Latest analysis script for IRF, new script to model imaging aberrations, modified plotting script for data from experiment.
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@ -1,12 +1,12 @@
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%% Parameters
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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"];
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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"];
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folderPath = "C:/Users/Karthik/Documents/GitRepositories/Calculations/Data-Analyzer/20/";
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%{
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run = '0140';
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folderPath = "C:/Users/Karthik/Documents/GitRepositories/Calculations/Data-Analyzer/";
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folderPath = strcat(folderPath, run);
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run = '0140';
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cam = 4;
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@ -16,7 +16,25 @@ span = [50, 50];
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fraction = [0.1, 0.1];
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pixel_size = 5.86e-6;
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removeFringes = true;
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removeFringes = false;
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%}
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folderPath = "C:/Users/Karthik/Documents/GitRepositories/Calculations/Imaging-Response-Function-Extractor/";
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run = '0096';
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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 = [1137, 2023];
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span = [500, 500];
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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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% 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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@ -36,8 +54,8 @@ for k = 1 : length(files)
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bkg_img = im2double(imrotate(h5read(fullFileName, append(groupList(cam), "/background")), angle));
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dark_img = im2double(imrotate(h5read(fullFileName, append(groupList(cam), "/dark")), angle));
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refimages(:,:,k) = subtract_offset(crop_image(bkg_img, center, span), fraction)';
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absimages(:,:,k) = subtract_offset(crop_image(calculate_OD(atm_img, bkg_img, dark_img), center, span), fraction)';
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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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@ -123,7 +141,7 @@ hold off;
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%% Helper Functions
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function ret = get_offset_from_corner(img, x_fraction, y_fraction)
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function ret = getBkgOffsetFromCorners(img, x_fraction, y_fraction)
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% image must be a 2D numerical array
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[dim1, dim2] = size(img);
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@ -135,7 +153,7 @@ function ret = get_offset_from_corner(img, x_fraction, y_fraction)
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ret = mean([mean(s1(:)), mean(s2(:)), mean(s3(:)), mean(s4(:))]);
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end
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function ret = subtract_offset(img, fraction)
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function ret = subtractBackgroundOffset(img, fraction)
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% Remove the background from the image.
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% :param dataArray: The image
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% :type dataArray: xarray DataArray
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@ -148,11 +166,11 @@ function ret = subtract_offset(img, fraction)
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x_fraction = fraction(1);
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y_fraction = fraction(2);
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offset = get_offset_from_corner(img, x_fraction, y_fraction);
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offset = getBkgOffsetFromCorners(img, x_fraction, y_fraction);
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ret = img - offset;
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end
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function ret = crop_image(img, center, span)
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function ret = cropODImage(img, center, span)
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% Crop the image according to the region of interest (ROI).
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% :param dataSet: The images
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% :type dataSet: xarray DataArray or DataSet
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@ -171,7 +189,7 @@ function ret = crop_image(img, center, span)
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ret = img(y_start:y_end, x_start:x_end);
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end
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function ret = calculate_OD(imageAtom, imageBackground, imageDark)
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function ret = calculateODImage(imageAtom, imageBackground, imageDark)
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% Calculate the OD image for absorption imaging.
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% :param imageAtom: The image with atoms
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% :type imageAtom: numpy array
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@ -264,4 +282,4 @@ function [optrefimages] = removefringesInImage(absimages, refimages, bgmask)
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% Compute optimised reference image
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optrefimages(:,:,j)=reshape(R*c,[ydim xdim]);
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end
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end
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end
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127
Estimations/ModellingImagingAberrations.m
Normal file
127
Estimations/ModellingImagingAberrations.m
Normal file
@ -0,0 +1,127 @@
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%% Zernike Polynomials
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resolution = 100; % Resolution
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plotZernike(2, 0, resolution) % Defocus (Z2^0)
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%%
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plotZernike(2, 2, resolution) % Astigmatism (Z2^2)
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%%
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plotZernike(3, 1, resolution) % Coma (Z3^1, x-direction)
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%%
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plotZernike(3, -1, resolution) % Coma (Z3^-1, y-direction)
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%%
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plotZernike(4, 0, resolution) % Spherical Aberration (Z4^0)
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%% Aberrated PSF
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C = [0.0, 0.0, 0.0, 0.0, 0.0]; % Zernike coefficients
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pupil_radius = 0.5; % Pupil radius (normalized)
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plotAberratedPSF(C, pupil_radius, resolution);
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function Z = computeZernikePolynomials(n, m, r, theta)
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% Zernike polynomial function for radial and angular coordinates (r, theta)
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% Input:
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% n - radial order
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% m - azimuthal frequency
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% r - radial coordinate (normalized to unit circle, 0 <= r <= 1)
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% theta - angular coordinate (angle in radians)
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%
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% Output:
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% Z - Zernike polynomial value at (r, theta)
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if n == 2 && m == 0
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% Defocus (Z2^0)
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Z = 2 * r.^2 - 1;
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elseif n == 2 && m == 2
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% Astigmatism (Z2^2)
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Z = r.^2 .* cos(2 * theta);
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elseif n == 3 && m == 1
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% Coma (Z3^1)
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Z = (3 * r.^3 - 2 * r) .* cos(theta);
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elseif n == 3 && m == -1
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% Coma (Z3^-1)
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Z = (3 * r.^3 - 2 * r) .* sin(theta);
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elseif n == 4 && m == 0
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% Spherical Aberration (Z4^0)
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Z = 6 * r.^4 - 6 * r.^2 + 1;
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else
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% Default to zero if no known Zernike polynomial matches
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Z = 0;
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end
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end
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function plotZernike(n, m, resolution)
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% n: radial order
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% m: azimuthal frequency
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% resolution: number of points for plotting
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% Create a grid of (r, theta) coordinates
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[theta, r] = meshgrid(linspace(0, 2*pi, resolution), linspace(0, 1, resolution));
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% Calculate the Zernike polynomial for the given (n, m)
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Z = computeZernikePolynomials(n, m, r, theta);
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% Convert polar to Cartesian coordinates for plotting
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[X, Y] = pol2cart(theta, r);
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% Plot the Zernike polynomial using a surface plot
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figure(1)
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clf
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set(gcf,'Position',[50 50 950 750])
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surf(X, Y, Z, 'EdgeColor', 'none');
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colormap jet;
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colorbar;
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title(sprintf('Zernike Polynomial Z_{%d}^{%d}', n, m), 'Interpreter', 'tex', 'FontSize', 16);
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xlabel('X', 'FontSize', 16);
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ylabel('Y', 'FontSize', 16);
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zlabel('Zernike Value', 'FontSize', 16);
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axis equal;
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shading interp;
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end
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function [theta, r, PSF] = modelPSF(C, pupil_radius, resolution)
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% C is the vector of Zernike coefficients [C_defocus, C_astigmatism, C_coma, C_spherical, ...]
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% resolution is the number of points for the grid (NxN grid)
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% pupil_radius is the radius of the pupil aperture
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% Create a grid of (r, theta) coordinates
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[theta, r] = meshgrid(linspace(0, 2*pi, resolution), linspace(0, 1, resolution));
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% Pupil function: 1 inside the pupil radius, 0 outside
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P = double(r <= pupil_radius); % 2D mask
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% Wavefront error from Zernike polynomials
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W = C(1) * computeZernikePolynomials(2, 0, r, theta) + ... % Defocus (Z2^0)
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C(2) * computeZernikePolynomials(2, 2, r, theta) + ... % Astigmatism (Z2^2)
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C(3) * computeZernikePolynomials(3, 1, r, theta) + ... % Coma (Z3^1, x-direction)
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C(4) * computeZernikePolynomials(3, -1, r, theta) + ... % Coma (Z3^-1, y-direction)
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C(5) * computeZernikePolynomials(4, 0, r, theta); % Spherical Aberration (Z4^0)
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% Fourier transform of the pupil function with aberrations
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PSF = abs(fftshift(fft2(P .* exp(1i * W)))).^2; % Intensity distribution
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end
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function plotAberratedPSF(C, pupil_radius, resolution)
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% C: Zernike coefficients [C_defocus, C_astigmatism, C_coma_x, C_coma_y, C_spherical]
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% pupil_radius: Radius of the pupil aperture
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% resolution: Number of points for plotting
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% Generate PSF using the updated modelPSF function
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[theta, r, PSF] = modelPSF(C, pupil_radius, resolution);
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% Convert polar to Cartesian coordinates for plotting
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[X, Y] = pol2cart(theta, r);
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figure(1)
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clf
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set(gcf,'Position',[50 50 950 750])
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surf(X, Y, PSF, 'EdgeColor', 'none');
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view(2); % 2D view
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axis equal tight;
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shading interp;
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colorbar;
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colormap jet;
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title('PSF', 'FontSize', 16);
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xlabel('X', 'FontSize', 16);
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ylabel('Y', 'FontSize', 16);
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end
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@ -1,26 +1,34 @@
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%% Parameters
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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"];
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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"];
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folderPath = "C:/Users/Karthik/Documents/GitRepositories/Calculations/Imaging-Response-Function-Extractor/0127/";
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folderPath = "C:/Users/Karthik/Documents/GitRepositories/Calculations/Imaging-Response-Function-Extractor/";
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cam = 5;
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run = '0096';
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% angle = 90 + 51.5;
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% center = [1700, 2300];
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angle = 90;
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center = [2035 1250];
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span = [255, 255];
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fraction = [0.1, 0.1];
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folderPath = strcat(folderPath, run);
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NA = 0.6;
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pixel_size = 4.6e-6;
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lambda = 421e-9;
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cam = 5;
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d = 0.61*lambda/NA;
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k_cutoff = 2*NA/lambda/1e6; % in units of 1/µm)
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angle = 0;
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center = [1137, 2023];
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span = [255, 255];
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fraction = [0.1, 0.1];
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removeFringes = true;
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NA = 0.6;
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pixel_size = 4.6e-6;
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lambda = 421e-9;
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% The diameter of the first dark concentric ring surrounding the central intensity peak of a point spread function (or Airy disk)
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d = 1.22 * (lambda / NA);
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% Abbe limit
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AbbeLimit = lambda / (2 * NA);
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% Maximum resolvable spatial frequency for the coherent case
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k_cutoff = (NA/lambda) * 1e-6; % (in units of 1/µm)
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removeFringes = false;
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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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@ -40,12 +48,12 @@ for k = 1 : length(files)
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bkg_img = im2double(imrotate(h5read(fullFileName, append(groupList(cam), "/background")), angle));
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dark_img = im2double(imrotate(h5read(fullFileName, append(groupList(cam), "/dark")), angle));
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refimages(:,:,k) = subtract_offset(crop_image(bkg_img, center, span), fraction);
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absimages(:,:,k) = subtract_offset(crop_image(calculate_OD(atm_img, bkg_img, dark_img), center, span), fraction);
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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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% Fringe removal
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if removeFringes
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optrefimages = removefringesInImage(absimages, refimages);
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@ -79,116 +87,109 @@ dy = pixel_size;
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xvals = (1:Nx)*dx*1e6;
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yvals = (1:Ny)*dy*1e6;
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Nyq_k = 1/dx; % Nyquist
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dk = 1/(Nx*dx); % Wavenumber increment
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kx = -Nyq_k/2:dk:Nyq_k/2-dk; % wavenumber
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kx = kx * dx; % wavenumber (in units of 1/dx)
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dvx = 1 / (Nx * dx); % reciprocal space increment in the X direction (in units of 1/dx)
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dvy = 1 / (Ny * dy); % reciprocal space increment in the Y direction (in units of 1/dy)
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Nyq_k = 1/dy; % Nyquist
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dk = 1/(Ny*dy); % Wavenumber increment
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ky = -Nyq_k/2:dk:Nyq_k/2-dk; % wavenumber
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ky = ky * dy; % wavenumber (in units of 1/dy)
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% Create the frequency axes
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vx = (-Nx/2:Nx/2-1) * dvx; % Frequency axis in X (in units of 1/dx)
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vy = (-Ny/2:Ny/2-1) * dvy; % Frequency axis in Y (in units of 1/dy)
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% Create the Wavenumber axes
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kx = 2*pi*vx; % Wavenumber axis in X
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ky = 2*pi*vy; % Wavenumber axis in Y
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% Create Circular Mask
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n = 2^8; % size of mask
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n = 2^8; % size of mask
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mask = zeros(n);
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I = 1:n;
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x = I-n/2; % mask x-coordinates
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y = n/2-I; % mask y-coordinates
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[X,Y] = meshgrid(x,y); % create 2-D mask grid
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R = 32; % aperture radius
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A = (X.^2 + Y.^2 <= R^2); % circular aperture of radius R
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mask(A) = 1; % set mask elements inside aperture to 1
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x = I-n/2; % mask x-coordinates
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y = n/2-I; % mask y-coordinates
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[X,Y] = meshgrid(x,y); % create 2-D mask grid
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R = 32; % aperture radius
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A = (X.^2 + Y.^2 <= R^2); % circular aperture of radius R
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mask(A) = 1; % set mask elements inside aperture to 1
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% Calculate Power Spectrum and plot
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figure('Position', [100, 100, 1200, 800]);
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figure(1)
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clf
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set(gcf,'Position',[100, 100, 1200, 800])
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% Create tiled layout with 2 rows and 3 columns
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t = tiledlayout(2, 3, 'TileSpacing', 'compact', 'Padding', 'compact');
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for k = 1 : length(od_imgs)
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mean_subtracted_od_imgs{k} = od_imgs{k} - mean_od_img;
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masked_img = mean_subtracted_od_imgs{k} .* mask;
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density_fft{k} = (1/numel(masked_img)) * abs(fftshift(fft2(masked_img)));
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density_noise_spectrum{k} = density_fft{k}.^2;
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% Subplot 1
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% subplot(2, 3, 1);
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subplot('Position', [0.05, 0.55, 0.28, 0.4])
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% Tile 1: Single-shot image
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nexttile(1);
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imagesc(xvals, yvals, od_imgs{k})
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xlabel('µm', 'FontSize', 16)
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ylabel('µm', 'FontSize', 16)
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xlabel('\mum', 'Interpreter', 'tex', 'FontSize', 16)
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ylabel('\mum', 'Interpreter', 'tex', 'FontSize', 16)
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axis equal tight;
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colorbar
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colormap jet; % (flip(jet))
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% set(gca,'CLim',[0 100]);
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colormap jet;
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set(gca,'YDir','normal')
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title('Single-shot image', 'FontSize', 16);
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% Subplot 2
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% subplot(2, 3, 2);
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subplot('Position', [0.36, 0.55, 0.28, 0.4])
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% Tile 2: Averaged density image
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nexttile(2);
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imagesc(xvals, yvals, mean_od_img)
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xlabel('µm', 'FontSize', 16)
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ylabel('µm', 'FontSize', 16)
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xlabel('\mum', 'Interpreter', 'tex', 'FontSize', 16)
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ylabel('\mum', 'Interpreter', 'tex', 'FontSize', 16)
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axis equal tight;
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colorbar
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colormap jet; % (flip(jet))
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% set(gca,'CLim',[0 100]);
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colormap jet;
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set(gca,'YDir','normal')
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title('Averaged density image', 'FontSize', 16);
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% Subplot 3
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% subplot(2, 3, 3);
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subplot('Position', [0.67, 0.55, 0.28, 0.4]);
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% Tile 3: Image noise = Single-shot - Average
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nexttile(3);
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imagesc(xvals, yvals, mean_subtracted_od_imgs{k})
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xlabel('µm', 'FontSize', 16)
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ylabel('µm', 'FontSize', 16)
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||||
xlabel('\mum', 'Interpreter', 'tex', 'FontSize', 16)
|
||||
ylabel('\mum', 'Interpreter', 'tex', 'FontSize', 16)
|
||||
axis equal tight;
|
||||
colorbar
|
||||
colormap jet; % (flip(jet))
|
||||
% set(gca,'CLim',[0 100]);
|
||||
colormap jet;
|
||||
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]);
|
||||
% Tile 4: Masked Noise
|
||||
nexttile(4);
|
||||
imagesc(xvals, yvals, mean_subtracted_od_imgs{k} .* mask)
|
||||
xlabel('µm', 'FontSize', 16)
|
||||
ylabel('µm', 'FontSize', 16)
|
||||
xlabel('\mum', 'Interpreter', 'tex', 'FontSize', 16)
|
||||
ylabel('\mum', 'Interpreter', 'tex', 'FontSize', 16)
|
||||
axis equal tight;
|
||||
colorbar
|
||||
colormap jet; % (flip(jet))
|
||||
% set(gca,'CLim',[0 100]);
|
||||
colormap jet;
|
||||
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)
|
||||
% Tile 5: DFT
|
||||
nexttile(5);
|
||||
imagesc(kx*1E-6, ky*1E-6, abs(log2(density_fft{k})))
|
||||
xlabel('k_x (\mum^{-1})', 'Interpreter', 'tex', 'FontSize', 16)
|
||||
ylabel('k_y (\mum^{-1})', 'Interpreter', 'tex', 'FontSize', 16)
|
||||
axis equal tight;
|
||||
colorbar
|
||||
colormap jet; % (flip(jet))
|
||||
% set(gca,'CLim',[0 100]);
|
||||
colormap jet;
|
||||
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)
|
||||
% Tile 6: Density Noise Spectrum = |DFT|^2
|
||||
nexttile(6);
|
||||
imagesc(kx*1E-6, ky*1E-6, abs(log2(density_noise_spectrum{k})))
|
||||
xlabel('k_x (\mum^{-1})', 'Interpreter', 'tex', 'FontSize', 16)
|
||||
ylabel('k_y (\mum^{-1})', 'Interpreter', 'tex', 'FontSize', 16)
|
||||
axis equal tight;
|
||||
colorbar
|
||||
colormap jet; % (flip(jet))
|
||||
% set(gca,'CLim',[0 100]);
|
||||
colormap jet;
|
||||
set(gca,'YDir','normal')
|
||||
title('Density Noise Spectrum = |DFT|^2', 'FontSize', 16);
|
||||
|
||||
title('Density Noise Spectrum', 'FontSize', 16);
|
||||
|
||||
drawnow;
|
||||
end
|
||||
|
||||
@ -198,25 +199,27 @@ end
|
||||
averagePowerSpectrum = mean(cat(3, density_noise_spectrum{:}), 3, 'double');
|
||||
|
||||
% Plot the average power spectrum.
|
||||
figure('Position', [100, 100, 1200, 500]);
|
||||
figure(2)
|
||||
clf
|
||||
set(gcf,'Position',[100, 100, 1500, 700])
|
||||
|
||||
subplot('Position', [0.05, 0.1, 0.4, 0.8]) % Adjusted position
|
||||
% Create tiled layout with 2 rows and 3 columns
|
||||
t = tiledlayout(1, 2, 'TileSpacing', 'compact', 'Padding', 'compact');
|
||||
|
||||
nexttile(1);
|
||||
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;
|
||||
radius = 3;
|
||||
% 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);
|
||||
@ -225,78 +228,74 @@ for ii = 1:length(centers)
|
||||
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)))
|
||||
imagesc(kx*1E-6, ky*1E-6, 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)
|
||||
xlabel('k_x (\mum^{-1})', 'Interpreter', 'tex', 'FontSize', 16)
|
||||
ylabel('k_y (\mum^{-1})', 'Interpreter', 'tex', '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)
|
||||
imagesc(kx*1E-6, ky*1E-6, abs(10*log10(averagePowerSpectrum)))
|
||||
xlabel('k_x (\mum^{-1})', 'Interpreter', 'tex', 'FontSize', 16)
|
||||
ylabel('k_y (\mum^{-1})', 'Interpreter', 'tex', '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
|
||||
% Fit
|
||||
nexttile(2);
|
||||
radialStep = 1; % in pixels
|
||||
[R, Profile] = getRadialProfile(averagePowerSpectrum, radialStep);
|
||||
kvec = (2 * pi) .* R(2:end) .* (sqrt(dvx^2 + dvy^2) * radialStep) * 1E-6; % in units of micrometers^-1
|
||||
NormalisedProfile = (Profile(2:end) - min(Profile(2:end)))./(max(Profile(2:end)) - min(Profile(2:end)));
|
||||
kmax = k_cutoff;
|
||||
|
||||
[xi, yi, profile] = improfile(image, [x1,x2], [y1,y2]);
|
||||
profile = (profile - min(profile))./(max(profile) - min(profile));
|
||||
ks = sqrt(kx.^2 + ky.^2);
|
||||
% Define the objective function to minimize (the difference between model and data)
|
||||
objectiveFunction = @(C, k) RadialImagingResponseFunction(C, k, kmax) - NormalisedProfile;
|
||||
|
||||
profile = profile(length(profile)/2:end);
|
||||
ks = ks(length(ks)/2:end);
|
||||
% Initial guess for the parameters [C1, C2, C3, C4, C5, C6]
|
||||
initialGuess = [2E6, 1E-6, 1E-6, 1E-6, 1E-6, 0.8];
|
||||
|
||||
n = 0.05;
|
||||
[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)])
|
||||
xlabel('k (1/µm)', 'FontSize', 16)
|
||||
% Set upper and lower bounds for the parameters (optional)
|
||||
lb = [-Inf, -Inf, -Inf, -Inf, -Inf, 0]; % Lower bounds
|
||||
ub = [Inf, Inf, Inf, Inf, Inf, 1]; % Upper bounds
|
||||
|
||||
% Perform the non-linear least squares fitting using lsqcurvefit
|
||||
options = optimoptions('lsqcurvefit', 'Display', 'iter'); % Display iterations during fitting
|
||||
[C_fit, resnorm] = lsqcurvefit(objectiveFunction, initialGuess, kvec, NormalisedProfile, lb, ub, options);
|
||||
|
||||
% Plot the fitted result against the data
|
||||
k_new = linspace(kvec(1), kvec(end), 1000);
|
||||
fittedProfile = RadialImagingResponseFunction(C_fit, k_new, kmax);
|
||||
|
||||
nexttile(2)
|
||||
plot(kvec, NormalisedProfile, 'o-', 'MarkerSize', 4, 'MarkerFaceColor', 'none', 'DisplayName', 'Radial (average) profile');
|
||||
hold on
|
||||
plot(k_new, fittedProfile, 'r-', 'DisplayName', 'Fitted Curve');
|
||||
set(gca, 'XScale', 'log'); % Setting x-axis to log scale
|
||||
xlabel('k_\rho (\mum^{-1})', 'Interpreter', 'tex', 'FontSize', 16)
|
||||
ylabel('Normalised amplitude', 'FontSize', 16)
|
||||
title('Radial profile', 'FontSize', 16);
|
||||
title('Modulation Transfer Function', 'FontSize', 16);
|
||||
legend('FontSize', 16);
|
||||
grid on;
|
||||
|
||||
|
||||
%% Helper Functions
|
||||
|
||||
function ret = get_offset_from_corner(img, x_fraction, y_fraction)
|
||||
function ret = getBkgOffsetFromCorners(img, x_fraction, y_fraction)
|
||||
% image must be a 2D numerical array
|
||||
[dim1, dim2] = size(img);
|
||||
|
||||
@ -308,7 +307,7 @@ function ret = get_offset_from_corner(img, x_fraction, y_fraction)
|
||||
ret = mean([mean(s1(:)), mean(s2(:)), mean(s3(:)), mean(s4(:))]);
|
||||
end
|
||||
|
||||
function ret = subtract_offset(img, fraction)
|
||||
function ret = subtractBackgroundOffset(img, fraction)
|
||||
% Remove the background from the image.
|
||||
% :param dataArray: The image
|
||||
% :type dataArray: xarray DataArray
|
||||
@ -321,11 +320,11 @@ function ret = subtract_offset(img, fraction)
|
||||
|
||||
x_fraction = fraction(1);
|
||||
y_fraction = fraction(2);
|
||||
offset = get_offset_from_corner(img, x_fraction, y_fraction);
|
||||
offset = getBkgOffsetFromCorners(img, x_fraction, y_fraction);
|
||||
ret = img - offset;
|
||||
end
|
||||
|
||||
function ret = crop_image(img, center, span)
|
||||
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
|
||||
@ -344,7 +343,7 @@ function ret = crop_image(img, center, span)
|
||||
ret = img(y_start:y_end, x_start:x_end);
|
||||
end
|
||||
|
||||
function ret = calculate_OD(imageAtom, imageBackground, imageDark)
|
||||
function ret = calculateODImage(imageAtom, imageBackground, imageDark)
|
||||
% Calculate the OD image for absorption imaging.
|
||||
% :param imageAtom: The image with atoms
|
||||
% :type imageAtom: numpy array
|
||||
@ -368,50 +367,6 @@ function ret = calculate_OD(imageAtom, imageBackground, imageDark)
|
||||
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
|
||||
@ -481,4 +436,50 @@ function [optrefimages] = removefringesInImage(absimages, refimages, bgmask)
|
||||
% Compute optimised reference image
|
||||
optrefimages(:,:,j)=reshape(R*c,[ydim xdim]);
|
||||
end
|
||||
end
|
||||
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 [R, Zr] = getRadialProfile(data, radialStep)
|
||||
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)/radialStep)+1;
|
||||
% very fast MatLab calculations:
|
||||
R = accumarray(Z_integer(:),abs(X(:)+1i*Y(:)),[],@mean);
|
||||
Zr = accumarray(Z_integer(:),data(:),[],@mean);
|
||||
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
|
||||
|
||||
Loading…
Reference in New Issue
Block a user