%% ===== D-S Settings =====
groupList          = ["/images/MOT_3D_Camera/in_situ_absorption", "/images/ODT_1_Axis_Camera/in_situ_absorption", ...
                      "/images/ODT_2_Axis_Camera/in_situ_absorption", "/images/Horizontal_Axis_Camera/in_situ_absorption", ...
                      "/images/Vertical_Axis_Camera/in_situ_absorption"];

folderPath         = "//DyLabNAS/Data/TwoDGas/2025/07/22/";

run                = '0021';

folderPath         = strcat(folderPath, run);

cam                = 5; 

angle              = 0;
center             = [1410, 2030];
span               = [200, 200];
fraction           = [0.1, 0.1];

pixel_size         = 5.86e-6;         % in meters
magnification      = 23.94;
removeFringes      = false;

ImagingMode        = 'HighIntensity';
PulseDuration      = 5e-6;            % in s

% Fourier analysis settings

% Radial Spectral Distribution
theta_min          = deg2rad(0);
theta_max          = deg2rad(180);
N_radial_bins      = 500;
Radial_Sigma       = 2;
Radial_WindowSize  = 5; % Choose an odd number for a centered moving average

% Angular Spectral Distribution
r_min              = 10;
r_max              = 20;
N_angular_bins     = 180;
Angular_Threshold  = 75;
Angular_Sigma      = 2;
Angular_WindowSize = 5;

zoom_size          = 50;             % Zoomed-in region around center

% Plotting and saving
scan_parameter              = 'ps_rot_mag_fin_pol_angle';
% scan_parameter              = 'rot_mag_field';

savefileName                = 'DropletsToStripes';
font                        = 'Bahnschrift';

if strcmp(savefileName, 'DropletsToStripes')
    scan_groups           = 0:1:40;
    titleString           = 'Droplets to Stripes';
elseif strcmp(savefileName, 'StripesToDroplets')
    scan_groups           = 40:-1:0;
    titleString           = 'Stripes to Droplets';
end

% Flags
skipNormalization           = true;
skipUnshuffling             = false;
skipPreprocessing           = true;
skipMasking                 = true;
skipIntensityThresholding   = true;
skipBinarization            = true;
skipMovieRender             = true;
skipSaveFigures             = false;
skipSaveOD                  = true;

%% ===== Load and compute OD image, rotate and extract ROI for analysis =====
% Get a list of all files in the folder with the desired file name pattern.

filePattern                    = fullfile(folderPath, '*.h5');
files                          = dir(filePattern);
refimages                      = zeros(span(1) + 1, span(2) + 1, length(files));
absimages                      = zeros(span(1) + 1, span(2) + 1, length(files));

for k = 1 : length(files)
    baseFileName = files(k).name;
    fullFileName = fullfile(files(k).folder, baseFileName);
    
    fprintf(1, 'Now reading %s\n', fullFileName);
    
    atm_img  = double(imrotate(h5read(fullFileName, append(groupList(cam), "/atoms")), angle));
    bkg_img  = double(imrotate(h5read(fullFileName, append(groupList(cam), "/background")), angle));
    dark_img = double(imrotate(h5read(fullFileName, append(groupList(cam), "/dark")), angle));
    
    if (isempty(atm_img)  && isa(atm_img, 'double')) || ...
       (isempty(bkg_img)  && isa(bkg_img, 'double')) || ...
       (isempty(dark_img) && isa(dark_img, 'double'))
        
        refimages(:,:,k) = nan(size(refimages(:,:,k)));  % fill with NaNs
        absimages(:,:,k) = nan(size(absimages(:,:,k)));
    else
        refimages(:,:,k)  = subtractBackgroundOffset(cropODImage(bkg_img, center, span), fraction)';
        absimages(:,:,k)  = subtractBackgroundOffset(cropODImage(calculateODImage(atm_img, bkg_img, dark_img, ImagingMode, PulseDuration), center, span), fraction)';
    end
end

% ===== Fringe removal =====

if removeFringes
    optrefimages               = removefringesInImage(absimages, refimages);
    absimages_fringe_removed   = absimages(:, :, :) - optrefimages(:, :, :);
    
    nimgs                      = size(absimages_fringe_removed,3);
    od_imgs                    = cell(1, nimgs);
    for i = 1:nimgs
        od_imgs{i}             = absimages_fringe_removed(:, :, i);
    end
else
    nimgs                      = size(absimages(:, :, :),3);
    od_imgs                    = cell(1, nimgs);
    for i = 1:nimgs
        od_imgs{i}             = absimages(:, :, i);
    end
end

%% ===== Get rotation angles =====
scan_parameter_values   = zeros(1, length(files));

% Get information about the '/globals' group
for k = 1 : length(files)
    baseFileName = files(k).name;
    fullFileName = fullfile(files(k).folder, baseFileName);
    info = h5info(fullFileName, '/globals');
    for i = 1:length(info.Attributes)
        if strcmp(info.Attributes(i).Name, scan_parameter)
            if strcmp(scan_parameter, 'ps_rot_mag_fin_pol_angle')
                scan_parameter_values(k) = 180 - info.Attributes(i).Value;
            else
                scan_parameter_values(k) = info.Attributes(i).Value;
            end
        end
    end
end

%% ===== Correlation of a single (highest) peak with a possible peak between 50-70 degrees from experiment data =====

fft_imgs              = cell(1, nimgs);
spectral_distribution = cell(1, nimgs);
theta_values          = cell(1, nimgs);

N_shots               = length(od_imgs);

% Compute FFT for all images
for k = 1:N_shots
    IMG                   = od_imgs{k};
    [IMGFFT, IMGPR]       = computeFourierTransform(IMG, skipPreprocessing, skipMasking, skipIntensityThresholding, skipBinarization);

    [Ny, Nx]              = size(IMG);
    dx                    = pixel_size / magnification;
    dy                    = dx;  % assuming square pixels

    x                     = ((1:Nx) - ceil(Nx/2)) * dx * 1E6;
    y                     = ((1:Ny) - ceil(Ny/2)) * dy * 1E6;

    dvx                   = 1 / (Nx * dx);
    dvy                   = 1 / (Ny * dy);
    vx                    = (-floor(Nx/2):ceil(Nx/2)-1) * dvx;
    vy                    = (-floor(Ny/2):ceil(Ny/2)-1) * dvy;

    kx_full               = 2 * pi * vx * 1E-6;
    ky_full               = 2 * pi * vy * 1E-6;

    mid_x                 = floor(Nx/2);
    mid_y                 = floor(Ny/2);
    fft_imgs{k}           = IMGFFT(mid_y-zoom_size:mid_y+zoom_size, mid_x-zoom_size:mid_x+zoom_size);

    kx                    = kx_full(mid_x - zoom_size : mid_x + zoom_size);
    ky                    = ky_full(mid_y - zoom_size : mid_y + zoom_size);

    [theta_vals, S_theta]    = computeAngularSpectralDistribution(fft_imgs{k}, r_min, r_max, N_angular_bins, Angular_Threshold, Angular_Sigma, []);
    spectral_distribution{k} = S_theta;
    theta_values{k}          = theta_vals;
end

% Convert spectral distribution to matrix (N_shots x N_angular_bins)
delta_nkr_all = zeros(N_shots, N_angular_bins);
for k = 1:N_shots
    delta_nkr_all(k, :) = spectral_distribution{k};
end

% Group by scan parameter values (e.g., alpha, angle, etc.)
[unique_scan_parameter_values, ~, idx]   = unique(scan_parameter_values);
N_params                                 = length(unique_scan_parameter_values);

% Define angular range and conversion
angle_range                              = 180;
angle_per_bin                            = angle_range / N_angular_bins;
max_peak_angle                           = 180;
max_peak_bin                             = round(max_peak_angle / angle_per_bin);

% Parameters for search
window_size                              = 10;
angle_threshold                          = 100;

% Initialize containers for final results
mean_max_g2_values                       = zeros(1, N_params);
skew_max_g2_angle_values                 = zeros(1, N_params);
var_max_g2_values                        = zeros(1, N_params);
kurt_max_g2_angle_values                 = zeros(1, N_params);
fifth_order_cumulant_max_g2_angle_values = zeros(1, N_params);
sixth_order_cumulant_max_g2_angle_values = zeros(1, N_params);

% Also store raw data per group
max_g2_all_per_group                     = cell(1, N_params);
std_error_g2_values                      = zeros(1, N_params);

for i = 1:N_params
    group_idx                  = find(idx == i);
    group_data                 = delta_nkr_all(group_idx, :);
    N_reps                     = size(group_data, 1);

    g2_values                  = zeros(1, N_reps);
    
    for j = 1:N_reps
        profile                = group_data(j, :);

        % Restrict search to 0–60° for highest peak
        restricted_profile     = profile(1:max_peak_bin);
        [~, peak_idx_rel]      = max(restricted_profile);
        peak_idx               = peak_idx_rel;
        peak_angle             = (peak_idx - 1) * angle_per_bin;

        if peak_angle < angle_threshold
            offsets            = round(50 / angle_per_bin) : round(70 / angle_per_bin);
        else
            offsets            = -round(70 / angle_per_bin) : -round(50 / angle_per_bin);
        end

        ref_window             = mod((peak_idx - window_size):(peak_idx + window_size) - 1, N_angular_bins) + 1;
        ref                    = profile(ref_window);

        correlations           = zeros(size(offsets));
        
        for k = 1:length(offsets)
            shifted_idx        = mod(peak_idx + offsets(k) - 1, N_angular_bins) + 1;
            sec_window         = mod((shifted_idx - window_size):(shifted_idx + window_size) - 1, N_angular_bins) + 1;
            sec                = profile(sec_window);

            num                = mean(ref .* sec);
            denom              = mean(ref.^2);
            g2                 = num / denom;

            correlations(k)    = g2;
        end

        [max_corr, max_idx]    = max(correlations);
        g2_values(j)           = max_corr;
    end

    % Store raw values
    max_g2_all_per_group{i}        = g2_values;
    
    % Compute cumulants
    kappa                      = computeCumulants(g2_values(:), 6);

    % Final stats
    mean_max_g2_values(i)                       = kappa(1);
    var_max_g2_values(i)                        = kappa(2);
    
    N_eff                                       = sum(~isnan(g2_values));
    std_error_g2_values(i)                      = sqrt(kappa(2)) / sqrt(N_eff);

    skew_max_g2_angle_values(i)                 = kappa(3);
    kurt_max_g2_angle_values(i)                 = kappa(4);
    fifth_order_cumulant_max_g2_angle_values(i) = kappa(5);
    sixth_order_cumulant_max_g2_angle_values(i) = kappa(6);

end

%% Plot PDF of order parameter

if ~skipSaveFigures
    % Define folder for saving images
    saveFolder = [savefileName '_SavedFigures'];
    if ~exist(saveFolder, 'dir')
        mkdir(saveFolder);
    end
end

figure(2);  % one persistent figure
set(gcf, 'Color', 'w', 'Position', [100 100 950 750])

for val = scan_groups
    % Find the index i that matches this scan parameter value
    i = find(unique_scan_parameter_values == val, 1);

    % Skip if not found (sanity check)
    if isempty(i)
        continue;
    end

    g2_vals = max_g2_all_per_group{i};
    g2_vals = g2_vals(~isnan(g2_vals));

    if isempty(g2_vals)
        continue;
    end

    % KDE estimation
    [f, xi] = ksdensity(g2_vals, 'NumPoints', 200);

    clf;
    histogram(g2_vals, 'Normalization', 'pdf', ...
        'NumBins', 10, ...
        'FaceAlpha', 0.3, ...
        'EdgeColor', 'none', ...
        'FaceColor', [0.3 0.5 0.8]);

    hold on;
    plot(xi, f, 'LineWidth', 2, 'Color', [0 0.2 0.6]);

    set(gca, 'FontSize', 16);
    title(sprintf('%s: \\boldmath$\\alpha = %.1f^{\\circ}$', titleString, val), ...
        'FontSize', 16, 'Interpreter', 'latex');

    xlabel('$\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', 'Interpreter', 'latex', 'FontSize', 14);
    ylabel('PDF', 'FontSize', 14);
    xlim([0.0, 1.5]);
    grid on;

    drawnow;

    % ==== Save Figure ====
    if ~skipSaveFigures
        % Create a filename for each averaged plot
        fileNamePNG = fullfile(saveFolder, sprintf('max_g2_analysis_param_%03d.png', val));
        
        % Save current figure as PNG with high resolution
        print(gcf, fileNamePNG, '-dpng', '-r300');  % 300 dpi for high quality
    else
        pause(0.5)
    end  
end

%% Plot all cumulants
figure(3)
set(gcf, 'Color', 'w', 'Position', [100 100 950 750])

scan_vals = unique_scan_parameter_values;

% Define font style for consistency
axis_fontsize  = 14;
label_fontsize = 16;
title_fontsize = 16;

% 1. Mean with error bars
subplot(3,2,1);
errorbar(scan_vals, mean_max_g2_values, std_error_g2_values, 'o-', ...
    'LineWidth', 1.5, 'MarkerSize', 6);
title('Mean of $\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', ...
    'Interpreter', 'latex', 'FontSize', title_fontsize);
xlabel('$\alpha$ (degrees)', 'Interpreter', 'latex', ...
    'FontSize', label_fontsize);
ylabel('$\kappa_1$', 'Interpreter', 'latex', ...
    'FontSize', label_fontsize);
set(gca, 'FontSize', axis_fontsize);
grid on;

% 2. Variance
subplot(3,2,2);
plot(scan_vals, var_max_g2_values, 's-', 'LineWidth', 1.5, 'MarkerSize', 6);
title('Variance of $\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', ...
    'Interpreter', 'latex', 'FontSize', title_fontsize);
xlabel('$\alpha$ (degrees)', 'Interpreter', 'latex', ...
    'FontSize', label_fontsize);
ylabel('$\kappa_2$', 'Interpreter', 'latex', ...
    'FontSize', label_fontsize);
set(gca, 'FontSize', axis_fontsize);
grid on;

% 3. Skewness
subplot(3,2,3);
plot(scan_vals, skew_max_g2_angle_values, 'd-', 'LineWidth', 1.5, 'MarkerSize', 6);
title('Skewness of $\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', ...
    'Interpreter', 'latex', 'FontSize', title_fontsize);
xlabel('$\alpha$ (degrees)', 'Interpreter', 'latex', ...
    'FontSize', label_fontsize);
ylabel('$\kappa_3$', 'Interpreter', 'latex', ...
    'FontSize', label_fontsize);
set(gca, 'FontSize', axis_fontsize);
grid on;

% 4. Kurtosis
subplot(3,2,4);
plot(scan_vals, kurt_max_g2_angle_values, '^-', 'LineWidth', 1.5, 'MarkerSize', 6);
title('Kurtosis of $\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', ...
    'Interpreter', 'latex', 'FontSize', title_fontsize);
xlabel('$\alpha$ (degrees)', 'Interpreter', 'latex', ...
    'FontSize', label_fontsize);
ylabel('$\kappa_4$', 'Interpreter', 'latex', ...
    'FontSize', label_fontsize);
set(gca, 'FontSize', axis_fontsize);
grid on;

% 5. 5th-order cumulant
subplot(3,2,5);
plot(scan_vals, fifth_order_cumulant_max_g2_angle_values, 'v-', 'LineWidth', 1.5, 'MarkerSize', 6);
title('Fifth-order cumulant of $\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', ...
    'Interpreter', 'latex', 'FontSize', title_fontsize);
xlabel('$\alpha$ (degrees)', 'Interpreter', 'latex', ...
    'FontSize', label_fontsize);
ylabel('$\kappa_5$', 'Interpreter', 'latex', ...
    'FontSize', label_fontsize);
set(gca, 'FontSize', axis_fontsize);
grid on;

% 6. 6th-order cumulant
subplot(3,2,6);
plot(scan_vals, sixth_order_cumulant_max_g2_angle_values, '>-', 'LineWidth', 1.5, 'MarkerSize', 6);
title('Sixth-order cumulant of $\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', ...
    'Interpreter', 'latex', 'FontSize', title_fontsize);
xlabel('$\alpha$ (degrees)', 'Interpreter', 'latex', ...
    'FontSize', label_fontsize);
ylabel('$\kappa_6$', 'Interpreter', 'latex', ...
    'FontSize', label_fontsize);
set(gca, 'FontSize', axis_fontsize);
grid on;

% Super title
sgtitle(sprintf('Cumulants of Peak Offset Angular Correlation - %s', titleString), ...
    'FontWeight', 'bold', 'FontSize', 16, 'Interpreter', 'latex');

%% ── Mean ± Std vs. scan parameter ──────────────────────────────────────

% Plot mean ± SEM
figure(1);
set(gcf, 'Color', 'w', 'Position',[100 100 950 750])
set(gca, 'FontSize', 14);   % For tick labels only
errorbar(unique_scan_parameter_values, ...       % x-axis
         mean_max_g2_values, ...                 % y-axis (mean)
         std_error_g2_values, ...                % ± SEM
         '--o', 'LineWidth', 1.8, 'MarkerSize', 6 );

set(gca, 'FontSize', 14, 'YLim', [0, 1]);
hXLabel = xlabel('$\alpha$ (degrees)', 'Interpreter', 'latex');
hYLabel = ylabel('$\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', 'Interpreter', 'latex');
hTitle  = title(titleString, 'Interpreter', 'tex');
% set([hXLabel, hYLabel], 'FontName', font);
set([hXLabel, hYLabel], 'FontSize', 14);
set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold');
grid on;

% Define folder for saving images
saveFolder = [savefileName '_SavedFigures'];
if ~exist(saveFolder, 'dir')
    mkdir(saveFolder);
end
save([saveFolder savefileName '.mat'], 'unique_scan_parameter_values', 'mean_max_g2_values', 'std_error_g2_values');

%% Helper Functions
function [IMGFFT, IMGPR] = computeFourierTransform(I, skipPreprocessing, skipMasking, skipIntensityThresholding, skipBinarization)
    % computeFourierSpectrum - Computes the 2D Fourier power spectrum 
    % of binarized and enhanced lattice image features, with optional central mask.
    %
    % Inputs:
    %   I           - Grayscale or RGB image matrix
    %
    % Output:
    %   F_mag       - 2D Fourier power spectrum (shifted)
    
    if ~skipPreprocessing
        % Preprocessing: Denoise
        filtered             = imgaussfilt(I, 10);
        IMGPR                = I - filtered; % adjust sigma as needed
    else
        IMGPR                = I;
    end
    
    if ~skipMasking
        [rows, cols]     = size(IMGPR);
        [X, Y]           = meshgrid(1:cols, 1:rows);
        % Elliptical mask parameters
        cx               = cols / 2;
        cy               = rows / 2;
        
        % Shifted coordinates
        x                = X - cx;
        y                = Y - cy;
        
        % Ellipse semi-axes
        rx               = 0.4 * cols;
        ry               = 0.2 * rows;
        
        % Rotation angle in degrees -> radians
        theta_deg        = 30;        % Adjust as needed
        theta            = deg2rad(theta_deg);
        
        % Rotated ellipse equation
        cos_t            = cos(theta);
        sin_t            = sin(theta);
        
        x_rot            = (x * cos_t + y * sin_t);
        y_rot            = (-x * sin_t + y * cos_t);
        
        ellipseMask      = (x_rot.^2) / rx^2 + (y_rot.^2) / ry^2 <= 1;
        
        % Apply cutout mask
        IMGPR            = IMGPR .* ellipseMask;
    end

    if ~skipIntensityThresholding
        % Apply global intensity threshold mask
        intensity_thresh = 0.20; 
        intensity_mask   = IMGPR > intensity_thresh;
        IMGPR            = IMGPR .* intensity_mask;
    end

    if ~skipBinarization
        % Adaptive binarization and cleanup
        IMGPR            = imbinarize(IMGPR, 'adaptive', 'Sensitivity', 0.0);
        IMGPR            = imdilate(IMGPR, strel('disk', 2));
        IMGPR            = imerode(IMGPR, strel('disk', 1));
        IMGPR            = imfill(IMGPR, 'holes');
        F                = fft2(double(IMGPR)); % Compute 2D Fourier Transform
        IMGFFT           = abs(fftshift(F))';  % Shift zero frequency to center
    else
        F                = fft2(double(IMGPR)); % Compute 2D Fourier Transform
        IMGFFT           = abs(fftshift(F))';  % Shift zero frequency to center
    end
end

function [theta_vals, S_theta] = computeAngularSpectralDistribution(IMGFFT, r_min, r_max, num_bins, threshold, sigma, windowSize)
    % 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);
    Theta     = atan2(Y - cy, X - cx); % range [-pi, pi]

    % Choose radial band
    radial_mask = (R >= r_min) & (R <= r_max);

    % Initialize angular structure factor
    S_theta     = zeros(1, num_bins);
    theta_vals  = linspace(0, pi, num_bins);

    % Loop through angle bins
    for i = 1:num_bins
        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
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 imageOD = calculateODImage(imageAtom, imageBackground, imageDark, mode, exposureTime)
%CALCULATEODIMAGE Calculates the optical density (OD) image for absorption imaging.
%
%   imageOD = calculateODImage(imageAtom, imageBackground, imageDark, mode, exposureTime)
%
%   Inputs:
%       imageAtom       - Image with atoms
%       imageBackground - Image without atoms
%       imageDark       - Image without light
%       mode            - 'LowIntensity' (default) or 'HighIntensity'
%       exposureTime    - Required only for 'HighIntensity' [in seconds]
%
%   Output:
%       imageOD         - Computed OD image
%

    arguments
        imageAtom       (:,:) {mustBeNumeric}
        imageBackground (:,:) {mustBeNumeric}
        imageDark       (:,:) {mustBeNumeric}
        mode            char {mustBeMember(mode, {'LowIntensity', 'HighIntensity'})} = 'LowIntensity'
        exposureTime    double = NaN
    end

    % Compute numerator and denominator
    numerator   = imageBackground - imageDark;
    denominator = imageAtom - imageDark;

    % Avoid division by zero
    numerator(numerator == 0)     = 1;
    denominator(denominator == 0) = 1;

    % Calculate OD based on mode
    switch mode
        case 'LowIntensity'
            imageOD = -log(abs(denominator ./ numerator));
            
        case 'HighIntensity'
            if isnan(exposureTime)
                error('Exposure time must be provided for HighIntensity mode.');
            end
            imageOD = abs(denominator ./ numerator);
            imageOD = -log(imageOD) + (numerator - denominator) ./ (7000 * (exposureTime / 5e-6));
    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