Polarimeter Receiver Prototyping and Testing for the South Pole Telescope Upgrade

Transcription

1 Polarimeter Receiver Prototyping and Testing for the South Pole Telescope Upgrade Constantinos Melachrinos June 5, 2009 Abstract Experimental evidence has so far been supportive for the inflationary Big Bang model of cosmology, while imposing other mysteries, such as the fact that dark matter and dark energy actually consist of 95% of the observable universe. The forthcoming upgrade of the South Pole Telescope, planned for 2010, will include a polarimeter with increased sensitivity compared to the current system. Measurements of the CMB polarization anisotropy to a high accuracy will describe the angular power spectrum of the B-mode polarization, which will help unravel some of the mysteries. We prototype and test a digital frequency multiplexed readout system for the SPT upgrade. The digital system has three advantages: it is able to reconstruct both the amplitude and the phase of the multiplexed signals, it has improved low frequency noise and increased multiplexing depth. We implement a prototype readout system and use it to characterize prototype detectors for the polarimeter. The system calibration and optical coupling measurements agree with expected results. The discrepancies are explained with systematic uncertainties. The noise spectrum is improved over the previous system, but further study is needed to minimize external factors and obtain the noise equivalent power. The readout system is robust and well-characterized to make measurements of detector parameters. 1 Introduction In this section, I will briefly explain current experimental efforts in cosmology, and their significance for the scientific community. Theoretical topics will include the Cosmic Microwave Background and dark matter. For the experimental efforts I will focus on astrophysics and telescopes. The South Pole Telescope, located in Antarctica, is a significant detector that aims to investigate the mysteries of dark energy and inflation. The 10 meter diameter telescope has been operating since 2007 and observes microwaves and millimeter waves, in frequencies between 70 and 300 GHz. Bolometers are used to detect the distortions of the cosmic microwave background (CMB), due to interactions between CMB photons and ionized gas in galaxy clusters, an effect first postulated by Sunyaev and Zel dovich [6]. Using a subset of the data, four previously unobserved galaxy clusters were discovered in October 2008 [8]. The current array on SPT is not polarization sensitive. Our upgrade plan is to install a polarimeter, that will enable the characterization of the angular power spectrum of the B-mode polarization to an unprecedented accuracy. Current sky maps with temperature anisotropies produced by WMAP can describe the temperature power spectrum up to multipoles of l 600. After the upgrade, the South Pole Telescope will be able to probe the spectrum to multipoles exceeding l Constraints on Ω m and Ω b will also constrain the properties of Dark Matter such as the neutrino mass. 1

2 The B-mode polarization spectrum is also sensitive to gravitational waves predicted by certain inflationary models. Even though the instrument s systematics and the foregrounds will most likely shadow the small gravitational signal, the search may prove fruitful. We will describe our prototyping and testing of a new fully digital polarimeter receiver, as opposed to the current semi-digital receiver. The full digitization of the readout multiplexing will enable the reconstruction of the phase of the signals, which will greatly increase the sensitivity of the polarimeter. 2 Principles of operation of fmux readout The MHz frequency domain multiplexed (fmux) readout system uses an array of bolometers to detect and measure the incident radiation in different frequencies. SQUIDs are then used to measure the current flowing through the bolometers. The operation of bolometers and SQUIDs is described below, followed by the description of the readout system. 2.1 Transition-Edge Sensor Bolometers Bolometers are the thermal detectors used to measure the cosmic microwave background. Fig. 1 shows a single bolometer and an array of bolometers as deployed to SPT. When radiation of power P is incident on the absorbing material of the bolometer, its temperature rises according to the formula: T b = T s + P G (1 e t τ ) (1) where G is the thermal conductance of the connection between the bolometer and a heat sink with temperature T s, and τ = C G is the intrinsic thermal time constant of the bolometer. A thermistor measures the temperature of the bolometer T b using a bias current. In order to increase the sensitivity of the temperature measurement, Transition-Edge Sensors (TES) are used. These sensors exploit the sharp change in electrical resistance between the normal and superconducting state of superconducting materials. The bias current for TES bolometers operates at the transition temperature for maximum sensitivity. The TES bolometers are held in their transition by a voltage bias. This has the benefit of putting the detector into a state of negative thermal feedback. The benefits are analogous to negative feedback in electronics (increased linearity, increased bandwidth), where the gain is given by the steepness of the normal to superconducting transition. Changes in incident optical power increase the temperature of the bolometer, which is measured as a change in the current though the bolometer. However, even when there is no incident optical power, a TES bolometer also detects noise arising from: a) the thermal fluctuations in the conductance between the bolometer and the heat sink, b) the resistance of the thermistor and c) the current bias used by the thermistor. Photon noise associated with the arrival of photons also contributes to the total noise. 2.2 Superconducting Quantum Interference Devices SQUIDs are used to measure the current flowing through the TES bolometers. Their operation depends on two superconducting phenomena: the Josephson effect and magnetic flux quantization in closed superconducting loops. A SQUID consists of a pair of Josephson junctions connected in parallel with a superconducting coil. An insulating layer also separates the junctions from the coil. When current passes through the superconductive coil, it induces a magnetic flux through the loop containing the junctions. This changes the phase difference across each of the junctions, changing the critical current It of the SQUID and its IV response. In fact, Series-Array SQUIDs (SSAs) are used because 2

3 Figure 1: Single bolometer and an array of bolometers they increase the signal-to-noise ratio compared to single SQUIDs. SSAs possess disadvantages such as increased sensitivity to trapped flux and background magnetic fields. The SSA is operated in a flux-locked feedback loop to improve its linearity and extend the dynamic range. The DC SQUID and a series array of SQUIDs are shown in Fig. 2 Figure 2: One DC SQUID and a series array of SQUIDs. 2.3 Readout Multiplexing Reading simultaneously arrays of thousands of bolometers is a technological challenge. Readout multiplexing combines signals from many sensors at cryogenic temperatures and gives one signal to be transmitted to the electronics at room temperature. This signal is then separated into the signals that combined earlier and allows their further analysis. There exist two main readout architectures: Time-Domain Multiplexing (TDM) and Frequency-Domain Multiplexing (FDM). In TDM the readout amplifier spends a fraction of its time at each sensor, whereas in FDM each sensor is biased at a unique frequency and the readout amplifier simultaneously processes all sensors. FDM is used because it requires one SQUID amplifier for readout, while TDM requires an additional SQUID amplifier for each of the sensors to act as the switch. Each TES bolometer is connected in series with an LC tuned filter which is tuned to a specific frequency and biased with alternating current. This way, signals from the remaining frequencies is suppressed, and the Nyquist noise is bandwidth limited. In our system there exist eight channels, operating at eight different frequencies, from 380 khz to 1 MHz. A sinusoidal bias, called carrier 3

4 comb, is sent to the LC filters to tune them at the appropriate frequencies. The sensor signal resides in sidebands above and below the carrier frequencies. A nulling comb is sent to cancel the carrier comb and permit only the signal to be detected by the SQUID pre-amplifier. This will be described in more detail in Section 3. The SQUID, then reads out the signal, which is then reconstructed in the different frequencies offline. This procedure is also shown in Fig. 3. Figure 3: The frequency-domain readout multiplexer 3 Upgrade from analog to digital fmux readout Recent technological advances have resulted in ADCs with increased speed and FPGAs with reduced power consumption and increased logic capabilities. These have made possible the manufacture of a digital signal processing system for biasing and reading out the multiplexed bolometers. In addition, there are two motivating factors in upgrading to a digital readout system: a) going to polarization requires two bolometers per pixel, so we would like to increase the number of bolometers per SQUID, b) the low frequency noise performance needs to be improved in order for us to measure the inflationary B-modes at low l. While the underlying principles of operation of the multiplexed readout system are the same, the digital system makes possible the reconstruction of the phase of the signals, faster processing and more flexible online detection. The digital system is shown in Fig. 4. The bolometers are biased with the carrier sinusoidal bias comb produced by a digital multi-frequency synthesizer (DMFS). Differences in incident radiation on the bolometers change the bolometer resistance and amplitude modulate the current through the bolometer. The sky-signal is thus detected in the sidebands of the bolometer s frequency of operation. The different signals in frequency-space are summed and connected to a single SQUID array, where a nulling sinusoidal bias comb, from a second DMFS, cancels the carrier comb, to allow only the signal to be detected at the SQUID. At the SQUID, the signal gets amplified and is transmitted to the digital multi-frequency demodulator (DMFD) where the signal is digitized and processed. In particular, a low pass filter and a chain of band defining FIR filters are put in series to decrease the 25MHz sampling rate to the 200Hz data rate that will be recorded. Special attention must be paid to maintain the low frequency signals while filtering and sub-sampling the wavelength to reduce the sampling rate. The output of the low pass filter is sent to first-in-first-out (FIFO) memory, where a processor gathers data from the rest of the DFMD modules on the FPGA and sends it over Ethernet to be stored to disc. Fig. 5 shows in detail this process. 4

5 Figure 4: The digital frequency-domain multiplexer readout system. Figure 5: The digital multi-frequency demodulator in detail. 5

6 Apart from the advantages outlined in the beginning of this section, the faster processing and ability to reconstruct the phase of the signal, the digital system is also modular. If one electronic board or wire fails, it only affects the specific components that it is connected to and not any other components. In addition, each board is autonomous in its operation, controlled by a central computer. The digital system also allows us to change the bandwidth of bolometer data using software, without the time consuming process of re-commissioning hardware. The low power dissipation at all stages in the digital system also permits the readout system to be considered for non-ground telescopes, such as ballon experiments. 4 Hardware implementation of digital fmux readout To be able to test the DfMux readout system, we first need to prototype it. The actual implementation includes cooling the SQUIDs to sub-kelvin temperatures, building the crate that hosts the DfMux board and setting up the communication between the board and a computer. 4.1 Cooling to sub-kelvin temperatures Operation at sub-kelvin temperatures ensures that no power is dissipated in the readout system, other than the signal. This is particularly important since we are operating at the superconducting transition temperature of the bolometers and even miniscule changes in temperature alter the I-V response of the bolometers. Since we want the bolometer sensitivity to provide us with an accurate measurement of the incident radiation, any amount of power would interfere with this measurement. To achieve sub-kelvin temperatures the Simon-Chase cooler is used [9], shown in Fig. 6. Figure 6: The Simon-Chase cooler. The cryocooler precools the 4 He to below the critical temperature 5.1 K. The sorbate is then pumped upon to give a heatsink at 0.85K for 3 He. The Intercooler 3 He buffers to reduce the heatload on the final Ultracooler 3 He which cools to the desired temperature of 250mK. The Simon-Chase cooler exploits the relatively weak van der Waals forces between the refrigerant gas (sorbate) and the sorbent material. We use charcoal as a sorbent, and 3 He and 4 He as the sorbate at different stages. To achieve sub-kelvin temperatures, the pump is heated to 45 K to desorb 6

7 (break the van der Walls forces) the sorbent gas from the sorbate. After desorption the sorbent gas condenses into the still, and then the pump is cooled again. This way, the adsorptivity of the sorbent increases and is pumped upon to reduce the vapour pressure of the sorbate. The temperature of the liquid is thus reduced further, typically to 0.3 K. More details on the Simon-Chase cooler can be found in reference [9] and the caption of Fig Building the crate The crate was assembled by ordering standard parts from suppliers. Table 1 shows the parts that we ordered. The crate can be used for up to twenty (20) boards simultaneously, but we are only testing one board. Item description Manufacturer Part # Quantity Price Remarks VME Backplane Vector Electronics VMEBP21J1 1 $ VMEBP21J1 and Technology VME Backplane Vector Electronics VMEBP21J2 1 $ VMEBP21J2 and Technology Vector card cage Vector Electronics CCA220-6U 1 $ CCA220-6U and Technology Power supply Astec Inc. see col.1 1 $1265 custom made MP8-3H-1H-1J-1J- 00 (+6V 78A, -6V 23A, +10V 18A, -10V 18A) AC Fan tray Bud Industries FT $ Table 1: This table shows the parts we order to assemble the crate that holds the DfMux. 4.3 Setting up communication between DfMux board and computer To control the DfMux board and take measurements, it is necessary to set up a way to communicate with the board. There are three ways to achieve this communication: using a web-based interface, using a set of Python classes, or using a Telnet session The web-based interface is accessible by connecting the board to the local network, which gives the board an IP address. This can, then, be accessed using any web browser. Using python is the most robust arrangement, and is therefore preferred. The interface classes are available through a SVN repository and they use Python version 2.5. The firmware for the DfMux is frequently upgraded, and is also available for download. The python scripts are used to make the measurements in Sec. 5, and are modifiable if needed. 7

8 5 Prototyping the digital fmux readout The digital fmux readout board was developed at McGill University and UC Berkeley for the Polar BEAR experiment. The same boards will be used for the polarization upgrade of SPT. Our goal is to demonstrate that the board performs as expected. Fig. 7 shows the board with its various components. The following tests will be done using the python scripts described in Sec Figure 7: The DfMux board with its various components as annotated. 5.1 Configuring SQUID array readout Before we use the SQUIDs for measurements, we need to make sure that their voltage-magnetic flux (V-Φ) response is described well. In particular, the flux quantization should be obvious, and the response should be monotonous. Fig. 8a shows the expected response of the SQUID tuning. Using the V-Φ response we can choose the optimal point at which to lock the feedback loop. The actual V-Φ response for a typical measurement session is shown in Fig. 8b. In this example, we chose to lock the feedback loop at SQUID bias 5.5V, flux bias 0, and voltage offset 5.25V. There, the curve is far from any sharp changes, and the response is monotonous. 5.2 Calibration To make sense of the measurements we perform with the DfMux, it is necessary to calibrate our measurements. In particular, we need to know the relationship of amplitude and gain for different frequencies as a function of the actual voltage that is transferred to the bolometers. In addition, we need to understand how many ADC counts are measured after demodulating the signal at the 8

9 Figure 8: The figure on the left shows the expected V-Φ response. The flux quantization, a characteristic of superconductive materials is obvious. The figure on the right shows the response from a typical measurement session. The flux quantization is obvious in both pictures. same frequency. These calibrations were performed at room temperature, and details are shown in Sec Further calibrations were necessary at cryogenic temperatures, to relate the measured power of the bolometers, with the applied power. Sec. 5.3 contains the discussion of these results. In the following, peak to peak voltage is used, unless noted. The relationship between rms voltage, used for calculating power, and peak to peak voltage is: V rms = V pk pk 2 2 (2) Calibration 300K We set up the DfMux readout system at room temperature and connected it to an oscilloscope. Using the interface described in Sec. 4.3, we sent carrier signals from the DfMux to the oscilloscope. Carrier signals of different amplitudes, frequencies or gains were sent, and we measured the peak to peak voltage on the oscilloscope, to derive a calibration relationship between the different factors. In particular, the amplitude scale of the DfMux corresponds to a fraction of the maximum voltage that the carrier signal can have, and hence varies linearly between 0 and 1. The carrier gain scale of the DfMux is a number between 0 and 3, and corresponds to increasing gain. Physically, the gain switch changes the number of resistors in parallel with the carrier signal and this way we can predict how the gain affects the voltage. The carrier signal is sinusoidal with a set frequency, and here we explore how much the frequency affects the measured voltage, even though it is not expected to vary significantly. The following paragraphs show each measurement and the results we obtained. Voltage as function of amplitude Keeping the gain at its maximum value (3), the peak to peak voltage was measured for four different amplitudes (0.25, 0.5, 0.75, 1). The procedure was repeated for four different frequencies (200, 600, 1000, 1600 khz) to understand whether there is a frequency dependence. Fig. 9 shows the results, which were fit to a linear relationship. The following formula can be used to get the peak to peak voltage, when the amplitude is known: V pk pk = C0(f) A + C1(f) (3) 9

10 The coefficients C0 and C1 depend on the frequency, as shown in fig. 10. The following formula is used to find the coefficients for any frequency in the range [0 1600] khz, and was found by using the results in fig. 10. C0(f) = 0.02 f (4) C1(f) = f (5) Using the above formulae, the peak to peak voltage can be expressed as a function of frequency for amplitude 1 as follows: V pk pk (mv ) = ( 0.02 f ) f = f(khz) (6) Figure 9: Voltage as function of amplitude for different frequencies and gain=3. Figure 10: The coefficients of the V=C0xA+C1 fit as functions of frequency Voltage as function of frequency Keeping the gain and amplitude constant at their maximum values (3 and 1, respectively), the peak to peak voltage was measured for the frequencies in the range [200, 1600] khz with 100 khz step size. The data were fit to a straight line to get the following: V (mv ) = f(khz) (7) 10

11 Fig. 11 shows the results. This particular fit is redundant with the previous subsection, where we derived a way to calculate the peak to peak voltage given any amplitude and frequency, but is included here nevertheless. However, it can be used as a consistency check with the previous method. Comparing equations 6 and 7 we can see that they have a very small difference, which can be attributed to the uncertainties of the measurements and the rounding errors involved in the various stages of the calculations. Both fits are shown in Fig. 12. Fig. 12 also shows the difference between the two ways of calculating the V pk pk as a function of frequency for amplitude=1, as a percentage from the value obtained with eq. 6. We see that the two fits are consistent to 0.4%. Figure 11: Voltage as function of frequency for amplitude=1 and gain=3. Figure 12: (left) Fits using two different methods for estimating V pk pk given the frequency. (right) Percentage difference of two ways of measuring voltage as function of frequency for amplitude=1 and gain=3. Voltage as function of gain The carrier gain can vary between its minimum (0) and maximum (3) values using the relation: 0 : 1 : 2 : 3 = 0.48 : 1.09 : 3.33 : 10 (8) These ratios are extracted by knowing which resistors are connected at each gain stage. We confirm this by varying the gain and measuring the peak to peak voltage at the maximum amplitude (1), 11

12 repeating this procedure for four different frequencies. The results are shown in Fig. 13. The peak to peak voltage at each gain level is divided by the voltage at maximum gain (3), and the result is multiplied by the ratio of this gain setting (10), to get the ratios for each frequency, and compare them to the expectations from Eq. 8. The results are shown in Fig. 14 and it is evident that the ratios are very close to the expected ratios, within 0.5% of the expected value. Figure 13: Voltage as function of gain for amplitude=1 at four different frequencies. Figure 14: (left) Ratio V(G=i)/V(G=3)*10 for amplitude=1 at four different frequencies, for comparison with the expected ratio. (right) Percentage difference of actual and expected ratios. When the DfMux detects a signal, it detects it as a number of ADC counts in time streams of data. The procedure we followed to calibrate ADC counts was to send a carrier signal at a certain frequency, then demodulate the signal at the same frequency, and send the demodulated signal back to the DfMux to detect. The number of ADC counts is proportional to the current through the bolometer, which is itself related to the power through the bolometer, according to Ohm s law. In the following, we calibrate the number of ADC counts as a function of demodulator phase, carrier amplitude, carrier and demodulator gain. The carrier signal was demodulated at the carrier frequency and the number of ADC counts for different phases φ was calculated. The procedure was repeated for different frequencies, amplitudes and gains, to get the dependencies of ADC counts in relation to these variables. Using the maximum gain on both the carrier and the demodulator gain leads to 12

13 saturation of the ADC counts. For this reason, using both maximum gains is avoided. Instead, we used maximum gain on the carrier gain (3) and minimum gain on the demodulator gain (0). ADC counts as function of demodulator phase and frequency For maximum gain in the carrier signal (3) and minimum gain in the demodulator (0), maximum amplitude (1) for the carrier signal and at four different frequencies, the ADC counts were measured for different demodulator phases in the range [0 360] degrees. A sinusoidal function was fit to these data for each frequency according to Eq. 9, and the results are shown in Fig. 15. fit : C = A cos ( 2π 360 φ + φ 0) (9) where A is the amplitude of the cosine and φ 0 is an additional phase factor in units of radians. φ is measured in degrees. For each frequency, there is an arbitrary phase φ 0 that determines at what Figure 15: ADC counts as function of demodulator phase for amplitude=1, carrier gain=3, demodulator gain=0 and different frequencies (300, 600, 900, 1200 khz). demodulator phase the maximum will occur. Besides this, the period and peak to peak amplitude of the sinusoidal response does not depend on frequency, as shown in Fig. 15. ADC counts as function of amplitude Keeping the frequency, carrier and demodulator gain and phase constant (600kHz, 3, 0 and 170 degrees (peak phase), respectively), the number of ADC counts were measured as a function of varying amplitude. The results are shown in Fig. 16. It is obvious that the number of ADC counts follows a linear relationship with varying amplitude, as expected. The following function was fit: fit : C = A (10) 13

14 The result is a linear dependence of the number of ADC counts on the amplitude, as expected. As Figure 16: ADC counts as function of carrier amplitude for carrier gain=3, demodulator gain=0, demodulator phase at the peak amplitude, and carrier/demodulator frequency 600 khz. shown in the previous section, the amplitude is itself proportional to the voltage of the signal. In Sec. 5.3, we will combine these measurements to calibrate the power. ADC counts as function of carrier and demodulator gain Keeping the frequency, amplitude, demodulator gain and phase constant (600kHz, 1, 0 and 135 degrees (peak phase), respectively), the number of ADC counts were measured as a function of varying carrier gain. The results are shown in Fig. 17a. It is obvious that the results follow the pattern expected by the ratio in Eq. 8. The procedure was repeated, but instead of varying the carrier gain, we kept it at its minimum (0) and varied the demodulator gain. The demodulator gain, like the carrier gain, can vary between its minimum (0) and maximum (3) according to the relation: 0 : 1 : 2 : 3 = 0.99 : 4.76 : : (11) This is done by switching certain resistors in parallel with the circuit on or off, depending on how much gain we want. The results are shown in Fig. 17b. It is obvious that the results follow the pattern expected by the ratio in Eq. 11. The percentage difference between the expected and actual functions, as a ratio of the difference of the values divided by the expected value, was measured to be less than 20% for all points, and is shown in Fig. 18. The calibration of ADC counts as a function of carrier and demodulator gain yielded the expected results. Combining the two calibrations, we obtained the ratio of ADC counts per volt. Our measurement yielded ADC ADC V, which is within 5% of the documented value of V. In addition, our measurement of voltage as a function of amplitude V bolo (µv ) = 16.5A[V rms ] is within 10% of the expected value V bolo (µv ) = 15.15A[V rms ], where A is the amplitude in a scale 0 to 1 and V bolo is the rms voltage in µv. In Sec. 5.4 we attempt to explain the systematic uncertainties in these measurements that could explain these small discrepancies. 5.3 Cryogenic calibration After calibrating the DfMux system at room temperature, the next step is to calibrate it at cryogenic temperatures, using a heater. Our goal in this section is to calculate the relationship between the 14

15 Figure 17: (left) ADC counts as function of carrier gain for carrier amplitude=1, demodulator phase at the peak amplitude, demodulator gain=0 and carrier/demodulator frequency 600 khz, (right) ADC counts as function of demodulator gain for carrier amplitude=1, demodulator phase at the peak amplitude, carrier gain=0 and carrier/demodulator frequency 600 khz. Figure 18: Percentage difference between expected and actual ADC counts as function of demodulator gain for carrier amplitude=1, demodulator phase at the peak amplitude, carrier gain=0 and carrier/demodulator frequency 600 khz. 15

16 applied power on the heater, and the power that the TES bolometer detects. We used the heater shown in Fig. 19. The bolometer has a transition temperature of 525mK, so for our cryogenic calibration we cooled the heater down to this temperature. We performed a network analysis which gave a frequency spectrum with a peak at 479kHz. This peak corresponded to the frequency of the LC-tuned filter of the SQUID that measured the power of the heater. The resistance of the heater was measured to be R heater = 0.92Ω. The cryogenic box contains the heater/tes structure and the SQUID, tuned Figure 19: The heater/tes bolometer structure used for the cryogenic calibrations in this section. The heater is used to inject power in the system, and serves as the known power, to compare to the power measured by the TES bolometer. at 479kHz. When current goes through the heater/tes, the SQUID detects it and we measure it as ADC counts using the DfMux system. Using the calibration from the previous section, we can transform ADC counts back to current through the bolometer. We used a potentiometer of ten 1MΩ resistors. By adjusting a clippy between the resistors, we could specify how many resistors are used to bias the circuit. The voltage used to bias the circuit and drive current I b was V=9.3V. The bias current I b was then I b = V R = 9.3V nmω, where n is the number resistors participating in the circuit. The applied power on the heater is P applied = Ib 2R heat. The measured power on the bolometer was found for each applied power using the following procedure. We applied a voltage bias on the heater starting at maximum amplitude (1), and measured the ADC counts at this voltage bias, which correspond to the current through the TES bolometer. Then the voltage bias was slowly changed to smaller fractions of the maximum amplitude, and the ADC counts were measured at each point. Ohm s law is obeyed at this stage, as seen in Fig. 20a. When the bolometer enters its transition state, further reduction on the voltage bias would not result in an Ohmic reduction in ADC counts or current. The resistance of the bolometer at this point was taken to be R normal = V I. We kept dropping the voltage bias and recording the current until the resistance fell to 0.85R normal. Fig. 20a shows the TES bolometer IV curve for varying potentiometer resistance, and hence varying applied power. The units of the axes are in ADC counts for the observed current and carrier amplitude for the observed voltage bias, as this is raw data. The data point R = 0MΩ refers to the case when no power was applied on the heater, the IV curve was obtained using the same way. Using the calibrations described in the previous sections, the number of ADC counts were transformed to current through the heater/tes structure, and the carrier amplitude was transformed to voltage across the bolometer. The bolometer power was then found using P bolo = IV. This was repeated for different applied power, and the resistance of the bolometer R = V/I was plotted as a 16

17 function of P bolo, as shown in Fig. 20b. In this calculation of the resistance we used the calibrated voltage and current, as explained in the final paragraph, and shown in Eq. 13. We see that the resistance of the bolometer as it falls in the transition is 0.5Ω. Figure 20: (left) The observed ADC counts as function of the carrier amplitude for different applied resistance. The data point R = 0MΩ refers to no applied power, (right) The resistance of the bolometer as a function of the observed power of the bolometers for different applied power. The data point R = 0MΩ refers to no applied power. The minimum power for each of the IV curves was taken to be the measured power at the transition. The data point R = 0MΩ, for which no power was applied, showed a non-zero measured power. This shows that the bolometer detects some power, even when none is applied at the heater, and is accounted for by subtracting it from the measured power. The relationship between the applied power and the measured power minus the power at P applied = 0 was linearly fit, and the results are shown in Fig. 21. The following function can be used to calculate applied power, knowing the measured power. P applied = (P bolo P bolo@(papplied =0)) (12) According to other measurements, the expected slope in this relationship is 0.94, which corresponds to a discrepancy less than 10%, which is attributed to systematic uncertainties. Sec. 5.4 contains a discussion on the systematics. One naive way to confirm our previous measurements, is to calculate the measured power using the two alternative formulae: P bolo = I 2 R = V 2 R, where the resistance of the bolometer is R = 0.5Ω. In principle, we should get the same relationship between the applied and measured power. Fig. 22a shows the results on the same plot. It is surprising why the different formulae for obtaining the power would give different measured power for the same applied power. In particular, the slopes are different; for P = I 2 R slope=0.265, for P = V 2 /R slope=2.618, and for P = IV slope= We suspect that the calibration obtained at room temperature is not exactly valid for cryogenic temperatures. For this reason, we apply a scale factor to the voltage and the current, as follows, to correct the power, and resistance:, where α = , and β = P bolo = αiβv = (αi) 2 (βv )2 R = R R bolo = βv αi The results of the correction are shown in Fig. 22b. 17 (13) (14)

18 Figure 21: The applied power as a function of the observed power of the bolometer, minus the observed power at zero applied power. Figure 22: (left) The applied power as a function of the observed power of the bolometer, minus the observed power at zero applied power. The observed power was calculated with three different formulae, and yields different slopes, (right) The observed power is now corrected, using Eq. 13 and the points all lie on the fit line. 18

19 5.4 Systematic Uncertainties The calibration was done under controlled conditions, where the input signal was specified by the DfMux, and the output was measured with an oscilloscope. Measuring the peak to peak voltage on the oscilloscope is not the most precise method, since the signal refreshes at a constant rate and the values change. Using the average function of the oscilloscope allowed for a less variable peak to peak voltage. However, this procedure was still not perfect. Many values of peak to peak voltage were measured for some data points, to get a feeling of the variance in the measurement. The standard deviation σ was found to be 2% of the peak to peak voltage value. The values taken for the peak to peak voltage were used to calibrate voltage as a function of frequency, amplitude and gain. Having a 2% systematic uncertainty on the voltage measurement translates into a nσ uncertainty in the fit parameters, where n is the number of data points used in the fit. For n=9 data points, the systematic uncertainty is estimated to be 6%. Comparing the fit parameters obtained with two different methods led to a 0.4% difference in the estimation of the offset, and a 6% difference in the estimation of the slope, in the relationship V = α f +β. This shows that our estimation for the systematic uncertainty of the slope is valid. When measuring the ADC counts, the DfMux readout system was used. Due to the electronics noise between the measurement of the ADC counts, and the streaming of the data to the computer, a systematic uncertainty was introduced. To estimate this, repeated measurements of ADC counts were performed, and their average difference was taken as the standard deviation. For this systematic uncertainty, σ was found to be 1% of the ADC counts measured. This contributed as a nσ=2% total systematic uncertainty in the parameter estimation involving ADC counts. Every time the SQUID is operated, the feedback loop needs to be locked with values that have minimum excess voltage, or equivalently, magnetic flux trapped in the loop. In addition, any excess voltage introduces a small impedance in the circuit, and an associated voltage drop, which complicates the voltage measurements. Every attempt is made to minimize the excess voltage, by selecting values on the V Φ curve to bias the SQUID. However, we can only input biases to three significant figures after the decimal point. The best we can usually achieve is an excess voltage of the order of 10 3 V in the feedback loop. This value is low enough to keep the feedback loop stable, but can introduce small systematic uncertainties in the measurements of the voltage, especially at low bias. This effect is smaller than 1% for all the measurements in this document. There exist other systematic uncertainties that we are currently unaware of. To estimate these uncertainties, we take the difference between the power calibration and the expected calibration (10%) to be the total systematic uncertainty. The quadratic difference between the known systematic uncertainties, as already calculated in this section, and the total uncertainty, is the systematic uncertainty due to unknown factors. In this case, assuming the voltage calibration systematic is 6%, the ADC calibration systematic is 2% and the total uncertainty to be 10%, the unknown uncertainty is: 6 Testing the DfMux σ unknown = 10 2 ( ) = 7.74% (15) After performing our calibrations at room and cryogenic temperatures, we can use the readout system to measure unknown properties of SPTpol candidate detectors. In particular, we are interested to measure the optical coupling of TES bolometers. The optical coupling of the bolometers is a measure of the target temperature dependence of the optical power measured by the bolometer. 19

20 6.1 Optical coupling For this measurement, we kept the temperature of the bolometer near its transition point, at 438mK. We pointed the bolometer at a target at room temperature, 300K. Then, we took the I V load curve, while varying the amplitude from full-scale to lower values, until the bolometer falls in its transition and the load curve is no longer Ohmic. We repeated this measurement using liquid nitrogen as target. Liquid nitrogen boils slowly at 77K, so for the duration of the measurement the target temperature was steady at 77K. The power of the bolometer was calculated using the formula P = IV, as in Sec Fig. 23a shows the measured power, as a function of the voltage of the bolometer, which were obtained after calibration for both targets. The resistance of the bolometer was also measured as R = V/I. Corrections were applied to voltage and current, to account for the discrepancy between the calibration at 300K and cryogenic temperatures, as explained in Sec Fig. 23b shows the resistance as a function of power. We see that for higher power, the resistance is near its maximum, but after the power reaches its minimum point, the resistance of the bolometer rapidly falls, as the bolometer becomes superconductive. The resistance of the bolometer was measured to be R 1.3Ω, hence this measurement confirms our calibration. The power at the minimum point is taken to be the optical power at the transition. The difference of the optical power at the transition between the two targets is a measure of the optical coupling of the bolometer. Here, it was found to be: P = P 77K P 300K = = 15.07pW (16) The expected power difference is found using the Rayleigh-Jeans law, which gives the power of Figure 23: (left) The measured power of the bolometer as a function of the voltage across it, for different bolometer temperatures and target temperatures. (right) The resistance of the bolometers as a function of the measured power. blackbody radiation at a given temperature: P = k T ν ɛ filters ɛ thermal ɛ beam (17), where k is Boltzmann s constant, T is the target temperature difference, ν is the frequency range and ɛs are efficiency factors. In particular, the frequency range is assumed to be flat, ν = GHz. ɛ filters takes into account the efficiency of each filter between the target blackbody and the detector. ɛ thermal is the thermal efficiency of the window between the blackbody target and 20

21 the dewar, and ɛ beam is the beam efficiency, or the fraction of the stereo-angle that the detector is observing, which is illuminated by the blackbody target. Table 2 shows the various efficiencies. The temperatures in front of each filter refer to the temperature at which the filter is located, when the dewar is cryogenic. According to this calculation, the expected difference in power P is equal to Efficiency description Fraction mk filter mk filter K filter K filter K filter 0.9 thermal 0.77 beam 0.95 Table 2: The efficiencies for the optical coupling measurement pW. Comparing the expected with the measured optical power, we find an agreement to within 1% Systematic uncertainties Even though our measurement agrees with the prediction to a very accurate extent, there still exist some identifiable systematic uncertainties. In Fig. 23a, after the detector reaches its transition, the power is supposed to stay constant at its minimum value. Instead, here the power of the bolometer rises. At the same time, in Fig. 23b, the resistance is supposed to fall as a straight line at the transition state of the bolometer. Instead, there is a zig-zag feature that cannot be explained. We attribute both these effects to systematic uncertainties. To quantify them, the extent of the rise of the power is taken to be the magnitude of the systematic uncertainty and is estimated at 25% for the 77K target, and 20% for the 300K target. The uncertainty due to the zig-zag feature is about 10%. The following section will focus on measuring the noise performance of the system, which is itself the systematic uncertainty. 6.2 Next steps - Measuring noise of digital fmux readout system The noise performance of the DfMux readout system is expected to be a significant improvement over the current analog system. As in any readout system there is a component of white noise, which should be negligible if DfMux is well optimized. In addition, the digital system gives a significant improvement in 1/f noise, which is dominated by DAC output transistors. This noise can be monitored, or subtracted when well-characterized. Fig. 24 shows the measured noise on sky from SPT, which we are trying to reduce with the upgraded system. All the previous work in this section was done to confirm that the DfMux readout system is equivalent to the analog system currently in use. The main improvement that is expected comes in the noise performance. After we confirmed that the DfMux works as expected, we attempted to take the noise spectrum. Having no target at the bolometers, and operating below and above the transition of the bolometers, we obtained time streams of data for a duration of 5 minutes. When we obtained the power spectrum of these, we found that there were four peaks in the frequency spectrum, that were harmonic with each other, that we could not explain, as shown in Fig. 25. To reduce this, we 21

22 Figure 24: This figure shows the noise as measured by SPT. The various contributions are separated and shown analytically. The overall noise is expected to be reduced with the upgraded digital readout system. Figure 25: The noise spectrum with the initial frequency peaks. 22

23 added a filter in the connection between the SQUID controller and the DfMux board. This succeeded in reducing this noise, which dominated the time stream. Following this, the noise spectrum was taken again, but this time the time-stream had some spikes we could not explain. After following up with the demodulated signal, we saw that the spikes persisted in the sinusoidal of the demodulated signal, as shown in Fig. 26. Moving the SQUID bias along the Figure 26: a) The noise time-stream (blue) and the demodulated signal (green), with spikes at 6000, and arb. time units, b) zooming in one of the spikes and showing both the noise and the demodulated signal, c,d) zooming in each spike. V Φ curve was also attempted, in hopes that we just hit a spike in the V Φ curve, but the spikes are still there. We are currently in the process of narrowing down further where these spikes could come from, and then attack the problem at its source. Our current two options for the noise source are either the DfMux readout system or the SQUID controller. Once we are no longer dominated by these peaks, we can take the noise spectrum and characterize it, identifying its components. The components of the noise will be johnson noise, phonon noise, electronic noise and photon noise, and each will give a noise equivalent power. Combining the noise equivalent powers of these sources will lead to an estimate of our sensitivity, or how long we need to operate the polarimeter to detect to a certain resolution. 23

24 7 Conclusions We have succeeded in prototyping the digital fmux readout system. The system is now calibrated and can be used to measure the properties of candidate detectors for the polarimeter upgrade. For example, the optical constants of a bolometer were measured with an accuracy better than 1%. Even though the DfMux already detects less noise than the current readout system, more work is needed to understand all the external sources of noise and minimize them. This will enable us to calculate the noise equivalent power, and combining it with the expected signal we can extract the sensitivity of our instrument. This SPT upgrade will make possible a more precise measurement of the CMB polarization anisotropies, which will describe the angular power spectrum of the B-mode polarization. Better measurements of the Ω m and Ω b cosmological constants will put constraints on Dark Matter properties, such as the neutrino mass. Gravitational wave B-mode detection will be possible for a specific gravitational wave model. Acknowledgements I would like to thank Prof. John Carlstrom for allowing me to work on this project. The completion of this project would have not been possible without the help and direction of Clarence Chang. Thanks to Lindsey Bleem and Abigail Crites for helping me learn the ropes. References [1] H. Spieler, Frequency Domain Multiplexing for Large Scale Bolometer Arrays, Monterey Far-IR, Sub-mm and mm Detector Technology Workshop proceedings, 2002, pp [2] T.M. Lanting et al., Frequency domain multiplexing for bolometer arrays, Nuclear Instruments and Methods in Physics Research A vol. 520, 2004, pp [3] T.M. Lanting, MUX Readout of Superconducting Bolometers, 2007 UC Berkeley Ph.D Thesis. [4] M. Dobbs, E. Bissonnette, and H. Spieler, Digital Frequency Domain Multiplexer for mm- Wavelength Telescopes, IEEE Transactions on Nuclear Science, TNS R2, 2008 [arxiv: v1]. [5] J. Ruhl et al.,the South Pole Telescope. In J. Zmuidzinas, W. S. Holland, and S. Withington, editors, Astronomical Structures and Mechanisms Technology. Edited by Antebi, Joseph; Lemke, Dietrich. Proceedings of the SPIE, Volume 5498, pp (2004)., pages 1129, Oct [6] R. Sunyaev and Y. Zeldovich. The spectrum of primordial radiation, its distortions and their significance. Comments Astrophys. Space Phys., 2:66, [7] E. Komatsu and U. Seljak. The Sunyaev-Zeldovich angular power spectrum as a probe of cosmological parameters. MNRAS, 336: , Nov astro-ph/ [8] Z. Staniszewski et a;. Galaxy clusters discovered with a Sunyaev-Zel dovich effect survey arxiv: [9] R.S. Bhatia et al., Closed cycle cooling of infrared detectors to 250 mk Cryogenics 42, 2002, pp