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. _____________________________