ADVANCED RADIO INTERFEROMETRIC IMAGING

Transcription

1 ADVANCED RADIO INTERFEROMETRIC IMAGING Hayden Rampadarath Based upon J. Radcliffe's DARA presentation Image courtesy of NRAO/AUI

2 INTR ODU CT ION In the first imaging lecture, we discussed the overall and basic theory or imaging. Thus far you have also only made a simple image. There are many different imaging methods, Their use are mainly determined by your science goals. In this lecture, we will be discussing (briefly) a couole of the different imaging methods Note, this is not an exhaustive list and there are many more.

3 INTR ODU CT ION Topics discussed: Recap of CLEAN Multi-scale or other deconvolution methods Wide-field imaging Multi-frequency Synthesis Review of Self-calibration using CLEAN components Primary beam correction Mosaicing Direction-dependent effects during imaging

4 INTR ODU CT ION After calibration the visibilities are represented by (+ errors): interferometer s geometrical vector sky position sky brightness (our image ) Want to determine from Nb: (l.m,n) notation is essentially the same as (x,y,z) coordinates used in the prev. talks

5 INTR ODU CT ION If we have a small field of view ( 1 l 2 m 2 1 ) 0 then w 0: Note: This is true for small fields of view that is confined to a few arceseconds

6 D E C O N VO LU T I O N This sampling function can be described by S(u,v) and is equal to 1 when the uv plane is sampled and zero otherwise: ID(l,m) is known as the dirty image and is related to the real sky brightness distribution by (using convolution theorem of FT): Where B is known as the dirty beam or the point spread function and is the FT of the sampling function.

7 THE DIRTY IMAGE Example VLA-A data targeting M82

8 DECONVOLUTION The Högbom algorithm (1974) 1. Find the strength and position of the brightest peak. 2. Subtract the dirty beam x peak strength x loop gain/damping factor position of the peak, the dirty beam B multiplied by the peak strength and a damping factor (usually termed the loop gain). 3. Go to 1. unless any remaining peak is below some user-specified level or number of interations reached. 4. Convolve the accumulated point source model with an idealized `CLEAN' beam (usually an elliptical Gaussian fitted to the central lobe of the dirty beam). 5. Add the residuals of the dirty image to the `CLEAN' image.

9 HÖGBOM CLEAN IN ACTION Hogbom CLEANED image 9

10 C LEAN IMAG E & MO DE L Hogbom CLEANED model 10

11 THE MANY FORMS OF CLEAN Maximum Entropy Method Cotton-Schwab Clark

12 D E C O N VO LV I N G D I F F U S E S T R U C T U R E Improved algorithm by Cornwell (2008) : multi-scale clean Fits small smooth Gaussian kernels (and delta functions) during a Högbom CLEAN iteration Implemented in CASA clean & tclean. Advised to use pixel scales corresponding to orders of the dirty beam size and avoid making scale too large compared to the image width/lowest spatial frequency. E.g. For example, if the synthesized beam is 10" FWHM and cell=2", try multiscale = [0,5,15] CASA tclean CASA clean

13 MULTI-SCALE CLEAN Multi-scale CLEANED image 13

14 MULTI-SCALE CLEAN Multi-scale CLEANED model 14

15 3. W I D E - F I E L D I M AG I N G A wide-field image is defined as: An image with large numbers of resolution elements across them Or multiple images distributed across the interferometer primary beam In order to image the entire primary beam you have to consider the following distorting effects: 1. Bandwidth smearing 2. Time smearing 3. Non-coplanar baselines (or the w term) 4. Primary beam response

16 BANDWIDTH SMEARING Given a finite range of wavelengths increasing radius pointing centre increasing radius Fringe pattern is ok in the centre but, with higher relative delay, different colours are out of phase BW smearing can be estimated using: Can be alleviated by observing and imaging with high spectral resolution with many narrow frequency channels gridded separately prior to Fourier inversion (reduces ). Detailed form of response depends on individual channel bandpass shapes

17 BANDWIDTH SMEARING Example e-merlin NVSS image Effect is radial smearing, corresponding to radial extent of measurements in uv plane

18 TIME SMEARING Not smeared Time-average smearing (de-correlation) produces tangential smearing Not easily parameterized. At declination +90 a simple case exists where percentage time smearing is given by: Smeared At other declinations, the effects are more complicated.

19 NON-COPLANAR BASELINES 2D Fourier Transform does not hold for new sensitive, wideband, wide-field arrays Non co-planar baselines becomes a problem i.e. l,m,w >> 0 Three-dimensional visibility fuction can be transformed to a three-dimensional image volume - this is not physical space since, & are direction cosines. The only non-zero values of I lie on the surface of a sphere of unit radius defined by

20 WIDE-FIELD IMAGING The sky brightness consisting of a number of discrete sources are transformed onto the surface of this sphere. The two-dimensional image is recovered by projection onto the tangent plane at the pointing centre So how do we achieve this? Two solutions available: i. Faceting - split the field into multiple images and stitch them together ii. w-projection - most used solution, effectively performs the above to recover Both available in CASA! I would advice only to use w-projection

21 W-PROJECTION Cornwell et al Recall: The curved sky is equvalent to the FT of the w-term, convolved with V(u,v) from a flat sky i.e. w=0

22 W-PROJECTION Cornwell et al Very dependent on zenith angle, co-planarity of array, field of view and resolution. Convolution theorem no longer works when w-terms present. CLEAN assumes constant PSF, but PSF changes (slightly) over the image. Solved with Cotton-Schwab algorithm (Schwab 1984) (used in CASA automatically).

23 W-PROJECTION The Cotton-Schwab + w-projection algorithm: 1) Make initial dirty image & central PSF - Perform minor iterations: Find peak Subtract scaled PSF at peak with small gain Repeat until highest peak ~80-90% decreased 2) Major iteration: Correct residual Predict visibility for current model Subtract predicted contribution and re-image CASA clean implementation

24 W-PROJECTION Take the GOODS-N field as observed by 1.4 GHz e-merlin Pointing centre Source 1 Source 2

25 W-PROJECTION Source 1: Near the pointing centre No w-projection w-projection Pretty much identical! Small field approximation holds and 2D FT suffices

26 W-PROJECTION Source 2: Away from the pointing centre No w-projection w-projection Small field approximation breaks and you need w-projection!

27 Cha ngeing the Pha se Centre Take the GOODS-N field as observed by 1.4 GHz e-merlin Pointing centre Source 1 Source 2

28 Cha ngeing the Pha se Centre Take the GOODS-N field as observed by 1.4 GHz e-merlin Note: changing the phase centre, helps with the wide-field problem. Thus won't need to use wprojection at. Can you see why? To image you can make a very wide image centred on, but this will require a very large image increased computation Or can change the phase centre to the position of This is done via rotating V(u,v) by the phase difference corresponding to the positional offset done via casa task 'fixvis' or the clean parameter 'phasecentre'.

29 M U LT I - F R E Q U E N CY S Y N T H E SI S Multi-frequency synthesis (MFS) means gridding different frequencies on the same uv grid Conway & Sault (1995) 29

30 M U LT I - F R E Q U E N C Y D E C O N V O L U T I O N Similar but not the same! (same name often used). Also known as multi-term deconvolution (as in CASA). Takes spectral variation into account during deconvolution Flux Density Assumed flat spectrum Actual source spectrum Frequency

31 M U LT I - F R E Q U E N CY D E C O N VO LU T I O N represents the sky emission in terms of a Taylor series about a reference frequency: A power model is used to describe the spectral dependence of the sky. One practical choice is a power law with emission. Useful for wideband, sensitive imaging. Incorporated in CASA in combination with multi-scale CLEAN as msmfs

32 M U LT I - F R E Q U E N CY D E C O N VO LU T I O N Multi-frequency deconvolution (or synthesis) is invoked in casa by selecting: mode = 'mfs' nterms = n where n = 1 or 2 nterms = 1 should be used if your source/target has a signal to noise ratio (SNR) < 20 nterms = 2 should only be used if your source/target has a SNR > 20

33 SELF-CALIBRATION USING CLEAN Clean components can be used as calibration model Often applied as: Phase calibration Shallow CLEAN (avoid CLEAN bias) Phase calibration Deep CLEAN Amplitude & phase calibration Deep CLEAN 33

34 S ELF-CALIBRATION USING CLEAN ALMA SV Data for IRAS16293 Band 6 34

35 PRIMARY BEAM CORRECTION Correction is required for the antenna response This is called primary beam correction (as opposed to the synthesized beam / psf ) For dishes, the primary beam is ~constant but can be very complex away from the FWHM. To correct for: multiply final image with the inverse beam! Scalar for total brightness, matrix for polarized

36 PRIMARY BEAM CORRECTION Complex sidelobe structure + asymmetries! Knockin primary beam holographic scan

37 PRIMARY BEAM CORRECTION Primary beam corrected JVLA+MERLIN image of GOODS-N Note the increased noise level towards the edge of the field

38 VA R I A B L E P R I M A RY B E A M S Primary beam of arrays can vary with time and frequency! Has to be accounted for during imaging if imaging the whole primary beam: A-projection (CASA has this for the JVLA + ALMA - VLBI arrays don t image the pb often!)

39 VARIABLE PRIMARY BEAM ary beam frequency variation for the UK Lovell Telescope G Image credit: Nick Wrigley 39

40 MOS AICING t if this is our primary beam and we want to see the FR-I galaxy to 40

41 MOS AICING can use multiple pointings and combine them with correct weightin 41

42 MOS AICING To create the mosaiced image Need to weight with 1/ = (primary beam)2 or Done in CASA with imagermode = 'mosaic'

43 D I R E C T I O N D E P E N D E N T C A L I B RAT I O N Direction dependent (DD) effects may need further corrections after imaging not a fully solved problem! Can be ionosphere, tropospheric, instrumental (e.g. a projection) Affects position, brightness & polarisation angles! Before DD cal After DD cal 43 Yattawata SAGECal (2007)

44 D I R E C T I O N D E P E N D E N T C A L I B RAT I O N Possible solutions: Image in small facets where DD's effects are constant Peeling For VLBI, Multi-source self-calibration (below) Pre-MSSC 44 Radcliffe et al Post-MSSC

45 SUMMARY Topics discussed: CLEAN When to use Multi-scale or other deconvolution methods The effect of and solution to w-terms Multi-frequency deconvolution Self-calibration using CLEAN components Primary beam correction Mosaicing Direction-dependent effects during imaging 45