Coherent Backscattering from Multiple Scattering Systems - KOPS ...

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5 Experiments E sample (t) / E half−space (t) 1 0.8 0.6 0.4 0.2 0 free space distribution half−space distribution −9.5 −9 −8.5 −8 −7.5 −7 −6.5 −6 log 10 (t [sec]) Figure 5.2: Comparison of the albedos. The time-dependent albedos A(t) of an absorbing cut-out of the free space (solid line) and respectively a half-space (dashed line) at the position of the sample are similar enough to replace the latter by the former in the calculation of the total albedo. Calculations for teflon sample with radius R = 20 mm, thickness L = 50 mm, diffusion coefficient D = 16500 m2 /s, absorption time τ = 3.3 ns, transport mean free path l ∗ = 220 µm, refractive index n = 1.35. be equal to one, meaning that the incoming light power P in is equal to the scattered power P out of a lossless sample. The albedo can therefore also be defined as A = P with losses P lossless = ∫ ∫ ∫ surface ∫ surface j with losses (⃗r ⊥ , t) d⃗r ⊥ dt j lossless (⃗r ⊥ , t) d⃗r ⊥ dt (5.3) In our multiple scattering samples, most of the loss of light energy is due to absorption. If it were the only reason for energy loss, the albedo could be easily calculated as A(τ) = 1 − 2(l∗ +z 0 ) e− √ Dτ (5.4) 2(l ∗ +z √ 0 ) Dτ with diffusion coefficient D, absorption time τ, and penetration depth z 0 . However, as the samples are not infinitely large, one can not a priori exclude that losses at the side and rear boundaries have significant influence on the photon distribution in the sample. Unfortunately there is no expression for the photon density distribution in a 3-dimensionally confined absorbing medium. Therefore we approximate the losses in a sample with finite radius R and thickness L by comparing the energy inside the non-absorbing infinite half- 46
5.1 Conservation of energy in coherent backscattering Calculation with free space photon density distribution: 0 t = 10 −11 s 0 t = 10 −10 s 0 t = 10 −9 s 1e8 z [mm] 10 20 30 10 20 30 10 20 30 1e6 1e4 40 40 40 1e2 50 −20 0 20 r [mm] 50 −20 0 20 r [mm] 50 −20 0 20 0 r [mm] Calculation with photon density distribution of the infinite half-space: 0 t = 10 −11 s 0 t = 10 −10 s 0 t = 10 −9 s 10 10 10 1e6 z [mm] 20 30 20 30 20 30 1e4 40 40 40 1e2 50 −20 0 20 r [mm] 50 −20 0 20 r [mm] 50 −20 0 20 0 r [mm] Figure 5.3: Calculated photon density distributions in the Teflon sample. The upper row shows the density distributions calculated as a cutout of free space, the lower row as a cutout of the infinite half-space. Note that the color axes are logarithmic. Assumed sample parameters: radius R = 20 mm, thickness L = 50 mm, diffusion coefficient D = 16500 m2 /s, absorption time τ = 3.3 ns, transport mean free path l ∗ = 220 µm, refractive index n = 1.35. 47
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Dissertation Coherent Backscatterin
Page 3 and 4: Ein kurzer Überblick Streuung ist
Page 5 and 6: Ein kurzer Überblick portweglänge
Page 7 and 8: Contents Ein kurzer Überblick i Da
Page 9 and 10: 1 Introduction There have been many
Page 11 and 12: 2 Theory In scattering theory, the
Page 13 and 14: 2.2 Single scattering - Mie theory
Page 15 and 16: 2.2 Single scattering - Mie theory
Page 17 and 18: 2.3 Random walk and diffusion scatt
Page 19 and 20: 2.3 Random walk and diffusion of pr
Page 21 and 22: 2.4 The influence of boundaries Fig
Page 23 and 24: 2.5 Photon flux from a surface The
Page 25 and 26: 2.6 On polarization and interferenc
Page 27 and 28: 2.6 On polarization and interferenc
Page 29 and 30: 2.7 The theory of coherent backscat
Page 31 and 32: 2.7 The theory of coherent backscat
Page 33 and 34: 3 Setups 3.1 Laser System The key p
Page 35 and 36: 3.2 Wide Angle Setup 1 .0 0 .8 h e
Page 37 and 38: 3.3 Small Angle Setup 1 0.998 0.996
Page 39 and 40: 3.3 Small Angle Setup Figure 3.6: T
Page 41 and 42: 3.4 Time Of Flight Setup Figure 3.8
Page 43 and 44: 4 Samples 4.1 Sample characterizati
Page 45 and 46: 4.1 Sample characterization techniq
Page 47 and 48: 4.2 The samples sample particle siz
Page 49 and 50: 4.2 The samples Figure 4.5: Fluidiz
Page 51 and 52: 5 Experiments 5.1 Conservation of e
Page 53: 5.1 Conservation of energy in coher
Page 57 and 58: 5.1 Conservation of energy in coher
Page 65 and 66: 5.2 The coherent backscattering con
Page 77 and 78: 6 Summary The focus of the work pre
Page 79 and 80: Bibliography [1] http://www.schneid
Page 81 and 82: Bibliography [34] E. Larose, L. Mar
Page 83 and 84: Figures and Tables Figures Backscat
Page 85 and 86: Figures and Tables Tables 4.1 Collo
Page 87 and 88: MATLAB codes Angular intensity dist
Page 89 and 90: Evaluation of the wide angle data E
Page 91 and 92: Evaluation of the wide angle data %
Page 93 and 94: Evaluation of the wide angle data f
Page 95 and 96: Evaluation of the small angle data
Page 97 and 98: Evaluation of the small angle data
Page 99: Evaluation of the small angle data
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