How to make a clean separation between CMB E and B modes with proper foreground masking

Understand

We investigate the E/B decomposition of CMB polarization on a masked sky.

• In real space, operators of E and B mode decomposition involve only differentials of CMB polarization.
• We may, therefore in principle, perform a clean E/B decomposition from incomplete sky data.
• Since it is impractical to apply second derivatives to observation data, we usually rely on spherical harmonic transformation and inverse transformation, instead of using real-space operators.