Coherent Backscattering from Multiple Scattering Systems - KOPS ...

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MATLAB codes % Derive experimental diffuson and cooperon exp_diffuson = diffuson (theta,l,R) * P_samp ; exp_diffuson_delta = diffuson (theta,l,R) * Perror_samp ; exp_cooperon = (corr_cone - exp_diffuson) / P_samp ; exp_cooperon_delta = ... sqrt ( (corr_cone_delta / P_samp).^2 ... + (exp_diffuson_delta / P_samp).^2 ... + ((corr_cone - exp_diffuson) / P_samp^2 * Perror_samp).^2 ) ; % Calculate theory curve theory_theta = 0 : 0.001*pi : pi/2 ; theory_cooperon = enhancement * cooperon (theory_theta,k,l,R,D,tau) ; %% Calculate energy e_theta = [ 0 , theta , pi/2 ] ; e_cooperon = [ 1 , exp_cooperon , 0 ] ; e_cooperon_delta = [ 0 , exp_cooperon_delta , 0 ] ; E = 2*pi ... * sum ( ( e_theta(:,2:end) - e_theta(:,1:end-1) ) ... * 1/2 .* ( e_cooperon(:,1:end-1) .* sin(e_theta(:,1:end-1)) ... + e_cooperon(:,2:end) .* sin(e_theta(:,2:end)) ) ) ; E_delta = 2*pi ... * sqrt ( sum ( ( 1/2 * ( e_theta(1,2:end) - e_theta(1,1:end-1) ) ... .* e_cooperon_delta(1:end-1) ).^2 ... .* sin (1/2 * ( e_theta(1,2:end) + e_theta(1,1:end-1) )) ... + ( 1/2 * ( e_theta(1,2:end) - e_theta(1,1:end-1) ) ... .* e_cooperon_delta(2:end) ).^2 ... .* sin (1/2 * ( e_theta(1,2:end) + e_theta(1,1:end-1) )) ) ) ; disp ([’E = ’,num2str(E),’+-’,num2str(E_delta)]) %% Plot data angles = theta / pi * 180 ; theory_angles = theory_theta / pi * 180 ; plot ( angles, exp_cooperon, ’b’, ... theory_angles, theory_cooperon, ’r’, ... angles, exp_cooperon+exp_cooperon_delta, ’:b’, ... angles, exp_cooperon-exp_cooperon_delta, ’:b’ ) xlabel (’scattering angle [deg]’) ylabel (’cooperon’) legend (’backscattering data’,’theory’) end 84
Evaluation of the wide angle data function d = diffuson (theta,l,R) z0 = 2/3 * l * (1 + R) / (1 - R) ; mu = cos(theta) ; d = ( mu .* (z0/l + mu./(mu+1)) ) ./ (z0/l + 1/2) ; end function c = cooperon (theta,k,l,R,D,tau) z0 = 2/3 * l * (1 + R) / (1 - R) ; mu = cos(theta) ; q = k * sin(theta) ; L_a = sqrt (D * tau) ; q_a = sqrt (q.^2 + 1/(D*tau)) ; c = ( l * (l + L_a)^2 * ( (1 - exp(-2*q_a*z0)) ./ ... (q_a*l) + 2*mu ./ (mu+1) ) ) ... ./ ( L_a^2 * ( l + (1 - exp(-2*z0/L_a)) * L_a ) * ... ( l*q_a + (mu+1) ./ (2*mu) ).^2 ) ; c_add = (8 * pi * a(k,l,R)) / (3 * k^2 * l * (l + 2 * z0)) * mu ./ (mu + 1) ; c = c - c_add ; end function a = a (k,l,R) theta = 0.00001*pi : 0.00001*pi : pi/2 ; z0 = 2/3 * l * (1 + R) / (1 - R) ; mu = cos(theta) ; q = k * abs(sin(theta)) ; E_A = trapz ( theta, ... 3/(8*pi) * 1./(q*l + (mu+1)./(2*mu)).^2 ... .* ( (1 - exp(-2*q*z0))./(q*l) + (2*mu)./(mu+1) ) ... .* sin(theta) ) ; E_BC = trapz ( theta, ... 1/(k*l)^2 * mu./(mu+1) ... .* sin(theta) ) ; a = E_A / E_BC ; end 85
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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
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3.3 Small Angle Setup 1 0.998 0.996
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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: Evaluation of the wide angle data %
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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