Hi Clem,
I think non-orthogonal pair angles can't - that is only an additional
calibration of the pair diff and getting it
systematically or randomly
wrong
across pairs can only mix E<->B.
This is true. Although I would phrase it as "not knowing your pol angles"
causes E->B. We don't need orthogonal pol angles to prevent E->B, we just
need to know them.
But what about polarization efficiency (epsilon)? If this differs between A
and B of pairs systematically or randomly that will
leak T-pol in the
timestream. And our analysis would not fix this even if we knew the per
detector efficiencies perfectly? However this effect is indistinguishable
from
relgain and would therefore deproject out.
I don't think this is correct. The way I always think about it is as
follows: the plot of response vs. pol angle for a given detector looks like
a sine wave of pi periodicity. The troughs are at T and the peaks are at
T+P. The height of this sine wave tells you P, and its phase tells you the
pol angle, alpha. For epsilon < 1, the troughs of the sine wave are still
T, but the peaks are now reduced. This is consistent with what's written
down in reduc_makesim, v = T + gamma*[Qcos(2 alpha) + Usin(2 alpha)], where
gamma = (1+epsilon)/(1-epsilon). Polarization efficiencies do not affect T
and so simply cannot leak T->P. What about E->B? The phase of the sine
waves are not affected either, and so the reconstructed pol angle will
never change. This is true whether we pair difference or not. What I think
*would* happen if epsilon were different for A and B is that if you make Q
and U maps from one A/B channel pair at one deck angle pair, it will have a
different calibration than the map at the 90 degree complementary deck
angle pair. Imagine epsilon_A = 1 and epsilon_B < 1. The pair difference
timestream for a continuous rotation around the pair centroid still has
maxima and minima at the right angles, but depending on whether A or B is
aligned with alpha the amplitude of the maximum is different.
Cross polar response is different, I think, and I think is more
complicated. In its simplest incarnation, the way I visualize it is the
sine wave now has troughs at T+x and peaks at T+P+x, though this might be
off base. Again the maxima and minima are in the right places but the
amplitude of the sine wave changes. I don't think this can leak E->B.
(Walt?) Most generally, I think cross polar response means that the beam,
including gain, is a function of polarization orientation ("Q and U
beams"). Again, if there is no polarization then the beam is the same at
all orientations and there won''t be any T->P. However, I think it can
cause E->B. If a detector can effectively point to a difference place on
the sky as a function of pol angle orientation, the maxima and minima can
be shifted around. This causes pol angle to be reconstructed incorrectly
and thus mix E->B.
-Chris
On Thu, Jul 2, 2015 at 11:48 AM, Clem Pryke <pryke(a)physics.umn.edu> wrote:
> Hi Chris,
>
> SPT are worrying about their T->P in their sims. In a pair differencing
> analysis what effects can and can't cause T->P?
>
> A/B beam mismatch of course can.
>
> I think non-orthogonal pair angles can't - that is only an additional
calibration of the pair diff and getting it
systematically or randomly
wrong
across pairs can only mix E<->B.
> But what about polarization efficiency (epsilon)? If this differs between A
and B of pairs systematically or randomly that will
leak T-pol in the
timestream. And our analysis would not fix this even if we knew the per
detector efficiencies perfectly? However this effect is indistinguishable
from
relgain and would therefore deproject out.
>
> Where is this possibility mentioned in your paper? Sec 9.7 talks about
> "Cross-polar response" but seems to say that this causes only E->B.
>
> I note that what I have written above is specifically contradicted in our
> Instrument Paper where it says:
>
> "The crosspolar response enters the analysis only as a small adjustment to
> the
> overall gain of the E and B polarization, but cannot create any false
> B-mode
> signal."
>
> That's certainly true so long as chi is equal for A and B of each pair.
> But is
> it really true when is differs between A and B?
>
> Clem
>
> --
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> Clem Pryke - Associate Professor - Physics
> University of Minnesota
> Room 318 Physics and Nanotechnology Building
> 115 Union Street SE, Minneapolis MN 55455
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>
>
>
--
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