Coherent Backscattering from Multiple Scattering Systems - KOPS ...

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3 Setups Figure 3.5: Small angle setup. A CCD camera captures the the backscattered radiation around backscattering direction. to 45 K below ambient temperature to reduce electronic noise. It turned out that the glass window that covers the CCD chip needs to be wedge shaped to avoid interferences in the glass, which cause a disturbing ripple structure on the CCD image. The camera offers exposure times between 30 ms and 183 min; to improve the signal-to-noise ratio, the backscattering data of our experiments are an average over a series of usually 100 pictures, taken with an exposure time of 0.5 s. The camera replaces an older 8-bit model with 580 × 740 pixels, which did not offer enough angular and intensity resolution for the planned experiments. The exchange of the camera improves the maximum intensity resolution by more than two orders of magnitude and the maximum angular resolution or respectively the maximum angular range by a factor of three. As the direct backscattering direction is blocked by the camera, a beamsplitter directs the laser beam onto the sample. The remaining part of the beam that passes straight through the beamsplitter must be dumped completely, as even weak backreflection will disturb the image on the camera. For similar reasons, a pellicle beamsplitter instead of a glass beamsplitter has to be used, as even anti-reflection coated surfaces of a glass plate would cause distinct ghost images. In contrast to the wide angle setup described in the previous section, where the sample is illuminated by a slightly divergent light beam, the incoming laser beam in the small angle setup is exactly parallel. Backscattered light with a certain scattering angle θ then forms a cone-shaped shell with a thickness that is determined by the diameter of the sample area illuminated by the incoming laser beam (fig. 3.6). The lens above the beamsplitter converges 30
3.3 Small Angle Setup Figure 3.6: The optical setup. Backscattered light with a certain scattering angle θ forms a cone-shaped shell, which is converged in the focal plane on a circle with radius r by the lens with focal length f . this ring of light on a circle in the focal plane, the radius of which is given by r = f · tan θ (3.1) where f is the focal length of the lens. Like in the wide angle setup, single scattering is blocked by a circular polarizer. In the small angle setup it is unnecessary to have a bendable polarizer foil, so a high-quality circular polarizer from an industrial optics manufacturer (AUC circular polarizer from B+W) can be used. These are available with larger diameters than usual polarizers offered by laboratory suppliers and provide extinction ratios up to 4000:1 [1]. 3.3.3 Sample average Solid samples like teflon or the titania powders have to be moved during the measurement to average over the speckle pattern. The method used in the wide angle setup, where the sample is simply rotated, however turned out to be inconvenient as the high-resolving camera picked up this rotational motion as a circular structure in the images. To have a larger ensemble to average over in the small angle experiments, the sample is therefore pulled on Lissajous loops by two motors with a frequency of several Hertz on each axis (fig. 3.7). 3.3.4 Data evaluation For the evaluation of the backscattering data the exact position of the tip of the coherent backscattering cone at θ = 0 has to be obtained from the CCD image. We do this by converting 31
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: 3.3 Small Angle Setup 1 0.998 0.996
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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