Image plane corrections

------------------>

S. Bhatnagar

NRAO, Socorro

The Measurement Equation

Generic Measurement Equation:

Data Corruptions Sky

:direction independent corruptions.

:image plane errors (direction dependent).

Jij is multiplicative in the Fourier domain

Jsij is multiplicative in the Image domain only if Jsi = Jsj

Hierarchy of algorithms

Unknowns of the problem: Jij ,Jsij, and IM.

Jsi = Jsj and independent of time

Imaging and calibration as orthogonal operations

Jsi (t) = Jsj (t) (Poln. squint, PB correction, etc.)

Jsij is multiplicative in the image plane for appropriate

(Cornwell,

EVLA Memo 62)

Hierarchy of algorithms

(Pointing offsets, PB variations, etc.)

Image plane effects not known a-priori

Pointing selfcal

Correct for Jsij during image deconvolution

W-Projection, PB-Projection

Simultaneous solver for Jij ,Jsij, and IM!!

(EVLA Memo 84)

(EVLA Memo 67)

(EVLA Memo 100)

General structure of imaging algorithms

Solve the normal equation

Compute the approx. update direction:

Update the model: (Steepest Descent minimization: Clean algorithm)

Compute residuals:

Transform implemented using FFT:

Incorporate the image plane effects in the transform operator: Forward/inverse transforms:

Iteratively solve the modified normal equation:

Motivation

Single pointing L-Band observations limited due to pointing/PB asymmetries ~10-20microJy/beam.

Next generation telescopes hope to do >10x better

Mosaicking dynamic range limited by pointing errors and azimuthally asymmetric PB/sidelobes.

Use of pixel basis for image representation: deconvolution errors: > 10mircoJy/beam

Frequency dependence of the sky & the instrument: 10-15microJy/beam (much greater than this when PB effects are included!)

Measured direction dependent effects

Eij as a function of direction is measured a-priori (nominal full beam polarimetric imaging)

Aperture Function: Ei different for each poln. product pq (pointing offsets correction)

Needs a solver: Pointing SelfCal

Asymmetric Primary Beams:

Power patterns

Model for VLA antenna power patters at L-band

(modeling code courtesy W.Brisken)

Stokes-I

Stokes-V

Variable side-lobe gain

Maximum

gain variations

at the location

of the sidelobes

Numerical errors:

Variations in the

peak of the sidelobe.

Image re-gridding

vs. direct evaluation

Error patterns

AvgPB - PB(to)

Azimuthal cuts at 50%, 10% and 1%

of the Stokes-I error pattern AvgPB - PB(to)

Simulations: Stokes-I

Stokes-I imaging with and without PB effects

(Polarization squint, Pointing offsets, PB rotation)

RMS ~15mJy/beam

RMS ~1mJy/beam

Simulations: Stokes-V

Stokes-V imaging with and without PB effects

(Polarization squint, Pointing offsets, PB rotation)

VLA L-Band C-array: Stokes-I

VLA L-Band C-array: Stokes-V

Pointing correction

Continuous lines: Typical antenna pointing offsets for VLA as a function of time (Mean between +/-25” and RMS of 5”).

Dashed lines: Residual pointing errors. RMS ~1”.

Model image using 59 sources from NVSS.

Flux range ~2-200 mJy

Details in EVLA Memo 84 (2004)

http://www.aoc.nrao.edu/evla/geninfo/memoseries/evlamemo84.pdf

Pointing SelfCal: “Unit” test

Test for the solver using simulated data

Red: Simulated pointing offsets t=60sec

Blue: Solutions t=600sec

Time lines: Research

Note on algorithm research, Aug. 2004

http://www.aoc.nrao.edu/~sbhatnag/Talks/AlgoDevelopment.ps

Major areas of work:

Scale sensitive deconvolution (Asp paper, 2004[2003])

Correction of PB effects (Poln., pointing, sidelobes,etc.)

Basic algo: Pointing Selfcal (2004), Imaging (early 2005)

Wideband imaging (will require the above)

Difficult to translate research into Project Management lingo (“deliverables”, etc.!) - still made an attempt!

“Demonstrable” progress: ~1 year

Tricky details: ~3 years (probably more)

Time lines: Development

Code development time much longer

Complexity – code base

Partly unavoidable

Improvements: Possible & Necessary

Use of simpler UI (UNIX command-line, inp/set/save/go)

Currently usable on real data (minus data selection)

Complexity – algorithm

Very difficult to predict (more difficult in evolving code-base)

Can run into dead-ends

Optimization and stability/robustness

From “working algorithm” to “usable implementation”

Stability/robustness/numerical testing: Time consuming & related to the code-base complexity/stability/evolution.

Progress so far

Use aperture function / eliminate re-gridding [Done]

Write the imaging and solver code [Done]

SelfCal <-> imaging iterations [Testing]

Component image model (Asp-Clean + PB-Projection + W-Projection) [Next!]

Is current deep L-band imaging pointing-error limited?

Mosaicking dynamic range limited by pointing errors?

Wide-band imaging

Use PB-projection to correct for PB scaling

MSF extensions: Freq. sensitive image plane modeling (Component based imaging)

Interesting extensions

Fast mosaicking

Use the pointing vector as the “offset” (Golap): Azimuthally symmetric PB

Use model for aperture illumination as a function of PA and pointing errors

Variable PB-sidelobes and pointing errors constitute the dominant error for mosaicking: Not included in existing simulations/imaging performance estimates

Wide band imaging

PB scaling contributes the dominant error: Not included in existing simulations

Use it with Component based sky model

Computing and I/O costs

Significant increase in run-time due to more sophisticated parameterization

Deconvolution: Fast transform (both ways)

E.g. limits the use of MCMC approach

Calibration: Fast prediction

Cost of computing residual visibilities is dominated by I/O costs for large datasets (~200GB for EVLA)

Deconvolution: Approx. 20 access of the entire dataset

Calibration: Each trial step in the search accesses the entire dataset

References

Hamaker, Bregman & Sault, 1996, A&AS, 117, 137

Cornwell, 1995, The Generic Interferometer: II Image Solvers, AIPS++ Note 184

Bhatnagar & Cornwell, 2004, Scale sensitive deconvolution of interferometric images, A&A, 426, 747-754, 2004 (astro-ph/0407225)

Cornwell, Golap & Bhatnagar, 2003, W-Projection: A new algorithm for non-coplanar baselines, Tech. rep., EVLA Memo 67

Brisken, 2003, Using Grasp8 To Study The VLA Beam, Tech. rep., EVLA Memo 58

Bhatnagar, Cornwell & Golap, 2004, Solving for the antenna based pointing errors, Tech. rep., EVLA Memo 84

Bhatnagar, Cornwell & Golap, 2006., Image plane corrections, EVLA Memo 100

http://www.aoc.nrao.edu/~sbhatnag/talks.html

Pointing SelfCal

Model image: deconvolved using entire data

Pixelated model image

Pointing SelfCal

Stokes-I imaging: Before and after pointing correction

Pieces of the puzzle

Efficient algorithms to correct for image plane effects

Approximate inverse transform (Vis -> Image)

Forward transform (accurate)

Decomposition of the sky in a more appropriate basis

Frequency sensitive

Solvers for the “unknown” image plane effects

As expensive as imaging!

Larger computers! (More memory, CPU power, fast I/O)

Known direction dependent effects

Non-coplanar baselines

Traditional approach: Faceting

W-projection: Visibility filtering (>10x faster)

W-projection: Example

L-Band, VLA C-array, ~40hr. integration (Fomalont et al.)

-RMS: ~15microJy, Peak: 40mJy

-Errors vary across the image (pointing?).

-Time varying first side-lobe not corrected.

Pointing SelfCal

Stokes-V imaging: Need to use component imaging?

Scale sensitive imaging: Asp-Clean

Pixel-to-pixel noise in the image is correlated

The scale of emission fundamentally separates signal (Io) from the noise (IN).

Asp-Clean (Bhatnagar & Cornwell, A&A,2004)

Search for local scale, amplitude and position

Sanjay Bhatnagar

2005-06-29T10:32:49

Sanjay Bhatnagar