LSST and the Dark Sector: Image LSST and the Dark Sector: Image processing challengesprocessing challenges

Tony Tyson

University of California, Davis

ADASS September 25, 2007

Dark Energy and Its SignaturesDark Energy and Its Signatures

Universe is 70% dark energy!

Cosmology and General Relativity Energy and matter. Space and time.

Space and time --- Hubble expansion

Supernovae – dL(z).

CMB and Baryon Oscillations – dA(z) and H(z).

Energy and matter --- Gravitational structure

Weak lensing – dA(z); growth of structure.

Galaxies and clusters – dA(z) and H(z);

growth of structure.

Weak Gravitational LensingWeak Gravitational Lensing

mass structure vs cosmic timemass structure vs cosmic time

7 billion lyr7 billion lyr

3 billion lyr3 billion lyr

dark matter

Cosmic shear vs redshiftCosmic shear vs redshift

Shift-and-stare imagingShift-and-stare imaging

Stars and galaxies are dis-registered between exposures. However, systematic errors in the CCD are registered in each frame.

Galaxy shape parameters: Galaxy shape parameters: filtered second moments of intensityfiltered second moments of intensity

),())(()sky(~

),()()sky(~

),()()sky(~

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2

2

0,

2

2

0,

2

yxgyyxxD

yxgyyD

yxgxxD

yxxyxy

yxxyy

yxxyx

Signal-matched filter: g(x,y) = galaxy profile

Surface brightness profile of galaxiesSurface brightness profile of galaxiesused for weak lensing with LSSTused for weak lensing with LSST

0.7 arcsecFWHM seeing

CConsider the average tangential component of the shear around circle C:

Contribution due to mass inside the circle:

But shear from a uniform sheet is zero, so:

Where:

r

C

True in general case, even for off-centered circle and for non-circular mass distributions!

C

R2

R1

3-D Mass Tomography

2x2 degree mass map from Deep Lens Survey

Comparing HST with SubaruComparing HST with Subaru

ACS: 34 min (1 orbit)PSF: 0.1 arcsec (FWHM)

2 arcmin

Comparing HST with SubaruComparing HST with SubaruSuprime-Cam: 20 minPSF: 0.52 arcsec (FWHM)

Statistical Weak Lensing:Statistical Weak Lensing:overcoming galaxy shape shot overcoming galaxy shape shot

noisenoise

Each source galaxy is prepared differently and has its own intrinsic ellipticity, before its image is lens distorted! So the source galaxy population has an intrinsic ellipticity distribution but averages out to zero over large areas. Rms ellipticity = 0.3

But we need to get ellipticity noise down to 0.003 on ten arcminute angular scales. -> average 10,000 galaxies.

WL shear power spectrum and WL shear power spectrum and statistical errorsstatistical errors

Signal

Noise

SNAP

LSST gastrophysics

LSST: fsky = 0.5, ng = 40

SNAP: fsky = 0.1, ng =100

Jain, Jarvis, and Bernstein 2006

Systematic error #1: PSF Systematic error #1: PSF ellipticityellipticity

Use foreground stars to define the PSF everywhere in the image. Then form the inverse transform (as a function of position in the image) which makes the stars round. i.e. convolve the image with this “rounding” matrix. Need enough unsaturated stars per square arcminute to fit a good PSF model.

Star shapes before

Convolution with rounding filter

But what’s left over?

Residual Subaru Shear Residual Subaru Shear CorrelationCorrelation

Test of shear systematics: Use faint stars as proxies for galaxies, and calculate the shear-shear correlation.

Compare with expected cosmic shear signal.

Conclusion: 300 exposures per sky patch will yield negligible PSF induced shear systematics.

Optimal Reconstruction of Galaxy Shapes:Optimal Reconstruction of Galaxy Shapes:

Stack-fit vs. Multi-fitStack-fit vs. Multi-fit

Dealing with Real DataDealing with Real Data

• Multiple observations of a given galaxy

– Different PSFs, field distortions, placement with Different PSFs, field distortions, placement with respect to pixels, placement relative to respect to pixels, placement relative to discontinuities, etc.discontinuities, etc.

The Stack-fit ApproachThe Stack-fit Approach

• Combine exposures into a stack

• Compare to (convolved) galaxy model

Galaxy on stack

Model x stack PSF

The Stack-fit ApproachThe Stack-fit Approach

• Benefits– Simple!

• Problems– Requires pixel interpolation systematics– Combines different seeings information lost– Discontinuous stack PSF harder to model– Does not provide desired accuracy

The Multi-fit ApproachThe Multi-fit Approach

• Compare (convolved) model to all exposures

symmetric shapelet

Original exposures

Model convolved with individual exposure PSFs

Model

Two flavors of co-measurementTwo flavors of co-measurement

For a given galaxy/star:For a given galaxy/star:

1. Measure its magnitude or shape on each image, then combine the measurements

2. Fit a model to all the images simultaneously

–more robust for faint objects which may have S/N~20 in the stack but ~1 in each image

–we adopt this method as our baseline design

–is mature for point-source photometry (used by 2MASS)

–we are developing it for galaxy shapes and extended-source photometry

The Multi-fit ApproachThe Multi-fit Approach

• Benefits– Uses full suite of information better accuracy

– Circumvents problems with stack-fit

• Problems– More complicated

– Slow scales with number of exposures

Challenges for Multi-fitChallenges for Multi-fit

• ~ 1022 floating point operations for fitting LSST data– Requires petascale computing resources– Competitive with transient object pipeline

• Improve efficiency?– Not clear how to beat linear scaling– Use stack when sufficient

• Including new exposures– Previous fit will provide useful starting point quicker

convergence

Multi-FitMulti-Fit

• Simultaneous fit to the data cube:

• Advantages:– uses all information. Weights better-seeing images appropriately.– handles image boundaries. PSF on a stacked image changes

abruptly at an image boundary.– each image PSF has less structure than the stacked image PSF– turns some systematics into random errors

MultiFit R&D Work to DateMultiFit R&D Work to Date

• Implementation 1:– Author: Chris Roat (currently at Google)

– C++, ROOT (particle physics) libraries

– website: beta.physics.ucdavis.edu/~croat/MultiFit/MultiFit.shtml

First results from Multi-FitFirst results from Multi-Fit

Increased stability for small galaxies Increased sample at high redshift

Chris Roat

MultiFit R&D Work to DateMultiFit R&D Work to Date

• Candidate Implementation 2: “glFit”– Authors: Bernstein, Nakajima, Rusin

– C++

– Shapelet-based, so convolutions are fast

– Implemented only for the single-image case

– Single-image fit takes 1 sec per galaxy with no speed optimization yet

MultiFit R&D Work to DateMultiFit R&D Work to Date

• Implementation 3:– Author: Jim Bosch (UC Davis)

– Models galaxies and PSFs as sums of Gaussians, so convolutions are fast.

– Real galaxies are not Gaussian, but this makes a good testbed.

– Upgrade to shapelets begun

– Requires 1 s per galaxy for data cube of 20 images, with no speed optimization yet, on 2 GHz desktop

– Being written in C++ and Python

R&D Work to Be DoneR&D Work to Be Done

• Quantify improvement of comeasurement over stacking for various science cases

• Speed optimization

• Extensive Monte Carlo tests

• Extend fitting to include other quantities: magnitudes, colors, etc.

Multi-Fit PipelineMulti-Fit Pipeline

Addressing Critical IssuesAddressing Critical Issues

WL shear reconstruction errors Show control to better than required precision using

existing new facilities Photometric redshift errors Develop robust photo-z calibration plan Undertake world campaign for spectroscopy

Photometry errors Develop and test precision flux calibration technique

Galaxy shape parameters: Galaxy shape parameters: normalizednormalized filtered second moments of filtered second moments of

intensityintensity

y)])g(x,y)(yxx([ / y)])g(x,y)(yx(xsky)(D[ I

y)]g(x,)y(y[ / y)]g(x,)y(ysky)(D[ I

y)]g(x,)x(x[ / y)]g(x,)x(xsky)(D[ I

00yx,

00yx,

xyxy

2

0yx,

2

0yx,

xyyy

2

0yx,

2

0yx,

xyxx

Ellipticity components:

e1 = Ixx-Iyy / Ixx+Iyy e2 = 2Ixy / Ixx+Iyy

Shear Shear from source ellipticity from source ellipticity

““Stretching factor” is the ratio of the two eigenvalues:Stretching factor” is the ratio of the two eigenvalues:

Weak Lens limit: Weak Lens limit:

ellipticityellipticity00

/ 2/ 2

Center on lens mass and then look at radial and tangential shear components: x,y to r, principal axis transform

II-I-Irrrr / I / I+I+Irr rr = = //

normalized projected 2-d mass densitynormalized projected 2-d mass density

Gauss-Laguerre ApproachGauss-Laguerre Approach

• Model: I(rbijij(r

• Advantages– Few assumptions ij related to physical

quantities

– Gal, PSF in same framework

Computational Details

• What it does– Some coordinate basis (position, size, e)

– Linear fit (over pixels) for b vector

– Alter ebasis (non-linear) and repeat

– Basis where b10, b20, b11 = 0 describes galaxy

• Run-time for convolved fit, single set of pixels:– ~5 galaxies per second on a few GHz processor

• Works well (Nakajima & Bernstein 2007)

LSST Precision on Dark LSST Precision on Dark Energy Energy

WL+BAO and Cluster counts give separate estimates. Both require wide WL+BAO and Cluster counts give separate estimates. Both require wide sky area deep survey.sky area deep survey.

Zhan 2006

p/= w0 + wa (1-a)

Comparison of Stage-IV facilities Comparison of Stage-IV facilities for DEfor DE