The REGLENS methodThe REGLENS method

Rachel Mandelbaum

STEP Workshop 2007

Collaborators: Christopher Hirata, Uros Seljak

Inputs required for methodInputs required for method

• List of object positions

• Postage stamps

• PSF as a function of position

• For all past science projects, used SDSS Photo pipeline to perform these tasks + get photometry, s/g separation, …

• Developing independent pipeline

Re-Gaussianization in detailRe-Gaussianization in detail

• Defining adaptive moments of PSF g using elliptical Gaussians that minimize:

• Trace = measure of size• PSF ellipticity:

Geneology of PSF Correction Schemes

Geneology of PSF Correction Schemes

Exact for Gaussian galaxiesand Gaussian PSFs whenusing weighted moments

Accounts for non-Gaussianityof galaxy profile if well-resolved

Same as previous method butwith linear-order correction forPSF non-Gaussianity

Perturbatively accounts for PSFnon-Gaussianity, then uses BJ02on "re-Gaussianized" image

re-GaussianizationHirata & Seljak, 2003

Section 2.4

Linear a4Hirata & Seljak, 2003

Appendix B

Linear PSF CorrectionBernstein & Jarvis 2002

Appendix C

Trivial covariancematrix summation

Re-Gaussianization, cont.Re-Gaussianization, cont.

• PSF g, best-fit Gaussian G (Mg), residual :

g = G + • Measured image I (MI):

I = Gf + f, or

I’= Gf = I-f

Re-gaussianization, cont.Re-gaussianization, cont.

• We want I’= Gf = I-f

• || << |G| compute f using f=elliptical Gaussian obtained via Mf = MI - Mg

• Construct I’ = galaxy image convolved with Gaussian PSF (at image level), compute moments MI’

Re-gaussianization, cont.Re-gaussianization, cont.

• Use BJ02 (linear) PSF correction on I’:• Shear coordinate system to get circular PSF• Use

• Resolution factor is defined using kurtosis

Weighting schemeWeighting scheme

• Weight by inverse shape + measurement error:

wi = 1

SN + e

• SN = <e2 - e >

2 2

22

Shear computationShear computation

• Weighted summation over individual galaxy ellipticities performed via

= ∑ wi ei

2 Ssh ∑ wi

• Shear responsivity Ssh computed using results from BJ02, Ssh ~ 1-erms

2

Object selectionObject selection

• Require R2 > 1/3

• Require r < 21.8 (SDSS) or S/N on shear measurement > 8.5 (STEP)

• Minimizes PSF dilution

• Avoids worst-case noise-rectification bias (Hirata, et. al. 2004)

Performance in simulationsPerformance in simulations

• Noiseless simulations (Hirata & Seljak, 2003):• Calibration bias <4% for deVauc, exponential

profiles, with varying magnitude as a function of apparent size

• STEP:• Mean calibration bias ~ -2% (averaged over

PSF)• Trends in calibration bias with apparent size,

magnitude: fainter, larger have more negative calibration bias

STEP vs. SDSSSTEP vs. SDSS

• Different PSF ellipticity effects in STEP than in SDSS data

• New, STEP-like (shapelets-based) simulations in SDSS:• Consistent PSF ellipticity effects with SDSS

data• Consistent shear calibration bias as with STEP,

including trends with apparent size• Account for difference: different PSF?

(skewness, substructure)

More method developmentMore method development

• Applying to co-added SDSS data using method optimized for shear measurement

• Convolve each image with kernel before addition to get the same, CIRCULAR PSF (sum of two Gaussians) in each image

• Preliminary results (ongoing with additional collaborators David Schlegel, Eric Huff @ LBL / Berkeley) indicate systematic shear eliminated to high precision

SummarySummary

• Method has been used for many science applications in SDSS g-g lensing, intrinsic alignments

• Further method development ongoing with simulations, coaddition pipeline

• Redshift distribution constraints completed• Approaching few percent precision for g-g

lensing and, eventually, cosmic shear on coadds