658 lines
24 KiB
Matlab
658 lines
24 KiB
Matlab
clear all
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close all
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%%
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groupList = ["/images/MOT_3D_Camera/in_situ_absorption", "/images/ODT_1_Axis_Camera/in_situ_absorption", ...
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"/images/ODT_2_Axis_Camera/in_situ_absorption", "/images/Horizontal_Axis_Camera/in_situ_absorption", ...
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"/images/Vertical_Axis_Camera/in_situ_absorption"];
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folderPath = "E:/Data - Experiment/2025/07/04/";
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run = '0016';
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folderPath = strcat(folderPath, run);
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cam = 5;
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angle = 0;
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center = [1430, 2040];
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span = [200, 200];
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fraction = [0.1, 0.1];
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pixel_size = 5.86e-6;
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removeFringes = false;
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% Fourier analysis settings
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% Radial Spectral Distribution
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theta_min = deg2rad(0);
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theta_max = deg2rad(180);
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N_radial_bins = 500;
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Radial_Sigma = 2;
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Radial_WindowSize = 5; % Choose an odd number for a centered moving average
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% Angular Spectral Distribution
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r_min = 10;
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r_max = 20;
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N_angular_bins = 180;
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Angular_Threshold = 75;
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Angular_Sigma = 2;
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Angular_WindowSize = 5;
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zoom_size = 50; % Zoomed-in region around center
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% scan_parameter = 'ps_rot_mag_fin_pol_angle';
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scan_parameter = 'rot_mag_field';
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% scan_parameter_text = 'Angle = ';
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scan_parameter_text = 'BField = ';
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savefolderPath = 'E:/Results - Experiment/B2.35G/';
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savefileName = 'Droplets';
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font = 'Bahnschrift';
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skipUnshuffling = true;
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if strcmp(savefileName, 'DropletsToStripes')
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scan_groups = 0:5:45;
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elseif strcmp(savefileName, 'StripesToDroplets')
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scan_groups = 45:-5:0;
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end
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skipPreprocessing = true;
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skipMasking = true;
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skipIntensityThresholding = true;
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skipBinarization = true;
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%% Compute OD image, rotate and extract ROI for analysis
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% Get a list of all files in the folder with the desired file name pattern.
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filePattern = fullfile(folderPath, '*.h5');
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files = dir(filePattern);
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refimages = zeros(span(1) + 1, span(2) + 1, length(files));
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absimages = zeros(span(1) + 1, span(2) + 1, length(files));
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for k = 1 : length(files)
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baseFileName = files(k).name;
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fullFileName = fullfile(files(k).folder, baseFileName);
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fprintf(1, 'Now reading %s\n', fullFileName);
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atm_img = double(imrotate(h5read(fullFileName, append(groupList(cam), "/atoms")), angle));
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bkg_img = double(imrotate(h5read(fullFileName, append(groupList(cam), "/background")), angle));
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dark_img = double(imrotate(h5read(fullFileName, append(groupList(cam), "/dark")), angle));
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refimages(:,:,k) = subtractBackgroundOffset(cropODImage(bkg_img, center, span), fraction)';
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absimages(:,:,k) = subtractBackgroundOffset(cropODImage(calculateODImage(atm_img, bkg_img, dark_img), center, span), fraction)';
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end
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% Fringe removal
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if removeFringes
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optrefimages = removefringesInImage(absimages, refimages);
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absimages_fringe_removed = absimages(:, :, :) - optrefimages(:, :, :);
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nimgs = size(absimages_fringe_removed,3);
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od_imgs = cell(1, nimgs);
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for i = 1:nimgs
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od_imgs{i} = absimages_fringe_removed(:, :, i);
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end
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else
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nimgs = size(absimages(:, :, :),3);
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od_imgs = cell(1, nimgs);
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for i = 1:nimgs
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od_imgs{i} = absimages(:, :, i);
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end
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end
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%% Get rotation angles
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scan_parameter_values = zeros(1, length(files));
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% Get information about the '/globals' group
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for k = 1 : length(files)
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baseFileName = files(k).name;
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fullFileName = fullfile(files(k).folder, baseFileName);
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info = h5info(fullFileName, '/globals');
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for i = 1:length(info.Attributes)
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if strcmp(info.Attributes(i).Name, scan_parameter)
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if strcmp(scan_parameter, 'ps_rot_mag_fin_pol_angle')
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scan_parameter_values(k) = 180 - info.Attributes(i).Value;
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else
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scan_parameter_values(k) = info.Attributes(i).Value;
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end
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end
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end
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end
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%% Unshuffle if necessary to do so
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if ~skipUnshuffling
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n_values = length(scan_groups);
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n_total = length(scan_parameter_values);
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% Infer number of repetitions
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n_reps = n_total / n_values;
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% Preallocate ordered arrays
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ordered_scan_values = zeros(1, n_total);
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ordered_od_imgs = cell(1, n_total);
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counter = 1;
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for rep = 1:n_reps
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for val = scan_groups
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% Find the next unused match for this val
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idx = find(scan_parameter_values == val, 1, 'first');
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% Assign and remove from list to avoid duplicates
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ordered_scan_values(counter) = scan_parameter_values(idx);
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ordered_od_imgs{counter} = od_imgs{idx};
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% Mark as used by removing
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scan_parameter_values(idx) = NaN; % NaN is safe since original values are 0:5:45
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od_imgs{idx} = []; % empty cell so it won't be matched again
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counter = counter + 1;
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end
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end
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% Now assign back
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scan_parameter_values = ordered_scan_values;
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od_imgs = ordered_od_imgs;
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end
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%% Run Fourier analysis over images
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fft_imgs = cell(1, nimgs);
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spectral_contrast = zeros(1, nimgs);
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spectral_weight = zeros(1, nimgs);
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N_shots = length(od_imgs);
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% Create VideoWriter object for movie
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videoFile = VideoWriter([savefileName '.mp4'], 'MPEG-4');
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videoFile.Quality = 100; % Set quality to maximum (0–100)
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videoFile.FrameRate = 2; % Set the frame rate (frames per second)
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open(videoFile); % Open the video file to write
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% Display the cropped image
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for k = 1:N_shots
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IMG = od_imgs{k};
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[IMGFFT, IMGPR] = computeFourierTransform(IMG, skipPreprocessing, skipMasking, skipIntensityThresholding, skipBinarization);
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[rows, cols] = size(IMGFFT);
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mid_x = floor(cols/2);
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mid_y = floor(rows/2);
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fft_imgs{k} = IMGFFT(mid_y-zoom_size:mid_y+zoom_size, mid_x-zoom_size:mid_x+zoom_size);
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[theta_vals, S_theta] = computeNormalizedAngularSpectralDistribution(fft_imgs{k}, r_min, r_max, N_angular_bins, Angular_Threshold, Angular_Sigma, []);
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[k_rho_vals, S_k] = computeRadialSpectralDistribution(fft_imgs{k}, theta_min, theta_max, N_radial_bins);
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S_k_smoothed = movmean(S_k, Radial_WindowSize); % % Compute moving average (use convolution) or use conv for more control
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spectral_contrast(k) = computeSpectralContrast(fft_imgs{k}, r_min, r_max, Angular_Threshold);
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spectral_weight(k) = trapz(theta_vals, S_theta);
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figure(1);
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clf
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set(gcf,'Position',[500 100 1000 800])
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t = tiledlayout(2, 2, 'TileSpacing', 'compact', 'Padding', 'compact'); % 1x4 grid
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% Calculate the x and y limits for the cropped image
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y_min = center(1) - span(2) / 2;
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y_max = center(1) + span(2) / 2;
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x_min = center(2) - span(1) / 2;
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x_max = center(2) + span(1) / 2;
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% Generate x and y arrays representing the original coordinates for each pixel
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x_range = linspace(x_min, x_max, span(1));
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y_range = linspace(y_min, y_max, span(2));
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% Display the cropped OD image
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ax1 = nexttile;
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imagesc(x_range, y_range, IMG)
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% Define normalized positions (relative to axis limits)
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x_offset = 0.025; % 5% offset from the edges
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y_offset = 0.025; % 5% offset from the edges
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% Top-right corner (normalized axis coordinates)
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hText = text(1 - x_offset, 1 - y_offset, [scan_parameter_text, num2str(scan_parameter_values(k), '%.2f')], ...
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'Color', 'white', 'FontWeight', 'bold', 'Interpreter', 'tex', 'FontSize', 20, 'Units', 'normalized', 'HorizontalAlignment', 'right', 'VerticalAlignment', 'top');
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axis equal tight;
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hcb = colorbar;
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colormap(ax1, 'hot');
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set(gca, 'FontSize', 14); % For tick labels only
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hL = ylabel(hcb, 'Optical Density');
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set(hL,'Rotation',-90);
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set(gca,'YDir','normal')
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set(gca, 'YTick', linspace(y_min, y_max, 5)); % Define y ticks
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set(gca, 'YTickLabel', flip(linspace(y_min, y_max, 5))); % Flip only the labels
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hXLabel = xlabel('x (pixels)', 'Interpreter', 'tex');
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hYLabel = ylabel('y (pixels)', 'Interpreter', 'tex');
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hTitle = title('OD Image', 'Interpreter', 'tex');
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set([hXLabel, hYLabel, hL, hText], 'FontName', font)
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set([hXLabel, hYLabel, hL], 'FontSize', 14)
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set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold'); % Set font and size for title
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% Plot the power spectrum
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ax2 = nexttile;
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imagesc(log(1 + abs(fft_imgs{k}).^2));
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% Compute center of the FFT image
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[ny, nx] = size(fft_imgs{k});
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cx = ceil(nx/2);
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cy = ceil(ny/2);
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% Define angles for the circle
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theta = linspace(0, 2*pi, 500);
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% Circle 1 at r_min
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x1 = cx + r_min * cos(theta);
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y1 = cy + r_min * sin(theta);
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% Circle 2 at r_max
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x2 = cx + r_max * cos(theta);
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y2 = cy + r_max * sin(theta);
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% Plot the circles
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hold on;
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plot(x1, y1, 'w--', 'LineWidth', 1.0); % Cyan for r_min
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plot(x2, y2, 'w--', 'LineWidth', 1.0); % Magenta for r_max
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plot([1, nx], [cy, cy], 'w--', 'LineWidth', 1.0); % white dashed horizontal line
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hold off;
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% Define normalized positions (relative to axis limits)
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x_offset = 0.025; % 5% offset from the edges
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y_offset = 0.025; % 5% offset from the edges
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axis equal tight;
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hcb = colorbar;
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colormap(ax2, Colormaps.inferno());
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set(gca, 'FontSize', 14); % For tick labels only
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set(gca,'YDir','normal')
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hXLabel = xlabel('k_x', 'Interpreter', 'tex');
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hYLabel = ylabel('k_y', 'Interpreter', 'tex');
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hTitle = title('Power Spectrum - S(k_x,k_y)', 'Interpreter', 'tex');
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set([hXLabel, hYLabel, hText], 'FontName', font)
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set([hXLabel, hYLabel], 'FontSize', 14)
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set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold'); % Set font and size for title
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% Plot the smoothed radial distribution
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nexttile
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plot(k_rho_vals, S_k_smoothed, 'LineWidth', 2);
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set(gca, 'FontSize', 14); % Tick labels
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set(gca, 'YScale', 'log'); % Logarithmic y-axis
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xlim([min(k_rho_vals), max(k_rho_vals)]);
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ylim([1, 1E8])
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hXLabel = xlabel('k_\rho', 'Interpreter', 'tex');
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hYLabel = ylabel('Magnitude (a.u.)', 'Interpreter', 'tex');
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hTitle = title('Radial Spectral Distribution - S(k)', 'Interpreter', 'tex');
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set([hXLabel, hYLabel], 'FontSize', 14, 'FontName', font);
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set(hTitle, 'FontSize', 16, 'FontWeight', 'bold', 'FontName', font);
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grid on;
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% Plot the angular distribution
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nexttile
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plot(theta_vals/pi, S_theta,'Linewidth',2);
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set(gca, 'FontSize', 14); % For tick labels only
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hXLabel = xlabel('\theta/\pi [rad]', 'Interpreter', 'tex');
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hYLabel = ylabel('Normalized magnitude (a.u.)', 'Interpreter', 'tex');
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hTitle = title('Angular Spectral Distribution - S(\theta)', 'Interpreter', 'tex');
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set([hXLabel, hYLabel, hText], 'FontName', font)
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set([hXLabel, hYLabel], 'FontSize', 14)
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set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold'); % Set font and size for title
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grid on
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drawnow
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pause(0.5)
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% Capture the current frame and write it to the video
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frame = getframe(gcf); % Capture the current figure as a frame
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writeVideo(videoFile, frame); % Write the frame to the video
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end
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% Close the video file
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close(videoFile);
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%% Helper Functions
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function [IMGFFT, IMGPR] = computeFourierTransform(I, skipPreprocessing, skipMasking, skipIntensityThresholding, skipBinarization)
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% computeFourierSpectrum - Computes the 2D Fourier power spectrum
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% of binarized and enhanced lattice image features, with optional central mask.
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%
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% Inputs:
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% I - Grayscale or RGB image matrix
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%
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% Output:
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% F_mag - 2D Fourier power spectrum (shifted)
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if ~skipPreprocessing
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% Preprocessing: Denoise
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filtered = imgaussfilt(I, 10);
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IMGPR = I - filtered; % adjust sigma as needed
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else
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IMGPR = I;
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end
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if ~skipMasking
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[rows, cols] = size(IMGPR);
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[X, Y] = meshgrid(1:cols, 1:rows);
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% Elliptical mask parameters
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cx = cols / 2;
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cy = rows / 2;
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% Shifted coordinates
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x = X - cx;
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y = Y - cy;
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% Ellipse semi-axes
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rx = 0.4 * cols;
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ry = 0.2 * rows;
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% Rotation angle in degrees -> radians
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theta_deg = 30; % Adjust as needed
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theta = deg2rad(theta_deg);
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% Rotated ellipse equation
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cos_t = cos(theta);
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sin_t = sin(theta);
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x_rot = (x * cos_t + y * sin_t);
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y_rot = (-x * sin_t + y * cos_t);
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ellipseMask = (x_rot.^2) / rx^2 + (y_rot.^2) / ry^2 <= 1;
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% Apply cutout mask
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IMGPR = IMGPR .* ellipseMask;
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end
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if ~skipIntensityThresholding
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% Apply global intensity threshold mask
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intensity_thresh = 0.20;
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intensity_mask = IMGPR > intensity_thresh;
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IMGPR = IMGPR .* intensity_mask;
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end
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if ~skipBinarization
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% Adaptive binarization and cleanup
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IMGPR = imbinarize(IMGPR, 'adaptive', 'Sensitivity', 0.0);
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IMGPR = imdilate(IMGPR, strel('disk', 2));
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IMGPR = imerode(IMGPR, strel('disk', 1));
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IMGPR = imfill(IMGPR, 'holes');
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F = fft2(double(IMGPR)); % Compute 2D Fourier Transform
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IMGFFT = abs(fftshift(F))'; % Shift zero frequency to center
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else
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F = fft2(double(IMGPR)); % Compute 2D Fourier Transform
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IMGFFT = abs(fftshift(F))'; % Shift zero frequency to center
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end
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end
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function [k_rho_vals, S_radial] = computeRadialSpectralDistribution(IMGFFT, thetamin, thetamax, num_bins)
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% IMGFFT : 2D FFT (should be fftshifted already)
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% thetamin : Minimum angle (in radians)
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% thetamax : Maximum angle (in radians)
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% num_radial_bins : Number of radial bins
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% sigma : Gaussian smoothing width (in bins)
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% Image size and center
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[ny, nx] = size(IMGFFT);
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[X, Y] = meshgrid(1:nx, 1:ny);
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cx = ceil(nx / 2);
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cy = ceil(ny / 2);
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dX = X - cx;
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dY = Y - cy;
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% Polar coordinates
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R = sqrt(dX.^2 + dY.^2); % radial coordinate
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Theta = atan2(dY, dX); % angle in radians [-pi, pi]
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% Angular mask (support wraparound from +pi to -pi)
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if thetamin < thetamax
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angle_mask = (Theta >= thetamin) & (Theta <= thetamax);
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else
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angle_mask = (Theta >= thetamin) | (Theta <= thetamax);
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end
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% Define full radial range: from center to farthest corner
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r_min = 0;
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r_max = sqrt((max([cx-1, nx-cx]))^2 + (max([cy-1, ny-cy]))^2);
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% Radial bins
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r_edges = linspace(r_min, r_max, num_bins + 1);
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k_rho_vals = 0.5 * (r_edges(1:end-1) + r_edges(2:end));
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S_radial = zeros(1, num_bins);
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% Power spectrum
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power_spectrum = abs(IMGFFT).^2;
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% Radial integration over selected angles
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for i = 1:num_bins
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r_low = r_edges(i);
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r_high = r_edges(i + 1);
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radial_mask = (R >= r_low) & (R < r_high);
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full_mask = radial_mask & angle_mask;
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S_radial(i) = sum(power_spectrum(full_mask));
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end
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end
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function [theta_vals, S_theta] = computeNormalizedAngularSpectralDistribution(IMGFFT, r_min, r_max, num_bins, threshold, sigma, windowSize)
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% Apply threshold to isolate strong peaks
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IMGFFT(IMGFFT < threshold) = 0;
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% Prepare polar coordinates
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[ny, nx] = size(IMGFFT);
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[X, Y] = meshgrid(1:nx, 1:ny);
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cx = ceil(nx/2);
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cy = ceil(ny/2);
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R = sqrt((X - cx).^2 + (Y - cy).^2);
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Theta = atan2(Y - cy, X - cx); % range [-pi, pi]
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% Choose radial band
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radial_mask = (R >= r_min) & (R <= r_max);
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% Initialize angular structure factor
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S_theta = zeros(1, num_bins);
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theta_vals = linspace(0, pi, num_bins);
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% Loop through angle bins
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for i = 1:num_bins
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angle_start = (i-1) * pi / num_bins;
|
||
angle_end = i * pi / num_bins;
|
||
angle_mask = (Theta >= angle_start & Theta < angle_end);
|
||
bin_mask = radial_mask & angle_mask;
|
||
fft_angle = IMGFFT .* bin_mask;
|
||
S_theta(i) = sum(sum(abs(fft_angle).^2));
|
||
end
|
||
|
||
% Smooth using either Gaussian or moving average
|
||
if exist('sigma', 'var') && ~isempty(sigma)
|
||
% Gaussian convolution
|
||
half_width = ceil(3 * sigma);
|
||
x = -half_width:half_width;
|
||
gauss_kernel = exp(-x.^2 / (2 * sigma^2));
|
||
gauss_kernel = gauss_kernel / sum(gauss_kernel);
|
||
% Circular convolution
|
||
S_theta = conv([S_theta(end-half_width+1:end), S_theta, S_theta(1:half_width)], ...
|
||
gauss_kernel, 'same');
|
||
S_theta = S_theta(half_width+1:end-half_width);
|
||
elseif exist('windowSize', 'var') && ~isempty(windowSize)
|
||
% Moving average via convolution (circular)
|
||
pad = floor(windowSize / 2);
|
||
kernel = ones(1, windowSize) / windowSize;
|
||
S_theta = conv([S_theta(end-pad+1:end), S_theta, S_theta(1:pad)], kernel, 'same');
|
||
S_theta = S_theta(pad+1:end-pad);
|
||
end
|
||
|
||
% Normalize
|
||
S_theta = S_theta / max(S_theta);
|
||
end
|
||
|
||
function contrast = computeSpectralContrast(IMGFFT, r_min, r_max, threshold)
|
||
% Apply threshold to isolate strong peaks
|
||
IMGFFT(IMGFFT < threshold) = 0;
|
||
|
||
% Prepare polar coordinates
|
||
[ny, nx] = size(IMGFFT);
|
||
[X, Y] = meshgrid(1:nx, 1:ny);
|
||
cx = ceil(nx/2);
|
||
cy = ceil(ny/2);
|
||
R = sqrt((X - cx).^2 + (Y - cy).^2);
|
||
|
||
% Ring region (annulus) mask
|
||
ring_mask = (R >= r_min) & (R <= r_max);
|
||
|
||
% Squared magnitude in the ring
|
||
ring_power = abs(IMGFFT).^2 .* ring_mask;
|
||
|
||
% Maximum power in the ring
|
||
ring_max = max(ring_power(:));
|
||
|
||
% Power at the DC component
|
||
dc_power = abs(IMGFFT(cy, cx))^2;
|
||
|
||
% Avoid division by zero
|
||
if dc_power == 0
|
||
contrast = Inf; % or NaN or 0, depending on how you want to handle this
|
||
else
|
||
contrast = ring_max / dc_power;
|
||
end
|
||
end
|
||
|
||
function ret = getBkgOffsetFromCorners(img, x_fraction, y_fraction)
|
||
% image must be a 2D numerical array
|
||
[dim1, dim2] = size(img);
|
||
|
||
s1 = img(1:round(dim1 * y_fraction), 1:round(dim2 * x_fraction));
|
||
s2 = img(1:round(dim1 * y_fraction), round(dim2 - dim2 * x_fraction):dim2);
|
||
s3 = img(round(dim1 - dim1 * y_fraction):dim1, 1:round(dim2 * x_fraction));
|
||
s4 = img(round(dim1 - dim1 * y_fraction):dim1, round(dim2 - dim2 * x_fraction):dim2);
|
||
|
||
ret = mean([mean(s1(:)), mean(s2(:)), mean(s3(:)), mean(s4(:))]);
|
||
end
|
||
|
||
function ret = subtractBackgroundOffset(img, fraction)
|
||
% Remove the background from the image.
|
||
% :param dataArray: The image
|
||
% :type dataArray: xarray DataArray
|
||
% :param x_fraction: The fraction of the pixels used in x axis
|
||
% :type x_fraction: float
|
||
% :param y_fraction: The fraction of the pixels used in y axis
|
||
% :type y_fraction: float
|
||
% :return: The image after removing background
|
||
% :rtype: xarray DataArray
|
||
|
||
x_fraction = fraction(1);
|
||
y_fraction = fraction(2);
|
||
offset = getBkgOffsetFromCorners(img, x_fraction, y_fraction);
|
||
ret = img - offset;
|
||
end
|
||
|
||
function ret = cropODImage(img, center, span)
|
||
% Crop the image according to the region of interest (ROI).
|
||
% :param dataSet: The images
|
||
% :type dataSet: xarray DataArray or DataSet
|
||
% :param center: The center of region of interest (ROI)
|
||
% :type center: tuple
|
||
% :param span: The span of region of interest (ROI)
|
||
% :type span: tuple
|
||
% :return: The cropped images
|
||
% :rtype: xarray DataArray or DataSet
|
||
|
||
x_start = floor(center(1) - span(1) / 2);
|
||
x_end = floor(center(1) + span(1) / 2);
|
||
y_start = floor(center(2) - span(2) / 2);
|
||
y_end = floor(center(2) + span(2) / 2);
|
||
|
||
ret = img(y_start:y_end, x_start:x_end);
|
||
end
|
||
|
||
function ret = calculateODImage(imageAtom, imageBackground, imageDark)
|
||
% Calculate the OD image for absorption imaging.
|
||
% :param imageAtom: The image with atoms
|
||
% :type imageAtom: numpy array
|
||
% :param imageBackground: The image without atoms
|
||
% :type imageBackground: numpy array
|
||
% :param imageDark: The image without light
|
||
% :type imageDark: numpy array
|
||
% :return: The OD images
|
||
% :rtype: numpy array
|
||
|
||
numerator = imageBackground - imageDark;
|
||
denominator = imageAtom - imageDark;
|
||
|
||
numerator(numerator == 0) = 1;
|
||
denominator(denominator == 0) = 1;
|
||
|
||
ret = -log(double(abs(denominator ./ numerator)));
|
||
|
||
if numel(ret) == 1
|
||
ret = ret(1);
|
||
end
|
||
end
|
||
|
||
function [optrefimages] = removefringesInImage(absimages, refimages, bgmask)
|
||
% removefringesInImage - Fringe removal and noise reduction from absorption images.
|
||
% Creates an optimal reference image for each absorption image in a set as
|
||
% a linear combination of reference images, with coefficients chosen to
|
||
% minimize the least-squares residuals between each absorption image and
|
||
% the optimal reference image. The coefficients are obtained by solving a
|
||
% linear set of equations using matrix inverse by LU decomposition.
|
||
%
|
||
% Application of the algorithm is described in C. F. Ockeloen et al, Improved
|
||
% detection of small atom numbers through image processing, arXiv:1007.2136 (2010).
|
||
%
|
||
% Syntax:
|
||
% [optrefimages] = removefringesInImage(absimages,refimages,bgmask);
|
||
%
|
||
% Required inputs:
|
||
% absimages - Absorption image data,
|
||
% typically 16 bit grayscale images
|
||
% refimages - Raw reference image data
|
||
% absimages and refimages are both cell arrays containing
|
||
% 2D array data. The number of refimages can differ from the
|
||
% number of absimages.
|
||
%
|
||
% Optional inputs:
|
||
% bgmask - Array specifying background region used,
|
||
% 1=background, 0=data. Defaults to all ones.
|
||
% Outputs:
|
||
% optrefimages - Cell array of optimal reference images,
|
||
% equal in size to absimages.
|
||
%
|
||
|
||
% Dependencies: none
|
||
%
|
||
% Authors: Shannon Whitlock, Caspar Ockeloen
|
||
% Reference: C. F. Ockeloen, A. F. Tauschinsky, R. J. C. Spreeuw, and
|
||
% S. Whitlock, Improved detection of small atom numbers through
|
||
% image processing, arXiv:1007.2136
|
||
% Email:
|
||
% May 2009; Last revision: 11 August 2010
|
||
|
||
% Process inputs
|
||
|
||
% Set variables, and flatten absorption and reference images
|
||
nimgs = size(absimages,3);
|
||
nimgsR = size(refimages,3);
|
||
xdim = size(absimages(:,:,1),2);
|
||
ydim = size(absimages(:,:,1),1);
|
||
|
||
R = single(reshape(refimages,xdim*ydim,nimgsR));
|
||
A = single(reshape(absimages,xdim*ydim,nimgs));
|
||
optrefimages=zeros(size(absimages)); % preallocate
|
||
|
||
if not(exist('bgmask','var')); bgmask=ones(ydim,xdim); end
|
||
k = find(bgmask(:)==1); % Index k specifying background region
|
||
|
||
% Ensure there are no duplicate reference images
|
||
% R=unique(R','rows')'; % comment this line if you run out of memory
|
||
|
||
% Decompose B = R*R' using singular value or LU decomposition
|
||
[L,U,p] = lu(R(k,:)'*R(k,:),'vector'); % LU decomposition
|
||
|
||
for j=1:nimgs
|
||
b=R(k,:)'*A(k,j);
|
||
% Obtain coefficients c which minimise least-square residuals
|
||
lower.LT = true; upper.UT = true;
|
||
c = linsolve(U,linsolve(L,b(p,:),lower),upper);
|
||
|
||
% Compute optimised reference image
|
||
optrefimages(:,:,j)=reshape(R*c,[ydim xdim]);
|
||
end
|
||
end
|