● MFS+SI MT-MFS+SI MT-MFS+ MT-MFS+ A-Projection WB A-Projection 2016, AJ (accepted) [arXiv:1605.07640] S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 5/20
Wide-band Wide-fjeld Imaging WB A-Projection + MT-MFS ● WB A-Projection for PB ● MT-MFS for sky ● (2011, ApJ, 739, L20 [arXiv:1106.2796v2]) S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 6/20
Full-Mueller (Polarization) WF-WB Imaging Direction Dependent (DD) Measurement Eq. (ME) in the ● image domain: Obs = [ M ] ⋅ [ I o ] I = [ [ Obs ] ⋅ [ 0 ] M 44 ] ● Diagonal: “pure” poln. products Obs o I I I I M 11 M 12 M 13 M 14 ● Off-diagonal: Include poln. leakage Obs o I Q I Q M 21 M 22 M 23 M 24 Obs o M 31 M 32 M 33 M 34 I U I U M 41 M 42 M 43 I V I V DD ME in the visibility domain: where A i = [ ● A q ] T ] ∗ [ V ij A p A p → q Obs = [ A i ⊗ A j o ] = [ A ij ] ∗ [ V ij o ] V ij A q → p Antenna Aperture Illumination S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 7/20
DD Efgects in Full-pol. Imaging DD “Mueller” matrix: ● [ Obs ] [ 0 ] Obs o I I I I Obs I Q o I Q = . Obs o I U I U I V I V Stokes Basis ● Affects DR at the 10 3-4 level ● PB Stokes-Q, -U is few% of Stokes-I [Jagannathan, Bhatnagar, Rau & Taylor] S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 8/20
DD Efgects in Full-pol. Imaging DD “Mueller” matrix: ● [ Obs ] [ 0 ] Obs o I I I I Obs I Q o I Q = . Obs o I U I U I V I V Stokes Basis ● Affects DR at the 10 3-4 level ● PB Stokes-Q, -U is few% of Stokes-I [Jagannathan, Bhatnagar, Rau & Taylor] S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 9/20
Issues in Wide-fjeld Wide-band Full-Pol. Imaging PB Efgects ● In-beam efgects : DD Leakage ● Parametric Aperture Illumination model (Holographic measurements ● not suffjcient) Pointing Errors ● Mosaic patterns ● Variations with frequency ● Frequency dependence of intrinsic Q and U ● Frequency dependence due to PB ● Computing load ● Fundamentally more expensive : Larger CF support ● Larger memory footprint: Fundamentally required, any which way you ● cut it S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 10/20
Full-pol. Imaging: In-beam Leakages Leakage (Ofg-diagonal elements of the Mueller matrix) ● Vary with direction (position in the beam), Parallactic Angle (time) and ● frequency Radial Slice for Stokes-I and I->Q Leakage [Jagannathan, Bhatnagar, Rau & Taylor] S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 11/20
Full-pol. Imaging: In-beam Leakages Leakage (Ofg-diagonal elements of the Mueller matrix) ● Vary with direction (position in the beam), Parallactic Angle (time) and ● frequency Radial Slice for Stokes-I and I->Q Leakage [Jagannathan, Bhatnagar, Rau & Taylor] S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 12/20
Full-pol. Imaging: Mosaic Sensitivity Pattern In-beam Stokes-Q pattern for a 11x11 point mosaick ● Heterogeneous case; rotation due to PA change also ignored ● The resulting pattern is combination of overlapping Clover-leaf pattern of each pointing • In-beam DD leakage spreads all across the mosaicked region. [Jagannathan, Bhatnagar, Rau & Taylor] S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 13/20
Full-pol. Imaging: PB Efgects Parametric model of antenna Aperture Illumination ● Difgerence between Ant6 and Ant10 in “homogeneous array” ● In the graph below: Optical effects should be independent of frequency (e.g. Poln. Squint) Mechanical effects should show linear trends (e.g. Antenna pointing errors) error Antenna pointing R-Beam Poln. Squint L-Beam Data: R. Perley Analysis: P.Jagannathan, S.Bhatnagar S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 14/20
Full-pol. Imaging: PB Efgects Parametric model of antenna Aperture Illumination ● Aperture Illumination ● Strongest effects Antenna size,Pointing errors ● Quadrapods ● Antenna-to-antenna variations ● [Kundert et al. IEEE Trans. (in review)] S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 15/20
Full-pol. Imaging: PB Efgects Parametric model of antenna Aperture Illumination ● Aperture Illumination ● Strongest effects Antenna size,Pointing errors ● Quadrapods ● Antenna-to-antenna variations ● [Kundert et al. IEEE Trans. (in review)] S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 16/20
Full-pol. Imaging: PB Efgects Parametric model of antenna Aperture Illumination ● Aperture Illumination ● Strongest effects Antenna size,Pointing errors ● Quadrapods ● Antenna-to-antenna variations ● [Kundert et al. IEEE Trans. (in review)] S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 17/20
Full-pol. Imaging: PB Efgects Parametric model of antenna Aperture Illumination ● Aperture Illumination ● Strongest effects Antenna size,Pointing errors ● Quadrapods ● Antenna-to-antenna variations ● [Kundert et al. IEEE Trans. (in review)] S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 18/20
Full-pol. Imaging: PB Efgects Parametric model of antenna Aperture Illumination ● Aperture Illumination ● Strongest effects Antenna size,Pointing errors ● Quadrapods ● Antenna-to-antenna variations ● [Kundert et al. IEEE Trans. (in review)] S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 19/20
Full-pol. Imaging: PB Efgects Parametric model of antenna Aperture Illumination ● Aperture Illumination ● Strongest effects Antenna size,Pointing errors ● Quadrapods ● Antenna-to-antenna variations ● [Kundert et al. IEEE Trans. (in review)] S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 20/20
Full-pol. Imaging: PB Efgects Parametric model of antenna Aperture Illumination ● Aperture Illumination ● Strongest effects Antenna size,Pointing errors ● Quadrapods ● Antenna-to-antenna variations ● [Kundert et al. IEEE Trans. (in review)] S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 21/20
Full-pol. Imaging: PB Efgects Parametric model of antenna Aperture Illumination ● Aperture Illumination ● Strongest effects Antenna size,Pointing errors ● Quadrapods ● Antenna-to-antenna variations ● [Kundert et al. IEEE Trans. (in review)] ● Cost equations ● Cheaper to fix the hardware? ● Cheaper to handle in post processing? S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 22/20
Full-pol. Imaging: PB Efgects EVLA Squint ● Expected: Lateral translation between RR- and LL-beams ● Measure: Translation + Rotation (~1 deg!) ● S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 23/20
Full-pol. Imaging: PB Efgects EVLA Squint ● Expected: Lateral translation between RR- and LL-beams ● Measure: Translation + Rotation (~1 deg!) ● S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 24/20
Full-pol. Imaging: Q/U vs. Frequency MFS approach to gain from WB sensitivity ● - PSF structure scales with frequency - Effective PSF amplitude also changes with frequency (Sp. Ndx., PB scaling) [Jagannathan, Bhatnagar, Rau & Taylor] S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 25/20
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