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Spatial deconvolution and inversion of 2D spectropolarimetric data. Asensio Ramos Ruiz Cobo Instituto de Astrofísica de Canarias. The Earth atmosphere strongly perturbs the ability to get good images and polarimetric data. - PowerPoint PPT Presentation
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Spatial deconvolution and inversionof
2D spectropolarimetric data
A. Asensio RamosB. Ruiz Cobo
Instituto de Astrofísica de Canarias
The Earth atmosphere strongly perturbs the ability toget good images and polarimetric data
But even the diffraction at the telescope modifies the observations
Motivation
Develop a fast method to invert spatially deconvolvedspectro-polarimetric observations from space
Image deconvolution
Richardson-Lucy algorithm(Richardson 1972, Lucy 1974)
Image formation ina linear system
Image deconvolution asa probabilistic problem
For Gaussian noise
Problems with image deconvolution
• Spectropolarimetric data has to be deconvolved frequency by frequency
• The signal-to-noise ratio in many frequencies is very small
• Maximum-likelihood deconvolution is very sensitive to noise
• Use a prior for images to diminish the effect of noise
Our prior for the signal
We write the Stokes profiles as a linear combination in an orthonormal basis
The linearity of the image formation leads to
Projecting on the basis and using the orthonormality of the basis, thedeconvolution reduces to deconvolving several ‘projected images’
Original Deconvolved
Original Deconvolved
Advantages
• Projected images are almost noiseless, so that the maximum-likelihooddeconvolution behaves much better
• If the basis set is sufficiently general, no relevant information is lost inthe truncation we use an empirical PCA basis
• The deconvolution process is computationally simple, unlike otherapproaches like that of van Noort (2012)
• Now any inversion scheme can be applied without stray-light correction
The contrast in the quiet regions increases from from 6.3% to 11.7%
OriginalDeconvolved
Penumbra – Magneto-convection in inclined magnetic field?
• MHD simulations reproduce penumbra as magneto-convection in inclinedmagnetic fielc (Rempel et al. 2009 a,b)
• Downward velocities with inverse polarities should be observed alongthe borders of penumbral filaments
• Convective downflow Scharmer et al. (2011), Scharmer & Henriqes (2012), Joshi et al. (2011)
• Reversed flux in outer penumbra Westendorp Plaza et al. (1997,2001)del Toro Iniesta et al. 2001
• Indirect indications in Stokes V Franz (2011)
Inversions present larger constrast in all quantities
Reversed polarity in the inner and outer penumbra
Downflow+reverse polarity (wrt umbra)
After deconvolution
Before deconvolution (2-component inversion)
Conclusions
• Fast regularizared deconvolution available
• Dispersed light almost disappears
• Inversion of 2D data
• Clear signatures of downflowing material with oppositepolarity in the penumbra