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" Fitting methods with direct convolution for shear measurements ."

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

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" Fitting methods with direct convolution for shear measurements ."

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  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 confidenceregions 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.

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