Mosaicing and Single-Dish Combination
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1 Mosaicing and Single-Dish Combination CASS Radio Astronomy School 2012 Lister Staveley-Smith (ICRAR / CAASTRO / UWA)
2 Outline Mosaicing with interferometers! Nyquist sampling! Image formation Combining with single-dish data! The short spacing problem! Image.v. Fourier plane combination
3 Observation type INTERFEROMETER! Single pointing! Multi-field! SINGLE DISH! ZERO SPACING! No!!! Yes!
4 Observation type INTERFEROMETER! Single pointing! Multi-field! SINGLE DISH! ZERO SPACING! No!!!!! Yes!!!
5 Observation type INTERFEROMETER! Single pointing! Multi-field! SINGLE DISH! ZERO SPACING! No!!!!! Yes!!!!!
6 Example Instruments INTERFEROMETER! Single pointing! Multi-field! JVLA ATCA SINGLE DISH! ZERO SPACING! No! Yes! MWA+PKS ALMA
7 Outline Mosaicing with interferometers! Nyquist sampling! Image formation Combining with single-dish data! The short spacing problem! Image.v. Fourier plane combination
8 Bibliography Ekers & Rots (1979) Image Formation, IAU Coll 49, 61. Cornwell (1988) A&A, 202, 316. Cornwell (1989) ASPC 6. Cornwell, Holdaway & Uson (1993) A&A, 271, 697. Sault, Staveley-Smith & Brouw (1996) A&A Suppl., 120, 375. Holdaway (1998) ASPC 180, ch.20. Gueth & Guilloteau (2000) ASPC 217, 291. Sault & Killeen, miriad manual, ch.21. Subrahmanyan (2004) MNRAS, 348, Bhatnagar, Golap & Cornwell (2005) ASPC 347, 96 Bunn & White (2007) ApJ, 655, 21. Hull et al. (2010) PASP, 122, Pety & Rodriguez-Fernandez (2010), A&A, 517, A12
9 Mosaicing with Interferometers Noun mosaic (plural mosaics) source: wiktionary 1. A piece of artwork created by placing colored squares (usually tiles) in a pattern so as to create a picture. 2. (genetics) An individual composed of two or more cell lines of different genetic or chromosomal constitution, but from the same zygote. 3. (botany) A viral disease of plants. 4. A composite picture made from overlapping photographs.
10 ASKAP correlator room (Photosynth by Staveley-Smith)
11 Galactic Centre: VLA (Yusef-Zadeh et al.)
12 1025 Why mosaic? Mosaicing is necessary to create an image larger than the field-of-view of the telescope: ATCA primary beam McClure-Griffiths
13 Nyquist sampling of sky D is dish diameter " 2D Rectangular grid Hexagonal grid!" = 16.5 at 21cm at ATCA!" = 19.0 at 21cm at ATCA
14 Super-Nyquist sampling OTF interferometry: ATCA+WBCORR: AT20G (Ekers et al.) ATCA+CABB: CORNISH-S (Hoare, Wieringa et al.) IRAM Plateau de Bure interferometer data dumped sky position primary beam
15 Step I: observe different pointings
16 Step 2: make individual images
17 Step 3: make combined image 1 P(x) Mosaicing equation: 0 I t (x) = W (x) # i # i P(x " x i )I i (x) P 2 (x " x i ) P is primary beam response; I i are the individual images. Also applies to PAFs
18 (de Blok et al.)
19 Comparison of u-v coverage Individual Extra u-v coverage in radial and azimuthal direction Mosaic
20 Mosaicing Fundamentals Background theory:! Ekers & Rots (1979) pointed out that one can think of a single dish as a collection of sub-interferometers. Fourier coverage diameter D D
21 Mosaicing Fundamentals Extending this formalism to interferometers shows that an interferometer doesn t just measure angular scales! =" / b it actually measures: " b + D < # < " b $ D b + D Fourier coverage b - D D D b
22 Why is u-v coverage improved?! interferometer beam Primary beam = Image domain
23 Why is u-v coverage improved? * baseline sampling illumination function = Fourier domain
24 Comparison of u-v coverage Individual Extra u-v coverage in radial and azimuthal direction Mosaic
25 Ways to combine multiple pointings! Combine dirty images, then deconvolve with spatially-variant beam! Deconvolve, then combine images*! Jointly deconvolve dirty images * potential loss of information, but recommended for discrete sources (primary beam errors less important)
26 Examples (SMC). Dirty image Linear mosaic of deconvolved images Joint deconvolution
27 Complications Planarity! Exact projection no problem with co-planar arrays; w-axis distortion over wide fields will occur with non-planar arrays (widefield imaging; Cornwell lecture on Fri). Bandwidth! Dealing with frequency-dependence of both primary beam and sky can be problematic (multi-frequency imaging; Urvashi lecture). Primary Beam and Pointing Doppler Off-axis! Good beam model needed; high dynamic range may require pointing self-calibration; OTF interferometry produces sausage-shaped beams! Doppler corrections are dependent on time and position, so not strictly applicable in visibility domain.! Off-axis calibration and polarimetry poor for some radio telescopes.
28 Outline Mosaicing with interferometers! Nyquist sampling! Image formation Combining with single-dish data! The short spacing problem! Image.v. Fourier plane combination
29 Merging Interferometer and Single-Dish Data +
30 Mosaicing Fundamentals Background theory:! Ekers & Rots (1979) pointed out that one can think of a single dish as a collection of sub-interferometers. Fourier coverage diameter D D
31 Single-dish/interferometer analogy -I Interferometer: Asymmetric crosscorrelations C ij (#) $ C ij (-#) % Complex visibilities V(&) Single dish: Symmetric auto-correlations % Real visibilities
32 Bibliography Stanimirovic (2002) ASP Conf. Series 278 Sault & Killeen (2003) Miriad Users Manual Holdaway (1999) ASP Conf. Series 180 Other work (partial list): Adler et al. (1992, ApJ, 392, 497); Bajaja & van Albada (1979, A&A, 75, 251); Cornwell, Holdaway & Uson (1993, A&A, 271, 697); Roger et al. (1984, PASA, 5, 560); Schwartz & Wakker (1991, ASP Conf. Ser. 19); Vogel et al. (1984, ApJ, 283, 655); Wilner & Welch (1994, 427, 898); Ye, Turtle & Kennicutt (1991, MNRAS, 249, 722); Kurono et al. (2009, PASJ, 61, 873)
33 The short (zero)-spacing problem UV plane PSF Braun & Walterbos (1985) ideal Central hole Typical interferometer. Negative bowl
34 Negative bowl HI in the E-arm of the LMC (ATCA 4x750 m) (post-mem deconvolution)
35 HIPASS2 1.4 GHz map (Calabretta et al. 2012)
36 Several ways to combine...! Combine data in IMAGE plane add dirty images (and beams), then deconvolve joint deconvolution*! Combine data in FOURIER plane combine interferometer uv data and single-dish pseudo-visibilities add transform of deconvolved interferometer and single-dish images* *good for mosaics
37 Merging interferometer and single-dish data v The Fourier (UV) plane Interferometer data u Single dish data Overlapping region
38 Combination in Image Plane (Stanimirovic et al. 1999) Combined image: I tot = w int I int + w sd f sd I sd Weights { w int = " sd " int + " sd
39 Combining dirty images (Stanimirovic 1999, 2002)!f (& weight) DECONVOLVE
40 Joint deconvolution Maximize entropy : Subject to (1) (2) % "= # $ I i ln I ( i ' * & M i e) i $ I D # B + I 2 int < N, int int i { } i 2 I D sd # B + I 2-0 $ sd 2. 1 < M, sd / i f sd 2 i This may be the best approach for ALMA or Mopra+ATCA data
41 Joint deconvolution (Stanimirovic 1999, 2002) Deconvolver
42 Combination in Fourier plane 1. Appropriately weight data in overlap region! E.g. taper interferometer Fourier-plane data with transform of SD beam! Multiply SD Fourier-plane data with transform of interferometer beam 2. Adjust flux density scales (relative calibration) 3. Add in Fourier plane!
43 merged Weighting function in Fourier plane (Sault & Killeen) Tapered ATCA Parkes
44 FT Example of Fourier plane combination: McClure-Griffiths et al. + f cal x FT -1 = FT
45 immerge (Fourier) linear combination (image) Comparing different methods using the SMC in HI at 169 km/s (Stanimirovic 2002) mosmem default image=parkes joint deconvolution
46 MWA 32T image MWA 32T (Hurley-Walker) Parkes 408 MHz, scaled to 150 MHz (Haslam) Hurley-Walker
47 Parkes ATCA +Parkes ATCA McClure-Griffiths
48 Check you understand your calibration Relative scaling of data in overlap region from immerge ( ' km/s HI in SMC)
49 ALMA uv coverage Ott
50 Complications Single dishes: Flux density and beam determination may be tricky Frequency-dependent beam properties Beam size may depend on elevation Flux density scale may depend on angular scale (e.g. HIPASS) Significant far-out sidelobes (main beam efficiency ~70%) Interferometers uv-coverage scales with frequency, especially if data flagged Pre-deconvolution PSF depends on position (mosaic) Post-deconvolution PSF varies with S/N ratio and angular scale Fourier plane coverage may be poor S/N may be low in overlap region
51 Cen A: 406 ATCA fields+ HIPASS2 (Feain et al 2011)
52 LMC: 1344 ATCA fields+pks (Kim et al. (2003)
53 Summary! Mosaicing essential for wide fields; modus operandi for ASKAP.! Single-dish data essential if your image has largescale structure approaching the interferometer primary beam size.! Parkes+ATCA: excellent 1-20 GHz; ALMA: excellent GHz.! For mosaicing and single dish combination, linear Fourier plane combination mostly works well! miriad and casa tasks (e.g. invert, image, immerge, feather) work well.
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