Coherent Backscattering from Multiple Scattering Systems - KOPS ...

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MATLAB codes position = regions(index).Centroid ; position = round (position) ; % position = center of mass of blob area; % position(1) = x, position(2) = y !!! %% Calculate profile or average mode_selector = ’average’ ; % alternative: ’profile’ if strcmp(mode_selector, ’average’) range = 1 ; % change value to average over a larger radial range [intensity,error,pixels] = ... calculate_average (matrix, errormatrix, position, range) ; else direction = 0 ; % change value to select other direction range = 1 ; % change value to average over a larger radial range [intensity,error,pixels] = ... calculate_profile (matrix, errormatrix, position, direction, range) ; end %% Display result plot ( pixels, intensity ) hold on plot ( pixels, intensity-error, ’:’ ) plot ( pixels, intensity+error, ’:’ ) hold off xlabel (’scattering angle [pixels]’) ylabel (’intensity [a.u.]’) end function [intensity,error,pixels] = ... calculate_average (matrix, errormatrix, position, range) % create carthesian coordinate system X = repmat(1:2048,2048,1) ; Y = X’ ; % shift origin of the coordinate system to ’position’ X = X - position(1) ; Y = Y - position(2) ; % turn carthesian coordinate system into polar coordinates [theta,rho] = cart2pol (X,Y) ; % range of theta: [-pi,pi] 88
Evaluation of the small angle data % reshape matrices into vectors matrix = reshape (matrix,[],1) ; errormatrix = reshape (errormatrix,[],1) ; rho = reshape (rho,[],1) ; % sort vectors for rho sorted = sortrows ([rho,matrix,errormatrix], 1) ; rho = sorted(:,1) ; matrix = sorted(:,2) ; errormatrix = sorted(:,3) ; % define ranges for the radial average rho = rho / range ; rho = round (rho) ; % radial = values of rho without repetitions, sorted in ascending order [radial,first] = unique (rho, ’first’) ; % first = first occurrence of each % unique value in rho [radial,last] = unique (rho, ’last’) ; % last = last occurrence of each % unique value in rho % average of the values of matrix and errormatrix weight = 1 ./ errormatrix.^2 ; weighted_matrix = matrix .* weight ; intensity = zeros (size(radial,1), 1) ; error = zeros (size(radial,1), 1) ; for k = 1 : size(radial,1) intensity(k) = sum ( weighted_matrix(first(k):last(k)) ) ... / sum ( weight(first(k):last(k)) ) ; error(k) = 1 / sqrt ( sum ( weight(first(k):last(k)) ) ) ... * 1 / sqrt ( last(k)-first(k)+1 ) ; end % define scale pixels = radial * range ; end function [intensity,error,pixels] = ... calculate_profile (matrix,errormatrix,position,direction,range) % calculate direction angle angle = direction / 180 * pi ; if angle < 0 angle = angle + 2 * pi ; % angles between 0 and 2*pi 89
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Dissertation Coherent Backscatterin
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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
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3.4 Time Of Flight Setup Figure 3.8
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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: Evaluation of the small angle data
Page 99: Evaluation of the small angle data
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