Assessment of a Rubidium ESFADOF Edge-Filter as ... - tuprints

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12 2 Remote Sensing of the Water Column: The Brillouin-Lidar ∆x = √ ( ( c 2 2 t c ∆t) + 2n H2 O 2n 2 ∆n H2 O) (2.2) H 2 O √ ( c 2 ( = ∆t) + x ∆n ) 2 H 2 O , (2.3) 2n H2 O n H2 O where ∆t represents the longest time uncertainty in the signal processing chain and ∆n H2 O the uncertainty in refractive index. State-of-the-art signal processing is available on a ns time scale [38], so that the dominant temporal uncertainty can be reduced to the pulse length τ. The last term of Eq. 2.2 accounts for the temperature and salinity dependence of the refractive index, which themselves are bound to uncertainties. However, it can be neglected for principal considerations, but has to be included in the final implementation of the signal post-processing, as its contribution increases with increasing penetration depth x. A pulse length of τ = 10 ns has been chosen in order to satisfy the tradeoff between the spatial resolution of the profile measurement and the accompanied accuracy limitations of the temperature measurement [17]. On the one hand, the pulse length defines the resolution cell beneath the water surface, which can be computed to ∆x = 1.13 m, when neglecting the refractive index contribution. But on the other hand, as the spectral width of the laser pulses are connected through the Fourier transform limit to their pulse length, they define the amount of additional spectral broadening of the Brillouin–scattering. Shorter pulse lengths would certainly increase the spatial accuracy of the depth profile, but would artificially broaden the spectral response of the Brillouin-scattering through the Fourier transform limit and hence decrease the accuracy of the temperature measurement (cf. Sec. 2.2.3). 2.2.2 Brillouin–Scattering As already mentioned in Sec. 2.1, the proposed Brillouin–lidar explores spontaneous Brillouin–scattering as the temperature tracer. It takes advantage of permanently available density fluctuations, which propagate with the speed of sound inside the medium. The latter is temperature dependent. Specifically, light propagating in water is inelastically scattered off these moving density fluctuations, where a momentum transfer to or from the sound waves occurs (cf. Fig. 2.2). First descriptions of the underlying physics have been independently given by Mandel’shtam in 1918 [27] and by Brillouin in 1921 [28]. A good overview on this topic can be found in the books of Fabelinskii [31] and Berne and Pecora [65]. The density fluctuations result in a modulation of the dielectric constant, which can be decomposed into two terms: (1) The first term originates from isentropic density fluctuations, which propagate at the speed of sound in all directions. They are responsible for the inelastic Brillouin–scattering. (2) The isobar fluctuations of the entropy do not propagate and result in the elastic Rayleigh– scattering [31, 65]. Thus, the Brillouin–scattering is sensitive to the local velocity of sound.
2.2 System Requirements 13 Fig. 2.2: Schematic drawing of the Brillouin-scattering: The incident light is inelastically scattered off permanently available density fluctuations, where the conservation of momentum translates into the depicted Bragg–condition. Due to the symmetry of the process, both propagation direction of the sound waves have to be considered, though only the blue shifted case, which results into a momentum transfer from the water to the light wave, is depicted. The isotropic scattering process covers the whole polar and azimuthal angles, φ and θ respectively. By decomposing the density fluctuations into Fourier components, it is possible to extract the resulting frequency shift ν B from the conservation of energy and momentum (cf. Fig. 2.2). Let k and ω denote the wavevector and the angular frequency of the incident light wave. Then, the scattered light wave, denoted by k ′ and ω ′ respectively, results from the conservation of energy and momentum ω ′ = ω ± ω S (2.4) k ′ = k ± k S , (2.5) where k S and ω S denote the wavevector and the angular frequency of the involved sound wave respectively. The ± sign accounts for the different propagation directions of the sound wave. When considering the fact, that the scattered wave vector changes only little in absolute value, i.e. that |k ′ | ≈ |k| = k is valid, the following relations hold for k S : k 2 S = ∣ ∣k ′ − k ∣ ∣ 2 = k’ 2 + k 2 − 2k ′ k = 4k 2 sin 2 θ 2 (2.6) k S = ±2ksin θ 2 = ±4π n H 2 O λ sin θ 2 . (2.7) It is obvious, that the scattered light wave undergoes a frequency change of ω S due to the mentioned conservation of energy and momentum (cf. Eqs. 2.4 and 2.5).
Page 1 and 2: INSTITUT FÜR ANGEWANDTE PHYSIK TEC
Page 3: Abstract Global and local climate c
Page 7: Pentru Alexandru şi Florina
Page 10 and 11: II Contents 4.3 Measurement Unit .
Page 12 and 13: 2 1 Introduction wide sea currents
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5 Discussion of the Experimental Re
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5.1 Overview of the Experimental Pa
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5.1 Overview of the Experimental Pa
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5.2 Vapor Cell I: 270 mT 95 5.2 Vap
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5.2 Vapor Cell I: 270 mT 97 0.20 5.
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5.2 Vapor Cell I: 270 mT 99 Fig. 5.
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5.2 Vapor Cell I: 270 mT 101 introd
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5.2 Vapor Cell I: 270 mT 103 Fig. 5
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5.2 Vapor Cell I: 270 mT 105 which
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0.15 ∆ν P = 0.98(2) GHz 5.2 Vapo
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5.3 ESFADOF Operational Limits 109
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cesses of the atomic vapor. This al
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Fig. 5.18: Rubidium Grotian energy
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5.4 Vapor Cell II: 500 mT 133 maxim
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5.4 Vapor Cell II: 500 mT 137 such
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6 Conclusion and Outlook The presen
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6 Conclusion and Outlook 141 pulses
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6 Conclusion and Outlook 143
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Appendix
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148 A Rubidium Atom 2. Relevant ato
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B Manufacturing process of Rb Vapor
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B Manufacturing process of Rb Vapor
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C Magnetic Field Strengths of the E
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D Tripod ECDL Fig. D.1: Schematic o
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160 References [10] G.L. Mellor and
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162 References [41] E.S. Fry, J. Ka
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164 References [69] Claude C. Leroy
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166 References [97] L. Goldberg, D.
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168 References [125] Cord Fricke-Be
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170 References [158] Triad Technolo
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172 References [186] M. Cheret, L.
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Curriculum Vitae Alexandru Lucian P
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178 1 Publications Conference Proce
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Supervised Theses Denise Stang, Wei
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184 1 Danksagung Bei Herrn Arno Wei
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