In this project I explore the locality of QU to EB translation. Specifically we carry out the following studies:

1. Derive real space convolution kernels on the sphere, which decompose Stokes QU to EB modes of polarization.
2. Derive real space convolution kernels on the sphere which separate Stokes QU parameters into those corresponding to E and B modes respectively.

The plot below depicts the different parts of the real space convolution kernel.

3. We study the spatial locality of these covolution kernels and study the effects of intentionally introduing radial cutoff on the kernels.
4. We apply these new methods on Planck 353 GHz polarization data.