Fitting methods with direct convolution for shear measurements'

1
"Fitting methods with direct convolution for
shear measurements."

• STEP Workshop
• August 2007
• M. Shmakova

2
Shear measurements with complex lensing maps
In complex notations
Shear 1-st order terms
S - sours to the T apparent image coordinates
2nd-st order terms
3
General Map
Flux after the lensing
Source Flux
is a transformation Jacobian
4
Shape measurements
For a single lensing plain
5
General transformation and PSF
Intrinsic
Lensing
6
Model method
Radial component of source
Map
Jacobian
Model
Poisson Noise
7
Model-fit-method
I. Lensing events are nonlinear at heart.
Precisely described by nonlinear maps
II. Follow the flow,
go forwards not backwards Galaxy model
lensing event effective PSF Image III.
Minimize norm
8
Model fit with PSF
Radial profile
M
a,b, d , centroid
MAP
PSF
Super-stack Image
Fit for Map parameters And compare with the real
image
9
Strong features

• Method is based on complex maps representing
  lensing.
• Possibility to use non-Gaussian PSFs
• Natural algorithm to search for non-linear effects

10
Fisher matrix and confidence regions estimation
Fisher matrix
Combined probability distribution
Each pixel data point f is a Gaussian
distribution for each pixel
Parameters of the model
Fisher matrix elements
11
Problems with the method

• Effective fit is possible only for single peak
  (up to noise ) galaxies
• Additional selection rules will reduce the
  number of galaxies reducing signal/noise
• Number of fitting parameters could be large
  depending on choice of radial profile.
• Fit could be difficult with non-linear behavior
  of parameters

12
Development

• Non-linear fit requires advanced optimization
  problem methods.
• Computational time advanced software
• Precise PSF knowledge is required

New fitting pipeline featuring main ideas of
Mathematica prototype is under development on
Python.