We present a derivation of the transformation between the Q and U Stokes parameters and the E and B scalar and pseudoscalar fields. We emphasize the geometrical properties that such transformation must satisfy. We present the E and B decompositions of some simple maps and of a model for a supernova remnant. We discuss the relative amplitudes of the E and B components, and argue that for generic random maps E and B should have roughly the same amplitudes.

• Received 10 June 2001

DOI:https://doi.org/10.1103/PhysRevD.64.103001