Looks like I already had this issue open @neurofractal @georgeoneill , so let's discuss here.

This is great news to hear [about field correction]! As you can see we've been doing some initial tests. I've been trying to work out whats the best approach for MNE-Python. We normally do a hard correction to the data (rather than having an online montage) and then update our 'compensation matrix' to update our forward modelling later. But I realise this is not in the nature of how the SSP filters work in MNE-Python (i.e. only activated when needed). This might need some thought.

Yes we'll have to be a bit careful. I have not looked at the math at all but doubt they are true orthogonal projection vectors, so wouldn't be good to call SSP; and I doubt they work like compensation matrices for CTF (which have some nice mathematical property -- like its inverse is its transpose or something like this, I'd have to check to remind myself). We can probably add a new constant for it -- we've wanted one before for the cross-talk correction for MEG data anyway, which is itself just a matrix multiply (that does not modify/reduce rank).

So I say in a second PR after #11257 is done let's get it doing what it needs to do -- probably as a matrix that can be applied (or not) just like a projection -- and then I can talk to some FIF folks about the right way to store the information.

I think the answer to both of the following is "yes", but just to check -- can the higher-order version also be described as just a matrix multiply? And they are not time-varying (i.e., just depend on sensor geometry, not sensor position as a function of time), right?

Uh oh!

ENH: Add offline homogeneous field correction for OPMs #10780

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