This document gives the conventions used by SHARP team to keep track of
the angle of polarization.  The purpose of this document is to establish
an agreed terminology for discussing these issues.  (For analyzing August
2005 data, we will use the grid tests to establish the correct value of
the HWP flag that determines the angle on the sky.)

___________________________
(1) direction for positive hwp motion
___________________________
The direction of positive half-wave plate motion is such that the angular
velocity vector of the half-wave plate points towards the SHARC-2
instrument.  This was recorded by Giles and Hua-bai in the instrument log
on August 8, 2005.
___________________________


___________________________
(2) Code in sharpsolve/sharpstokes:
___________________________
Q = H(0) - V(0)
-Q = H(45) - V(45)

U = H(22.5) - V(22.5)
-U = H(67.5) - V(67.5)

then flip sign of U
___________________


____________________
(3) Code in sharpsum:
____________________
ANG = 2 * (PAR + EL - HWP)

***NOTE added in April 2006***
***The sign in front of HWP has been changed (see later postings)***

HWP is a flag that can be added to take into
account the arbitrary offset

PAR is the Parallactic Angle

EL is the elevation

Q_out = Q_in * cos(ANG) - U_in * sin(ANG)
U_out = U_in * cos(ANG) + Q_in * sin(ANG)
_____________________

_____________________
(4) Giles' calculation at 14,000 feet:
_____________________
PHI_SKY = - PHI_INSTRUMENT + (PAR + EL)

with the following definitions:

PHI_SKY is angle of E-vector on sky, increasing E from N

PHI_INSTRUMENT is angle of E-vector at SHARP input, as 
viewed by someone looking down the Nasmyth tube from
the Nasmyth platform.  The angle is zero when the E-vector
is vertical and increases as the E-vector is rotated 
counter-clockwise.
_____________________________