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Anisa T . Bajkova Central (Pulkovo) Astronomical Observatory of RASPowerPoint Presentation

Anisa T . Bajkova Central (Pulkovo) Astronomical Observatory of RAS

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### MULTI-FREQUENCY SYNTHESIS TECHNIQUE IN RADIO INTERFEROMETRIC IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

Anisa T. Bajkova

Central (Pulkovo) Astronomical Observatory of RAS

MFS in VLBI IMAGING USING GENERALIZED MAXIMUM ENTROPY METHODassumes mapping at several observing radio frequencies simultaneously to improve UV-coverage, so MFS is a tool of rapid aperture synthesis. MFS is possible due to measurement of UV-coordinates of visibility function in wavelengths.

The main problem of MFS is spectral dependence of a source brightness distribution and in order to avoid possible artifacts in the image it is necessary to fulfill spectral correction during the deconvolution stage of the image formation (CLEAN or MEM).

The most important works on MFS IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

- Conway, J.E., Cornwell T.J., Wilkinson P.N. MNRAS, 1990, 246, 490.
- Conway, J.E. Proc. IAU Coll. 131, ASP Conf. Ser., 1991, 19, 171.
- Cornwell, T.J. VLB Array Memo 324, 1984, NRAO, Socorro, NM.
- Sault, R.J., Wieringa, M.H. A&A, Suppl. Ser., 1994, 108, 585.
- Sault, R.J., Oosterloo, T.A. astro-ph/0701171v1, 2007.
- Likhachev, S.F., Ladygin, V.A., Guirin, I.A. Radioph. & Quantum Electr., 2006, 49, 499.

are based on CLEAN deconvolution algorithm for spectral correction of images (double-deconvolution algorithm [1,2,4,5], vector-relaxation algorithm [6]).

The aim of this work: IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

Development and investigation of a new MFS deconvolution algorithm based on maximum entropy method for effective solving spectral variation problem in broad-band frequency region and estimation of a spectral index distribution over a source.

CLEAN or MEM ? IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

Bob Sault

The answer is image dependent:

- “High quality” data, extended emission, large images
Maximum entropy

- “Poor quality” data, confused fields, point sources CLEAN

Importance of MFS for Russian Radio Astronomy IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

- Three-element Russian
“Quasar” VLBI network (Svetloye, Zelenchukskaya, Badary)

- Future Space-Ground
high-orbit“Radioastron”

mission

In both cases we have sparse UV- coverages, insufficient for imaging radio sources with complicated structure

Improving UV-coverage IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

(a) (b)

Four element radio Interferometer:Svetloe, Zelenchukskaya, Badary, Matera (a) single frequency synthesis (b) multi-frequency synthesis

Space-Ground Radio Interferometer “Radioastron” IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

Spectral variation IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

Bob Sault IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

Maximum entropy image deconvolution principle:

Of all the possible images consistent with the observed data, the one that has the maximum entropy is most likely to be the correct one.

Maximum Entropy Method IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

Discrete form of practical MEM:

Visibility function constraints: IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

Reconstruction using Generalized Maximum Entropy Method IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD(GMEM)

The Lagrange method: IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

Solution: IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

Unconditional optimization problem: IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

Simulation results IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

30%

SFS

UV-planes

а б

90%

60%

в г

Fig.1

a IMAGING USING GENERALIZED MAXIMUM ENTROPY METHODbc

Fig.2

Model distributions of the source (a), first -order spectral map (b) and spectral index (c) (0<α(x,y)<0.8), size of maps 128x128

Contour levels: 0.0625,0.125,0.25,0.5,1,2,4,8,16,32,64,99 %

а б в

Fig.3

Reconstructed images using (a) SFS; (b) МFS (30%),α(x,y)=0; (c) MFS α(x,y)≠0

Contour levels: 0.0625,0.125,0.25,0.5,1,2,4,8,16,32,64,99 %

SFS without spectral correction 2 3

а b

cd

4 5 I1(x,y) α(x,y)

ef

hi

Рис.8

MFS (90%, 9 frequencies) significant noise in data (visibility function)

Contour levels: 0.25,0.5,1,2,4,8,16,32,64,99%

Modelling 3C120

Model of 3C120 at 8.2 GHz Spectral index distribution

Reconstructed images: -2.1 < α(x,y)<0.8,

frequency bandwidth=30%, nonlinear spectral correction with N=4

Reconstructed images: -2.1 < α(x,y)<0.8,

frequency bandwidth=60%, nonlinear spectral correction

with N=4

SFS MFS (bandwidth=±30%) MFS (bandwidth=±60%)

UV-coverage for Radioastron mission (U,V in 108 wavelengths)

Image synthesis by Radioastron MFS (bandwidth=±30%) MFS (bandwidth=±60%)

Model

SFS

MFS with spectral correction MFS without spectral correction

Image synthesis by Radioastron MFS (bandwidth=±30%) MFS (bandwidth=±60%)

Source model SFS MFS(±30%)(α(x,y)=0)

MFS(±30%)( α(x,y)≠0) MFS(±30%)( α(x,y)≠0) MFS(±60%)( α(x,y)≠0)

(without spectral correction) (linear spectral correction N=2) (nonlinear spectral correction N=4)

CONCLUSION MFS (bandwidth=±30%) MFS (bandwidth=±60%)

We proposed and investigated simple and effective MFS-deconvolution technique based on the Generalized Maximum Entropy Method which allows to provide accurate spectral correction of images in wide frequency band and reconstruct both source brightness and spectral index distributions.

The results obtained will be published in

Astronomy Reports (2008), v.85, N 12.

THANK YOU FOR ATTENTION! MFS (bandwidth=±30%) MFS (bandwidth=±60%)

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