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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.

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slide1

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

Anisa T. Bajkova

Central (Pulkovo) Astronomical Observatory of RAS

slide2
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).

the most important works on mfs
The most important works on MFS
  • 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
The aim of this work:

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.

slide5
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
importance of mfs for russian radio astronomy
Importance of MFS for Russian Radio Astronomy
  • 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
Improving UV-coverage

(a) (b)

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

slide11
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.

maximum entropy method
Maximum Entropy Method

Discrete form of practical MEM:

simulation results
Simulation results

30%

SFS

UV-planes

а б

90%

60%

в г

Fig.1

slide20
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 %

slide21
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 %

slide22
Io(x,y) I1(x,y) α(x,y)

2

а bc

3

def

Fig.4

(Frequency band30%)

slide23
2

а bc

3

def

4

Fig.5(60%)

ghi

slide24
2

а bc

3

def

4

Fig.6 (90%)

ghi

slide25
а bc

Fig.7

MFS (90%), 27 frequences

slide26
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%

modelling 3c120
Modelling 3C120

Model of 3C120 at 8.2 GHz Spectral index distribution

slide28
Reconstructed images: -2.1 <α(x,y)<0.8,

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

slide29
Reconstructed images: -2.1 <α(x,y)<0.8,

frequency bandwidth=60%, nonlinear spectral correction

with N=4

slide31
SFS MFS (bandwidth=±30%) MFS (bandwidth=±60%)

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

slide32
Image synthesis by Radioastron

Model

SFS

MFS with spectral correction MFS without spectral correction

slide33
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)

conclusion
CONCLUSION

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.

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