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5 Experiments is lower than 1 (fig. 5.5). At the wings of the backscattering cone an intensity cutback appears that balances the intensity enhancement of the cone. However, the effect of α (B+C) c is significant only for small kl ∗ . For kl ∗ 10 its influence is negligible, and the backscattering cone is well described by the cooperon α (A) c given in eqn. 2.15. In this regime the diffuson can be found from the large angle wings of the backscattering data [55]. For small kl ∗ the diffuson is hidden by the intensity cutback, and the proceeding devised above has to be used to extract the cooperon from the data. Small kl ∗ however means strongly scattering dense samples, where the scattering particles are in touching distance. In such systems, near-field effects become important for the scattering process. Strictly speaking, the random walk model developed for dilute systems and the deduction of the transport mean free path from the intensity distribution of Mie scattering and the anisotropy parameter 〈cos θ〉 are no longer valid. The kl ∗ obtained by fitting with the theory from Akkermans and Montambaux will therefore certainly have the correct order of magnitude, but might deviate slightly from the real value. 5.1.4 The results of the test experiments To test the theoretical prediction made above, the coherent backscattering cones of various samples were measured with the wide angle setup. The diffusion coefficients lay in the range between 13 m2 /s and 250 m2 /s (see tab. 4.1), so that we expected to observe extremely wide backscattering cones with kl ∗ close to unity and a distinct intensity cutback as well as narrow cones with high kl ∗ where no cutback is visible. As the albedos of the titania samples are basically 1, the albedo mismatch of sample and reference is mainly given by the albedo of the teflon block. The latter was calculated with all three diffusion coefficients D = 27500 m2 /s, D = 16500 m2 /s, and D = 13300 m2 /s that can be derived from time of flight and small angle backscattering experiments, as discussed in sec. 4.2.2. The data quality of the wide angle backscattering experiments varies strongly, as the wide angle setup is extremely sensitive to parasitically scattered light. However, as stated above, the backscattering cone is evidentially caused by interference, so that the total amount of backscattered power must be the same both for the coherent and the incoherent addition of ∫ π/2 0 a c (θ) sin θ dθ dφ of the cooperon is the backscattered intensity, and the integral E = ∫ 2π 0 necessarily zero. E can therefore be used as a criterion to judge the quality of the experimental data. Furthermore, it is also possible to substantiate the method to calculate the albedo that was developed earlier. In fig. 5.6 one observes that the data are approximately centered at E = 0 if the albedo is calculated with D = 16500 m2 /s and D = 13300 m2 /s, but are shifted to E ≈ −0.1 sterad for an albedo calculated with D = 27500 m2 /s. Therefore the data on average suggest conservation of energy for precisely those values of the diffusion coefficient which are obtained from the small angle measurements (see sec. 5.2.2). This strongly indicates that the values for the albedos are correct, although as proof further experiments on samples with other albedos than teflon or titania are necessary. 52
5.1 Conservation of energy in coherent backscattering 7 6 5 # 4 3 2 1 0 −0.7−0.6−0.5−0.4−0.3−0.2−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 integrated cooperon E [sterad] 7 6 5 # 4 3 2 1 0 −0.7−0.6−0.5−0.4−0.3−0.2−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 integrated cooperon E [sterad] 7 6 5 # 4 3 2 1 0 −0.7−0.6−0.5−0.4−0.3−0.2−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 integrated cooperon E [sterad] Figure 5.6: Distribution of backscattered energies. The distribution of backscattered light energies E centers around E ≈ 0 if D = 13300 m2 /s (top) and D = 16500 m2 /s (center) are used to calculate the albedo of teflon. For D = 27500 m2 /s (bottom) the distribution is clearly shifted away from zero, so that conservation of energy would not be obeyed in this case. Consequently, for all further evaluations the diffusion coefficient obtained from the small angle experiments, D = 13300 m2 /s, is used. 53
Page 1 and 2:
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 and 54: 5.1 Conservation of energy in coher
Page 59: 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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