Coherent Backscattering from Multiple Scattering Systems - KOPS ...

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MATLAB codes end if n == 1 p1 = 0 ; p = 1 ; t = mu ; % because t = n * mu * p - (n+1) * p1 = 1 * mu * 1 - 2 * 0 else p0 = p1 ; p1 = p ; p = (2*n-1) / (n-1) * mu .* p1 - n / (n-1) * p0 ; t = n * mu .* p - (n+1) * p1 ; end S1 = S1 + (2*n+1) / (n*(n+1)) * (an*p + bn*t) ; S2 = S2 + (2*n+1) / (n*(n+1)) * (an*t + bn*p) ; S11 = 1/2 * ( S2 .* conj(S2) + S1 .* conj(S1) ) ; S33 = 1/2 * ( S1 .* conj(S2) + S2 .* conj(S1) ) ; I1 = S11 ; I2 = 1/2 * ( S11 + S33 ) ; % intensity after the scattering particle % after second transmission of circular polarizer plot (angle,I1,angle,I2) xlabel (’scattering angle [deg]’) ylabel (’intensity [a.u.]’) legend (’after scatterer’,’after circular polarizer’) end function J = J (n,x) J = sqrt(x*pi/2) * besselj(n+1/2,x) ; end function H = H (n,x) H = sqrt(x*pi/2) * ( besselj(n+1/2,x) + i * bessely(n+1/2,x) ) ; end function dJ = dJ (n,x) dJ = sqrt(pi/(2*x)) * ( (1+n) * besselj(n+1/2,x) - x * besselj(n+3/2,x) ) ; end function dH = dH (n,x) dH = sqrt(pi/(2*x)) * ( (1+n) * ( besselj(n+1/2,x) + i * bessely(n+1/2,x) ) ... - x * ( besselj(n+3/2,x) + i * bessely(n+3/2,x) ) ) ; end 80
Evaluation of the wide angle data Evaluation of the wide angle data This MATLAB script calibrates and displays the data of the wide angle setup (secs. 3.2 and 5.1), calculates the integrated cooperon E, and draws a theory curve which can be fitted to the data by varying the value for the transport mean free path l ∗ . Each data set consists of a series of reference measurements at different incoming laser powers and one measurement with the sample itself. The data are stored in ASCII files which contain the diode signals and their errors. The diode positions (in degrees) are read <strong>from</strong> the file ‘diode angles.dat’. The filenames of the data files contain the average incoming laser powers and their errors (in arbitrary units), which are measured by the power meter in the setup. The albedo mismatch ℵ = A reference /A sample has to be calculated <strong>from</strong> eqn. 5.6, diffusion coefficient D and absorption time τ are measured in time of flight experiments (sec. 3.4), and the effective refractive index n eff is calculated using eqn. 4.1. With the variable ‘enhancement’ the height of the theoretical cone can be adapted to that of the measured one. function wide_angle_evaluation %% Initialize variables and load files file_samp = ’C:\Examples\example_0.100+-0.001.dat’ ; % sample file path_ref = ’C:\Examples\’ ; % path reference files name_ref = ’teflon_01_0.200+-0.001.dat’ ; % arbitrary reference file wavelength = 590e-9 ; D = 15 ; tau = 2e-9 ; n_eff = 1.58 ; l = 500e-9 ; aleph = 0.890 ; enhancement = 0.9 ; % laser wavelength % diffusion coefficient of the sample % absorption time of the sample % effective refractive index of the sample % transport mean free path for theory fit % albedo mismatch % enhancement of the backscattering cone % angular positions of the photodiodes angles = load (’C:\Examples\diode_angles.dat’,’-ascii’) ; theta = angles * pi / 180 ; % sample file data_samp = load (file_samp,’-ascii’) ; parts = regexp (file_samp, ’_|+-|.dat’, ’split’) ; P_samp = parts ( size(parts,2) - 2 ) ; P_samp = str2double (P_samp:,1) ; Perror_samp = parts ( size(parts,2) - 1 ) ; Perror_samp = str2double (Perror_samp:,1) ; 81
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Dissertation Coherent Backscatterin
Page 3 and 4:
Ein kurzer Überblick Streuung ist
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Ein kurzer Überblick portweglänge
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Contents Ein kurzer Überblick i Da
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1 Introduction There have been many
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2 Theory In scattering theory, the
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2.2 Single scattering - Mie theory
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2.2 Single scattering - Mie theory
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2.3 Random walk and diffusion scatt
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2.3 Random walk and diffusion of pr
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2.4 The influence of boundaries Fig
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2.5 Photon flux from a surface The
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2.6 On polarization and interferenc
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2.6 On polarization and interferenc
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2.7 The theory of coherent backscat
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2.7 The theory of coherent backscat
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3 Setups 3.1 Laser System The key p
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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 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: MATLAB codes Angular intensity dist
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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