This memo gives a description of the new procedure to determine the value
of the flag "HWP" and to monitor its stability. Also, I give some some
results of this procedure, from the July run.
August 30, 2006 (modified August 17, 2007; changes marked with ***)
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A. Quick-Check Procedure, to monitor stability of "HWP":
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(1) Mount a grid with wires vertical in front of a cold load, as shown in
SHARP installation video. Use level to ensure accuracy within one degree.
(***if you put grid on the exit aperture then you can change the ZA of the
telescope to level the grid***)
Vertical wires corresponds to Phi_Inst_cor = 90 (see April 13 memo for
definition of Phi_Inst_cor).
(2) Measure the hwp angle at which the V-channel has its lowest signal.
Call this hwp angle "V_null".
(***set gains to low; see cheatsheet***)
(***you should level with a warm-load in front of the LN-2 bucket before
each reading***)
Note that all SHARP hwp angles can be expressed in two ways:
(a) "actual values of hwp angle", which are the actual numbers read on the
encoder. I will refer to the V_null expressed in this way as
"V_null_encoder"
and
(b) "relative values of hwp angle", which are measured relative to the
first hwp angle used for data-taking. (The first angle was 50 degrees for
the July 2006 run.) I will refer to the V-null expressed in this way
"V_null_rel".
(3) Note that HWP = 2 * V_null_rel
(***so we can write: HWP = 2 * (V_null_encoder - "first-angle") ***)
(this is derived below)
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B. Procedure used to measure "HWP" accurately
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For a precise measurement of "HWP" we need to take a few standard
polarimetry files and do a fit, rather than just finding the "null" of V
as described in (A) above. The reason is that there might be systematic
deviations from a perfect sine curve.
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C. Results from the July 2006 run
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From an inspection of the notes made in the instrument log during the July
2006 run, we crudely estimate the V_null for each quick-check:
date value
of of
quick-check V_null_encoder
7/13 93-94
7/16 93-94
7/17 90-91
7/18 92-93
7/20 92-93
It can be seen that there are no large problems with encoder slipping, but
fits could be done to more precisely locate the minimum to probe this
further.
We can derive a value of "HWP" from these data by taking an average:
V_null_encoder (avg.) is 92.5
V_null_rel is 92.5 - 50 = 42.5
estimate for HWP is 2*(42.5) = 85
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D. Derivation of the relationship HWP = 2 * V_null_rel
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The derivation has two steps:
(1) Think through the relationship between V_null_rel and Phi_Inst_raw
The April 13 memo gives the definition of Phi_Inst_raw in terms of Q and
U, and also tells how Q and U are calculated from the raw measurements of
H and V as a function of hwp angle. From this info, the following Table
can be constructed:
V_null_rel Q U Phi_Inst_raw
0 + 0 0
22.5 0 - 135
45 - 0 90
67.5 0 + 45
From this Table we see that Phi_Inst_raw = -2 * V_null_rel
(2) Relate Phi_Inst_raw to HWP:
The following two expressions come from April 13th memo:
Phi_Inst_cor = -1.0 * Phi_Inst_raw + Instrument_Offset
Instrument_Offset = -HWP - 90
Thus, for vertical wires, we have:
Phi_Inst_raw = -HWP
Putting the results of (1) and (2) together, we get the desired
relationship between V_null_rel and HWP.