Image plane corrections

Pointing Correction

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S. Bhatnagar (NRAO, Socorro)

T.J.Cornwell (ATNF), K.Golap (NRAO, Socorro)

The Measurement Equation

Generic Measurement Equation:

Data Corruptions Sky

Jij are the direction independent corruptions.

JSij are the image plane errors (direction dependent).

where Eij = FT[JSij]. Unknowns: Jij ,JSij, and IM.

SelfCal: Given IM and knowing Eij

Deconvolution: Given Jij and Eij,

Visibility correction

In the absence of direction dependent errors

Observed data is corrected as

Imaging is done using the corrected visibilities

Imaging and calibration are decoupled

Antenna independent direction dependent corruptions (e.g. Primary beam effects) can be written as multiplicative terms in the image domain.

This can be used in an iterative deconvolution scheme to make IM which is corrected for JS (VLA Poln. squint correction, mosaicking, etc.)

Visibility correction

For effects which are separable as antenna based effects

When , effects of JijS cannot be reduced to the convolution of the visibility plane by a single function.

Visibility domain filters vary across the visibility plane.

Visibility inversion

V,I : The visibility and image vectors

A: The Measurement Matrix

E: The direction dependent effect in the Fourier plane

To use FFT for Fourier transforming, re-sampling is done by convolutional gridding

Major cycle:

Minor cycle:

Direction dependent effects can be incorporated in imaging by using EA as the transform operator

Pieces of the puzzle

Efficient algorithms to include image plane effects during deconvolution

Forward transform (Vis -> Image) (no less accurate than the PSF used for deconvolution)

Inverse transform (accurate)

Decomposition of the sky in an appropriate basis

Solvers for the “unknown” image plane effects

Larger computers! (More memory, CPU power)

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.

Measured direction dependent effects

Eij as a function of direction is measured a priori

Aperture Function: Eij separate for each poln. product pq

Needs a solver: Pointing SelfCal

Asymmetric Primary Beams:

PB-projection

Visibility filters computed for 15o PA increments.

Azimuthally symmetric Primary Beams.

Typical NVSS field: Peak 190mJy

Full beam polarimetry: Squint corrected Stokes-V imaging

Aperture function

Model for VLA antenna illumination at L-band

(courtesy W.Brisken)

Variable side-lobe gain

PB-projection: Stokes-I

Stokes-I imaging with and without PB effects

(Polarization squint, Pointing offsets, PB rotation)

PB-Projection: Stokes-V

Stokes-V imaging with and without PB effects

(Polarization squint, Pointing offsets, PB rotation)

Pointing Solver: Motivation

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

EVLA L-band sensitivity: 1microJy/beam

Mosaicking dynamic range limited by pointing errors.

Significant fraction of ALMA observation will be mosaicking observations.

Significantly increased computing:

Each iteration involves expensive visibility prediction

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

Pointing correction

RMS: 15microJy/beam vs. 1microJy/beam

Peak: 250microJy vs. 5 microJy

Model image as components

Details in EVLA Memo 84 (2004)

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

Pointing SelfCal

Model image: deconvolved using entire data

Pixelated model image

Pointing SelfCal

Stokes-I imaging: Before and after pointing correction

Pointing SelfCal

Stokes-V imaging: Need to use component imaging?

Use illumination patterns (work in progress)

Where to from here...

Eliminate aperture function re-gridding

SelfCal <-> imaging iterations

Component based imaging and prediction (Asp-Clean + PB-Projection + W-Projection)

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

Mosaicking dynamic range limited by pointing errors?

Wide-band imaging (EVLA memo #?)

Use PB-projection to correct for PB scaling

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

Wide-band continuum imaging

EVLA bandwidth ratio of 2:1

Sky emission, the Primary Beams, etc. are a function of frequency.

Ideas: Apply PB effects during predict using pb-projection.

Parameterized sky model for prediction.

Combining Scale sensitive + frequency sensitive deconvolution with image plane corrections.

Computing and I/O costs

Significant increase in run-time due to more sophisticated parameterization

Deconvolution: Fast evaluation of

Calibration: Fast evaluation of

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

Solutions: Analytical approximations, caching, Parallel computing and I/O,...

Wide-band imaging: The problem

IF1 – IF2: 50MHz apart

Spectral index? Frequency dependence of the PBs?

EVLA bandwidth ratio of 2:1

General approach for imaging

Design filters to be used as Gridding Convolution Functions (GCF) for accurate forward transform (major cycle)

Use an approximation for the inverse transform to compute the update direction (minor cycle)

Major cycle:

Minor cycle:

Sanjay Bhatnagar

2005-06-29T10:32:49

Sanjay Bhatnagar