Abstract
The cosmic microwave background radiation (CMB) is now firmly establishedas a fundamental and essential probe of the geometry, constituents, and birth ofthe observable universe. The CMB is a potent observable because it can bemeasured with precision and accuracy. Just as importantly, theoretical models ofthe universe can predict the characteristics of the CMB to high accuracy, andthose predictions can be directly compared to observations. There are multipleaspects associated with making a precise measurement. In this chapter, we focuson optical components for the instrumentation used to measure the CMBpolarization and temperature anisotropy. We begin with an overview of generalconsiderations for CMB observations and discuss common concepts used inthe community. We next consider a variety of alternatives available for adesigner of a CMB telescope. Our discussion is guided by the ground- andballoon-based instruments that have been implemented over the years. In thesame vein, we compare the arc-minute resolution Atacama CosmologyTelescope (ACT) and the South Pole Telescope (SPT). CMB interferometersare presented briefly. We conclude with a comparison of the four CMBsatellites, Relikt, COBE, WMAP, and Planck, to demonstrate a remarkableevolution in design, sensitivity, resolution, and complexity over the past30 years.
Keywords:
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- 1.
The factor of \(\ell (\ell + 1)/2\pi \) (Bond and Efstathiou 1984), as opposed to the possibly more natural \(\ell (2\ell + 1)/4\pi \) (Peebles 1994), is derived from the observation that the cold dark matter model, without a cosmological constant, approaches \(\ell (\ell + 1)\) at small \(\ell \) for a scalar spectral index of unity. Needless to say, the model that gave rise to the now-standard convention does not describe nature. Another choice would be \({(\ell + 1/2)}^{2}\) because the wavevector \(k \rightarrow \ell + 1/2\) at high \(\ell \). There is not a widely agreed upon letter for the plotted power spectrum. We use \(\mathcal{B}\) for both “bandpower” and J. R. \(\mathcal{B}\)ond who devised the convention. The term bandpower refers to averaging the \({\mathcal{B}}_{\ell }\) over a band in \(\ell \).
- 2.
- 3.
The Airy beam profile is given by \(B(\theta ) = {[2{J}_{1}(x)/x]}^{2}\) where x = πDsin(θ)/λ and J 1 is a Bessel function. The value of 1. 22λ/D is the angular separation between the maximum and the first null. For small angles, θ 1/2 = 1. 03λ/D. The total solid angle is \(2\pi \int \nolimits \nolimits {B}_{n}(\theta )\sin (\theta )d\theta \). To make the integral simple and avoid considering the difference between projecting onto a plane versus a sphere, we consider the limit of small θ. Then, \(\Omega = 8{\lambda }^{2}/\pi {D}^{2}{ \int \nolimits \nolimits }_{0}^{\infty }{[{J}_{1}(\pi Dx/\lambda )]}^{2}{x}^{-1}dx = {\lambda }^{2}/A\).
- 4.
In a close packed array, this may be approximated having the pixel size smaller than λ. Such a spatial mode would support two polarizations.
- 5.
The inflation-generated gravity waves also contribute to the temperature anisotropy and thus can be constrained by such measurements.
- 6.
1 pWatt = 10− 12 W.
- 7.
Spatial turbulence in the atmosphere is parametrized in terms of a Kolmogorov spectrum (Tatarskii 1961; Church 1995; Lay and Halverson 2000) that depends on the spatial wave number q as either q − 11/3 or q − 8/3 depending on whether the turbulent layer is three- or two-dimensional. Thus at large angular scale, low q, atmospheric fluctuations can be quite large.
- 8.
For bolometric systems on can simply imagine the difference of two intensity measurements. For coherent or interferometric systems, the square law detector outputs the product of two differently polarized electric fields.
- 9.
For example, the BLAST balloon payload (Pascale et al. 2008), which had frequency bands between 600 and 1,200 GHz, had a centered Cassegrain system with a 2-m aperture primary providing a resolution of 30′′ at the highest frequency.
- 10.
Currently, record duration for a science payload in an Antarctic flight is close to 42 days (Seo et al. 2008). NASA is developing capabilities for flights of 100 days.
- 11.
Note that parameterizing the detector spacing or the feedhorn aperture in units of the focal ratio, F, times the wavelength, λ, provides sufficient information to approximate the aperture efficiency, spillover efficiency, and other relevant optical quantities for estimating the mapping speed.
- 12.
Throughput calculations assume (10.6) taking the entrance aperture diameter and the total FOV available by the optical system of the experiment. A significantly smaller throughput value can be obtained by taking the throughput per detector element and multiplying by the number of detectors implemented. We opt for the first version because our primary interest in this chapter is in the overall optical design independent of the choice of detector spacing on the focal plane.
- 13.
- 14.
The term “powered” reflectors refers to reflectors with focusing properties, rather than flat reflectors used to only fold the path of the beam.
- 15.
Graham (1973) first suggested introducing such a tilt in a decentered Cassegrain telescope to eliminate the cross polarization introduced by the asymmetrical configuration of the two reflectors. Subsequently, Mizuguchi and Yokoi (1974) and Mizugutch and Yokoi (1975), and later others (e.g., Mizugutch et al. 1976; Mizuguchi et al. 1978; Dragone 1978), made the idea more quantitative, expanded it to a Gregorian system, and to a system with more than two reflectors. (Some papers are published with Mizugutch in place of Mizuguchi.) The primary motivation in these studies remained the elimination of cross polarization at the center of the FOV. Thus, a decentered Cassegrain or Gregorian optical system with a tilt between the axes of symmetry of the primary and secondary is sometimes referred to as a “Mizuguchi-Dragone telescope.” In a series of publications in the early 1980s, Dragone analyzes aberrations in decenetered reflecting system. It so happens that the tilt that cancels cross polarization also cancels astigmatism.
- 16.
In a parallel development, Vokurka (1980) proposed a ‘crossed configuration’ made of two cylindrically parabolic mirrors for an improved compact test range antenna. This crossed concept was expanded by Dudok and Fasold (1986) - also in the context of compact test range antenna - to a Cassegrain system similar to the one proposed earlier by Dragone, albeit without the various tilts and shape changes that reduce aberrations.
- 17.
Differential gain also arises when other factors in the system affect gain between two polarization states, for example, when two independent detectors that are sensitive to the two polarization states have different responsivities.
- 18.
A 1.2 K nearly unpolarized signal is generated by the 0.5% emissivity. This signal is differentially polarized at the 1% level.
- 19.
The 2.7 K CMB monopole can also lead to a polarized signal through instrumental polarization. However, the magnitude of this signal is a constant across the observation, and since essentially all CMB polarimeters are differential, they are not sensitive to this overall offset.
- 20.
- 21.
We note that this optimization approach in which the conic constants of both reflectors are simultaneously optimized across a flat focal plane is different from the optimization discussed in Hanany and Marrone (2002), where the focal plane shape and position were optimized to provide the largest DLFOV.
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Acknowledgments
The authors are collaborators on just a subset of the instruments discussed in this chapter. We have learned about other optical system through papers and talking with colleagues, though all errors are of course ours. We would especially like to thank Elia Battistelli, Cynthia Chiang, Nils Halverson, Bill Jones, Akito Kusaka, Jeff McMahon, Lucio Piccirillo, Jon Sievers, Suzanne Staggs, Ed Wollack, and Sasha Zhiboedov for discussions and suggestions that improved this chapter. Ed Wollack in particular made numerous helpful comments. We also thank Chaoyun Bao, Angela Glenn, Michael Milligan, and Keith Thompson for help with the figures.
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Hanany, S., Niemack, M., Page, L. (2013). CMB Telescopes and Optical Systems. In: Oswalt, T.D., McLean, I.S. (eds) Planets, Stars and Stellar Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5621-2_10
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