Polarization Efficiency Analysis: December 2006 run - part I

For the December 2006 observing run we measured the polarization efficiency and HWP zero angle with two wire grids in series using a differential measurement with a cold and warm load. The optical path was essentially

The differential measurement was undertaken by "leveling the hardware" of the SHARC-2 camera with the warm load (a piece of eccosorb) and in front of the aperture and then recording data with the cold load. The leveling procedure was repeated each time the HWP was moved. The details of the data analysis for this data can be found in my document on the July 2006 polarization efficiency measurements.

Due to some procedural errors we have 3 different set-ups for this test.

  1. a set of data using the 450 μm HWP but the 350 μm SHARC-2 filter without a nylon screen.
  2. a set using the 450 μm HWP and SHARC-2 filter, without nylon
  3. a set using the 450 μm HWP and SHARC-2 filter, with 1/16 inches of nylon inserted between the cold/warm load and the aperture.

Set (1) resulted in a polarization efficiency of about 75 - 76 % and a significant offset of the sine wave from zero (18 % in the case of vertical grid wires). This low efficiency and the offset are likely due to the drop in HWP efficiency expected from using it at the wrong wavelength (Novak et al. 1989, PASP, 101, 215).


Set (2) resulted in a polarization efficiency of about 96 % with a modest offset of the sine wave (~ 5 -- 6 %). The offset is likely due to the effects of loading effects on relative pixel gains. If the pixel gains in the H and V arrays do not vary by the same amount then the result is a false polarization. In the November 2006 results I worked out the expected form for the resulting polarization signals in H and V. From those the polarization signal is given by
.
where P is the polarization, θ is the HWP angle, and f = Gv/Gh is the ratio of the gains in the H and V arrays. (Note the error in the plot to the right. The legend reads "f = Gh/Gv" whereas the value given is actually "f = Gv/Gh"

A fit of the data (shown at right) to the 3 free parameters above yields P = 97.0 and 97.3 %, δ = -36.8° and +30.4°, and f = 0.86 and 0.88. The two sets of numbers are for tests in which the calibration grid had the wires oriented vertically and diagonally (45° CW from vertical looking towards the sky).


Set (3) resulted in a polarization efficiency of 98% with negligible offset. The decrease in efficiency without the nylon sheet (set-up 2) is most likely due to changes in detector loading. The data to the right is for the calibration grids with wires rotated 45° CW from vertical looking towards the sky).
The best estimate of δ with respect to vertical from the above data is -36.7° = 233.3°. Following the calculations from November we get

V_null_encoder = 233.3°.
V_null_rel = 233.3 - 200 = 33.3°
HWP zero angle = 2 × 33.3 = 67°

Last updated by John Vaillancourt. 2006-Dec-14.
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