17th SOT meeting2006. 4.17-20. NAOJ

Milne-Eddington Stokes Inversion
for Spectro-Polarimeter (SP)T. Yokoyama (U. Tokyo)
Y. Katsukawa, M. Shimojo (NAOJ)
K. Shimada, T. Sekii, S. Tsuneta, K. Ichimoto (NAOJ)
T. Shimizu (JAXA/ISAS)

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Objective of this sub-project
Development of a profile-fitting program based on theMilne-Eddington model••

It is for generating data-maps of the magnetic fields for the usage ofthe quick analysis. The maps will be released on the data server inthe SOLAR-B Science Center.
It will be a template for the development of the software that is formore sophisticated fitting procedure of the Stokes-profile analysis.

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Development of the new code•

The HAO “inversion” code is one of the best famous codes for theMilne-Eddington-model fitting.
– It is a very efficient and powerful code. However, ...
• It is very complicated. Hard to understand the calculation flows.
• Basically it assumes an input data format suitable for the ASP.

••

We develop a new code under the following guiding principles.
– The basic algorithm will be the same as that of the HAO code.
– FITS file I/O– Fast enough to use for daily processing of the B-field maps
– Portable to various architectures.
– Easy to follow the procedures in the code.
The code is developed by modifying and extending– PIKAIA by the HAO group– MELANIE by H. Socas-Navarro

3/10Outline of the fitting procedure
1. genetic algorithm(by Katsukawa)

Initial-guess parameters

2. Fitting the Stokes profiles by
the nonlinear least-square method(Levenberg-Marquardt method)(by Yokoyama)

Calibrated Stokes profiles(I/O of Fits format by Shimojo)

Vector field maps

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••
•

•

Genetic algorithm is a searchtechnique by iterating thegeneration, the selection andthe mutation of solutions.
Robust but slow.
Our strategy– Based on PIKAIA by HAO
group– simplify the profilecalculation procedures– reduce # of freeparameters– reduce # of used points inthe profile data
performance:15msec/pixel@ Intel Xeon 3.6GHz

first-guess by SOTgenetic code

Derivation of initial-guess data by the genetic algorithm“correct” solution (Final fitting
results by the HAO inversion
code)
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Nonlinear least-square fitting of the Stokes profiles••

Nonlinear least-square fitting (Levenberg-Marquardt method) is done toobtain the final results.
Development strategy– based on MELANIE by Socas-Navaro (performance:>100msec/pixel)– tune as much as possible• relax the convergence condition– MELANIE: iterate while the residual (χ2) is decreasing– SOT-fit: iterate while the reduction rate of the residual is greater than 1%• Remove the redundant calculations– calculations of Voigt functions• Optimize the value of parameters (e.g. λ) in the Levenberg-Marquardtmethod• etc. etc.

••

Performance: 15-25msec/pixel @ Intel Xeon 3.6GHz
Still there remain bugs....
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Nonlinear least-square fitting of the Stokes profiles•

Fitting free parameters (12 parameters)– Field strength– Field inclination– Field azimuth– Doppler shift– Doppler width– Damping parameter– Line strength– Source function– Source function gradient– Macro-turbulence– Stray-light fraction (filling factor)– Stray-light shift

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Test 1/2
• A test fitting is done by using the dataset observed by ASP.
• Performance: 30msec/pixel (Intel Xeon 3.6GHz) for(genetic plus fitting) procedures. It takes 8 hrs forgenerating a (1k*1k-pixels) map.

results by the SOT-fit

results by the HAO code
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Test 2/2•••

Fit the test model profiles thatare generated by using theknown sets (~100,000 sets) of
parameters and by using theMilne-Eddington model withadditional noise on them.
The fitted results distribute near
the “correct answer”. The
degree of scatter increases asincreasing the noise level.
On the other hand, there seems
to be a systematic fitting error
when the correct field strengthis less than ~500 Gauss. In thiscase, there is a tendency of theoverestimation of the fieldstrength.

noise level: 0%, 0.1%, 0.2%
1000G
2000G
100G
500G
Field strength

Inclination

Verticaldottedlines :
“Correctanswer”

Stray-light fraction (filling factor)

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Summary••••

We are developing a profile-fitting program based on the MilneEddington model.
The obtained maps are roughly consistent with those by HAO
code.
The performance is 30 msec / pixel. This rate is enough toproduce magnetic field maps from the downlinked data of
SOT/SP without a long delay.
There still remain bugs and some issues to be solved.

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