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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 1/20
ALMA Future Sc. Program Development WorkshopAug. 2016, Charlottesville
Wide-field Wide-band Full-polarization Imaging:
Impact of Direction Dependent PB effects
S. Bhatnagar, U. Rau, P. Jagannathan, K. Kundart
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 2/20
What is wide-field?
“True” sky
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 3/20
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 effects for higher source spectral index will become significant at lower bandwidth ratios
● Empirical Dynamic range :
● Spectral line imaging, by definition, does not require wide-band imaging algorithms
Iα
100
S( ν)∝( ν / νo)−0.7
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 4/20
Wide-band Wide-field 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 different PA), in-beam polarization is large (AA)
PB “Spectral Index” PB Frequency dependence(blue curve)
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 5/20
Wide-band Wide-field Imaging● Characterization of the (WB) A-Projection + MT-MFS
MFS+SI MT-MFS+SI
MT-MFS+A-Projection
MT-MFS+WB A-Projection
2016, AJ (accepted) [arXiv:1605.07640]
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 6/20
Wide-band Wide-field Imaging● WB A-Projection + MT-MFS
● WB A-Projection for PB
● MT-MFS for sky
(2011, ApJ, 739, L20 [arXiv:1106.2796v2])
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 7/20
Full-Mueller (Polarization) WF-WB Imaging● Direction Dependent (DD) Measurement Eq. (ME) in the
image domain:
● DD ME in the visibility domain:
IObs= [ M ]⋅[ I o ]
[I IObs
IQObs
IUObs
IVObs ] = [
M 11 M 12 M 13 M 14
M 21 M 22 M 23 M 24
M 31 M 32 M 33 M 34
M 41 M 42 M 43 M 44]⋅[
I Io
IQo
IUo
IV0 ]
● Diagonal: “pure” poln. products● Off-diagonal: Include poln. leakage
where Ai = [ A p A p→ q
Aq→ p Aq]V ij
Obs = [ Ai⊗A jT ] ∗[V ij
o ] = [ Aij ] ∗[V ijo ]
Antenna Aperture Illumination
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 8/20
DD Effects in Full-pol. Imaging● DD “Mueller” matrix:
Stokes Basis
[Jagannathan, Bhatnagar, Rau & Taylor]
● Affects DR at the 103-4 level● PB Stokes-Q, -U is few% of Stokes-I
. [I I
o
IQo
IUo
IV0
][I I
Obs
IQObs
IUObs
IVObs
] =
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 9/20
DD Effects in Full-pol. Imaging● DD “Mueller” matrix:
Stokes Basis
[Jagannathan, Bhatnagar, Rau & Taylor]
● Affects DR at the 103-4 level● PB Stokes-Q, -U is few% of Stokes-I
. [I I
o
IQo
IUo
IV0
][I I
Obs
IQObs
IUObs
IVObs
] =
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 10/20
Issues in Wide-field Wide-band Full-Pol. Imaging● PB Effects
● In-beam effects : DD Leakage
● Parametric Aperture Illumination model (Holographic measurements not sufficient)
● 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
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 11/20
Full-pol. Imaging: In-beam Leakages● Leakage (Off-diagonal elements of the Mueller matrix)
● Vary with direction (position in the beam), Parallactic Angle (time) and frequency
[Jagannathan, Bhatnagar, Rau & Taylor]
Radial Slice for Stokes-I and I->Q Leakage
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 12/20
Full-pol. Imaging: In-beam Leakages● Leakage (Off-diagonal elements of the Mueller matrix)
● Vary with direction (position in the beam), Parallactic Angle (time) and frequency
[Jagannathan, Bhatnagar, Rau & Taylor]
Radial Slice for Stokes-I and I->Q Leakage
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 13/20
Full-pol. Imaging: Mosaic Sensitivity Pattern
[Jagannathan, Bhatnagar, Rau & Taylor]
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.
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 14/20
Full-pol. Imaging: PB Effects● Parametric model of antenna Aperture Illumination
● Difference between Ant6 and Ant10 in “homogeneous array”
R-Beam
L-Beam
Data: R. PerleyAnalysis: P.Jagannathan, S.Bhatnagar
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)
Po
ln. S
qu
int
An
tenn
a p
oin
ting
erro
r
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 15/20
Full-pol. Imaging: PB Effects● Parametric model of antenna Aperture Illumination
[Kundert et al. IEEE Trans. (in review)]
Aperture Illumination
● Strongest effects● Antenna size,Pointing errors● Quadrapods● Antenna-to-antenna variations
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 16/20
Full-pol. Imaging: PB Effects● Parametric model of antenna Aperture Illumination
[Kundert et al. IEEE Trans. (in review)]
Aperture Illumination
● Strongest effects● Antenna size,Pointing errors● Quadrapods● Antenna-to-antenna variations
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 17/20
Full-pol. Imaging: PB Effects● Parametric model of antenna Aperture Illumination
[Kundert et al. IEEE Trans. (in review)]
Aperture Illumination
● Strongest effects● Antenna size,Pointing errors● Quadrapods● Antenna-to-antenna variations
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 18/20
Full-pol. Imaging: PB Effects● Parametric model of antenna Aperture Illumination
[Kundert et al. IEEE Trans. (in review)]
Aperture Illumination
● Strongest effects● Antenna size,Pointing errors● Quadrapods● Antenna-to-antenna variations
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 19/20
Full-pol. Imaging: PB Effects● Parametric model of antenna Aperture Illumination
[Kundert et al. IEEE Trans. (in review)]
Aperture Illumination
● Strongest effects● Antenna size,Pointing errors● Quadrapods● Antenna-to-antenna variations
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 20/20
Full-pol. Imaging: PB Effects● Parametric model of antenna Aperture Illumination
[Kundert et al. IEEE Trans. (in review)]
Aperture Illumination
● Strongest effects● Antenna size,Pointing errors● Quadrapods● Antenna-to-antenna variations
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 21/20
Full-pol. Imaging: PB Effects● Parametric model of antenna Aperture Illumination
[Kundert et al. IEEE Trans. (in review)]
Aperture Illumination
● Strongest effects● Antenna size,Pointing errors● Quadrapods● Antenna-to-antenna variations
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 22/20
Full-pol. Imaging: PB Effects● Parametric model of antenna Aperture Illumination
[Kundert et al. IEEE Trans. (in review)]
Aperture Illumination
● Strongest effects● Antenna size,Pointing errors● Quadrapods● Antenna-to-antenna variations
● Cost equations● Cheaper to fix the hardware?● Cheaper to handle in post processing?
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 23/20
Full-pol. Imaging: PB Effects● EVLA Squint
● Expected: Lateral translation between RR- and LL-beams
● Measure: Translation + Rotation (~1 deg!)
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 24/20
Full-pol. Imaging: PB Effects● EVLA Squint
● Expected: Lateral translation between RR- and LL-beams
● Measure: Translation + Rotation (~1 deg!)
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 25/20
Full-pol. Imaging: Q/U vs. Frequency● MFS approach to gain from WB sensitivity
[Jagannathan, Bhatnagar, Rau & Taylor]
- PSF structure scales with frequency- Effective PSF amplitude also changes with frequency (Sp. Ndx., PB scaling)
![Page 26: ALMA Future Sc. Program Development Workshop · S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 3/20 What do we call wide-band? When fractional](https://reader033.vdocument.in/reader033/viewer/2022060505/5f1e285f61133241350591bd/html5/thumbnails/26.jpg)
S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 26/20
Full-pol. Imaging: Q/U vs. Frequency● MFS approach to gain from WB sensitivity
[Jagannathan, Bhatnagar, Rau & Taylor]
- PSF structure scales with frequency- Effective PSF amplitude also changes with frequency (Sp. Ndx., PB scaling)
PSF( xo)Continuum=∑νI (xo , ν)PSF(x−xo ,ν)
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 27/20
Full-pol. Imaging: Q/U vs. Frequency● Possible to use MT approach on Q and U for low RM cases
● Polynomial model (a la MT-MFS) tested for RM = -25 to +25
● Even easier for ALMA frequency range
[Jagannathan, Bhatnagar, Rau & Taylor]
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 28/20
The Hot-spots
GriddingDe-Gridding
ImageReconstruction
(ConvolutionsOf large images)
SupplyConvolutionFunctions
FFT
2
1
3Data
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 29/20
The Hot-spots
GriddingDe-Gridding
ImageReconstruction
(ConvolutionsOf large images)
SupplyConvolutionFunctions
FFT
2
1
3Data
Data scatter + Multi-process computing VsMulti-thread CPU computing
70-80% of the compute load!70-80% of the compute load!(The major cycle)(The major cycle)
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 30/20
The Hot-spots
GriddingDe-Gridding
ImageReconstruction
(ConvolutionsOf large images)
SupplyConvolutionFunctions
FFT
2
1
3Data
Data scatter + Multi-process computing VsMulti-thread CPU computing
70-80% of the compute load!70-80% of the compute load!(The major cycle)(The major cycle)
Compute and cache VsCompute on demand(on the GPU/FPGA)
Can dominate the memoryCan dominate the memoryfootprintfootprint
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 31/20
The Hot-spots
GriddingDe-Gridding
ImageReconstruction
(ConvolutionsOf large images)
SupplyConvolutionFunctions
FFT
2
1
3Data
Data scatter + Multi-process computing VsMulti-thread CPU computing
70-80% of the compute load!70-80% of the compute load!(The major cycle)(The major cycle)
Compute and cache VsCompute on demand(on the GPU/FPGA)
Can dominate the memoryCan dominate the memoryfootprintfootprint
Compute and cache VsCompute on demand(on the GPU/FPGA)
Minor cycle compute loadMinor cycle compute load(Can dominate the total run-time)(Can dominate the total run-time)
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 32/20
Algorithm architecture
FLOPS
I/O
Mem
ory
FLOPS-to-Mem Ratio
More memory per FLOP
Lesser memory per FLOPS
GPUs?
Algorithm design● Move towards algorithms with higher compute-to-I/O ratio● Use cheap massively parallel h/w (low memory footprint at the cost of higher computing)
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S. Bhatnagar: ALMA Future Science Program Development Workshop, Aug. 24 – 25, 2016, CV 33/20
Issues in Wide-field Wide-band Full-Pol. Imaging● PB Effects
● Develop parametric models for antenna aperture illumination
● Extend full Mueller imaging tools for heterogeneous array case
– Full-pol imaging for EVLA under test as part of P. Jagannathan’s thesis
● Variations with frequency
● Assess extension of MT-MFS for full pol.
– Improved multi-scale algorithms in general
● Assess the range of freq. dependencies of the PB to be included
● Computing load
● Computing: Parallel processing on a routine basis
● Memory footprint: Use heterogeneous hardware (CPUs + GPUs, etc.)
● Use Cloud Computing as an effective development platform.