3.1 Far-field optical characterization of Bicep2
3.1.1 Far-field beam mapping
Far-field beam maps are made possible by the fact that Bicep2 has a relatively close far-field distance, of order ⇠100 m. We can thus make maps of the far-field response using ground-based calibrators, a distinct advantage of small-aperture experiments. Far-field maps have been made in the Caltech synchrotron highbay and at the South Pole station. The Caltech synchrotron highbay measurements were critical for verifying the optical health of the telescope prior to deployment. The calibration data acquired at the South Pole serve as our archival calibration data and will be the focus of our characterization discussion below. To fully capture the rich complexity of the optical response of the telescope, wide field-of-view maps with high signal to noise are required.
Maps of the Bicep2optical response were made with primarily two source configurations. The first used a broadband amplified noise source. This source consists of a terminating resistor coupled to a chain of amplifiers and frequency doublers, yielding a ⇠ 1⇥106 K microwave source, PIN- switched at 18 Hz. Beam maps were taken with circular and linear polarizers at the output, in both an open-waveguide and horn-coupled configuration. While the maps yielded excellent signal-to-noise, the extreme source brightness led to gain non-linearity in a number of detectors. The source is also highly non-thermal. An example map is shown in Figure 3.1. This map was made with a circularly polarized broadband amplified noise source. This map, with a noise floor at roughly 75dB below the peak height of the beam, was made in 12 hours of data-taking.
The second source configuration consisted of a chopped reflector, referred to as “thermal source”
beam maps. A large-aperture chopper was placed in front of a mirror reflecting the cold South Pole sky, which typically has a zenith temperature of 12 K. The chopper, covered with eccosorb sitting at ambient temperature, modulated the optical signal through the aperture at a rate of 10-18 Hz. This data set proved to yield a much more repeatable and linear main beam response than the microwave noise source. While this came at the sacrifice of signal-to-noise, we still find the map depth sufficient to characterize the main beam performance.
Due to the mechanical restrictions of the mount, the telescope cannot observe ground-based calibrators directly. As a result, a folding flat mirror was required to redirect the telescope’s beam to the roof of the Martin A. Pomerantz Observatory (MAPO) at a distance of roughly 200 m (Figure 3.3). Microwave sources were mounted to a mast roughly 10 m above the roof. The use of the folding flat mirror introduces additional free parameters in the pointing model for these beam maps, which
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Figure 3.1: Beam map of the Bicep2 far-field response made with a broadband amplified noise source, centered and co-added over all operational channels. Plotted is the logarithmic irradiance in dB. The map, made with the Al TES, spans well over 6 orders of magnitude. Besides the main beam, pickup from the ground is apparent (betweenEL= 5 and 2 deg).
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Figure 3.2: Simulated beam map of theBicep2far-field response made with Zemax physical optics.
The optical model does not include the forebaffle, which has the effect of cutting down large angular response. The measured main beam shape and Airy rings are well-matched by simulations.
64 we will describe in detail in Appendix C.
Figure 3.3: Bicep2at the Dark Sector Laboratory at the South Pole. For beam mapping calibration measurements, a folding flat mirror was mounted above the telescope to redirect the beam to a nearby calibration source (not pictured).
The Bicep2beam maps are collected in anAZ ELraster pattern at a single DK angle. In most cases, full rasters were acquired at two or more DK angles. This is a powerful test: beam features that rotate with the telescope can be identified and assessed in this scheme.
When beam mapping, data is collected at a high data rate (relative to the science data taking rate), typically 150 Hz. With the source chopped at ⇠18 Hz, we acquire many samples over every chop cycle. Azimuthal scans during mapping are driven at scan rate of 2 /s. This ensures that many chops are acquired over the main beam. The telescope encoder data, the detector data and reference chop are acquired synchronously.
The beam map analysis proceeds in three steps: deconvolution, demodulation, then map making.
The purpose of the deconvolution step is primarily to account for any group delay that results from a time asymmetric filter that is applied to the data. Typically, the digital Butterworth filter that is applied to science data is disabled. However, in some cases it is desirable to take data with this filter enabled, which has a 3 dB point at 137 Hz. The group delay is accounted for by applying a simple shift to the data stream. A full deconvolution is not necessary, as the beam features are modulated at much lower frequencies.
In the second step, the data is demodulated using a phase-locked square-wave reference chop that is fed from the optical source. The demodulation works essentially by multiplying the reference chop to the detector time series and taking sums over individual chop cycles, resulting in one data point per cycle.
The final, and most complicated step, is the map making itself. This requires a three-dimensional
pointing model that translates raw encoder counts to apparent detector location on the sky. This pointing model is documented in Appendix C. Once all of the per-detector maps have been con- structed in ground-fixed coordinates, they can be stacked for higher signal-to-noise, or differenced to form pair-difference maps. In the construction of these maps, the centroid ofAandB are assumed to be the same.