hires 2014 conference stellar surfaces with optical interferometry fabien baron brian kloppenborg...
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HIRES 2014 CONFERENCE
Stellar surfaces with optical interferometry
Fabien BaronBrian Kloppenborg
CHARA, Georgia State University
John MonnierUniversity of Michigan
HIRES 2014 CONFERENCE
Stellar surfaces with optical interferometry
Magical Tips and tricks for imaging
Fabien BaronBrian Kloppenborg
CHARA, Georgia State University
John MonnierUniversity of Michigan
HIRES 2014 CONFERENCE
Magic lesson 1: learning the ropes
HIRES 2014 CONFERENCE
We have a dataset
We want to show a set of probable images
And have some sort of error map for features (“Is this spot real ?”)
What do we want from imaging ?
HIRES 2014 CONFERENCE
We have a dataset
We want to show a set of probable images
And have some sort of error bar on image features
E.g. “Is this spot real ?”
What do we want from imaging ?
This means software that can build error maps
HIRES 2014 CONFERENCE
We have a dataset
We want to show a set of probable images
And have some sort of error map for features (“Is this spot real ?”)
Can be model-based or “model-independent”
By model-independent we actually mean…
What do we want from imaging ?
HIRES 2014 CONFERENCE
We have a dataset
We want to show a set of probable images
And have some sort of error map for features (“Is this spot real ?”)
Can be model-based or “model-independent”
By model-independent we actually mean … lots of identical model parameters, e.g. image pixels
Want to maximize the probability of the image i, knowing the data D and a model of image formation M
What do we want from imaging ?
Posterior probability
HIRES 2014 CONFERENCE
Applying Bayes theorem
WARNING !
MATH TRICKERY
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Applying Bayes theorem jargon
Posterior probability
Likelihood
Prior
Taking the log of these expressions, we find the “best” image as
This is classic regularized maximum likelihood
Evidence
Note: this expression is made up
HIRES 2014 CONFERENCE
Common issues with likelihood
Data is not uncorrelated (see M. Ireland talk)
Ill-posed problem
Need for regularization Multimodal due to missing phase
Non-convex criterion
HIRES 2014 CONFERENCE
Common issues with likelihood
Data is not uncorrelated (see M. Ireland talk)
Ill-posed problem
Need for regularization Multimodal due to missing phase
Non-convex criterion
HIRES 2014 CONFERENCE
Common issues with likelihood
Data is not uncorrelated (see M. Ireland talk)
Ill-posed problem
Need for regularization Multimodal due to missing phase
Non-convex criterion Convexification !
HIRES 2014 CONFERENCE
Common issues with likelihood
Data is not uncorrelated (see M. Ireland talk)
Ill-posed problem
Need for regularization Multimodal due to missing phase
Non-convex criterion Convexification !
HIRES 2014 CONFERENCE
Common issues with likelihood
Data is not uncorrelated (see M. Ireland talk)
Ill-posed problem
Need for regularization Multimodal due to missing phase
Non-convex criterion Convexification !
Experience shows suboptimal images
We will have to deal with the non-convex criterion…
HIRES 2014 CONFERENCE
Magic lesson 2: making the criterion smaller, aka minimization…
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Minimizing the criterion
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Minimizing the criterion
Approach 2. Monte Carlo Markov Chain•Stochastic global minimization, resilient to local minima, error maps
•Simulated annealing, parallel tempering, nested sampling
•Can use non-differentiable, non-convex regularizers
•MACIM (Ireland 2006), SQUEEZE (Baron 2010, https://gitorious.org/squeeze)
230 Ghz images
Rusen et al., 2014 (EHT simulations)
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Magic lesson 3: dispel illusions
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What a supergiant should look like…
Chiavassa et al., 2010
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But actually imaging spots or convection cells is hardBetelgeuse: COAST 1997 (Young et al., 2000)
HIRES 2014 CONFERENCE
More recent software helps
Betelgeuse: COAST 1997 & 2004 data (Young et al., 2000 and 2004)
Images from reanalysis in Chiavassa et al., 2010
HIRES 2014 CONFERENCE
Beware underfitting…
Betelgeuse: IOTA 2005 data (Haubois et al., 2009)
Images from reanalysis in Chiavassa et al., 2010Terrible chi2 > 10 , Model and image not compatible
HIRES 2014 CONFERENCE
Or barely fitting because of calibration issues
VX Sgr: 2008 AMBER data (Chiavassa et al., 2010)
Image reconstruction too difficult
Model and image do not show the same spots
Bad chi2
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If only…
VX Sgr: 2008 AMBER data (Chiavassa et al., 2010)
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Model and imaging should give the same answers
RS Per, T Per: MIRC 2007 leftover data (Baron et al., 2014)
All chi2 < 1.5
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Artefact detection
Total variation Uniform disc regularizer• Generate a model of the supergiant as you think it may be
• Simulate the observations of this object, copying the uv coverage and signal to noise from the original data
• This allows to detect artefacts from the reconstruction process and to improve the regularization
HIRES 2014 CONFERENCE
Too many Wizards in the kitchen
AZ Cyg
IAU Interferometry Beauty Contest
(Baron et al., 2012)
Truth/Model
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Magic lesson 4: regularizing the optimization
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• Lots of regularizers/priors to choose from:
Choice of regularizer(s)
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• But not that many good ones
Choice of regularizer(s)
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Maximum Entropy (note: positivity built-in)
Choice of regularizer(s)
Total variation (Chen 1999, Strong 2003)
Spot regularizer(non-convex)
Image plane Gradient plane
HIRES 2014 CONFERENCE
Sparsity: an image is “sparse” in a basis if it can be expressed as a small number of non-zero coefficients in this basis
For a sparse image, optimal image reconstruction can be achieved (Candes 2007, Donoho 2008) by minimizing the number of non-zero coefficients in the sparsity basis
This leads to regularizers based on the norm
Buzzword alert ! Restricting space: Compressed Sensing, Sparsity
Sparsity in image plane = minimizes the number of lit-up pixels
Sparsity of gradient = favors zones of uniform flux
How do you objectively choose the best sparsity basis ???
HIRES 2014 CONFERENCE
Application of Compressed sensing (SQUEEZE)
Baron et al., 2012, in prep
Isotropicwavelets
Arclets
Gradient
Sparsity basis
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Magic lesson 5: controlling (prior) space
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Priors
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Imaging with the wrong priors: flat prior
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Imaging with the wrong priors: flat prior, constrained short baselines with PTI data
HIRES 2014 CONFERENCE
Imaging with the wrong priors: elliptical prior, too small
HIRES 2014 CONFERENCE
Imaging with the wrong priors: elliptical prior, too large
HIRES 2014 CONFERENCE
Imaging with the wrong priors: elliptical prior, wrong angle
HIRES 2014 CONFERENCE
Imaging with the wrong priors: elliptical prior, just right !
HIRES 2014 CONFERENCE
First resolved image of a main sequence star (beyond Sun)
Monnier et al., 2007
HIRES 2014 CONFERENCE
MIRC
2 Rsun
MIRC Observations of Rapid Rotators
from recent review by Ming Zhao
Regulus
Che et al. 2011
Alderamin
Zhao et al. 2009
Bet Cas
Che et al. 2011
Altair
Monnier et al. 2007
Rasalhague
Zhao et al. 2009
Rapid rotator magic
B8V A5IV A7V A7V-IV F2IV
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Magic lesson 6: controlling your weight
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Choice of regularization weight
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SHUSH !The correct approach would be to marginalize µ !
µ take not take a single value but is described by P(µ)
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Finding the optimal µ: hard… unless you know the solution
Classic,But vague…And non-Bayesian
Renard et al., 2011
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Finding the optimal µ: hard… unless you know the solution
Kluska et al., 2014L-curve: imprecise
Note: bad convergence of MIRAdue to local minima
HIRES 2014 CONFERENCE
MSE (Mean Square Error)Pixel-to-pixel comparison
DSSIM (Structural Similarity) (Wang 2004; Loza 2009)•More natural/human-like metric•Subdivides the images to be compared into small subdomains and check for correlation•Metric has more tunable parameters…
• like dynamic range, window size
Finding the optimal µ: hard… even if you know the solution
Not always obvious which is the best…
HIRES 2014 CONFERENCE
● So, how do we select regularizers, regularization weights, compressed sensing basis, Christmas presents ?
● Bayesian model selection compares the probabilities of two models:
● The ratio of “evidences” determines which model is more probable
● Computing the evidence is non-trivial, and should be done by the optimization engine
● Model fitting (SIMTOI, Nested Sampling, Skilling 2006)
● Imaging (SQUEEZE, parallel tempering, Neal 2002)
Regularization with model selection
HIRES 2014 CONFERENCE
Magic lesson 7: controlling time and shapes
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beta Lyrae: typical datasets
Zhao et al., 2008CHARA/MIRC 4T
2013Jun23
Baron et al., in prep.CHARA/MIRC 6T
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beta Lyrae: images (2007)
Zhao et al., 2008
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beta Lyrae: imaging and modeling circa 2007
“Modeling” (ahem !)Image reconstruction based on snapshot imaging
1 mas
0.5 mas
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beta Lyrae: typical data, model, image (2013)
Image reconstruction software and data got better
But a better model would furtherimprove the image
Much cleaner image with flat prior
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Algol: images could be better....
23 nights from 2006 to 2011, 4T data only
Period 2.87 days
Split into time chunks, giving 55 images of the inner binary
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Algol: close-up on the inner pair
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Ideally we would use all time chunks to constrain the geometry of the stars
Need to depart from snapshot imaging and do time dependent imaging
HIRES 2014 CONFERENCEPixellation on spheroids
Basic Healpix Healpix + Roche surface
Back of Roche surface Image/Model fitting with Gravity Darkening
HIRES 2014 CONFERENCE
SImulation and Modeling Tool for Optical Interferometry
Roche Lobe Geometryw/ Healpix tesselation
Oblate spheroids w/ gravity darkening
Spots!
Limb darkening
Obscuration
Photometric & Interferometric Data
Live Parameter Updating
& Rendering
Animation
Smooth edges via. multi-sample anti-aliasing
HIRES 2014 CONFERENCE
SIMTOI: Advancing Model fittingGPU Computing Backend:
– OpenCL Interferometry Library (liboi)
– Extremely fast, 300 chi2 / second
– Derived from the GPU Accelerated Image Reconstruction program(Baron & Kloppenborg, 2010)
Features:
– Uses Roche Equations → stellar surface
– Uses temperatures rather than fluxes
– Gravity and Limb darkening
– Multiple systems with occulation
– Orbits and corresponding light curves
– Rotation (differential possible)
– Starspots
Minimization Options:
– Levenberg-Marquardt, grid search, Nelder-Mead simplex (amoeba)
– Bayesian model selection with nested sampling (Feroz et al., 2012)
Data Types:
– OIFITS
– Light curves
– RV
HIRES 2014 CONFERENCE
Symbiotic CH Cygdeparture from circular disc ?
Pedretti et al., 2009
Need for model selection
Number of spots on rotating giant ?
Parks et al., 2015 (submitted)
Model
SQUEEZE
BSMEM
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Modeling the disc of eps Aur
Kloppenborg et al. 2010
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Model selection for eps Aur
Kloppenborg et al., 2015 (submitted)
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Model selection for eps Aur: SIMTOI results
Cylinder 1 -86412 260
Ringed Disk 2 -22472 69
Ringed Disk 2 3 -26602 93
Ringed Disk 3 4 -22620 67
Pascucci Disk 5 -19354 50
Andrews Disk 6 -19303 49
Pascucci Disk w/ clearing
7 -19158 51
Tilted Pascucci Disc
8 -17607 50
Log Z Chi2r
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Work in progress: imaging on a sphere
Merges SQUEEZE and SIMTOI Useful to study other hard-to-model
effects such as rapidly evolving spots, proximity effect, interacting discs
To integrate light-curve inversion, radial velocities, Doppler information
Imaging spots on a stellar surface with
wavelets
Fairly hard !