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
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