Calculations/Data-Analyzer/extractAutocorrelation.m

%% Parameters

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     = "E:/Data - Experiment/2025/05/22/";

run            = '0078';

folderPath     = strcat(folderPath, run);

cam            = 5; 

angle          = 0;
center         = [1375, 2020];
span           = [200, 200];
fraction       = [0.1, 0.1];

pixel_size     = 5.86e-6;
removeFringes  = false;

scan_parameter      = 'rot_mag_fin_pol_angle';
% scan_parameter      = 'rot_mag_field';
scan_parameter_text = 'Angle = ';
% scan_parameter_text = 'BField = ';

font          = 'Bahnschrift';

skipPreprocessing           = true;
skipMasking                 = true;
skipIntensityThresholding   = true;
skipBinarization            = true;

%% 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));
    
    refimages(:,:,k)  = subtractBackgroundOffset(cropODImage(bkg_img, center, span), fraction)';
    absimages(:,:,k)  = subtractBackgroundOffset(cropODImage(calculateODImage(atm_img, bkg_img, dark_img), center, span), fraction)';

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, '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

%% Extract g2 from experiment data

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

N_bins                = 32;
Threshold             = 75;
Sigma                 = 2;
N_shots               = length(od_imgs);

% Display the cropped image
for k = 1:N_shots
    IMG              = od_imgs{k};
    [IMGFFT, IMGPR]  = computeFourierTransform(IMG, skipPreprocessing, skipMasking, skipIntensityThresholding, skipBinarization);
    
    % Calculate the x and y limits for the cropped image
    y_min            = center(1) - span(2) / 2;
    y_max            = center(1) + span(2) / 2;
    x_min            = center(2) - span(1) / 2;
    x_max            = center(2) + span(1) / 2;
    
    % Generate x and y arrays representing the original coordinates for each pixel
    x_range          = linspace(x_min, x_max, span(1));
    y_range          = linspace(y_min, y_max, span(2));
    
    [rows, cols]     = size(IMGFFT);
    zoom_size        = 50;             % Zoomed-in region around center
    mid_x            = floor(cols/2);
    mid_y            = floor(rows/2);
    fft_imgs{k}      = IMGFFT(mid_y-zoom_size:mid_y+zoom_size, mid_x-zoom_size:mid_x+zoom_size);
    
    [theta_vals, S_theta]    = computeNormalizedAngularSpectralDistribution(fft_imgs{k}, 10, 20, N_bins, Threshold, Sigma);
    spectral_distribution{k} = S_theta;
    theta_values{k}          = theta_vals;
end

% Create matrix of shape (N_shots x N_bins)
delta_nkr_all = zeros(N_shots, N_bins);
for k = 1:N_shots
    delta_nkr_all(k, :) = spectral_distribution{k};
end

% Grouping by scan parameter value (e.g., alpha)
[unique_scan_parameter_values, ~, idx] = unique(scan_parameter_values);

% Number of unique alpha values
N_alpha = length(unique_scan_parameter_values);

% Preallocate result arrays
g2_all      = zeros(N_alpha, N_bins);
g2_error_all = zeros(N_alpha, N_bins);

for i = 1:N_alpha
    group_idx  = find(idx == i);                  % Indices of 20 shots for this alpha
    group_data = delta_nkr_all(group_idx, :);     % (20 x N_bins) array

    for dtheta = 0:N_bins-1
        temp = zeros(length(group_idx), 1);
        for j = 1:length(group_idx)
            profile         = group_data(j, :);
            profile_shifted = circshift(profile, -dtheta, 2);

            num   = mean(profile .* profile_shifted);
            denom = mean(profile)^2;

            temp(j) = num / denom - 1;
        end
        g2_all(i, dtheta+1)       = mean(temp);
        g2_error_all(i, dtheta+1) = std(temp) / sqrt(length(group_idx));  % Standard error
    end
end

% Reconstruct theta axis from any one of the stored values
theta_vals = theta_values{1};  % assuming it's in radians

% Number of unique alpha values
nAlpha = size(g2_all, 1);

% Generate a colormap with enough unique colors
cmap = sky(nAlpha);  % You can also try 'jet', 'turbo', 'hot', etc.

figure(1); 
clf;
set(gcf,'Position',[100 100 950 750])
hold on;
legend_entries = cell(nAlpha, 1);

for i = 1:nAlpha
    errorbar(theta_vals/pi, g2_all(i, :), g2_error_all(i, :), ...
        'o-', 'Color', cmap(i,:), 'LineWidth', 1.2, ...
        'MarkerSize', 5, 'CapSize', 3);
    legend_entries{i} = sprintf('$\\alpha = %g^\\circ$', unique_scan_parameter_values(i));
end
ylim([-1.5 3.0]);  % Set y-axis limits here
set(gca, 'FontSize', 14);
hXLabel = xlabel('$\delta\theta / \pi$', 'Interpreter', 'latex');
hYLabel = ylabel('$g^{(2)}(\delta\theta)$', 'Interpreter', 'latex');
hTitle  = title('B = 2.45 G - Droplets to Stripes', 'Interpreter', 'tex');
legend(legend_entries, 'Interpreter', 'latex', 'Location', 'bestoutside');
set([hXLabel, hYLabel], 'FontName', font)
set([hXLabel, hYLabel], 'FontSize', 14)
set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold');  % Set font and size for title
grid on;

%% Extract g2 from simulation data

Data                        = load('E:/Results - Numerics/Data_Full3D/PhaseDiagram/ImagTimePropagation/Theta0/HighN/aS_9.562000e+01_theta_000_phi_000_N_712500/Run_000/psi_gs.mat','psi','Params','Transf','Observ');

% Data                        = load('E:/Results - Numerics/Data_Full3D/PhaseDiagram/ImagTimePropagation/Theta40/HighN/aS_9.562000e+01_theta_040_phi_000_N_508333/Run_000/psi_gs.mat','psi','Params','Transf','Observ');

Params = Data.Params;
Transf = Data.Transf; 
Observ = Data.Observ; 

if isgpuarray(Data.psi)
    psi = gather(Data.psi);
else
    psi = Data.psi;
end
if isgpuarray(Data.Observ.residual)
    Observ.residual = gather(Data.Observ.residual); 
else
    Observ.residual = Data.Observ.residual; 
end

% Axes scaling and coordinates in micrometers
x = Transf.x * Params.l0 * 1e6; 
y = Transf.y * Params.l0 * 1e6;
z = Transf.z * Params.l0 * 1e6;

dx = x(2)-x(1); dy = y(2)-y(1); dz = z(2)-z(1);

% Calculate frequency increment (frequency axes)
Nx           = length(x);       % grid size along X 
Ny           = length(y);       % grid size along Y 
dx           = mean(diff(x));   % real space increment in the X direction (in micrometers)
dy           = mean(diff(y));   % real space increment in the Y direction (in micrometers)
dvx          = 1 / (Nx * dx);  % reciprocal space increment in the X direction (in micrometers^-1)
dvy          = 1 / (Ny * dy);  % reciprocal space increment in the Y direction (in micrometers^-1)

% Create the frequency axes
vx           = (-Nx/2:Nx/2-1) * dvx;  % Frequency axis in X (micrometers^-1)
vy           = (-Ny/2:Ny/2-1) * dvy;  % Frequency axis in Y (micrometers^-1)

% Calculate maximum frequencies
% kx_max       = pi / dx;
% ky_max       = pi / dy;

% Generate reciprocal axes
% kx           = linspace(-kx_max, kx_max * (Nx-2)/Nx, Nx);
% ky           = linspace(-ky_max, ky_max * (Ny-2)/Ny, Ny);

% Create the Wavenumber axes
kx           = 2*pi*vx;  % Wavenumber axis in X
ky           = 2*pi*vy;  % Wavenumber axis in Y 

% Compute probability density |psi|^2
n = abs(psi).^2;

nxz = squeeze(trapz(n*dy,2));
nyz = squeeze(trapz(n*dx,1));
nxy = squeeze(trapz(n*dz,3));

skipPreprocessing           = true;
skipMasking                 = true;
skipIntensityThresholding   = true;
skipBinarization            = true;

font          = 'Bahnschrift';
% Extract g2

N_bins                      = 90;
Threshold                   = 75;
Sigma                       = 2;

IMG                         = nxy;

[IMGFFT, IMGPR]             = computeFourierTransform(IMG, skipPreprocessing, skipMasking, skipIntensityThresholding, skipBinarization);

[theta_vals, S_theta]       = computeNormalizedAngularSpectralDistribution(IMGFFT, 10, 35, N_bins, Threshold, Sigma);

g2_all = zeros(1, N_bins);  % Preallocate

for dtheta = 0:N_bins-1
    profile         = S_theta;
    profile_shifted = circshift(profile, -dtheta, 2);

    num   = mean(profile .* profile_shifted);
    denom = mean(profile)^2;

    g2_all(dtheta+1) = num / denom - 1;
end

figure(2);
clf
set(gcf,'Position',[500 100 1000 800])
t = tiledlayout(2, 2, 'TileSpacing', 'compact', 'Padding', 'compact'); % 1x4 grid

% Display the cropped OD image
nexttile
plotxy = pcolor(x,y,IMG');
set(plotxy, 'EdgeColor', 'none');
cbar1 = colorbar;
cbar1.Label.Interpreter = 'latex';
colormap(gca, Helper.Colormaps.plasma())
xlabel('$x$ ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14)
ylabel('$y$ ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14)
title('$|\Psi(x,y)|^2$', 'Interpreter', 'latex', 'FontSize', 14) 

% Plot the power spectrum
nexttile;
imagesc(kx, ky, log(1 + abs(IMGFFT).^2));
axis square;
hcb = colorbar;
colormap(gca, Helper.Colormaps.plasma())
set(gca, 'FontSize', 14);   % For tick labels only
set(gca,'YDir','normal')
hXLabel = xlabel('k_x', 'Interpreter', 'tex');
hYLabel = ylabel('k_y', 'Interpreter', 'tex');
hTitle  = title('Power Spectrum - S(k_x,k_y)', 'Interpreter', 'tex');
set([hXLabel, hYLabel], 'FontName', font)
set([hXLabel, hYLabel], 'FontSize', 14)
set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold');  % Set font and size for title

% Plot the angular distribution
nexttile
plot(theta_vals/pi, S_theta,'Linewidth',2);
set(gca, 'FontSize', 14);   % For tick labels only
hXLabel = xlabel('\theta/\pi [rad]', 'Interpreter', 'tex');
hYLabel = ylabel('Normalized magnitude (a.u.)', 'Interpreter', 'tex');
hTitle = title('Angular Spectral Distribution - S(\theta)', 'Interpreter', 'tex');
set([hXLabel, hYLabel], 'FontName', font)
set([hXLabel, hYLabel], 'FontSize', 14)
set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold');  % Set font and size for title
grid on

nexttile
plot(theta_vals/pi, g2_all, 'o-', 'LineWidth', 1.2, 'MarkerSize', 5);
set(gca, 'FontSize', 14);
ylim([-1.5 3.0]);  % Set y-axis limits here
hXLabel = xlabel('$\delta\theta / \pi$', 'Interpreter', 'latex');
hYLabel = ylabel('$g^{(2)}(\delta\theta)$', 'Interpreter', 'latex');
hTitle  = title('Autocorrelation', 'Interpreter', 'tex');
set([hXLabel, hYLabel], 'FontName', font)
set([hXLabel, hYLabel], 'FontSize', 14)
set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold');  % Set font and size for title
grid on;

%% 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] = computeNormalizedAngularSpectralDistribution(IMGFFT, r_min, r_max, num_bins, threshold, sigma)
    % 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 the angular structure factor array
    S_theta = zeros(1, num_bins); % Pre-allocate for 180 angle bins
    % Define the angle values for the x-axis
    theta_vals = linspace(0, pi, num_bins);

    % Loop through each angle bin
    for i = 1:num_bins
        angle_start = (i-1) * pi / num_bins;
        angle_end   = i * pi / num_bins;
        
        % Define a mask for the given angle range
        angle_mask  = (Theta >= angle_start & Theta < angle_end);
        
        bin_mask    = radial_mask & angle_mask;

        % Extract the Fourier components for the given angle
        fft_angle   = IMGFFT .* bin_mask;
        
        % Integrate the Fourier components over the radius at the angle
        S_theta(i)  = sum(sum(abs(fft_angle).^2)); % sum of squared magnitudes
    end
    
    % Create a 1D Gaussian kernel
    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); % normalize
    
    % Apply convolution (circular padding to preserve periodicity)
    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); % crop back to original size
    
    % Normalize to 1
    S_theta = S_theta / max(S_theta);
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