Coherent Backscattering from Multiple Scattering Systems - KOPS ...

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3 Setups Figure 3.2: Wide angle setup. 256 photodiodes arranged in a semicircle around the sample capture the the backscattered radiation over a range of nearly 180 ◦ . the sample around an axis parallel to the incoming laser beam, providing a sample average which eliminates the speckle pattern. 3.2.1 Optical setup The intensity of the coherent backscattering cone varies rapidly around the backscattering direction, while the variations at larger scattering angles are comparatively slow. Accordingly, the angular resolution of the setup has to be rather high in the center, while at larger angles the diodes can be set further apart. To meet these requirements, for angles θ < 9.75 ◦ eight photodiode arrays with 16 photodiodes each (S5668 from Hamamatsu) are used, yielding an angular resolution of 0.15 ◦ . For angles θ > 9.75 ◦ , single photodiodes (S4011 from Hamamatsu) provide angular resolutions of 0.7 ◦ for 9.75 ◦ < θ < 19.55 ◦ , ∼ 1 ◦ for 19.55 ◦ < θ < 60 ◦ and ∼ 3 ◦ for 60 ◦ < θ < 85 ◦ . Still, it is not possible ro resolve the very tip of the cone at θ ≈ 0, as this is the position where the laser beam passes through the diode arc. For this task the small angle setup (see sec. 3.3) has to be used. The desired angular resolution also implies some prerequisites for the optical setup: The laser source has to be imaged completely on a single photodiode, without any light of a certain scattering angle missing its diode or even illuminating a neighboring one. On the other hand, the incoming laser beam is supposed to have a considerable width at the sample surface to avoid finite size effects [32]. Therefore the incoming laser beam is first widened and parallelized by a telescope, and then focussed on the point between the photodiodes, diverging again on its way to the sample. Light scattered with a certain scattering angle is then focussed again when it reaches the photodiodes. 26
3.2 Wide Angle Setup 1 .0 0 .8 h e lic ity c o n s e rv in g h e lic ity b re a k in g 0 .6 c o o p e ro n 0 .4 0 .2 0 .0 -9 0 -6 0 -3 0 0 3 0 6 0 9 0 s c a tte rin g a n g le [d e g ] Figure 3.3: Polarizer effectiveness. The circular polarizer foil is only about 97% effective, so that each polarization channel contains 3% of the other channel. The resulting small cone with an enhancement of 0.03 can easily be observed in the helicity breaking channel. Due to some missing data points at θ ≈ 0 the enhancement of 0.97 in the helicity conserving channel is more difficult to read from the graph. 3.2.2 Suppression of single scattering The enhancement of the coherent backscattering cone, I m /(I m + I s ), depends on the intensities of both singly (I s ) and multiply (I m ) scattered light, where single scattering results in a lowered backscattering enhancement. To study the backscattering of multiply scattered light in detail, single scattering has to be suppressed sufficiently. According to the theorem of reciprocity (see sec. 2.6), interference of multiple scattered waves is only possible for the parallel or respectively the helicity conserving polarization channel. As explained in sec. 5.2.3, the sequence ‘polarizer – scatterer(s) – polarizer’ which is necessary to select the channel with the backscattering cone simultaneously blocks single scattering if circular polarizers are used. The wide angle setup is therefore equipped with a bendable circular polarization foil (J53-333 from 3M), which is placed at the entrance of the setup and in front of the diodes. This polarizer foil blocks about 97% of the single scattered intensity (fig. 3.3). 3.2.3 Diode calibration As each of the photodiodes is read by its own electronic circuit, it is necessary to calibrate the diodes to make up for different gains of the processing electronics [22, 23, 47]. This is done by 27
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: 3 Setups 3.1 Laser System The key p
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 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:
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