3D ELECTRON DENSITY RECONSTRUCTION FROM THE SECCHI CORONAGRAPHS and EUVI ONBOARD STEREO: 3D ELECTRON DENSITY RECONSTRUCTION FROM THE SECCHI CORONAGRAPHS and EUVI ONBOARD STEREO Jeffrey Newmark, John Cook
Naval Research Laboratory
(202) 767-0244 newmark@nrl.navy.mil
Outline: Outline SECCHI 3D Reconstruction and Visualization Website:
http://stereo.nrl.navy.mil/3drv/3dindex.html
Presentation Based on SECCHI Consortium Meeting, April 2004, CA
Overview of 3D related activities by consortium
Details of selected activities
Heliospheric Imager – overview, science planning, CMEs
SMEI – not STEREO, early results, prelude for HI
Conclusions
SECCHI Science Overview: SECCHI Science Overview SECCHI SPD 2003 <#>
Methodologies: Methodologies MHD modeling
Forward Fitting
Requires parameterization of model
Number of parameters could be large
2D projection is given, only 3D coordinates need to be constrained by 2nd STEREO image
Strategy: develop tool with automated 2D-parameterization of curvi-linear features (loops, filaments, fluxropes, sigmoids, postflare loops, etc.)
3D coordinate can be first constrained by a-priori model (potential field, force-free, simple geometries, and then iteratively refined with projections from 2nd image, starting with the most unique and unambigous tie-points.
Examples: Stereoscopy (most suitable for EUVI early in the mission), inclusion of magnetic field
Inversion
Inversions generally are coarse because of data noise, ambiguities, non-uniqueness
Advantage of inversions: they are model-independent, non-parametric
Examples: Tomography, Pixon reconstruction
Combination - None, one, or both methods yield a good fit to data,
disproves both models, confirms one model, or ambiguous choice
SECCHI Group Activities (1): SECCHI Group Activities (1) NRL
3D Reconstruction of White Light Coronagraph Images from Multiple Viewpoints – Cook, Newmark, Reiser, Yahill – Tomography, Pixon reconstruction, 3D data cube rendering
Differential Emission Measure (DEM) Tool for EUVI – Cook, Newmark – comparison with forward fitting models
Streamer Simulation – Vourlidas, Marque, Howard, Thernisien – model comparison to data, 3D data cube rendering
CME Mass and Energetics Toolbox – Vourlidas, Thernisien, Howard – based on LASCO tools
JPL
Tie Point Tool – De Jong, Liewer, Hasll, Lorre – manual stereoscopy
SynLOS: synthetic LOS Tool for SECCHI white Light Images – Liewer, Hall, Lorre – 3D data cube rendering
LMSAL/Rice
3D Reconstruction of Stereoscopic Images from EUVI – Aschwanden, Lemen, Wuelser, Alexander – forward modeling and constraint time series
SECCHI Group Activities (2): SECCHI Group Activities (2) ROB
Computer Aided CME Tracking (CACTus) – Robbrecht, Berghmans, Lawrence, Van der Linden – pipeline processing automated CME catalog – based on LASCO – not reconstruction tool presently
Computer Aided EIT Wave and Dimming Detection – Podladchikova, Berghmans, Zhukov - pipeline processing automated EIT waves and dimming regions catalog – based on EIT – not reconstruction tool presently
Solar Weather Browser (SWB) – Nicula, Berghmans, Van der Linden – browse tool, not reconstruction tool presently
(Apparent) Velocity Map Construction – Hochedez, Gissot – full motion analysis software of EUV and WL using optical flow techniques – tracking, detection, stereoscopic reconstruction
MPS (formerly MPAe)
Finite Element Tomography Code (FETOC) – Inhester – 3D tomography inversion code – coronal magnetic filed model can be used as a constraint
Stereoscopy of EUV loops – Portier-Fozzani (Athens), Inhester – parameterized, forward fitting loop model
Reconstruction of coronal magnetic fields (LINFF, NONLINFF) – Wiegelmann, Inhester – 3D coronal magnetic field from boundary data, interfaces to provide reconstructed field for stereoscopy and tomography
SECCHI Group Activities (3): SECCHI Group Activities (3) MPS/UB cont.
Real-time and 3D visualization of STEREO images – Bothmer, Kraupe, Schwenn, Podlipnik, Cremades, Wiegelmann – planetarium display
3D Structure of CMEs: Origin, Internal Magnetic Field Configuration and Near-Sun Evolution – Bothmer, Cremades, Tripathi – comparison of model prediction (magnetic field + H-alpha based) and data
JHU/APL – Automatic solar feature recognition and classification – Rust, Bernasconi, LaBonte – solar filaments, sigmoids, chirality, and CMEs – EUVI – helicity is important for 3D modeling
Obs. de Paris – Combining Nancay Radio heliograph with SECCHI instruments – Pick, Kerdraon – identification of emitting coronal structures, source regions
SMEI (not SECCHI, but related to HI) - Jackson, Tappin, Hick, Webb – IPS and Thomson scattering Modeling/Tomography – solar wind model dependent, low resolution, developed from techniques based on Helios data
SECCHI Group Activities: MHD Modeling: SECCHI Group Activities: MHD Modeling NRL – Klimchuk, Antiochos, DeVore, Karpen, Lopez-Fuentes, Lynch, MacNeice, Magara, Patsourakos
MHD CME initiation and propagation, Coronal loop structure, Coronal heating, Loop plasma evolution (incl. Prominences), Coronal hole evolution, Flux emergence, Active region structure
3D Visualization - Heliospace package, Developed with ARL (Tim Hall), Based on FAST (NASA/Ames)
SAIC – Mikic, Linker, Riley, Lionello – coronal and Heliospheric timde dependent MHD model = MAS
Univ. Alabama – Wu – MHD models
GSFC CCMC – hosts models
Specific Examples: Specific Examples
NRL 3D WL: Reconstruction: NRL 3D WL: Reconstruction Strategy: Apply 3D tomographic electron density reconstruction techniques to solar features from low corona through heliosphere to 1 AU. Utilize Brightness, polarized brightness, temporal, 2D white light coronagraph images and synthetic models from 2/3 vantage points, construct (time dependent) 3D electron density distribution.
Focus: Use theoretical CME models and existing LASCO observations prior to STEREO launch in order to predict the range of conditions and features where reconstruction techniques will be applicable.
Goal: Provide a practical tool that will achieve ~daily CME 3D electron density models during the STEREO mission.
Study realistic complexities: Input Synthetic Models -> density structures (uniform vs. cavity vs. “realistic”), K/F corona, time dependence
NRL 3D WL: Key Aspects : NRL 3D WL: Key Aspects Renderer - Physics (Thomson scattering), tangential and radial polarization brightness, total brightness, finite viewer geometry, optically thin plasma.
Reconstruction Algorithm - PIXON (Pixon LLC), Pina, Puetter, Yahil (1993, 1995) - based upon minimum complexity, non-parametric, locally adaptive, iterative image reconstruction. Roughly analogous to multiscale (wavelet) methods (not as closely related to maximum entropy).
chosen for speed (large # voxels, up to 10^9): small number of iterations, intelligent guidance to declining complexity per iteration. Sample times have been 32x32x32 <15 minutes, 64x64x64 ~60 minutes, 128x128x128~6 hrs, (1 GHz PC).
Minimum complexity: With this underdetermined problem, we make minimal assumptions in order to progress. Another possibility is forward modelling, i.e. parameter fitting. Complementary approach.
Visualization - 3D electron density distribution, time dependent (movies), multiple instrument, multiple spacecraft, physics MHD models.
3D Reconstruction: CME model (J. Chen)Three Orthogonal Viewpoints: Rendered Data (1): 3D Reconstruction: CME model (J. Chen) Three Orthogonal Viewpoints: Rendered Data (1)
3D Reconstruction: CME model (J. Chen)Three Orthogonal Viewpoints: Rendered Data (2): 3D Reconstruction: CME model (J. Chen) Three Orthogonal Viewpoints: Rendered Data (2)
3D Reconstruction: CME model (J. Chen)Three Orthogonal Viewpoints: Image Visualization: 3D Reconstruction: CME model (J. Chen) Three Orthogonal Viewpoints: Image Visualization
3D Reconstruction: CME model (J. Chen)Three Ecliptic Viewpoints: Image Visualization: 3D Reconstruction: CME model (J. Chen) Three Ecliptic Viewpoints: Image Visualization
3D Reconstruction: CME model (J. Chen)Two Viewpoints: Image Visualization: 3D Reconstruction: CME model (J. Chen) Two Viewpoints: Image Visualization
NRL 2: Determining the Ne for a CME: NRL 2: Determining the Ne for a CME For a transient event, such as a CME, the problem of determining K is quite straightforward, since we are only interested in the excess mass.
In this case we use a pre-event image to subtract the entire background from the image that contains the event.
Knowing the electron density, a simple conversion calculates the mass
Note: calculating the total excess mass only counts mass that comes up from below the occulting disk – it does not consider mass that has been transported from lower to higher heights, all within the field of view of that coronagraph
This procedure has been automated, and only needs to know the times of the event, the radial height of the leading edge, the central latitude or position angle and the angular span. Vourlidas et al 2003 has derived the following plot of the results of calculating the mass of over 4000 LASCO CMES
NRL 2: Determining Ne for a Coronal Structure: NRL 2: Determining Ne for a Coronal Structure To calculate the electron density in a non-transient structure requires a different technique.
We have developed two different approaches, one using polarized brightness observations and the other using total brightness observations. The software for both of these approaches is available in the LASCO software tree.
In both techniques, a radial cut through the pB or Bt corona, at a particular position angle, is obtained and then fit to a polynomial. Using an assumption of spherical symmetry, we then can then perform the inversion.
The pB technique was developed by van de Hulst in the 1950s and has been used for many years by many groups. It depends on the assumption that pB = K, ie that all the other sources contributing to the observations are not polarized. This is usually not a bad assumption inside of about 3-4 solar radii.
The Bt technique was developed by Hayes et al (2001). It depends on knowledge of each of the contributions given earlier.
NRL 2: Forward Modeling: NRL 2: Forward Modeling Another technique we have started on is to assume a structure and then empirically generate a good fit to the observations. The difficultly with this approach is that the structure is only as good as your imagination and that many different structures may be equally suitable (or unsuitable)
This procedure allows you to specify the location in solar coordinates of a structure or combination of structures that are present in the corona and then allows you to view the resulting brightness image that would be generated from any angle. The structures must be expressed analytically.
We currently have various structures defined to represent possible streamer structures (slabs with a gaussian density, constant density cross section or gaussian-ellipsoid cross sections; a warped current sheet), a coronal hole.
We will be adding structures of possible CME representations – cone, spherical shell, ellipsoidal shell are currently envisioned.
We will also be making it more “user-friendly”.
JPL: SynLOS - Hemisphere CME at 20° viewed from SC at -30°: JPL: SynLOS - Hemisphere CME at 20° viewed from SC at -30°
CME at 20° x y -30° HI2 R=48 Rsun HI1 R=32 Rsun COR2 R=4 Rsun sc sc sc sc FOV of COR2 & dat cube FOV of HI2 & data cube FOV of HI1 & data cube
(Sun in center of 1 AU circle) earth earth
JPL: Stereoscopy: Tie Point Tool: JPL: Stereoscopy: Tie Point Tool Classical Stereoscopy: Determine 3D location of a “Feature” identified in both images of a stereo pair using triangulation
Minimum platform-independent tool (Now Exists):
Manual placement of tie points in displayed stereo image pair
Computation of 3D location of feature in heliographic coordinate system (uses program xyzsun) Can be used to trace out loops (EUVI) and to compute 3D velocities of features from time series of stereo images, e.g., CME velocities (CORs and HIs)
Slide22: LMSAL: Forward-fit Algorithm for Stereo Image Pair 1. Selection of structure-rich multi-wavelength
image from TRACE, EIT, and/or Yohkoh database
(with filament, flare, CME, fluxropes, etc.) 2. Tracing linear features (loops, filaments, fluxropes)
in 2D: s(x,y) 3. Inflation from 2D to 3D with prescription z(x,y)
s(x,y) -> s(x,y,z) 4. Physical model of structures: T(s), n(s), p(s), EM(s) 6. Line-of-sight integration EM(x’,y’)=EM(x’,y’,z’)dz’
and convolution with instrumental response function 5. Geometric rotation to different stereo angles
EM(x,y,z) -> EM(x’,y’,z’) http://www.lmsal.com/~aschwand/ppt/2002_Paris_stereo.ppt
Slide23: LMSAL: 3D Geometry [x(s),y(s),z(s)]
of coronal coronal structures, such as
filaments, loops, arcades, flares, CMEs, … - Geometric definitions :
1-dim parametrization along magnetic field lines
is in low-beta plasma justified --> [x(s),y(s),z(s)]
- Cross-sectionial variation for loops, --> A(s)
- Start with tracing in 2D in first STEREO image --> [x(s),y(s)]
- Model for 3D inflation z(s),
e.g. semi-circular loops with vertical stretching factor
z(s)=sqrt[(x(s)^2 + y(s)^2]*q_stretch
- Forward-fitting to second STEREO image to determine q_stretch
Slide24: STEREO - A STEREO - B
Slide25: LMSAL: Tracing linear features : --> [x(s),y(s)] High-pass
filtering Feature tracing,
reading coordinates,
spline interpolation
Slide26: Step 3:
3D Inflation: z=0 -> z(x,y)
- model (e.g. semi-circular loops)
- magnetic field extrapolation
- curvature minimization in 3D s(x,y) LMSAL
s(x,y,z)
Slide27: * LMSAL: 3D Fitting: F[x(s),y(s),z(s)]
Volume rendering of coronal structures Flux fitting in STEREO image
Volume filling of flux tube with sub-pixel sampling
Render cross-sections by superposition of loop fibers with sub-pixel
cross-sections: A=Sum(A_fiber), with w_fiber<pixel
Loop length parametrization with sub-pixel steps ds<pixel
Flux per pixel sampled from sub-pixel voxels of loop fibers
Slide28: LMSAL: Forward-Fitting of Arcade Model with 200 Dynamic Loops Observations from TRACE 171 A : Bastille-Day flare 2000-July-14
Slide29: * LMSAL: 4D Fitting: F[x(s),y(s),z(s),t]
of coronal coronal structures - Flux fitting in STEREO image #1 at time t1 : - Flux fitting in STEREO image #2 at time t1
- Sequential fitting of images #1,2 at times t = t2, t3, …. , tn
Slide30: LMSAL: 5D Model: DEM [x(s),y(s),z(s),T(s),t]
with dynamic physical model
Ingredients for flare loop model :
- 3D Geometry [x(s), y(s), z(s)]
- Dynamic evolution [x(s), y(s), z(s), t]
- Heating function E_heat(s)
- Thermal conduction -F_cond(s)
- Radiative loss E_rad(s) = -n_e(s)^2 [T(s)]
-> Differential emission measure distribution dEM(T,t)/dT
-> Line-of-sight integration EM(T)= n_e(z,T,t)^2 dz (STEREO angle)
-> Instrumental response function R(T)
-> Observed flux F(x,y,t)= EM(T,t) * R(T) dT
-> Flux fitting of 5D-model onto 3D flux F(x,y,t)
for two stereo angles (4D) and multiple temperature filters (5D)
Slide31: Eva Robbrecht
David Berghmans
Gareth Lawrence
Royal Observatory of Belgium ROB CACTus Computer Aided CME Tracking
Slide32: time distance from Sun time distance from Sun S W N E The catalyst θ r ROB
Slide33: ROB: Sample Output (test data Nov ’03)
Slide34: J-F Hochedez, Royal Observatory of Belgium EIT 304, Shutterless June 2003 Example of a EUV solar images decomposition
Wavelet transform & segmentation
Classification based on object parameters
Possibility of tracking objects
Application to SECCHI: tiepoints ROB
Slide35: ROB: Sample LASCO images:
Slide36: ROB: Developmental Solar Data Browser:
MPS: Magnetic fields toolsThomas Wiegelmann and Bernd Inhester: MPS: Magnetic fields tools Thomas Wiegelmann and Bernd Inhester STEREO/SECCHI has no magnetograph. Why do we develop magnetic field tools then?
Magnetic field dominates and structures the solar corona (magnetic pressure >> plasma pressure)
Coronal magnetic field is useful/necessary for Tomography and Stereoscopy.
Photospheric magnetic field data are (will be) available e.g. from Kitt Peak, SOHO/MDI (SOLIS, Solar-B)
MPS: Magnetic fields and coronal tomography: MPS: Magnetic fields and coronal tomography Use only line of sight density integrals.
Use only magnetic field data.
Use both line of sight density integrals and magnetic field as regularization operator.
MPS: Magnetic field outlines the coronal plasma: MPS: Magnetic field outlines the coronal plasma EIT-image and projected magnetic field lines. Planed is (for SECCHI) to project the magnetic field on both images => magnetic Stereoscopy
3D magnetic field lines, linear force-free field with α · L=2
Slide40: MPS: Global Potential Field reconstruction
MPS: Summary magnetic fields: MPS: Summary magnetic fields Potential magnetic fields and linear force free fields are popular due to their mathematic simplicity and available data. (e.g. from MDI on SOHO, Kitt Peak)
Nonlinear force free fields are necessary to describe active regions exactly. More challenging both observational and mathematical.
A consistent 3D model of the solar corona requires tomographic inversion and magnetic reconstruction in one model.
Slide42: NRL: MHD 2.5D Spherical Breakout P. J. MacNeice et al, ApJ, in press – properties of model
Lynch et al, ApJ submitted – comparison with observations
NRL: MHD: Density (top), Brightness (bottom): NRL: MHD: Density (top), Brightness (bottom)
NRL: MHD: 3D Spherical Breakout: NRL: MHD: 3D Spherical Breakout Nonaxisymmetric multipolar field
3D generalization of previous work Visualization uses interpolation onto Cartesian grid
NRL: MHD: Corona Loop Structure: NRL: MHD: Corona Loop Structure TRACE 171 Image
Extrapolated Flux Tube
Lopez-Fuentes & Klimchuk
NRL: MHD: 3D Spherical Breakout: NRL: MHD: 3D Spherical Breakout B_radial, flux, density, temperature
B_radial, flux, grid
SAIC: MAS Model Highlights: SAIC: MAS Model Highlights
SAIC: MAS Model Highlights (cont.): SAIC: MAS Model Highlights (cont.)
SAIC: MHD Model of the Corona and Heliosphere: SAIC: MHD Model of the Corona and Heliosphere
Slide51: SAIC: 3D CME Eruption:
Magnetic Field Topology
Synoptic Map: Synoptic Map
Heliospheric Imager (HI): Heliospheric Imager (HI)
Slide56: HI Operations Document – R. Harrison
HI Image Simulation – C. Davis & R. Harrison
HI Operations Scenarios – R. Harrison & S. Matthews
HI Beacon Mode Specification – S. Matthews
Heliospheric Imager
Slide57: HI in a nutshell:
First opportunity to observe Earth-directed CMEs along the Sun-Earth line in interplanetary space - the first instrument to detect CMEs in a field of view including the Earth!
First opportunity to obtain stereographic views of CMEs in interplanetary space - to investigate CME structure, evolution and propagation.
Method: Occultation and baffle system, with wide angle view of the heliosphere, achieving light rejection levels of 3x10-13 and 10-14 of the solar brightness. Heliospheric Imager
Slide58: HI in a nutshell: Door Radiator Forward Baffles Inner Baffles HI-1 HI-2 Heliospheric Imager
Slide59:
Heliospheric Imager
Slide60: HI – Image Simulation HI Point Spread Function & noise included.
Not included: Earth/Moon HI-2 Simulated Image - nominal exposure (60 s) - non-shutter effect included. F-corona & stray light Stellar ‘background’ down to 13th mag. Planets Saturation of brightest planets & stars Cosmic rays The story so far... HI2 Occulter
Slide61: HI- Simulation Movies 512 x 512
Considerations – HI FOV, CMEs: Considerations – HI FOV, CMEs HI common volume observed highly dependent on angular position (mission duration).
Temporal confusion from voxels whose emission observed at the CCDs originates at different times: light travel time differences across the field of view.
Both of the above optimal with Earth directed plasma
CME speed = 800 km/s vs. summed exposure time
Voxel identification confusion in reconstructions with temporal development
Resolution of features: approximately the number of pixels crossed in HI summed individual exposures.
HI-1 (35”/pixel) => 30 min. summing, 36x36 pixels (Sun-Earth line, 45º velocity)
HI-2 (120”/pixel) => 60 min. summing, 32x32 pixels (Sun-Earth line, 90º velocity)
Slide63: SMEI Early Results
Conclusions: Conclusions Useful 3D reconstructions are achievable!
There are real limitations that we must understand and that will define which reconstructions are possible.
The reconstructions are significantly improved with the addition of a third viewpoint to the reconstruction, such as could be provided during the STEREO mission by an operating LASCO coronagraph on the SOHO spacecraft.
Application to SECCHI will require substantial effort and collaboration; we appreciate all help on scientific preparations.
Funding?
Web Site: http://stereo.nrl.navy.mil/ (follow link to 3D R&V). This contains past presentations and all necessary details to test reconstruction methods on sample problems.
Slide69: BACKUP SLIDES
3-D Reconstruction Using the Pixon Method: 3-D Reconstruction Using the Pixon Method The problem is to invert the integral equation with noise:
But there are many more model voxels than data pixels.
And the reconstruction significantly amplifies the noise.
All reconstruction methods try to overcome these problems by restricting the model; they differ in how they do that.
A good first restriction is non-negative n(r).
Non-Negative Least-Squares (NNLS) fit.
Minimum complexity (Ockham’s razor): restrict n(r) by minimizing the number of parameters used to define it.
The number of possible parameter combinations is large.
An exhaustive parameter search is not possible.
The Pixon method is an efficient iterative procedure that approximates minimum complexity by finding the smoothest solution that fits the data (details: Puetter and Yahil 1999).
New modification: Adaptive (Hierarchical) Gridding
K-Corona Physics: Thomson Scattering: K-Corona Physics: Thomson Scattering K-corona arises from Thomson scattering of
Photons by hot coronal electrons. The scattered
radiation is polarized. The sun as an extended
source modifies the scattering process.
K-Corona Physics: Emission Coefficients: K-Corona Physics: Emission Coefficients Separate scattered radiation into tangentially
and radially polarized light. The tangential
emission coefficient (ph s-1 cm-3 sr-1 ) may be
written as:
And the radial emission coefficient is:
Where we explicitly account for extended sun
limb darkening
PIXON: Adaptive (Hierarchical) Gridding: PIXON: Adaptive (Hierarchical) Gridding Naïve voxel size at the resolution of the projected detector pixels results in 109 voxels.
This is computationally unmanageable (or at least very time consuming).
The number of voxels greatly exceeds the number of independent data points, which is only 4x106.
We propose to solve both problems by using a hierarchical 3-D grid, which is coarse where the (projected) data show n(r) to be smooth and is progressively refined where the data require n(r) to be more structured.
While the Pixon method does not require an adaptive grid, it can take advantage of it in imposing maximum smoothness to increase computational speed by a more efficient calculation.
3D Reconstruction: CME model (J. Chen)Three Ecliptic Viewpoints: Rendered Data (1): 3D Reconstruction: CME model (J. Chen) Three Ecliptic Viewpoints: Rendered Data (1)
3D Reconstruction: CME model (J. Chen)Three Ecliptic Viewpoints: Rendered Data (2): 3D Reconstruction: CME model (J. Chen) Three Ecliptic Viewpoints: Rendered Data (2)
3D Reconstruction: CME model (J. Chen)Two Viewpoints: Rendered Data: 3D Reconstruction: CME model (J. Chen) Two Viewpoints: Rendered Data 37° Spacecraft Separation