Spatial deconvolution and inversion of 2D spectropolarimetric data

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