EB-convolution mixes the input Q/U sky components in harmonic domain by mapping
a^E_lm -> a^E_lm cos(2psi) + a^B_lm sin(2psi)
and
a^B_lm -> a^B_lm cos(2psi) - a^E_lm sin(2psi).
The cos(2psi) and sin(2psi) terms are evaluated separately and co-added. In the absence of a HWP, the sin(2psi) term is zero and the second polarized convolution can be omitted.
Re-interpret the TEB convolution:
a^E_lm -> a^E_lm cos(2psi) + a^B_lm sin(2psi)
and
a^B_lm -> a^B_lm cos(2psi) - a^E_lm sin(2psi)
.The
cos(2psi)
andsin(2psi)
terms are evaluated separately and co-added. In the absence of a HWP, thesin(2psi)
term is zero and the second polarized convolution can be omitted.