MULTI-FREQUENCY SYNTHESIS TECHNIQUE IN RADIO INTERFEROMETRIC IMAGING USING GENERALIZED MAXIMUM ENTRO...
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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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Anisa t bajkova central pulkovo astronomical observatory of ras

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

Anisa T. Bajkova

Central (Pulkovo) Astronomical Observatory of RAS


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).


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.


Anisa t bajkova central pulkovo astronomical observatory of ras

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


Anisa t bajkova central pulkovo astronomical observatory of ras

Space-Ground Radio Interferometer “Radioastron”


Spectral variation

Spectral variation


Anisa t bajkova central pulkovo astronomical observatory of ras

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:


Visibility function constraints

Visibility function constraints:


Reconstruction using generalized maximum entropy method gmem

Reconstruction using Generalized Maximum Entropy Method(GMEM)


Anisa t bajkova central pulkovo astronomical observatory of ras

The Lagrange method:


Solution

Solution:


Anisa t bajkova central pulkovo astronomical observatory of ras

Unconditional optimization problem:


Simulation results

Simulation results

30%

SFS

UV-planes

а б

90%

60%

в г

Fig.1


Anisa t bajkova central pulkovo astronomical observatory of ras

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 %


Anisa t bajkova central pulkovo astronomical observatory of ras

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 %


Anisa t bajkova central pulkovo astronomical observatory of ras

Io(x,y) I1(x,y) α(x,y)

2

а bc

3

def

Fig.4

(Frequency band30%)


Anisa t bajkova central pulkovo astronomical observatory of ras

2

а bc

3

def

4

Fig.5(60%)

ghi


Anisa t bajkova central pulkovo astronomical observatory of ras

2

а bc

3

def

4

Fig.6 (90%)

ghi


Anisa t bajkova central pulkovo astronomical observatory of ras

а bc

Fig.7

MFS (90%), 27 frequences


Anisa t bajkova central pulkovo astronomical observatory of ras

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


Anisa t bajkova central pulkovo astronomical observatory of ras

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

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


Anisa t bajkova central pulkovo astronomical observatory of ras

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

frequency bandwidth=60%, nonlinear spectral correction

with N=4


Modelling radioastron mission

Modelling Radioastron mission


Anisa t bajkova central pulkovo astronomical observatory of ras

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

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


Anisa t bajkova central pulkovo astronomical observatory of ras

Image synthesis by Radioastron

Model

SFS

MFS with spectral correction MFS without spectral correction


Anisa t bajkova central pulkovo astronomical observatory of ras

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.


Thank you for attention

THANK YOU FOR ATTENTION!


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