study o horizontal flows in solar active regions

THESIS DISSERTATIONTHESIS DISSERTATION

Study of horizontal flows in solar active regions

high-resolution image reconstruction techniquesbased on

Santiago Vargas Domínguez

Supervisors: Valentín Martínez Pillet & Jose A. Bonet

La Laguna, Tenerife - Dic 2008

La Laguna, Tenerife - Dic 2008

THESIS DISSERTATIONTHESIS DISSERTATION


high-resolution image reconstruction techniques


Supervisors: Valentín Martínez Pillet & Jose A. Bonet

based on


La Laguna, Tenerife - Dec 18, 2008


high-resolution image reconstruction techniques

based on

THESIS THESIS DISSERTATIONDISSERTATION

Supervisors: Jose Antonio Bonet & Valentín Martínez Pillet

PART 1 Defining a method for in-flight calibration of IMaX aberrations

PART 2 Study of proper motions in solar active regions

Outline

PART 1Defining a method for in-flight calibration of IMaX aberrations

Aim at:Perform numerical simulations to identify and evaluate possible optical error sources in the IMaX instrument.Develop an in-flight calibration method to characterize the aberrations affecting the images in IMaX.Describe and test the robustness of the calibration method.

Outline


IntroductionImage restoration techniquesIn-flight calibration of IMaX aberrationsConclusions

PART 1 Defining a method for in-flight calibration of IMaX aberrations d) Conclusions

c) In-flight calibration of IMaX aberrations

a) Introductionb) Image restoration techniques

Trying to explain the Trying to explain the physics of the Sun requires physics of the Sun requires

to resolve very tiny to resolve very tiny structuresstructures

PART 1 Defining a method for in-flight calibration of IMaX aberrations d) Conclusions



Earth’s atmosphere can be considered

as an isotropic turbulent medium

Atmospheric turbulence is a major problem we encounter in ground-based observations affecting the image

quality


a) Introductiona) Introduction

Image degradation is generally described as the combination of 3 main contributions

Structures smearing (blurring)

Global displacements of the image (image motion)

Distortion of structures caused by differential image motion in different patches (stretching)

seeing

First problem to deal with if interested on high resolution

data


a) Introduction

Solutions:

Space observatories

SOHO

HINODE

Elevated cost of launching,

maintenance and updating

Adaptive Optics

Only pursues low-order corrections

Limited to an isoplanatic patch of a few arcsec


a) Introduction

Solutions :

Space observatories

Adaptive OpticsPost-facto techniquesPowerful numerical codes for image restoration developed in the last decade.They require a specific observing strategy


a) Introduction

Image Image formationformation

X

Y

Object plane Image

plane

Object plane Image

plane


a) Introduction

Text

+

Point in the object plane

observed as a spot

on the image plane

Object plane Image

plane

X

Y

Airy spotImage Image

formationformation


a) Introduction

TextText

Point Spread Function

Space variantVariability of the transmission system

For a extended object (e.g Sun)

Intensity at each point has a contribution from

the neighborhood

Image Image formationformation

PSF =


a) Introduction

TextText

Image restorationImage restoration

Image restoration fits into the Inverse Problem in Physics that can be considered as the solution of the Fredholm Inhomogeneous equation of the 1st kind.

The kernel is the PSF

Using the convolution theorem,

True objectwhere q is the vectorial notation for the coordinates in the image points

Isoplanatic assumption

Optical Transfer Function (OTF)


a) Introduction

TextText

Noise Noise contribution and contribution and

filteringfiltering

Restoration filter (Wiener-Helstrom)

Additive noise

Some models for SNR are commonly assumed (Collados, 1986)

Phase Diversity Phase Diversity techniquetechnique


b) Image restoration techniquesa) Introduction

d) Conclusions


focus-defocus image pairsPSFsnoise additive termstrue object

Noise terms force a statistical solution of the problem

The PD technique was first proposed as a new method to infer phase aberrations working with images of extended incoherent objects formed through an optical system (Gonsalves & Childlaw, 1979).


b) Image restoration techniquesa) Introduction

d) Conclusions


Phase Diversity Phase Diversity techniquetechnique

Error metric to be minimized (Paxman et all, 1992)

OTF is the auto-correlation of the generalized pupil

function

Joint phase aberration

Zernikes

Parametrized by the expansion in Zernike polynomials.Non-linear optimization techniques (SVD) are used to minimize the error metric and get the vector, S1, S2 and Io


b) Image restoration techniques

Restoration techniquesRestoration techniques

MFBDMulti-Frame

Lofdahl, 2002, 1996

Blind Deconvolution

MOMFBDMulti-Object Multi-Frame

Van Noort, Rouppe van der Voort & Löfdahl, 2005

PDPhase Diversity

Results coming up in a few minutes !!!!


a) Introduction

d) Conclusions

c) In-flight calibration of IMaX aberr.b) Image restoration techniques

Imaging Magnetograph eXperiment

Instituto de Astrofísica de Canarias

Instituto de Astrofísica de Andalucía

Instituto Nacional de Técnica Aeroespacial

Grupo de Astronomía y Ciencias del Espacio


a) Introduction

d) Conclusions


SUNRISEBallon-borne 1-m solar

telescope Aims at: High-resolution Spectro-polarimetric observations of the solar atmosphereTo be flown:

In the framework of NASA Long Duration Ballon Program in 2009 in circumpolar trajectories at 35-40 km.Consist of:Telescope , Image Stabilisation and Light Distribution System

, IMaX Sunrise Filter Imager (SUFI)


c) In-flight calibration of IMaX aberr.

spsp



ISLiD - Image Stabilisation and Light Distribution System

For simultaneous observations with all science instruments based on di-electric dichroic beam splitters.Includes the Correlator and Wavefront Sensor

IMaX - Imaging Magnetograph eXperimentMagnetograph providing fast cadence two-dimensional maps of complete magnetic field vector and the LOS velocity as well as white-light images with high-spatial resolution.

SUFI - Sunrise Filter ImagerFiltegraph for high-resolution images in the visible and the UV spectral lines.



IMaX description

Aim at:Provide magnetograms of extended solar regions by combining high temporal cadence and polarimetric precision, working as:

High-efficient image acquisition system

Near diffraction limited imager

High resolving power spectrograph

High sensitivity polarimeter



Cameras

Etalon

Electronics box

A glass-plate can be optionally intercalated in one of the IMaX imaging channels to get simultaneous focus-defocus image-pairs, i.e. Phase Diversity (PD) image-pairs, from which an estimate of the aberrations will be possible in post-processing by means of a PD inversion code.Assuming a long-term variation in the aberrations, their calibration could be performed with a cadence of one hour. A burst of 25-30 PD-pairs in the continuum would be enough each time.



Calibration of aberrations in IMaX

We have included in IMaX a system to calibrate the image degradation during the flight that should allow a correction of the residual aberrations in the science images.

diversity


a) Introduction

d) Conclusions


Strategy



Testing the robustness of the calibration method

Evaluate the robustness of the method versus a variety of aberration assumptions

Isoplanatic patch

True object

Synthetic image (Vöegler et al. 2005)



Testing the robustness of the calibration method

Simulate the formation of PD image-pairs produced by 1-m telescope and a given set of aberrations. 30 for diff. photon

noise realizationsImage-pairs are inverted with the PD code.

Set of averaged aberrations retrieved from inversions are compared to input aberrations.



Identifying error sourcesThe contribution from the error sources can be mathematically represented through the generalized pupil function,

Phase diverse

Transmission function over pupil

Main polishing

error Phase error from etalon

Low-order aberrations

Atm. aberration (IMaX=0)



Quantifying error sources contributionFirst step is the compilation of data from the design and specifications of all different components



Low-order aberrations (LOA)

Empirical measurements for the assembled instrument.



Amplitude in double-pass

Phase in double-pass| H(,) | e (,)

Etalon Screens



Main mirror polishing errors

Ripple screenHigh-order aberrations

Average power spectrum matches a von Karman power

spectrum



Phase Diversity plate



Detector contribution

A detector element performs a spatial integration of the irradiance falling onto its surface



Simulations

We classify error contributions in 3 groups:

Low-order aberrations (LOA)

High-order aberrations (HOA)

Detector contribution & Noise



Simulations

ERROR SOURCE

CONTRIBUTIONEXPERIMENT

1 2 3 4

rms-ripple 0, 2/60, 2/28 waves

rms-LOA0, 1/12, 1/7, 1/4, 1/3, 1/2

waves

rms-noise 10-3 x continuum signal

rms-etalon 1/26 waves

Etalon amplitude | H(,) | ≠ 1

CCD 12 m/pix

PD-defocus

DEGRADATION/INVERSION8.51 mm (PV 1.00) / 8.51

mm9.00 mm (PV 1.06) / 8.51

mm

A pessimistic case for IMaX + ISLiD + Telescope performance



Error contribution

srms-ripple=2/60rms-etalon=/26rms-noise=10-3

CCD

rms-LOA=/5

Focus image of a PD-pair True object(from 30 realizations)

RESULTSRESULTS

Degraded Restored True



d) Conclusionsc) In-flight calibration of IMaX aberrations

A method for the in-flight calibration of aberrations in IMaX has been proposed.The robustness of the method has been tested by numerical experiments simulating different aberration components.Sources of aberration have been modeled and added in every subsequent experiment.The repercussion of every new added ingredient in the final result from the inversions has been evaluated.

In the PART 1 of this work:

The calibration method has proved to give satisfactory results even in under pessimistic aberration conditions



d) Conclusionsc) In-flight calibration of IMaX aberrations

Main conclusions are:The PD-code does not accurately reproduce the shape of the WFE but provides reliable OTFs for satisfactory restorations.Inhomogeneities in the etalon transmission are converted into some extra errors in the resulting wavefront that partially compensate the loss of contrast caused by unsensed HOA.Experiment 3 validates the method proposed to calibrate the errors in the images of IMaXThe amount of defocus (diversity) produced by the PD plate is a critical parameter for an optimal performance of the PD code. An error of 0.5 mm in the determination of the diversity value can caused an over restoration of about 5%.

PART 2Study of proper motions in solar active regions

Aim at:

Analysis of horizontal proper motions, at a photospheric level, around solar active

regions from ground-based and space high-resolution time series.

Nearly 1000000 images have been Nearly 1000000 images have been used for this study !!!used for this study !!!

Outline

Solar active regionsProper motions in a complex ARMoat flows surrounding sunspotsFlow field around solar poresConclusions

PART 2 Study of proper motions in solar active regions

a) Solar active regionsb) Proper motions in a complex AR

d) Flow field around solar porese) Conclusions

c) Moat flows surrounding sunspots

PART 2 Study of proper motions

in solar active regions

Are the evident manifestation of the solar activity

Sunspots

Are interpreted as complex structures having strong magnetic fields that inhibit the plasma convection (temperature lower

than the surrounding photosphere)

a) Solar active regionsb) Proper motions in a complex AR





Structure of Sunspots The responsible for the origin and structure is

believed to be the toroidal magnetic flux in the solar interior (Schüssler et al, 2002)

Cluster (spaguetti) : Mag. field divides into many separate flux Parker, 1979 tubes in the first Mm below the surface

Models

Monolithic : Mag. field underneath the solar surface is Cowling, 1957 confined to a single flux tube.

a) Solar active regionsPART 2 Study of proper

motions in solar active

regions

UmbraCoolest part of the

sunspots~ 3500 - 5000 K

Strong Mag.F inhibits convectionVertical magnetic field; more inclined at umbra-penumbra boundary

~ 2000 - 3500 Gauss in average

Energy radiation 20% photosphere

Features (umbral dots, light bridges)

PenumbraFilamentary bright/dark

structure

The first one has been extensively tested 2 different orientations of mag. field coexist

Energy radiation 75% photospheric

Mag. Field inner part: ~1500 Gauss outer part: ~700 Gauss

Vertical component (~60-70 deg)Horizontal component

Different models try to explain the structure of the penumbra: Uncombed, Gappy, MISMAS.



regions

Evershed Flow

Associated to an observational effect in the penumbra registered as a global wavelength shift for spectral lines forming in the penumbrae of sunspots.



regions

Photosphere surrounding sunspots

Convective flows & large-scale plasma circulation plays and important role in dynamics and evolution of solar active regions (Schrijver & Zwaan 2000).

Granular convective pattern surrounding sunspots is perturbed by the presence of magnetic elements, moving magnetic features (MMF).

MMF’s move radially outward through an annular cell called “moat”. (Sheeley 1972, Harvey & Harvey 1973).



regions

Moat flow

(Meyer et al. 1974)

Could be:

Typical cell scale of up to 104 km.

A supergranule.

Center occupied by a sunspot.

(Nye et al. 1988)

Excess temperature and pressure generated have been proposed as origin of moat.

Sunspot would act as a blocking agent to the upward propagation of heat from below.

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Averaged horizontal velocities [m s-1]



regions

+ Young spots

♢ Old Spots

Sobotka & Roudier, 2007





a) Solar active regionsb) Proper motions in a complex solar AR

Observations1m - Solar Swedish Tower

(SST) Roque de los Muchachos Observatory, La

Palma.

NOAA AR10786 9-Jul-2005

G-band, G-cont 7:47 – 9:06 UT

DC

G-band δ-configuration sunspot


in solar active regions d) Flow field around solar pores

e) Conclusions


a) Solar active regionsb) Proper motions in a complex solar AR

Processing

Flat-fielding & dark-current substraction

Image restoration MOMFBD + PD

De-rotation and alignment

De-stretching and p-modes

filtering

Time series

G-band and G-cont

428 images each

Cadence: 10.0517 s

71 minutes

FOV 57.8” x 34.4”

Image restoration MOMFBD + PD

Low quality

Medium quality

Good quality

Restored quality

Nº Images : 428 Duration : 71 minutes Cadence : 10.0517 s Pixel size : 0.041 “/pix

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MoatNo Moat

Exploding granules draggedby the moat flow (elongated)

Recurrent exploding granules



b) Proper motions in a complex solar AR

Map of displacements

We have used the G-band series to study proper motions of the structures by local correlation technique (LCT)

Finding local concordances between two frames (correlation window).First applied by November & Simon (1988) to measure proper motions in solar granulation.Used at diff. spatial scales to study solar dynamics (e.g supergranulation Shine,Simon & Hurlburt, 2000)

Gaussian tracking window FWHM = 0.78” (half of typical granular size)

Map of horizontal displacements averaged over the whole series

[Mm]




General description of proper motions

Neutral LinesFlowmap

Exploding granules

SOUP magnetogramsMOMFBD+PD

Combining 1500 images

SNR=200Resolution: 0.2 “/pix




Moats

Vmoats = 0.67 km/sVh > 0.4 km/s

Moats are closely associated with the presence of a penumbra.

Low velocity threshold: 400 m/s




None of the pores is associated with any moatlike flow.

Strong neutral line Not clear evidence of moat flow Moats are absent in granulation regions located next to penumbral sides paralell to the direction of the filaments.




Conclusions

We have detected strong outflows (moats) associated to penumbrae (mean speed 0.67 km/s, rms=0.32 km/s)

Furthermore, moats do not developed in directions transversal to the penumbral filaments.

Evidence suggestive of a link between moat flow and flows aligned with penumbral

filaments (EF)

Umbral core sides with no penumbrae do not display moat flows.

Neutral lines are seem to play a role in the inhibition of moat flows in places where they are expected to be generated.




Recent findings by Sainz Dalda & Martínez Pillet (2005), and Ravindra (2006) establish that the penumbral filaments extend beyond the photometric sunspot boundary and cross the region dominated by the moat flow. Cabrera Solana et al (2006) found Evershed clouds as precursors of MMFs around sunspots.




b) Proper motions in a complex AR


a) Solar active regions

Extend the sample of solar active regions to consolidate the previous conclusions.

Aim at:

i.e establish whether the moat-penumbrae relation is sistematically found in other active regions.

By using:

Gound-based high-resolution observations

7 different sunspots series.

Sunspots with different penumbral configurations.




b) Proper motions in a complex ARc) Moat flows surrounding sunspots


1m - Solar Swedish Tower (SST) S1 AR440, 22 Aug 2003

S2 AR608, 10 May 2004

S5 AR789, 13 Jul 2005

S6 AR813, 04 Oct 2005

S3 AR662, 20 Aug 2004

S7 AR893, 10 Jun 20061

2

345

6

7

Observations

S4 AR662, 21 Aug 2004

Restoration MFBD/MOMFB

Time series > 40 min




Masking moats in 8 steps

1. Select the FOV to analyze.2. Create a binary mask for the sunspots.

3. Compute the proper motions by LCT.

4. De-project velocities.

5. Create a binary mask using a velocity threshold.

6. Apply the mask to the flowmap in 3.

7. Create a binary mask of moats.

8. Plot the final flow map showing the moat flows.




Moat flows around sunspots (flowmaps)

Penumbral filaments extending radially from the umbra

Peculiar regions




Penumbral filaments curved, tangential to

sunspot border No moatlike flows




Neutral lines affecting the flow behaviour




Conclusions

Moat flows are oriented following the direction of the penumbral filaments.

Umbral core sides with no penumbra do not display moat flows.

Moat do not develop in the direction transverse to the penumbral filaments.

No evidence of moats following penumbral filaments when having a change in the magnetic polarity.


e) Conclusions





d) Flow field around solar pores

Observing and analyzing pores. Since they do not have penumbra at all, our main conclusions. about moat-penumbra relation can be tested.

Aim at:

By using:

Gound-based and space observations.

Pores time series.


e) Conclusions




Ground-based observationsSST

30 Sep 2007

Study of proper motions in solar active regions

Active region NOAA 10971

Standard reduction and processing

MOMFBD reconstructions

G-band time series (50 min)

MOMFBD restorations

d) Flow field around solar poresStudy of proper motions in solar active regions


General description of proper motions


Exploding granules


Space observationsHINODE

1 June 2007

30 Sep 2007


Coordinated obs. with SST

Alignment and subsonic filtering

60 min

14 hours

HINODE during14 hours


Long-term evolution of the velocity field



Distribution of horizontal speeds

Velocity magnitudes

Low< 0.3 km/s



Velocity distribution around solar pores



Pore center

Radial directions

Inward (-)

Outward (+)

t

r

r


Flow mapGradients

Radial directionsCos

Mask


Results

InOut

FOVFOV

Cos Cos


Outflows display larger velocity magnitudesInflows display lower velocity magnitudes

Conclusions

First time we tested our algorithms in HINODE data. Flows calculated from different solar observations are coherent and show the overall influence of exploding events in the granulation around pores.

Motions toward the pores in their nearest vicinityare dominant and are observed systematically.

These motions are basically influenced by external plasma flows deposited by the exploding events.

Definitely, there are no signs of moatlike flows around the pores.


d) Flow field around solar poresc) Moat flows surrounding sunspots




e) Conclusions

Overall Conclusions

The required software for restoration/inversion of IMaX images has been implemented in the context of this thesis and we make it available for the team.

Our simulations validate the method proposed to calibrate the errors in the images of IMaX.


We have developed a method for the in-flight calibration of aberrations in IMaX.

Note: Only 4 slides left !!

Moats do not appear in directions transversal to the penumbral filament ones.

All detected properties for moats are also applicable to the Evershed Flow.

Moats develop following the direction of the penumbral filaments in granulation surrounding sunspots.

There are no signs of moatlike flows around the pores.

Overall ConclusionsPART 2 Study of proper motions in solar active regions

Moats are found to be directly correlated to the presence of penumbra in sunspots.

Neutral lines seem to play a role in the inhibition of moats.

Before this work ....

So what ???

Final fate of the EF unknown.

Origin of moat flow unclear.

After this work ....

EF transforms into moat flow.

In agreement with Local Helioseismology (f-modes) evidence: moat flow is only 2

Mm deep.

Acknowledgments

Seidel aberrations

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Using the map of average velocities we study the evolution of passive corks homogeneously distributed in the FOV

Study of convective cells


Space observationsHINODE

1 June 2007

30 Sep 2007


Coordinated obs. with SST

Alignment and subsonic filtering

60 min

14 hours

Moat Granulation

Vh km/s

Threshold used when

plotting velocities !!!







De-projection of horizontal velocities

Measured proper motions are in fact projections of the real horizontal velocities in the sunspot plane onto the plane perpendicular to LOS

Sunspot SystemObserving System

€

v' 2 = v 2 sin2 φ + cos2 φ cos2θ ⎛

⎝ ⎜

⎞

⎠ ⎟

€

tanφ'=tanφ

cosθ




Proper motions inside penumbrae

Link between the moat flow and flows along the penumbral filaments (Evershed flow).

Recent findings by Sainz Dalda & Martínez Pillet (2005), Cabrera Solana et al (2006) and also Ravindra (2006) establish that the penumbral filaments extend beyond the photometric sunspot boundary and cross the region dominated by

the moat flow.


d) Flow field around solar poresc) Moat flows surrounding sunspots




e) Conclusions


Pore center

Radial directions

Inward (-)

Outward (+)

t

r

r

What for ????

The material presented here comes from the analysis of images in the continuum with short exposure times ~10 ms (static atmosphere) and combining many images (~100 continuum, ~1500 SOUP) but still low SNR values are reached.

IMaX will do polarimetry with:

negligible atmospheric turbulence, high SNR, diffraction limit, during hours and furthermore double spatial resolution (from 0.2 to 0.1 arcsec)

Why using speckle ????

The speckle summation has been employed as a way (resource) to determine the robustness of the calibration method we propose to characterize the aberrations in IMaX.

though

in the real case IMaX images are be meant to restored as single PD-pairs with no speckle summation at all.

Image blurring permitted for an instrument can be specified by the diameter of the blur spot or angle subtended by it.

For instance, we can select the angle as the value of the diffraction cut-off that is slightly greater than the Airy FWHM.

Nevertheless this criterion is quite severe and some more flexible ones establish the limit of the defocus tolerance based on the loss of intensity in the central part of the PSF.

Defocus Tolerance

Why PD if it does not reproduce exactly the

WFE ??

We get reliable OTFs to solve our deconvolution problem.

Because

The error metric depends directly on this OTF.

Dispersion of coefficients is low and we do not expectcancellations in the WFE. Repeatability

We have inverted real images for different noise realizations and the dispersion of the wavefront is small.

Why uncorrelated signal and noise assumption ??

Photon noise is certainly a function of the intensity

there are some other noise contributions: Readout and noise related to the fluctuations in

atmospheric transparency which are not

Nevertheless,

Uncorrelated noise and signal is in general a useful approximation giving good results in

simulations

Small-scale irregularities in the wavefront error are notdetectable by the PD-code if we use a finite (rather low) number of Zernike terms.

Please goto Pag 78.

This limitation mainly produces stray-light over the restored image and consequently a loss of contrast.This effect is tolerable within certain margins, and fixes constraints to the polishing quality in the SUNRISE main mirror and the inhomogeneities in the IMaX etalon.

The residual errors in the proposed calibration method induce, in turn,

errors in the subsequent restoration

mean (it - ir) < 2.5% loss of contrast < 5%

IMaX case

study o horizontal flows in solar active regions

Education

image quality

imax instrument

inflight calibration

new method

differential image motion

phase aberrations

true object whereqis

extended object e