The side lobes are higher in the center of the focal plane and fall off radially. The width varies radially across the focal plane, with the greatest widths in the center of the focal plane.
The Journey to Modern Cosmology
The Expanding Universe
Even before the highly accurate measurements of the density of the universe that can be made today, in the 1960s and 1970s it was believed that 0.01 ≤Ωtotal ≤10. The Friedmann equation will be important in the discussion of the motivations for an inflationary universe in §1.3.
The Homogenous, Isotropic Universe
During these early times the density of the universe was so high that matter was in approximately thermal equilibrium at every point in space. If the predictions of the Big Bang model are correct, the universe should be filled with radiation from a cold blackbody, with a temperature that is inversely proportional to the scale factor a.
Problems with Standard Cosmology
- The Flatness Problem
- The Horizon Problem
- Magnetic Monopoles
- A Solution to the Problems
Why should the density of the universe immediately after the big bang be so close to the critical density? In this model, an exponential expansion of the universe occurs while the universe is trapped in a false vacuum state.
Inflation Theory
Basics
A decreasing Hubble radius means that large scales entering the universe at this time were within the horizon before inflation, and thus had time to become homogeneous. To solve the cosmological problems outlined in the previous section, we not only want the universe to expand exponentially, but also to expand over a sufficiently long period of time.
Slow-roll Inflation
As mentioned in §1.1.1, for cosmological calculations we usually assume that the energy-momentum tensor is of the form describing a perfect fluid. This is the same situation as described at the end of §1.3.1, which, as we have already pointed out, results in an accelerated expansion of the universe.
Perturbations
The density fluctuations caused by inflation are adiabatic (by this we mean that the perturbations in the density of all components of the universe are correlated), Gaussian and uncorrelated (ie the phases of the Fourier modes describing the fluctuations on different scales are not correlated). The existence of tensor perturbations is one of the most important predictions of the theory of inflation, as it can be verified observationally by measurements of the polarization of the cosmic microwave background (it will be explained in the next section).
How to Detect Inflation
CMB Temperature Anisotropies
We typically multiply this quantity by `(`+ 1) for plots of the CMB power spectrum (see Fig. 1.3). One of the most notable features of the CMB power spectrum is the series of peaks.
CMB Polarization
- Stokes Parameters
- Thomson Scattering
This vibration re-radiates light with a direction of polarization parallel to the direction of oscillation. These B-lensing modes come from the gravitational lensing of the E-mode spectrum from all the matter between us and the CMB.
Predicted Polarization Spectra
The contribution of inflationary gravitational waves to the B-mode spectrum peaks on angular scales of about two degrees, while gravitational lensing of the CMB causes B-modes on smaller angular scales.
Polarized Foregrounds
Synchrotron Radiation
Dust
The optimal 2% of the sky has polarized dust emission that is an order of magnitude smaller than the nominal field. Large-scale (` ≤ 10) polarized dust emission is expected to be at least an order of magnitude brighter than ther= 0.03 primordial B-mode spectrum at 90GHz.
Honorable Mentions
Our field of view will include the clearest 2% of the sky accessible by a McMurdo flyby, where the polarized dust emission is expected to be an order of magnitude smaller than the levels shown in the left panel of Fig. One of the characteristics of the dust magnet is that its polarization direction will change with frequency, and thus it should be able to be separated from the CMB signal [58].
CMB Polarization Measurements
The BB curve shows both the inflationary gravitational wave and lens components. a) The B-mode map observed by the BICEP2 telescope. Much of the optical and telescope design is based on the very successful BICEP1 [91] and BICEP2 [69] experiments.
The Cryostat
Installing these blankets is painstaking and slow due to their proximity to very delicate parts (eg the shaders). A finite element analysis of the SPIDER flight cryostat shows that the flight cryostat meets all these requirements [41].
Inserts
- Cold Plate
- Truss
- Lenses
- Cooled Optics Sleeve
- Magnetic Shielding
- Filters, Shaders, and Windows
Early in the creation of the SPIDER lens, we discovered that the AR coating process was significantly changing the shape of the lens (see Fig. 2.5). A significant portion of the power from the SPIDER beam ends up in this cold stop (approximately 25%).
Half-wave Plates
Instead of a hot-press adhesive, the AR coating process for the 90GHz waveplates uses a small drop of adhesive (Eccobond 24) in the center of the quartz to attach it to the sapphire. Later tests of the HWPs were performed in the SPIDERtest cryostat and the flight cryostat.
Focal Plane
The FPU is supported by eight stainless steel heat capacity blocks, which provide the cooling path from the FPU to the 10 stp-liter3He refrigerator (made by Simon Chase Research). This cooling path is purposefully designed to be slow, to silently thermally disconnect the FPU from the fridge.
TES Bolometers
Microfabrication
Gold heat sink frame and island gold layer - deposited by e-beam evaporation and patterned by lift-off. The input radiation excited electric fields horizontally across holes cut from the niobium ground plane.
Bolometer Theory
- Thermal Model
- Electrical Model
For small signals, the resistance of the TES can be expanded to first order as R(T, I)≈R0+ ∂R. This equation shows the dependence of the TES resistance on both the temperature and the electric current.
SQUIDS
All components on the right side of the diagram are outside the cryostat at room temperature. Summing coil SQ1 supplies current to the second SQUID stage (SQ2) for each of the 16 columns in the FPU.
Multi-Channel Electronics
Part of the tuning process for the SPIDER system involves choosing a single TES bias for all TESs in a column that gets as many detectors as possible at the transition.
Ballooning
The Gondola
In addition to the nacelle frames, this diagram also shows the sunshades and two star cameras on the bottom of the cryostat. The nacelle design is also driven by the need for the cryostat to survive the impact shock when the payload detaches from the balloon at the end of flight.
Pointing Systems
CSBF provides an impact damping system that will attach to the bottom of the payload to control some of the forces during landing. The nacelle is designed to protect the cryostat in the event of a rollover after landing.
Observing Strategy
Frequency Coverage
These requirements are based on the need to maintain pointing accuracy as the weight (and center of mass) of the payload changes during flight (either due to falling ballast or helium evaporation). Both panels show the same part of the sky in equatorial coordinates, smoothed with a 30-angle beam.
Sky Coverage
Full air temperature and polarization maps are then simulated using the synfast program, which is part of the HEALPix software package. These maps are then smoothed by a Gaussian beam of the same width as the SPIDERbeam (which has been measured to be approximately Gaussian).
Relative Gain Uncertainty
Spectral Differences
The spectrum of each detector was measured in the test cryostat or the flight cryostat (see §4.5). An archive version of this measurement will also be performed in the flight cryostat prior to flight.
Beam Systematics
- Differential Beam Width
- Differential Pointing
- Differential Ellipticity
- Measuring the Beam Function
The simulation found that the residuals for this value of the differential ellipticity were negligible at the angular scales that SPIDER cares about. It is possible to try to measure the beam function B` (and thus the width) of the SPIDER detectors without mapping the beams directly.
HWP Non-Idealities
Ghosting
A highly reflective HWP can cause ghost beams that have amplitudes up to 10% of the main beam amplitude, which can cause a large contamination of the time course of each detector. That is, a ghost contamination of 1% indicates that the ghost beam has an amplitude of 1% of the time course of the main detector.
Telescope and Detector Pointing
In Palestine, Texas, we tested the fully integrated pointing system during SPIDER's pre-flight integration and expect to be able to reconstruct the pointing system within our benchmark. That camera's aiming solution is accurate to within a minute of arc, which meets our benchmark target.
Polarization Rotation Systematics
The BICEP1 experiment used this technique to improve their physical measurements of absolute polarization angle [56]. The relative polarization angle (which determines the cross-polar response, ) is the angle between two detectors in a pair.
Polarized Sidelobes
To keep this systematic effect to only a few percent, the calibration target for the accuracy of the absolute polarization angle is set to <1◦ [62]. The BB spectrum derived from the SPIDER sidelobe model is much weaker at low multipoles and essentially negligible at l-80, which is the angular scale of the inflation peak.
Cross-Talk
Noise
Noise Model
- Photon Noise
- Johnson Noise
- Thermal Fluctuation Noise
- Amplifier Noise
- Excess Noise
It is a function of TES temperature and typically has a value between 0.5 and 1. Although not a major contribution to the total noise of the SPIDER detectors, it leads to a total amplifier noise NEI of about 45 pA /√.
Total Noise
Our measured noise slightly exceeds the noise predicted by the model, especially at kilohertz frequencies, where we see "excess noise" in our noise spectra (see the gray spectrum in Figure 3.12). The main concern with the excess noise is that it will be diverted back into the science band, as a significant amount of power from the excess noise exceeds the Nyquist frequency of our readout system.
Expected Performance
So, while an individual Planck detector has lower noise than an individual SPIDER detector, SPIDER has so many more detectors on the sky (thousands, up to Planck's eight) that the final map depth for SPIDER is expected to be lower. SPIDER is expected to have smaller error bars than both BICEP2 and Planck at multipoles corresponding to the peak of the gravitational wave spectrum.
Conclusion
The characterization of the SPIDER instrument consists of measurements of the optical efficiency, detector device parameters, mm-wave spectral bands, noise and beams. We use our measurements of the SPIDER detectors to help select good detectors for deployment and to feed information back to the manufacturing team that will help improve the detectors.
The Loadcurve
If the temperature on the island increases, the resistance of the TES will also increase and the Joule power will decrease, cooling the island. As the temperature on the island decreases, the resistance of the TES decreases and the Joule power increases, causing the island to warm up.
Measuring Device Parameters
The parameter Go will mainly influence the slope of the fit, while β will influence the curvature. A measurement of the device parameters is only possible during dark runs (when the focal plane is covered by a 300 mK plate) or on the (always) dark TES detectors.
Optical Efficiency
A complete description of the optical efficiency as a function of frequency requires the detector's spectral passband, F(ν). Plots of the optical responses and efficiencies of each detector can be found in Figs.
Bandpass Spectra
The FTS
Interferograms and Spectra
If the blue lines are the wires of the wire grid, ˆpoints along the wires, ˆbpoints perpendicular to the wires, ˆxpoints east in figure. In addition, we divide the spectra by ν2 to correct for the blackbody emission from the source.
Noise
Optical and Electrical Gain
Differential Pointing
The differential pointing in the vertical (y) direction is believed to be caused by gradients in the films used to fabricate the detectors. -5.9), our aircraft detectors have typical differential pointing values of 2-3% and are well within our benchmark values. a) An example of the beams from an A/B pair and their difference beam from SPIDER Run 8.0 (an early test of X3) in the Caltech test cryostat.
Differential Width
Differential Ellipticity
Beam Steer
From this we concluded that the beam steering is a problem in tile manufacturing and is not related to the optical elements in the SPIDER telescope. Furthermore, we see that the effect does not propagate into the far field of the telescopes, as can be seen in the far field maps mentioned earlier. a) An example of a near-field beam map where the beam shows significant misalignment.
Other Beam Effects
Sidelobes
Near Sidelobes
Comparison of mean beam profiles to 1 degree for maps taken with a thermal source and a rotating polarized source (RPS). Inner corner' refers to pixels near the center of the focal plane (in the inner corner of the tile).
Far Sidelobes
During our deployment to Palestine, Texas, we attempted to get a rough measurement of the far side lobes by scanning the cryostat over an amplified sound source. The 90GHz IMPATT source was mounted on the roof of the tall cabinet and pointed down toward SPIDER.
Using Beam Maps to Test Half-Wave Plates
Beam Effects
The points for HWP=0-HWP=45 (green) show a small deviation from zero in the vertical direction.
Ghosts
Most is transmitted through the HWP as the main beam (black), but a small portion is reflected back through the optics (green) and then bounces off the FPU and exits the optical assembly as a fog beam (red). .
Diffuse Scattering
Polarization Efficiency and Rotation
Caltech Measurement
- Polarization Dependence of Beam Centers
Palestine Measurement
Current Status
Suggestions for future work
Simulations
Preparation for flight
The Future of CMB Polarimetry
Conclusion
S PIDER noise model with a comparison to an actual noise spectrum. The blue
A forecast of the S PIDER statistical error bars on the B-mode spectrum in
A simplified version of the detector circuit diagram. The voltage V BIAS is
Optical Efficiency in pW/K RJ for all FPUs (test cryostat)
Histograms of optical efficiency in pW/K RJ for all FPUs (test cryostat)
Optical Efficiency in % for all FPUs (test cryostat)
Histogram of optical efficiency in % for all FPUs (test cryostat)
Normal resistance in mΩ for all FPUs (test cryostat)
Histograms of normal resistance in mΩ for all FPUs (test cryostat)
Diagrams of the FTS and the wire grid beam splitter
Histograms of bandcenter in GHz for all FPUs (flight cryostat). Figures cour-
Estimated spectral bandwidths (fractional) for all FPUs (flight cryostat). Fig-
Detector bandpass spectra vs. atmosphere at 30km for all FPUs (flight cryo-
Example noise spectra at two different biases
Noise equivalent current and noise equivalent power versus TES resistance
The relative optical and relative electrical gains plotted against each other
Beam widths for all FPUs
Histogram of beam widths (FWHM) for all FPUs
Beam ellipticity for all FPUs
Histograms of beam ellipticity for all FPUs
Differenced beam maps showing the change in differential pointing between
Differential pointing for all FPUs
Histograms of differential beam ellipticity for all FPUs
A-B pointing differences for all FPUs
Differential beam width for all FPUs
Histograms of differential beam width for all FPUs
Differential beam ellipticity for all FPUs
Histograms of differential beam ellipticity for all FPUs
Material Properties for S PIDER optics
S PIDER Systematics Table
HWP Parameters used for simulations
Noise Budget for 90GHz and 150GHz detectors
Device Parameters for all FPUs
Optical Efficiencies for all FPUs
Bandcenters and Bandwidths for all FPUs
Beam Parameters for all FPUs
Differential Beam Parameters for all FPUs
Polarization Efficiency and Rotation Measurement I
Polarization Efficiency and Rotation Measurement II
