Polarization Efficiency Analysis: November 2006 run - part I

For the November run I tried measuring the polarization efficiency and HWP zero angle with a single calibration grid in 3 separate set-ups:

1. M3 → aperture → perpendicular grid → SHARP → SHARC-II
2. M3 → perpendicular grid → aperture → SHARP → SHARC-II
3. M3 → grid ~22.5° from perpendicular → aperture → SHARP → SHARC-II

• In set-up (1) I found that rotating the HWP greatly changed the detector loading at all points across the focal plane. This was most likely due to a polarized load on the detectors due to reflections off the wire grid. This required a true differential measurement between a hot and cold load (done by "leveling hardware").
• In set-up (2) I did not observe a large change in loading across the focal plane so I attempted a non-differential measurement (hardware was leveled only at the first HWP angle). However, I measured a polarization efficiency of only 50 - 60% and the sine-curve had a significant zero-offset (see gain-difference discussion below). Most likely there still exist polarized reflections off the calibration grid in the area of the aperture.
• In set-up (3) I again did not observe a large change in loading across the focal plane so I attempted a non-differential measurement. I measured a polarization efficiency of 94 - 100 %

The plots below show an interesting systematic in this measurement. The data on H-V and S = (H-V)/(H+V) vs. HWP angle show a measurable offset along the y-axis. In addition, the H+V vs. HWP angle shows a distinct periodicity. My working theory had been that this is due to differences in the H and V gains (the January 2006 RGM has been applied to the data). That is, the polarization f-factor is clearly not unity. However, this hypothesis does consistently agree with all the data. Or rather, the offset varies dramatically from dataset to dataset, which is not what I would have expected for the f-factor. I have outlined the theory below anyway in the hopes that someone else might have some more ideas.

Consider the orthogonal signals are given by:
H = 0.5 I G_h [ P (cos 4θ + 1) + (1-P) ] and
V = 0.5 I G_v [ P (1 - cos 4θ) + (1-P) ]
where I is the total unpolarized intensity, P is the polarization, θ is the HWP angle, and G_h,v are the H and V array gains. I have assumed the arbitrary phase is zero for simplicity.

Now we have
H - V = 0.5 I [ P (G_h + G_v) cos 4θ + (G_h - G_v) ],
H + V = 0.5 I [ P (G_h - G_v) cos 4θ + (G_h + G_v) ]

From these equations we can see that if G_h = G_v then H(θ) - V(θ) and S(θ) should be symmetric about zero and H(θ) + V(θ) should be a constant. The data are clearly not consistent with the assumption G_h = G_v (especially for the low polarization found for set-up 2). The H(θ) - V(θ) and S(θ) data are consistent with the relations above. However, the H(θ) + V(θ) data exhibit a periodicity which differs from the expected 90°, but it is also clearly not random. I currently have no explanation for this.

The zero-offsets and H+V period are consistent between the two tests taken while the calibration grid wires were near-vertical. However, when the wires are horizontal, not only does the polarization level change, but so does the odd periodicity of H+V.

The H+V periodicity is not as obvious as in the differential data, but I think it is there. The differential data is much noisier than the non-differential data; I think the periodicity is just buried in the noise. I strongly suspect that much of this noise is due to the cold load not being replaced in the same spot (distance from detectors) for each HWP angle. I suggest blocking the cold load with warm eccosorb rather than removing/replacing the LN2 dewar for such differential tests in the future.

If the gain-difference hypothesis alone is correct I would have expected to get similar measurements for the f-factor despite the different measurement techniques. It may be that there is just a large error on the offset terms. But right now I can't rule out something else.

Figures above --- Left: Data for set-up #2 with calibration grid wires near-horizontal. Right: Data for set-up #3 with calibration grid wires near-vertical. Note that I have left the error bars off this plot and out of the fit so the parameter uncertainties and χ² reported in the plots are not realistic.