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

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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 VLBIassumes 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).

- 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]).

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 ?

Bob Sault

The answer is image dependent:

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

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

- 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

(a) (b)

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

Space-Ground Radio Interferometer “Radioastron”

Bob Sault

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.

Discrete form of practical MEM:

The Lagrange method:

Unconditional optimization problem:

30%

SFS

UV-planes

а б

90%

60%

в г

Fig.1

abc

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 %

Io(x,y) I1(x,y) α(x,y)

2

а bc

3

def

Fig.4

(Frequency band30%)

2

а bc

3

def

4

Fig.5(60%)

ghi

2

а bc

3

def

4

Fig.6 (90%)

ghi

а bc

Fig.7

MFS (90%), 27 frequences

SFSwithout 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%

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

Model

SFS

MFS with spectral correction MFS without spectral correction

Image synthesis by Radioastron

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)

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.