hires 2014 conference stellar surfaces with optical interferometry fabien baron brian kloppenborg...

HIRES 2014 CONFERENCE

Stellar surfaces with optical interferometry

Fabien BaronBrian Kloppenborg

CHARA, Georgia State University

John MonnierUniversity of Michigan


Stellar surfaces with optical interferometry

Magical Tips and tricks for imaging

Fabien BaronBrian Kloppenborg

CHARA, Georgia State University

John MonnierUniversity of Michigan


Magic lesson 1: learning the ropes


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 ?


We have a dataset


And have some sort of error bar on image features

E.g. “Is this spot real ?”


This means software that can build error maps


We have a dataset



Can be model-based or “model-independent”

By model-independent we actually mean…



We have a dataset



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


Posterior probability


Applying Bayes theorem

WARNING !

MATH TRICKERY


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


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




Ill-posed problem


Non-convex criterion Convexification !




Ill-posed problem


Non-convex criterion Convexification !

Experience shows suboptimal images

We will have to deal with the non-convex criterion…


Magic lesson 2: making the criterion smaller, aka minimization…


Minimizing the criterion


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)


Magic lesson 3: dispel illusions


What a supergiant should look like…

Chiavassa et al., 2010


But actually imaging spots or convection cells is hardBetelgeuse: COAST 1997 (Young et al., 2000)


More recent software helps

Betelgeuse: COAST 1997 & 2004 data (Young et al., 2000 and 2004)

Images from reanalysis in Chiavassa et al., 2010


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


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


If only…

VX Sgr: 2008 AMBER data (Chiavassa et al., 2010)


Model and imaging should give the same answers

RS Per, T Per: MIRC 2007 leftover data (Baron et al., 2014)

All chi2 < 1.5


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


Too many Wizards in the kitchen

AZ Cyg

IAU Interferometry Beauty Contest

(Baron et al., 2012)

Truth/Model


Magic lesson 4: regularizing the optimization


• Lots of regularizers/priors to choose from:

Choice of regularizer(s)


• But not that many good ones



Maximum Entropy (note: positivity built-in)


Total variation (Chen 1999, Strong 2003)

Spot regularizer(non-convex)

Image plane Gradient plane


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 ???


Application of Compressed sensing (SQUEEZE)

Baron et al., 2012, in prep

Isotropicwavelets

Arclets

Gradient

Sparsity basis


Magic lesson 5: controlling (prior) space


Priors


Imaging with the wrong priors: flat prior


Imaging with the wrong priors: flat prior, constrained short baselines with PTI data


Imaging with the wrong priors: elliptical prior, too small


Imaging with the wrong priors: elliptical prior, too large


Imaging with the wrong priors: elliptical prior, wrong angle


Imaging with the wrong priors: elliptical prior, just right !


First resolved image of a main sequence star (beyond Sun)

Monnier et al., 2007


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


Magic lesson 6: controlling your weight


Choice of regularization weight


SHUSH !The correct approach would be to marginalize µ !

µ take not take a single value but is described by P(µ)


Finding the optimal µ: hard… unless you know the solution

Classic,But vague…And non-Bayesian

Renard et al., 2011


Finding the optimal µ: hard… unless you know the solution

Kluska et al., 2014L-curve: imprecise

Note: bad convergence of MIRAdue to local minima


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…


● 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


Magic lesson 7: controlling time and shapes


beta Lyrae: typical datasets

Zhao et al., 2008CHARA/MIRC 4T

2013Jun23

Baron et al., in prep.CHARA/MIRC 6T


beta Lyrae: images (2007)

Zhao et al., 2008


beta Lyrae: imaging and modeling circa 2007

“Modeling” (ahem !)Image reconstruction based on snapshot imaging

1 mas

0.5 mas


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


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


Algol: close-up on the inner pair


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


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


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


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


Modeling the disc of eps Aur

Kloppenborg et al. 2010


Model selection for eps Aur

Kloppenborg et al., 2015 (submitted)


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


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 !

hires 2014 conference stellar surfaces with optical interferometry fabien baron brian kloppenborg...

Documents