3.3 Noise
3.3.5 Atmospheric
We now examine data collected on the telescope during the October 2012 engineering run in order to char- acterize the atmospheric noise. Figure 3.16 shows the power spectral density calculated from the timestream Vˆ(t)of an on-resonance carrier centered on a representative Band 1 resonator. Note that this is the raw data without filtering or noise removal. The timestream was collected during a 20-minute-long observation in which the telescope performed raster scans across a very faint source. The impact of the source on the individual resonator PSDs is negligible. Prior to calculating the PSD we rotated the timestream to the am- plitude and phase basis and divided by the carrier amplitude. For comparison, Figure 3.16 also shows the PSD of the off-resonance carrier that is closest in microwave frequency to the on-resonance carrier. If mul- tiplicative electronics noise dominated then in these units the on-resonance and off-resonance PSDs would be identical, and this does indeed appear to be the case at intermediate temporal frequencies in the amplitude direction. However, there is clearly excess noise present in the on-resonance data. We know that the noise that dominates at higher frequencies is due to TLS based on our results from the previous section. But at low frequencies, the PSDs clearly transition to a much steeper spectrum that has a slope consistent withν−8/3. In Section 2.3.2.3 we showed that the K-T thin screen model for atmospheric noise predicts exactly aν−8/3 scaling in the 2D regime, which holds ifν2∆hsinhavg|w|e.
In addition, the noise fluctuations that exhibit this steepν−8/3spectrum occur in a well-defined direction in the complex plane. We examined the angleθ1(ν)of the eigenvector corresponding to the largest eigenvalue of the cross-power spectral density matrix for the on-resonance data. This technique was introduced in Section 3.3.4 where we employed it to the study of TLS noise. At low frequenciesθ1(ν)converges to a fixed value that is slightly rotated from the frequency direction. This is exactly what one would expect for atmospheric noise, which would lie in the quasi-particle direction.
We have shown that the noise fluctuations that dominate the on-resonance timestreams at low frequencies have aν−8/3 spectrum and appear in a direction in the complex plane that is roughly consistent with the quasi-particle direction. One final expectation of atmospheric noise discussed in Section 2.3.2.3 is that it
Amplitude PSD [dBc / Hz]
ν [Hz]
Phase PSD [dBc / Hz]
ν [Hz]
ν -8/3
ν -8/3
Figure 3.16: Power spectral density of the noise affecting an on-resonance carrier (red) and off-resonance carrier (black) in the amplitude (top) and phase (bottom) direction in units of dBc/Hz. The on-resonance carrier was centered on a Band 1 resonator on L120210.2L with a resonant frequency fres=3.06174 GHz.
The off-resonance carrier was separated by approximately 4 MHz from the on-resonance carrier. The data was collected during a 20-minute-long observation in which the telescope performed raster scans across a faint source. The elevation angle of the telescope wase=70◦and the atmospheric opacity at 225 GHz was τ225=0.075. The blue and purple lines denote aν−8/3scaling with temporal frequency normalized to the value of the PSD at 50 mHz.
Orthogonal Correlations Quasi-particle Correlations
Figure 3.17: Pearson correlation coefficients between the 327 on-resonance carriers probing L120210.2R and L120210.2L. Only the carriers centered on antenna coupled resonators are shown. The quasi-particle direction is shown on the left and the orthogonal direction is shown on the right. Dashed black lines separate the different readout boards. Solid black lines separate the different detector arrays: L120210.2R corresponds to carriers numbered 0-161, and L120210.2L corresponds to carriers numbered 162-326. The correlation coefficients were calculated in the Fourier domain using only temporal frequencies between 0.02 Hz and 0.20 Hz. The data was collected during a 20-minute-long observation in which the telescope performed raster scans across a faint source. The elevation angle of the telescope wase=35◦and the atmospheric opacity at 225 GHz wasτ225=0.12.
should be correlated across detectors. In order to investigate whether the steep low-frequency noise is corre- lated, we use the weighted mean ofθ1(ν)at low frequencies as an estimate of the quasi-particle direction ˆθqp. We rotate the timestreams to the quasi-particle and orthogonal basis. We then calculate the Pearson correla- tion coefficients between all on-resonance carriers in this basis. The correlation coefficients are calculated in the Fourier domain using only frequencies between 0.02 Hz and 0.20 Hz where the noise of interest dom- inates. The results are presented in Figure 3.17. Directing our attention first to the quasi-particle direction we find that the majority of detectors are almost perfectly correlated with each other. Apart from a handful of anomalous detectors, this high degree of correlation persists across observing band, readout board, and detector array. Next, examining the orthogonal direction, we see that it looks similar to the correlation ma- trices for the off-resonance carriers presented in Figure 3.11. The crucial piece of evidence is that detectors on different arrays are highly correlated in the quasi-particle direction, but almost completely uncorrelated in the orthogonal direction (as is the case for off-resonance carriers). This means that the low-frequency noise appearing in the quasi-particle direction cannot be multiplicative electronics noise.
We have shown that noise due to fluctuations in atmospheric emission dominates at low frequencies and appears in a well-defined direction in the complex plane. The high degree of correlation over the focal plane and between different observing bands bodes well for the atmospheric noise removal.
Chapter 4
MUSIC Detector Characterization
4.1 Introduction
We have calibrated the full instrument model described in Chapter 2 using the procedure outlined in Chapter 3 for the detectors on the science-grade MUSIC arrays. This chapter presents the results of the calibration procedure. The science-grade arrays were fabricated in 2012. The yield from the initial fabrication run was lower than expected, with many of the arrays suffering from feedline discontinuities. These discontinuities were, for the most part, eliminated in subsequent fabrication runs by improving the cleaning process between fabrication steps. In total, six arrays were produced that have both feedline continuity and high resonator yield. Recall that a single array is 6×12 pixels, with each pixel sensitive to four bands, for a total of 288 resonators. Approximately 95% of the designed resonators are identified in network analyzer sweeps for each of the six arrays. The arrays are subdivided into two half-bands, with 144 resonators per half-band. The lower half-band contains resonators between approximately 3−3.4 GHz and the upper half-band contains resonators between approximately 3.6−4.0 GHz. The two half-bands share a HEMT and coaxial cable, but are read-out using different electronic boards. The division is a result of the approximately 450 MHz bandwidth of the readout electronics, which is set by the sampling rate of the ADC.
The detector arrays are identified by a name of the format L[DATE].[WAFER# ][L/R], where [DATE] is the date that the array was fabricated, [WAFER#] is an integer that differentiates between wafers produced on that date, and [L/R] indicates whether the array was on the left/right side of the wafer. The position of the detector arrays in the focal plane unit (FPU) has not changed since September 20, 2012. All results presented in this thesis were collected after that date, so we will often refer to the arrays by their position in the FPU, which has two rows (A-B) and four columns (1-4). In most cases, we will quote separate results for the lower and upper half band. As an example, A2L and A2U refer to the lower and upper half band of the detector array in row A, column 2.