Image Processing for Weak Lensing

Wentao LuoSHAO

May 14, 2014 NAOC

Contents

• Weak Gravitational Lensing

• Accurate image processing—PSF correction

• Reconstruct the density field using weak lensing.

2 2 2 22 2

2 2 2 2 21 1 2

2 2(1 ) (1 )

{ ( )[ cos ( ) ]}k

ds c dt ac c

dw f w d d

2

2dl

c

Hilbert et al 2009

3

2observer

sourcet dl

c Time delay:

Deflection angle:

Narayan & Bartelmann

1997

2 ( )ij ij

i j

A

1 2

2 1

1

1A

1 2i

Jacobian

Narayan & Bartelmann 1997

int 2e e R

int 2e e R

2e R

Point Spread Function

<e_psf>~0.45 for SDSS while shear signal ~0.01

Methods

• Traditional methods 2, Re-Gaussianization (Hirata & Seljak

2003) 3, Rounding Kernel (Bernstein & jarvis

2002) 4, Shapelets (Refregier 2000)

• Jun Zhang 2008; Jun Zhang 2010; Jun Zhang, WTL & Sebastien. Foucaud 2014

Re-Gaussianization

Rounding Kernel

The Structure of Our Pipeline

Input Input imageimage

PSF PSF imageimage

BJ02BJ02 Image Image convolved convolved

with with KernelKernel

re-re-GaussianizGaussianized imageed imageHS03HS03

Bernstein & Jarvis 2002; Hirata & Seljak 2003

RR

ee++,e,exx

OutOutputput

Testing

SHERA Mandelbaum et al 2011

Deconvole HST psf, re-convolve SDSS PSF

SDSS pixelsize+SDSS noise

Reality is cruel!!

Jun Zhang Methods

GREAT3 Results

---------------------------------------------------------------

Conclusion

• Accurate image processing is the first step for weak lensing study

• Simulations to test your pipeline• We can use real data to do the

comparison among various methods• Potential systematic from image

itself• Moving to real data