Merge branch 'master' of https://git.physi.uni-heidelberg.de/karthik/Calculations
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Karthik
commit
a27ad2d256
@ -4,14 +4,15 @@ groupList = ["/images/MOT_3D_Camera/in_situ_absorption", "/images/ODT_1_Axis
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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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run = '0072';
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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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% center = [1137, 2023];
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center = [1141, 2049];
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span = [255, 255];
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fraction = [0.1, 0.1];
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@ -109,7 +110,6 @@ 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(1)
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clf
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@ -193,12 +193,12 @@ for k = 1 : length(od_imgs)
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drawnow;
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end
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%% Compute the average 2D spectrum and do radial averaging to get the 1D spectrum
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%% Compute the average 2D spectrum
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% Compute the average power spectrum.
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averagePowerSpectrum = mean(cat(3, density_noise_spectrum{:}), 3, 'double');
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% Plot the average power spectrum.
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% Plot the average power spectrum and the 1-D Radial Imaging Response Function
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figure(2)
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clf
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set(gcf,'Position',[100, 100, 1500, 700])
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@ -223,7 +223,7 @@ yc = centers(:,2);
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[yDim, xDim] = size(averagePowerSpectrum);
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[xx,yy] = meshgrid(1:yDim,1:xDim);
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mask = false(xDim,yDim);
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for ii = 1:length(centers)
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for ii = 1:size(centers, 1)
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mask = mask | hypot(xx - xc(ii), yy - yc(ii)) <= radius;
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end
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mask = not(mask);
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@ -272,7 +272,7 @@ initialGuess = [2E6, 1E-6, 1E-6, 1E-6, 1E-6, 0.8];
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% Set upper and lower bounds for the parameters (optional)
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lb = [-Inf, -Inf, -Inf, -Inf, -Inf, 0]; % Lower bounds
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ub = [Inf, Inf, Inf, Inf, Inf, 1]; % Upper bounds
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ub = [Inf, Inf, Inf, Inf, Inf, 1]; % Upper bounds
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% Perform the non-linear least squares fitting using lsqcurvefit
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options = optimoptions('lsqcurvefit', 'Display', 'iter'); % Display iterations during fitting
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@ -285,14 +285,200 @@ fittedProfile = RadialImagingResponseFunction(C_fit, k_new, kmax);
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nexttile(2)
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plot(kvec, NormalisedProfile, 'o-', 'MarkerSize', 4, 'MarkerFaceColor', 'none', 'DisplayName', 'Radial (average) profile');
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hold on
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plot(k_new, fittedProfile, 'r-', 'DisplayName', 'Fitted Curve');
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plot(k_new, fittedProfile, 'r-', 'DisplayName', 'Fit');
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set(gca, 'XScale', 'log'); % Setting x-axis to log scale
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xlabel('k_\rho (\mum^{-1})', 'Interpreter', 'tex', 'FontSize', 16)
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ylabel('Normalised amplitude', 'FontSize', 16)
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title('Modulation Transfer Function', 'FontSize', 16);
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title('Imaging Response Function', 'FontSize', 16);
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legend('FontSize', 16);
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grid on;
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%% 2-D Imaging Response Function fit
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% Get the size of the matrix
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[nRows, nCols] = size(averagePowerSpectrum);
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% Compute the center index
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centerRow = round(nRows / 2);
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centerCol = round(nCols / 2);
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% Remove the central DC component by setting it to zero
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averagePowerSpectrum(centerRow, centerCol) = 0;
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% Define the objective function for fitting
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function residuals = fitImagingResponse(params, averagePowerSpectrum)
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% Calculate the ImagingResponseFunction with the given parameters
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M = ImagingResponseFunction(params);
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% Compute the residuals as the difference between the matrices
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residuals = M(:) - averagePowerSpectrum(:); % Flatten both matrices
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end
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% Initial guess for parameters (from your example)
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initialParams = [0.65, 0.1, 0.1, 0.1, 0.1, 0.1, 1E-6, 1E-8, 80];
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% Set options for the optimizer (optional, helps with debugging)
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options = optimoptions('lsqnonlin', 'Display', 'iter', 'MaxFunctionEvaluations', 5000);
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% Perform the fitting using lsqnonlin
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optimalParams = lsqnonlin(@(params) fitImagingResponse(params, averagePowerSpectrum), initialParams, [], [], options);
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AstigmatismCoefficient = optimalParams(2);
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SphericalAberrationCoefficient = optimalParams(3);
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DefocussingCoefficient = optimalParams(5);
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% Compute the best-fit M using the optimized parameters
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bestFitM = ImagingResponseFunction(optimalParams);
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residuals = fitImagingResponse(optimalParams, averagePowerSpectrum);
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% Plot the fitted result
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figure(3)
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clf
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set(gcf,'Position',[100, 100, 1500, 500])
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% Create tiled layout with 2 rows and 3 columns
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t = tiledlayout(1, 3, 'TileSpacing', 'compact', 'Padding', 'compact');
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nexttile(1);
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imagesc(abs(10*log10(averagePowerSpectrum)))
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axis equal tight;
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colorbar
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colormap(flip(jet));
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title('Average Density Noise Spectrum', 'FontSize', 16);
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grid on;
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nexttile(2);
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imagesc(abs(10*log10(bestFitM)))
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axis equal tight;
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colorbar
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colormap(flip(jet));
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title('Fitted Imaging Response Function', 'FontSize', 16);
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grid on;
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nexttile(3);
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resmat = reshape(residuals, size(bestFitM));
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imagesc(abs(10*log10(resmat)))
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axis equal tight;
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colorbar
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colormap(flip(jet));
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title('Fit residuals', 'FontSize', 16);
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grid on;
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%% 3-D Plot of Density Noise Spectrum
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figure(4)
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clf
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set(gcf,'Position',[100, 100, 1500, 700])
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surf(10 * log10(averagePowerSpectrum));
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shading interp; % Creates a 3D surface plot
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xlabel('X-axis', 'FontSize', 16);
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ylabel('Y-axis', 'FontSize', 16);
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zlabel('Rescaled amplitude (a.u.)', 'FontSize', 16);
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title('Imaging Response Function', 'FontSize', 16);
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colorbar; % Shows the color scale
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% Set axis limits based on the size of the averagePowerSpectrum
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[xSize, ySize] = size(averagePowerSpectrum);
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xlim([1, xSize]);
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ylim([1, ySize]);
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zlim([min(10 * log10(averagePowerSpectrum(:))), max(10 * log10(averagePowerSpectrum(:)))]); % Optional for Z-axis limits
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%% Decompose in Zernike Polynomial basis
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N = size(averagePowerSpectrum, 1);
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[X, Y] = meshgrid(linspace(-1, 1, N));
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max_n = 6; % Adjust based on your needs
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basis = [];
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orders = [];
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for n = 0:max_n
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for m = -n:2:n
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% Generate Zernike polynomial for (n, m)
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Z = zernike_polynomial(n, m, X, Y);
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% Flatten and store valid points
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basis = [basis, Z(mask)];
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orders = [orders; [n, m]];
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end
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end
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data = 10 * log10(averagePowerSpectrum);
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valid_data = data(mask);
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% Solve Ax = b (A = basis matrix, b = data)
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coeffs = basis \ valid_data(:);
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% Reconstruct the surface using the coefficients
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reconstructed = basis * coeffs;
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reconstructed_surface = zeros(size(X));
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reconstructed_surface(mask) = reconstructed;
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figure(5)
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clf
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set(gcf,'Position',[100, 100, 1500, 700])
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% Create tiled layout with 2 rows and 3 columns
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t = tiledlayout(1, 3, 'TileSpacing', 'compact', 'Padding', 'compact');
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nexttile(1);
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imagesc(data); title('Imaging Response Function', 'FontSize', 16);
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axis square;
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colorbar
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colormap(jet);
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grid on;
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nexttile(2);
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imagesc(reconstructed_surface); title('Reconstructed with Zernike', 'FontSize', 16);
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axis square;
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colorbar
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colormap(jet);
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grid on;
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nexttile(3);
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imagesc(data - reconstructed_surface); title('Residuals', 'FontSize', 16);
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axis square;
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colorbar
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colormap(jet);
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grid on;
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disp('Zernike Coefficients:');
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disp('---------------------');
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for i = 1:length(coeffs)
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fprintf('Order (n=%d, m=%d): Coefficient = %.4f\n', orders(i,1), orders(i,2), coeffs(i));
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end
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% Plot Zernike Coeffecients
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% Find the index of the (n=0, m=0) term
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idx_remove = find(orders(:,1) == 0 & orders(:,2) == 0);
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% Remove the Z_0^0 term from coefficients and orders
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coeffs_filtered = coeffs;
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coeffs_filtered(idx_remove) = [];
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orders_filtered = orders;
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orders_filtered(idx_remove, :) = [];
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% Generate labels for filtered modes (n, m)
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labels_filtered = cell(length(coeffs_filtered), 1);
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for i = 1:length(coeffs_filtered)
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labels_filtered{i} = sprintf('(%d, %d)', orders_filtered(i,1), orders_filtered(i,2));
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end
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figure(6)
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clf
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set(gcf,'Position',[100, 100, 1500, 700])
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bar(coeffs_filtered, 'FaceColor', [0.2, 0.6, 0.8]); % Customize bar color
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ylim([-1.0, 1.0])
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title('Zernike Coefficients', 'FontSize', 16);
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xlabel('Zernike Mode (n, m)', 'FontSize', 16);
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ylabel('Coefficient Value', 'FontSize', 16);
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xticks(1:length(coeffs_filtered)); % Set x-ticks for all coefficients
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xticklabels(labels_filtered); % Assign (n, m) labels
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xtickangle(45); % Rotate labels for readability
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grid on;
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%% Helper Functions
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function ret = getBkgOffsetFromCorners(img, x_fraction, y_fraction)
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@ -439,25 +625,48 @@ function [optrefimages] = removefringesInImage(absimages, refimages, bgmask)
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end
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function [M] = ImagingResponseFunction(B)
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x = -100:100;
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y = x;
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x = -128:127;
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y = x;
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[X,Y] = meshgrid(x,y);
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R = sqrt(X.^2+Y.^2);
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PHI = atan2(X,Y)+pi;
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%fit parameters
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tau = B(1);
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R = sqrt(X.^2+Y.^2);
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PHI = atan2(X,Y)+pi;
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% Fit parameters
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tau = B(1);
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alpha = B(2);
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S0 = B(3);
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phi = B(4);
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beta = B(5);
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S0 = B(3);
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phi = B(4);
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beta = B(5);
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delta = B(6);
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A = B(7);
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C = B(8);
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a = B(9);
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U = heaviside(1-R/a).*exp(-R.^2/a^2/tau^2);
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A = B(7);
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C = B(8);
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a = B(9);
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U = heaviside(1-R/a).*exp(-R.^2/a^2/tau^2);
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THETA = S0*(R/a).^4 + alpha*(R/a).^2.*cos(2*PHI-2*phi) + beta*(R/a).^2;
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p = U.*exp(1i.*THETA);
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M = A*abs((ifft2(real(exp(1i*delta).*fftshift(fft2(p)))))).^2 + C;
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p = U.*exp(1i.*THETA);
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M = A*abs((ifft2(real(exp(1i*delta).*fftshift(fft2(p)))))).^2 + C;
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end
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function [p] = exitPupilFunction(B)
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x = -128:127;
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y = x;
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[X,Y] = meshgrid(x,y);
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R = sqrt(X.^2+Y.^2);
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PHI = atan2(X,Y)+pi;
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% Fit parameters
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tau = B(1);
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alpha = B(2);
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S0 = B(3);
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phi = B(4);
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beta = B(5);
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delta = B(6);
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A = B(7);
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C = B(8);
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a = B(9);
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U = heaviside(1-R/a).*exp(-R.^2/a^2/tau^2);
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THETA = S0*(R/a).^4 + alpha*(R/a).^2.*cos(2*PHI-2*phi) + beta*(R/a).^2;
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p = U.*exp(1i.*THETA);
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end
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function [R, Zr] = getRadialProfile(data, radialStep)
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@ -483,3 +692,29 @@ function [RadialResponseFunc] = RadialImagingResponseFunction(C, k, kmax)
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end
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RadialResponseFunc = C(6) * 1/2 * A .* RadialResponseFunc;
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end
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function R = zernike_radial(n, m, rho)
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% Compute radial part of Zernike polynomial for radial order n and azimuthal order m
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R = zeros(size(rho));
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for k = 0:(n - abs(m))/2
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coeff = (-1)^k * factorial(n - k) / ...
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(factorial(k) * factorial((n + abs(m))/2 - k) * factorial((n - abs(m))/2 - k));
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R = R + coeff * rho.^(n - 2*k);
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end
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end
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function Z = zernike_polynomial(n, m, X, Y)
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% Convert Cartesian coordinates to polar coordinates
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[theta, rho] = cart2pol(X, Y);
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rho(rho > 1) = 0; % Restrict to unit disk
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% Compute radial component
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R = zernike_radial(n, m, rho);
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% Compute azimuthal component (sine/cosine terms)
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if m >= 0
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Z = R .* cos(m * theta);
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else
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Z = R .* sin(-m * theta);
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end
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end
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