1. " Fitting methods with direct convolution for shear measurements." STEP Workshop August 2007 M. Shmakova

2. Shear measurements with complex lensing maps Shear – 1-st order terms 2nd-st order terms S - sours to the T –apparent image coordinates In complex notations:

3. General Map is a transformation Jacobian: Source Flux Flux after the lensing

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. 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:Model-fit-method

8. Model fit with PSF M a,b, d, centroid MAP Radial profile PSF Fit for Map parameters And compare with the real image Super-stack Image

9. Strong features Method is based on complex maps representing lensing. Method is based on complex maps representing lensing. Possibility to use non-Gaussian PSFs Possibility to use non-Gaussian PSFs Natural algorithm to search for non-linear effects 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 Effective fit is possible only for single peak (up to noise ) galaxies Additional selection rules will reduce the number of galaxies reducing signal/noise 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 Fit could be difficult with non-linear behavior of parameters

12. Non-linear fit requires advanced “optimization problem” methods. Non-linear fit requires advanced “optimization problem” methods. Computational time – advanced software Computational time – advanced software Precise PSF knowledge is required Precise PSF knowledge is required New fitting pipeline featuring main ideas of Mathematica “prototype” is under development on Python. Development