Coherent Backscattering from Multiple Scattering Systems - KOPS ...

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5 Experiments Figure 5.16: Correction of the scattering angle. Left: Multiply scattered light from the medium with effective refractive index n eff enters the container wall (refractive index n glass ) with scattering angle θ ms . At the container–air interface this light is refracted. The scattering angle measured at the CCD camera is therefore θ CCD . Right: Singly scattered light from a particle with refractive index n particle in water is refracted at both surfaces of the container walls. The reason for this at first surprising observation is that the polarizer removes only the central maximum of the backscattered intensity distribution around θ = 0, which for the large particles in the fluidized bed is only about 0.2 ◦ wide. The singly scattered light is refracted at both surfaces of the acrylic glass wall of the container (fig. 5.16). The scattering angle at the CCD camera and the original scattering angle θ ss at the particle are therefore related like ( ) nair θ ss = arcsin · sin θ CCD ≈ n water n air n water · θ CCD (5.9) This means that the signal at the CCD camera contains two superimposed contributions, which require different corrections to obtain the real scattering angles! The contribution of single scattering As explained before, the circular polarizer in the setup removes the central maximum of single scattering, but leaves the rest of its intensity pattern more or less unaltered. If the refractive indices of particles and water and the size distribution of the particles are known exactly, the intensity distribution of single scattering can be calculated using Mie theory (fig. 5.15), and can then be subtracted from the data. The background illumination of the backscattering image however is rather non-uniform and can therefore not be removed completely. This makes it an extremely delicate task to choose the correct parameters for the Mie distribution to subtract (fig. 5.17). We adapt the Mie distribution to the first order maximum and minimum of the azimuthally averaged data, where the variance of the data is still comparatively low. 64
5.2 The coherent backscattering cone in high resolution intensity [a.u.] 4000 3000 2000 1000 data profiles (f = 43%) data average (f = 43%) n water = 1.334 , n particle = 1.519 . n water = 1.334 , n particle = 1.520 n water = 1.334 , n particle = 1.521 n water = 1.334 , n particle = 1.522 n water = 1.334 , n particle = 1.523 n water = 1.333 , n particle = 1.519 n water = 1.333 , n particle = 1.520 n water = 1.333 , n particle = 1.521 n water = 1.333 , n particle = 1.522 n water = 1.333 , n particle = 1.523 0 −1000 −2000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 scattering angle θ CCD [deg] Figure 5.17: Measured data and calculated Mie distributions. Due to non-uniform background lighting the data vary strongly for angles larger than 0.3 ◦ and can not be fitted properly. To get a reliable scaling, the Mie distributions were scaled to fit the first order minimum and maximum of the azimuthally averaged data, whose heights are marked in the graph. The first maximum of the calculated Mie distributions is shifted towards smaller scattering angles, which shows that the particle size distribution used for the calculations is slightly wrong. 65
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 65 and 66: 5.2 The coherent backscattering con
Page 71: 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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