3.2 Un-modeled beam residuals
3.2.2 Far sidelobes
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Near sidelobes are measured using the far-field beam maps acquired with a circularly polarized broadband microwave noise source (plotted in Figure 3.1). As before, maps are created assuming a common centroid forAandB. In order to isolate sources of polarized sidelobes, maps were co-added over individual detector pairs, tiles, or over the entire focal plane. Investigating these maps with different levels of co-addition enables the identification of mismatch that is unique to detector pairs, or common to a tile or the entire focal plane.
Figure 3.10 illustrates the polarization fraction of the beam out to 2 degrees from the beam center, co-added over tiles. Near the first Airy null, we find that the polarization fraction increases sharply. At larger radii, we can see that the polarization fraction is periodically discontinuous, leaving the impression of radial annuli. The periodicity corresponds to the same periodicity as the Airy rings. While the polarization fraction is high, the integrated power is relatively small; roughly 5% of the integrated optical power lies outside of the first Airy null. The source of the polarization of these sidelobes is not currently understood. In amplitude, the primary source of near sidelobe mismatch is a polarized first Airy ring, which can be seen in Figure 3.11 at roughly 0.8 degrees from the beam centroid. This is apparent in beam maps as well as in this azimuthally averaged radial profile. Further out in radius from1 5degrees, the azimuthally averaged polarized fraction of the sidelobe is roughly1 10%.
Because of the complex nature of the near sidelobe pattern, predicting the resulting level of temperature-to-polarization leakage in power spectra is non-trivial, though it is not a completely in- tractable problem. Efforts to construct models of the near sidelobe patterns as inputs to simulations are ongoing, and may ultimately be a necessary test to assess the potential polarization leakage from mismatched sidelobes.
Tile 2
0.4 0.2 0 0.2 0.4
2 1 0 1 2
Tile 3
0.4 0.2 0 0.2 0.4
2 1 0 1 2
2 1 0 1 2
degrees Tile 4 2
1 0 1 2
degrees
Tile 1
Figure 3.10: Polarized fraction of near sidelobes. Outside of the main beam, the near sidelobes are highly polarized (up to 50%), but contain little integrated power. Sharp discontinuities in the polarized fraction occur near Airy nulls. The polarization of the near sidelobes is not predicted by optical models and is not currently understood.
was rastered in a pattern covering its full range of motion. Beginning at vertical (EL = 90), the telescope slewed through 360 degrees inAZ at a fixedDK angle. The elevation was then lowered in increments of 0.5 degrees down to the elevation limit, repeating the azimuthal scan at every step. To cover as much of the field-of-view as possible, the DK was rotated by 180 degrees at the elevation minimum. The scan was continued at interstitial elevation steps back up to vertical, repeating the same azimuthal scan at each step.
These far sidelobe maps were acquired with many combinations of instrument and source con- figurations. Some of these different source configurations were necessary because the dynamic range required of the measurement (roughly 10 orders of magnitude) exceeds the dynamic range of the instrument, even on the Al transition. With the microwave source full-open, the detectors came unlocked when within a few degrees of the main beam. It was thus necessary to “stitch” two or more measurements together at different source amplitudes. These multiple measurements make it possible to probe deeply for far sidelobe response, and to measure the amplitude relative to the main beam. Maps were acquired with and without the co-moving forebaffle (described in Section 2.7.3) to assess the performance of the baffling scheme.
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
10 6 10 5 10 4 10 3 10 2 10 1 100
Radius from beam center (degrees)
Peaknormalizedamplitude A pol, azimuthally averaged B pol, azimuthally averaged Difference
Figure 3.11: Measured near sidelobes, azimuthally averaged about the beam center co-added over allAandB detectors. The difference is plotted in red.
A further complication of these measurements is the polarization of the source configuration. As the telescope rotates inAZ, the polarization state of the source projected onto the polarization axes of the detectors rotates as well. For this reason, maps were acquired using two orthogonal linear polarizations to fully reconstruct the co-polar and cross-polar response for all detectors.
The map construction proceeds in much the same way as described in Section 3.1.1. We employ a similar pointing model, as described in Appendix C, to account for parallax effects, but with no folding flat mirror. Using the reconstructed pointing information, maps are binned in ground-fixed AZ and EL.
Far sidelobe maps are plotted in Figure 3.12. As with previous maps, these have been co-added over allAandB detectors in the focal plane separately. The annular high noise stripe in the figure is the result of the bright source driving the detectors out of lock. When this happens, the detectors continuously ramp through the full range of the feedback loop. These channels are then cut, resulting in a strip with much less integration depth than the rest of the map. Similarly, the beam center is not accurately measured in these maps due to the same dynamic range issue.
Several obvious features are present in this data: first, a square-ish pattern can be seen at a radius of roughly 15 degrees from the main beam. Secondary reflections within the optical chain of the instrument are responsible for this excess pickup. These secondary reflections (anthropomorphically referred to as “little buddies”) are an optical artifact caused by reflections offthe focal plane. They manifest themselves as ghost images of the main beam mirrored through the optical axis. This is what gives rise to the square pattern when co-added over detectors: Since the detectors are arranged in a square pattern across the focal plane, so too will be the “little buddies.” Similar optical ghosts were found inBicep1and measured to have an integrated amplitude of -22 dB (Chiang 2008). Due
40 20 0 20 40 degrees
B Polarization
60 40 20 0
40 20 0 20 40
40 20 0 20 40
degrees APolarization
Figure 3.12: Measured far sidelobes co-added over A polarized detectors (left) and B polarized detectors (right). The maps are presented in a gnomonic map projection, with the topocentric zenith at r= 0. AZ = 0runs along the positivexaxis. Prominent features in these maps include:
i) an annular stripe at a radius of⇠28degrees, which is a data-taking artifact of losing lock on the bright source, ii) a square-shaped diffuse pattern around the main beam from optical ghost images (or “little buddies”), and iii) diffuse pickup at wide angles that results from scattering within the optics, as well as secondary reflections within the telescope.
to improved anti-reflection coating, the integrated power in the ghost beam has been reduced to
< 30 dB, relative to the detector’s main beam. Crucially, for both Bicep1 and Bicep2, these ghosts were measured to be largely unpolarized, and thus not a significant contributor to spurious polarization. Because of the scan pattern of the far sidelobe measurement (repeated at 180 degrees relative to the original scan), the amplitude of this feature appears artificially doubled in Figure 3.12.
The second obvious feature in these maps is diffuse pickup between roughly 15 and 30 degrees from the beam center. At larger radii from the main beam, the optical response drops considerably. This is the co-moving forebaffle at work: wide angle response is largely rejected, and within measurement uncertainty consistent with zero. The diffuse pickup that is within the solid angle defined by the forebaffle has contributions from scattering from various optical components as well as secondary reflections within the telescope. The diffuse pickup from secondary reflections within the optics chain is seen as a sharp focus in the aperture plane, which has been measured with near-field beam maps.
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