V-terms inclusion

[mj-gomes]

Hi,

I received a suggestion from Margherita Lembo to include the V terms in the HWP calculus (and we would have to also insert them in the mapmaker(s)).

Right now we always consider no circular polarization, therefore the hwp_sys code and - I believe - also the mapmakers only work for IQU (@anand-avinash I think for BrahMap is also the case, but correct me if I'm wrong).

This addition would allow to study models which could induce conversion from linear to circular polarization. This is, I believe, not important for the simulations for the KDP2, but I'm opening the discussion so that we keep it in mind for later.

It wouldn't be hard to implement this in hwp_sys, but I am not sure about BrahMap. We would have to have a V map. Is this something easy to add @anand-avinash ?

[anand-avinash]

It should be easy to implement in BrahMap - I just have to create a new pointing operator with an extra term and a new preconditioner for the same. But do we know what the detector response would be to the circular polarization? That is, what would be the signal model if we include circular polarization?

[mj-gomes]

The tod equation in hwp_sys code actually comes from a model including V, from which I ignored the terms in V (see eq. 2.1 in https://arxiv.org/pdf/2308.00967).