Calculations/Imaging Response Function Extractor/extractIRF.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 = "C:/Users/Karthik/Documents/GitRepositories/Calculations/IRF/0044/";

cam      = 5; 

angle    = 90 + 51.5;
center   = [1700, 2300];
span     = [255, 255];
fraction = [0.1, 0.1];

NA         = 0.6;
pixel_size = 4.6e-6;
lambda     = 421e-9;

d = lambda/2/pi/NA;
k_cutoff = NA/lambda/1e6;

%% 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  = im2double(imrotate(h5read(fullFileName, append(groupList(cam), "/atoms")), angle));
    bkg_img  = im2double(imrotate(h5read(fullFileName, append(groupList(cam), "/background")), angle));
    dark_img = im2double(imrotate(h5read(fullFileName, append(groupList(cam), "/dark")), angle));
    
    refimages(:,:,k)  = subtract_offset(crop_image(bkg_img, center, span), fraction);
    absimages(:,:,k)  = subtract_offset(crop_image(calculate_OD(atm_img, bkg_img, dark_img), center, span), fraction);

end
%% Fringe removal

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

%% Compute the Density Noise Spectrum

mean_subtracted_od_imgs = cell(1, length(od_imgs));
mean_od_img             = mean(cat(3, od_imgs{:}), 3, 'double');

density_fft             = cell(1, length(od_imgs));
density_noise_spectrum  = cell(1, length(od_imgs));

[Nx, Ny] = size(mean_od_img);
dx       = pixel_size;
dy       = pixel_size;

xvals        = (1:Nx)*dx*1e6;
yvals        = (1:Ny)*dy*1e6;

Nyq_k    = 1/dx;                   % Nyquist
dk       = 1/(Nx*dx);              % Wavenumber increment
kx       = -Nyq_k/2:dk:Nyq_k/2-dk; % wavenumber
kx       = kx * dx;                % wavenumber (in units of 1/dx)

Nyq_k    = 1/dy;                   % Nyquist
dk       = 1/(Ny*dy);              % Wavenumber increment
ky       = -Nyq_k/2:dk:Nyq_k/2-dk; % wavenumber
ky       = ky * dy;                % wavenumber (in units of 1/dy)

% Create Circular Mask
n = 2^8;                  % size of mask
mask = zeros(n);
I = 1:n; 
x = I-n/2;                % mask x-coordinates 
y = n/2-I;                % mask y-coordinates
[X,Y] = meshgrid(x,y);    % create 2-D mask grid
R = 32;                   % aperture radius
A = (X.^2 + Y.^2 <= R^2); % circular aperture of radius R
mask(A) = 1;              % set mask elements inside aperture to 1


% Calculate Power Spectrum and plot
figure('Position', [100, 100, 1200, 800]);
clf

for k = 1 : length(od_imgs)
    mean_subtracted_od_imgs{k} = od_imgs{k} - mean_od_img;
    masked_img                 = mean_subtracted_od_imgs{k} .* mask;
    density_fft{k}             = (1/numel(masked_img)) * abs(fftshift(fft2(masked_img)));
    density_noise_spectrum{k}  = density_fft{k}.^2;

    % Subplot 1
    % subplot(2, 3, 1);
    subplot('Position', [0.05, 0.55, 0.28, 0.4])
    imagesc(xvals, yvals, od_imgs{k})
    xlabel('µm', 'FontSize', 16)
    ylabel('µm', 'FontSize', 16)
    axis equal tight;
    colorbar
    colormap (flip(jet));
    % set(gca,'CLim',[0 100]);
    set(gca,'YDir','normal')
    title('Single-shot image', 'FontSize', 16);
    
    % Subplot 2
    % subplot(2, 3, 2);
    subplot('Position', [0.36, 0.55, 0.28, 0.4])
    imagesc(xvals, yvals, mean_od_img)
    xlabel('µm', 'FontSize', 16)
    ylabel('µm', 'FontSize', 16)
    axis equal tight;
    colorbar
    colormap (flip(jet));
    % set(gca,'CLim',[0 100]);
    set(gca,'YDir','normal')
    title('Averaged density image', 'FontSize', 16);
    
    % Subplot 3
    % subplot(2, 3, 3);
    subplot('Position', [0.67, 0.55, 0.28, 0.4]);
    imagesc(xvals, yvals, mean_subtracted_od_imgs{k})
    xlabel('µm', 'FontSize', 16)
    ylabel('µm', 'FontSize', 16)
    axis equal tight;
    colorbar
    colormap (flip(jet));
    % set(gca,'CLim',[0 100]);
    set(gca,'YDir','normal')
    title('Image noise = Single-shot - Average', 'FontSize', 16);
    
    % Subplot 4
    % subplot(2, 3, 4);
    subplot('Position', [0.05, 0.05, 0.28, 0.4]);
    imagesc(xvals, yvals, mean_subtracted_od_imgs{k} .* mask)
    xlabel('µm', 'FontSize', 16)
    ylabel('µm', 'FontSize', 16)
    axis equal tight;
    colorbar
    colormap (flip(jet));
    % set(gca,'CLim',[0 100]);
    set(gca,'YDir','normal')
    title('Masked Noise', 'FontSize', 16);
    
    % Subplot 5
    % subplot(2, 3, 5);
    subplot('Position', [0.36, 0.05, 0.28, 0.4]);
    imagesc(kx, ky, abs(log2(density_fft{k})))
    xlabel('1/dx', 'FontSize', 16)
    ylabel('1/dy', 'FontSize', 16)
    axis equal tight;
    colorbar
    colormap (flip(jet));
    % set(gca,'CLim',[0 100]);
    set(gca,'YDir','normal')
    title('DFT', 'FontSize', 16);
    
    % Subplot 6
    % subplot(2, 3, 6);
    subplot('Position', [0.67, 0.05, 0.28, 0.4]);
    imagesc(kx, ky, abs(log2(density_noise_spectrum{k})))
    xlabel('1/dx', 'FontSize', 16)
    ylabel('1/dy', 'FontSize', 16)
    axis equal tight;
    colorbar
    colormap (flip(jet));
    % set(gca,'CLim',[0 100]);
    set(gca,'YDir','normal')
    title('Density Noise Spectrum = |DFT|^2', 'FontSize', 16);

    drawnow;
end

%% Compute the average 2D spectrum and do radial averaging to get the 1D spectrum

% Compute the average power spectrum.
averagePowerSpectrum = mean(cat(3, density_noise_spectrum{:}), 3, 'double');

% Plot the average power spectrum.
figure('Position', [100, 100, 1200, 500]);
clf

subplot('Position', [0.05, 0.1, 0.4, 0.8]) % Adjusted position
imagesc(abs(10*log10(averagePowerSpectrum)))
axis equal tight;
colorbar
colormap(flip(jet));
% set(gca,'CLim',[0 1e-7]);
title('Average Density Noise Spectrum', 'FontSize', 16);
grid on;
centers = ginput;
radius = 6;
% Plot where clicked.
hVC  = viscircles(centers, radius, 'Color', 'r', 'LineWidth', 2);
xc = centers(:,1);
% xc = [78.2600, 108.3400, 128.8200, 150.5800, 181.3000];
yc = centers(:,2);
% yc = [131.3800, 155.7000, 128.8200, 101.3000, 126.2600];
[yDim, xDim] = size(averagePowerSpectrum);
[xx,yy] = meshgrid(1:yDim,1:xDim);
mask = false(xDim,yDim);
for ii = 1:length(centers)
	mask = mask | hypot(xx - xc(ii), yy - yc(ii)) <= radius;
end
mask = not(mask);

x1 = 1;
y1 = 1;
x2 = 256;
y2 = 256;

% Ask user if the circle is acceptable.
message = sprintf('Is this acceptable?');
button = questdlg(message, message, 'Accept', 'Reject and Quit', 'Accept');
if contains(button, 'Accept','IgnoreCase',true)
    image = mask.*averagePowerSpectrum;
    image(image==0) = NaN;
    imagesc(kx, ky, mask.*abs(10*log10(averagePowerSpectrum)))
    hold on
    line([kx(x1),kx(x2)], [ky(y1),ky(y2)], 'Color','white', 'LineStyle','--', 'LineWidth', 4);
    % imagesc(kx, ky, 10*log10(averagePowerSpectrum))
    % imagesc(kx, ky, log2(averagePowerSpectrum))
    % imagesc(kx, ky, averagePowerSpectrum)
    xlabel('1/dx', 'FontSize', 16)
    ylabel('1/dy', 'FontSize', 16)
    axis equal tight;
    colorbar
    colormap(flip(jet));
    % set(gca,'CLim',[0 1e-7]);
    title('Average Density Noise Spectrum', 'FontSize', 16);
    grid on;
elseif contains(button, 'Quit','IgnoreCase',true)
    delete(hVC); % Delete the circle from the overlay.
    image = averagePowerSpectrum;
    imagesc(kx, ky, abs(10*log10(averagePowerSpectrum)))
    % imagesc(kx, ky, 10*log10(averagePowerSpectrum))
    % imagesc(kx, ky, log2(averagePowerSpectrum))
    % imagesc(kx, ky, averagePowerSpectrum)
    xlabel('1/dx', 'FontSize', 16)
    ylabel('1/dy', 'FontSize', 16)
    axis equal tight;
    colorbar
    colormap(flip(jet));
    % set(gca,'CLim',[0 1e-7]);
    title('Average Density Noise Spectrum', 'FontSize', 16);
    grid on;
end

subplot('Position', [0.55, 0.1, 0.4, 0.8]) % Adjusted position
% [r, Zr] = radial_profile(averagePowerSpectrum, 1);
% Zr = (Zr - min(Zr))./(max(Zr) - min(Zr));
% plot(r, Zr, 'o-', 'MarkerSize', 4, 'MarkerFaceColor', 'none');
% set(gca, 'XScale', 'log'); % Setting x-axis to log scale

[xi, yi, profile] = improfile(image, [x1,x2], [y1,y2]);
profile   = (profile - min(profile))./(max(profile) - min(profile));
ks        = sqrt(kx.^2 + ky.^2);

profile   = profile(length(profile)/2:end);
ks        = ks(length(ks)/2:end);

n    = 0.15;
[val,slice_idx]=min(abs(ks-n));
ks        = ks(1:slice_idx);
profile   = profile(1:slice_idx);
plot(ks, profile, 'b*-');
% plot(profile, 'b*-');
grid on;
% xlim([min(ks) max(ks)])
title('Radial average of Density Noise Spectrum', 'FontSize', 16);
grid on;


%% Helper Functions

function ret = get_offset_from_corner(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 = subtract_offset(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 = get_offset_from_corner(img, x_fraction, y_fraction);
    ret    = img - offset;
end

function ret = crop_image(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 = calculate_OD(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 [R, Zr] = radial_profile(data,radial_step)
    x = (1:size(data,2))-size(data,2)/2;
    y = (1:size(data,1))-size(data,1)/2;
    % coordinate grid:
    [X,Y] = meshgrid(x,y);
    % creating circular layers
    Z_integer = round(abs(X+1i*Y)/radial_step)+1;
    % very fast MatLab calculations:
    R  = accumarray(Z_integer(:),abs(X(:)+1i*Y(:)),[],@mean);
    Zr = accumarray(Z_integer(:),data(:),[],@mean);
end

function [M] = ImagingResponseFunction(B)
    x = -100:100;
    y = x;
    [X,Y] = meshgrid(x,y);
    R = sqrt(X.^2+Y.^2);
    PHI = atan2(X,Y)+pi;
    %fit parameters
    tau = B(1);
    alpha = B(2);
    S0 = B(3);
    phi = B(4);
    beta = B(5);
    delta = B(6);
    A = B(7);
    C = B(8);
    a = B(9);
    U = heaviside(1-R/a).*exp(-R.^2/a^2/tau^2);
    THETA = S0*(R/a).^4 + alpha*(R/a).^2.*cos(2*PHI-2*phi) + beta*(R/a).^2;
    p = U.*exp(1i.*THETA);
    M = A*abs((ifft2(real(exp(1i*delta).*fftshift(fft2(p)))))).^2 + C;
end

function [RadialResponseFunc] = RadialImagingResponseFunction(C, k, kmax)
    A = heaviside(1-k/kmax).*exp(-C(1)*k.^4);
    W = C(2) + C(3)*k.^2 + C(4)*k.^4;
    RadialResponseFunc = 0;
    for n = -30:30
        RadialResponseFunc = RadialResponseFunc + besselj(n,C(5)*k.^2).^2 + besselj(n,C(5)*k.^2).*besselj(-n,C(5)*k.^2).*cos(2*W);
    end
    RadialResponseFunc = C(6)*1/2*A.*RadialResponseFunc;
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