Latest analysis routine.

Imaging-Response-Function-Extractor/extractIRF.m

@@ -193,12 +193,12 @@ for k = 1 : length(od_imgs)
     drawnow;
 end
 
-%% Compute the average 2D spectrum and do radial averaging to get the 1D spectrum
+%% Compute the average 2D spectrum
 
 % Compute the average power spectrum.
 averagePowerSpectrum = mean(cat(3, density_noise_spectrum{:}), 3, 'double');
 
-% Plot the average power spectrum.
+%% Plot the average power spectrum and the 1-D Radial Imaging Response Function
 figure(2)
 clf
 set(gcf,'Position',[100, 100, 1500, 700])
@@ -272,7 +272,7 @@ initialGuess       = [2E6, 1E-6, 1E-6, 1E-6, 1E-6, 0.8];
 
 % 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
+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
@@ -285,14 +285,87 @@ 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');
+plot(k_new, fittedProfile, 'r-', 'DisplayName', 'Fit');
 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('Modulation Transfer Function', 'FontSize', 16);
+title('Imaging Response Function', 'FontSize', 16);
 legend('FontSize', 16);
 grid on;
 
+%% 2-D Imaging Response Function fit
+
+% Get the size of the matrix
+[nRows, nCols] = size(averagePowerSpectrum);
+
+% Compute the center index
+centerRow = round(nRows / 2);
+centerCol = round(nCols / 2);
+
+% Remove the central DC component by setting it to zero
+averagePowerSpectrum(centerRow, centerCol) = 0;
+
+% Define the objective function for fitting
+function residuals = fitImagingResponse(params, averagePowerSpectrum)
+    % Calculate the ImagingResponseFunction with the given parameters
+    M = ImagingResponseFunction(params);
+
+    % Compute the residuals as the difference between the matrices
+    residuals = M(:) - averagePowerSpectrum(:); % Flatten both matrices
+end
+
+% Initial guess for parameters (from your example)
+initialParams = [0.65, 0.1, 0.1, 0.1, 0.1, 0.1, 1E-6, 1E-8, 80];
+
+% Set options for the optimizer (optional, helps with debugging)
+options       = optimoptions('lsqnonlin', 'Display', 'iter', 'MaxFunctionEvaluations', 5000);
+
+% Perform the fitting using lsqnonlin
+optimalParams                  = lsqnonlin(@(params) fitImagingResponse(params, averagePowerSpectrum), initialParams, [], [], options);
+AstigmatismCoefficient         = optimalParams(2);
+SphericalAberrationCoefficient = optimalParams(3);
+DefocussingCoefficient         = optimalParams(5);
+
+% Compute the best-fit M using the optimized parameters
+bestFitM  = ImagingResponseFunction(optimalParams);
+
+residuals = fitImagingResponse(optimalParams, averagePowerSpectrum);
+
+% Plot the fitted result
+
+figure(3)
+clf
+set(gcf,'Position',[100, 100, 1500, 500])
+
+% Create tiled layout with 2 rows and 3 columns
+t = tiledlayout(1, 3, 'TileSpacing', 'compact', 'Padding', 'compact');
+
+nexttile(1);
+imagesc(abs(10*log10(averagePowerSpectrum)))
+axis equal tight;
+colorbar
+colormap(flip(jet));
+title('Average Density Noise Spectrum', 'FontSize', 16);
+grid on;
+
+nexttile(2);
+imagesc(abs(10*log10(bestFitM)))
+axis equal tight;
+colorbar
+colormap(flip(jet));
+title('Fitted Imaging Response Function', 'FontSize', 16);
+grid on;
+
+nexttile(3);
+resmat = reshape(residuals, size(bestFitM));
+imagesc(abs(10*log10(resmat)))
+axis equal tight;
+colorbar
+colormap(flip(jet));
+title('Fit residuals', 'FontSize', 16);
+grid on;
+
+
 %% Helper Functions
 
 function ret = getBkgOffsetFromCorners(img, x_fraction, y_fraction)
@@ -439,25 +512,48 @@ function [optrefimages] = removefringesInImage(absimages, refimages, bgmask)
 end
 
 function [M] = ImagingResponseFunction(B)
-    x = -100:100;
+    x     = -128:127;
-    y = x;
+    y     = x;
     [X,Y] = meshgrid(x,y);
-    R = sqrt(X.^2+Y.^2);
+    R     = sqrt(X.^2+Y.^2);
-    PHI = atan2(X,Y)+pi;
+    PHI   = atan2(X,Y)+pi;
-    %fit parameters
+    
-    tau = B(1);
+    % Fit parameters
+    tau   = B(1);
     alpha = B(2);
-    S0 = B(3);
+    S0    = B(3);
-    phi = B(4);
+    phi   = B(4);
-    beta = B(5);
+    beta  = B(5);
     delta = B(6);
-    A = B(7);
+    A     = B(7);
-    C = B(8);
+    C     = B(8);
-    a = B(9);
+    a     = B(9);
-    U = heaviside(1-R/a).*exp(-R.^2/a^2/tau^2);
+    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);
+    p     = U.*exp(1i.*THETA);
-    M = A*abs((ifft2(real(exp(1i*delta).*fftshift(fft2(p)))))).^2 + C;
+    M     = A*abs((ifft2(real(exp(1i*delta).*fftshift(fft2(p)))))).^2 + C;
+end
+
+function [p] = exitPupilFunction(B)
+    x     = -128:127;
+    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);
 end
 
 function [R, Zr] = getRadialProfile(data, radialStep)