4.2 Science-grade Arrays
4.2.2 FTS
We collected FTS data over the course of three days, between 2013/07/27 and 2013/07/29. We obtained 22 datasets in total, varying the position of the SPIDER FTS apparatus with respect to the cryostat window. We collected an IQ sweep and re-centered the carriers on-resonance approximately every other dataset. For each dataset, the carriage carrying the mirror was set to scan the central 280 mm of the 300 mm long stage, and then return. This was repeatedNcycle=8−12 times, so that each dataset containedNscan=16−24 interferograms.
For each scan, the carriage followed a trapezoidal velocity profile in which it accelerated at 2.5 mm/sec/sec to a maximum velocity of 8.75 mm/sec/sec, traveled at constant velocity for approximately 250 mm, and then decelerated at 2.5 mm/sec/sec. There was no difference in the resulting spectra between forward and backward scans.
The FTS was only capable of illuminating a small fraction of the detectors at once (roughly one device half-band). In an attempt to obtain bandpasses for all detectors, we collected 22 datasets over a grid of positions relative to the center of cryostat window. Our control over the position of the apparatus was fairly crude and not entirely repeatable, so the following alignment process was carried out before collecting each dataset. We set the carriage to the center of the stage, where the two paths of the FTS have equal lengths. This is the location where constructive interference is maximum and is commonly referred to as the white light fringe. We began collecting data and monitored it in real time for a subset of detectors that were evenly spaced over the particular device half-band that we hoped to illuminate at that particular apparatus position. We then waved a room temperature EccosorbR wand back-and-forth in front of the FTS LN2load. If the detectors were well coupled to the LN2load, then the difference in temperature between the room temperature wand and the LN2load created a noticeable signal in the detector timestreams. We fine tuned the position of the apparatus so that the room-temperature-wand signal was maximized in a significant number of the detector timestreams. The central part of the focal plane unit was much easier to illuminate than the edges. The lower half-bands of A2, A3, B2, and B3 were easily aligned and have high-quality spectra. In order to align the upper half-bands of these four detector arrays, we had to direct the FTS beam into the cryostat at an angle.
This was accomplished by rotating the cryostat slightly with respect to vertical. After doing so, we were able to obtain high-quality spectra for the upper half-bands of A2, A3, B2, and B3. In order to align the A4 and B4 detector arrays, we had to direct the FTS beam into the cryostat at an angle orthogonal to the rotational freedom of the cryostat. This was achieved by adjusting the angle of the last mirror with respect to horizontal from 45◦to 50◦. While the room-temperature-wand signal was observed in the detector timestreams for these two arrays, few interferograms were detected, and we were only able to obtain spectra for a handful of detectors. The number of detectors on each device half-band that measured at least one interferogram is presented in the top panel of Figure 4.4.
Figure 4.4:Top: The number of resonators on each device half-band that were probed during the FTS mea- surements (blue) and measured at least one interferogram (green). Bottom: The median band center and effective band width for the resonators on each device half-band. The different colors denote the four MU- SIC observing bands. The gray boxes denote the designed bandpasses.
We focus on datasets that have a white light fringe clearly visible in at least one detector timestream. Of the 22 datasets, 15 satisfy this criteria. Analysis of each dataset proceeds as follows:
• We determine the frequency directionθbfreqand conversion factorAbfreqfor each resonator from the most recent IQ sweep using the technique outlined in Section 3.3.4. We rotate the data to the frequency direction and convert to fractional resonant frequency fluctuations. We apply all further analysis to the frequency component alone.
• We examine the half-band-averaged timestreams by eye in order to determine the location of theNscan
white light fringes.
• We extract a 28.5 second block of time centered on each white light fringe from the timestream. This corresponds to the 250 mm where the carriage was traveling at its maximum velocity (8.75 mm/sec).
• We fit a polynomial to each block of time and then subtracted it to remove the large scale features caused by changes in loading as the mirror moved across the stage.
• We apply a Hanning window to each block of time and then calculated the PSD. We average the PSDs for theNscan blocks of time together to obtain a final estimate of the PSD for each resonator for each dataset.
• We run a peak finding algorithm on the PSDs. We apply a cut on the peak-height-to-continuum ratio, peak width, and peak location to find the actual spectra.
• We take the square root of the PSD.
• We mask the peaks and fit the continuum noise level to the model given by Equation (3.24). We subtract the best fit model and then normalize by the maximum value to obtain an estimate of the transmission.
• We use Equation (3.14) to convert from temporal frequency to millimeter-wave frequency. We then multiply the millimeter-wave frequency by a factor of 1.0261 to correct for velocity miscalibration (see Section 3.2.4).
If a resonator has spectra in multiple datasets, then we average them together, weighting by the peak-height- to-continuum ratio.
We calculate the band center and effective bandwidth for each resonator as
νmm ,ant=
RFTS(ν)νdν
RFTS(ν)dν ∆νmm ,ant=
Z
FTS(ν)dν, (4.2) whereFTS(ν)denotes the measured bandpass. The median values of these two quantities are illustrated in Figure 4.4 and presented in Table 4.3 for each device half-band. We also display the average bandpass in Figures 4.5-4.6. In both the figures and the table we compare the measured bandpasses to the designed bandpasses.
Figure 4.5: MUSIC bandpasses for the L120210.2R and L120210.2L detector arrays. The different colors denote the four observing bands. The solid-filled regions show the measured bandpasses and the hashed-filled regions show the designed bandpasses. Overlaid on each plot is the atmospheric transmission spectrum at the CSO for 1.68 mm precipitable water vapor (historical median). The measured bandpasses were obtained by averaging over all detectors on the specified device half-band.
Figure 4.6: MUSIC bandpasses for the L120309.4L and L120427.1L detector arrays. The different colors denote the four observing bands. The solid-filled regions show the measured bandpasses and the hashed-filled regions show the designed bandpasses. Overlaid on each plot is the atmospheric transmission spectrum at the CSO for 1.68 mm precipitable water vapor (historical median). The measured bandpasses were obtained by averaging over all detectors on the specified device half-band.
Table 4.3: The median band centers and effective band widths for four of the MUSIC detector arrays.
νmm,ant[GHz]
Device ID Position Band 0 Band 1 Band 2 Band 3
Designed 151.3 226.1 289.3 345.8
L120210.2R A2 147.6 218.2 279.3 335.9
L120210.2L B2 148.3 217.8 280.2 334.7
L120309.4L A3 137.1 198.2 237.0 278.9
L120427.1L B3 144.2 212.8 257.2 303.1
νmm,ant[Measured / Designed]
Device ID Position Band 0 Band 1 Band 2 Band 3
L120210.2R A2 0.98 0.96 0.97 0.97
L120210.2L B2 0.98 0.96 0.97 0.97
L120309.4L A3 0.91 0.88 0.82 0.81
L120427.1L B3 0.95 0.94 0.89 0.88
∆νmm,ant[GHz]
Device ID Position Band 0 Band 1 Band 2 Band 3
Designed 34.3 44.5 33.8 20.7
L120210.2R A2 20.5 26.5 17.6 13.6
L120210.2L B2 18.0 23.5 16.0 12.4
L120309.4L A3 14.5 16.0 17.1 14.2
L120427.1L B3 11.7 20.0 14.1 10.7
∆νmm,ant[Measured / Designed]
Device ID Position Band 0 Band 1 Band 2 Band 3
L120210.2R A2 0.60 0.60 0.52 0.66
L120210.2L B2 0.53 0.53 0.47 0.60
L120309.4L A3 0.42 0.36 0.51 0.68
L120427.1L B3 0.34 0.45 0.42 0.52
We find that the measured band centers shifted downward in frequency by'3% from the designed band centers for the A2 and B2 array. This downward shift was caused by an increase in the ratio of the dielectric constantεto the thicknessdof the Si3N4dielectric used for the science-grade detector array. Measurements of theε test devices on the A2 detector array confirm this explanation, showing an increase of 6% inε/d between the final engineering-grade tiles and the science-grade tiles, as discussed in Section 4.2.1. The impact of this shift on the 150, 225, and 290 GHz observing bands is minimal; however, the 345 GHz band shifted far enough that it has significant overlap with a water absorption line at'325 GHz. As a result, the sensitivity of the 345 GHz observing band is noticeably degraded.
Clearly something more insidious is affecting the A3 and B3 band centers. We find that for these two detector arrays, the ratio of the measured to designed band center is band dependent. This results in the 150 and 225 GHz band spilling into each other, and the 345 GHz band being far from the desired location.
This variation in the location of the band centers makes analysis of science data collected with these arrays difficult. Although we were unable to obtain FTS measurements for a significant number of detectors on the A4 and B4 arrays, measurements of the response to hot and cold loads suggest that the bandpasses for these arrays exhibit similar behavior to that seen in A3 and B3. Because of this, we have chosen to pursue science observations with the A2 and B2 arrays only. The remainder of this thesis will focus on calibration of the detectors on the A2 and B2 arrays.
The effective bandwidth ranges from 47% to 66% of the designed bandwidth for the A2 and B2 detectors.
The is due to modest fringing, clearly visible in Figures 4.5-4.6. Simulations of the bandpass filter, which are also shown in Figures 4.5-4.6, do not display fringes. Vector network analyzer measurements at microwave frequencies of a scaled version of the bandpass filter design are also free of fringes [102]. This suggests that the source is not the actual filter, but rather the optical chain. Based on the frequency separation of adjacent fringes, we suspect that the fringing originates from standing waves in the dielectric filters.