> I want to write out some visibilities which show > the difference betwen an observation with a fixed gain of > unity vs one where the gain varies around unity. Since the > gains are just real scalars as f(t) I would have thought that > I would get equivalent results by > > 1) just computing the total gain (including variable component) > and then subtract 1 from it. Then just get the expected difference > visibility from the usual > > Meq.MatrixMultiply(ns.G(p),ns.E(src),ns.K(p,src),\ > ns.B(src),ns.Kt(q,src),ns.Et(src),ns.Gt(q)) > > I was expecting to get exactly the same result by > > 2) computing visibilities based on the total gain (including > time variations), then computing visibilities using just > an (implicit) gain of 1, and then subtracting the visibilities > computed with gain 1 from those computed with the total gain. > > However, from the images I seem to get +ve differences in one > case and negative holes in the other! Whereas I would > expect consistency - either +ve or -ve. > > I must be missing something ...
Well, you caught me at a good moment, I was just looking at differential trees... Anyway, I think you forgot that gain enters the ME twice. Essentially the first case computes:
(G_p-1)X(Gt_q-1) = G_p*X*Gt_q - X*Gt_q - G_p*X + X
which is not the same thing at all as the second (correct) case, G_p*X*Gt_q - X.
> Ah - right :) So the ME is not necessarily distributive!
That's a good way of putting it. It _is_ w.r.t. the sky though. It's non-distributive and non-linear w.r.t. Jones terms.
Cheers, Oleg