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Updated to plot convolution of aberrated psf with an object

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Karthik 2025-02-22 05:16:38 +01:00
parent cfc6b7ec9a
commit 2f8f8d02fe
1 changed files with 78 additions and 31 deletions
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109
Estimations/ModellingImagingAberrations.m
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@ -1,22 +1,37 @@
%% Zernike Polynomials %% Compute and plot Zernike Polynomials
resolution = 100; % Resolution NumberOfGridPoints = 100; % Resolution
plotZernike(2, 0, resolution) % Defocus (Z2^0) plotZernike(2, 0, NumberOfGridPoints) % Defocus (Z2^0)
%% %%
plotZernike(2, 2, resolution) % Astigmatism (Z2^2) plotZernike(2, 2, NumberOfGridPoints) % Astigmatism (Z2^2)
%% %%
plotZernike(3, 1, resolution) % Coma (Z3^1, x-direction) plotZernike(3, 1, NumberOfGridPoints) % Coma (Z3^1, x-direction)
%% %%
plotZernike(3, -1, resolution) % Coma (Z3^-1, y-direction) plotZernike(3, -1, NumberOfGridPoints) % Coma (Z3^-1, y-direction)
%% %%
plotZernike(4, 0, resolution) % Spherical Aberration (Z4^0) plotZernike(4, 0, NumberOfGridPoints) % Spherical Aberration (Z4^0)
%% Aberrated PSF %% Compute and plot Aberrated PSF, Image
C = [0.0, 0.0, 0.0, 0.0, 0.0]; % Zernike coefficients NumberOfGridPoints = 1024; % Number of grid points per side
pupil_radius = 0.5; % Pupil radius (normalized) PupilRadius = 0.010; % Radius of pupil [m]
Length = 0.5; % Total size of the grid [m]
GridSpacing = Length / NumberOfGridPoints; % Grid spacing [m]
Wavelength = 421e-9; % Optical wavelength [m]
ImageDistance = 0.7; % Image distance [m]
plotAberratedPSF(C, pupil_radius, resolution); % Generate PSF
C = [0.3, 0.2, 0.1, -0.1, 0.4]; % Zernike coefficients
[X, Y, PSF] = generateAberratedPSF(C, PupilRadius, NumberOfGridPoints, GridSpacing);
plotAberratedPSF(X, Y, PSF);
% Generate object
Object = generateObject(Wavelength, ImageDistance, NumberOfGridPoints, GridSpacing);
% Convolve the object with the PSF to simulate imaging
Image = convolveObjectWithPSF(abs(Object).^2, PSF, 1);
%% Functions
function Z = computeZernikePolynomials(n, m, r, theta) function Z = computeZernikePolynomials(n, m, r, theta)
% Zernike polynomial function for radial and angular coordinates (r, theta) % Zernike polynomial function for radial and angular coordinates (r, theta)
@ -50,13 +65,13 @@ function Z = computeZernikePolynomials(n, m, r, theta)
end end
end end
function plotZernike(n, m, resolution) function plotZernike(n, m, NumberOfGridPoints)
% n: radial order % n: radial order
% m: azimuthal frequency % m: azimuthal frequency
% resolution: number of points for plotting % NumberOfGridPoints: number of points for plotting
% Create a grid of (r, theta) coordinates % Create a grid of (r, theta) coordinates
[theta, r] = meshgrid(linspace(0, 2*pi, resolution), linspace(0, 1, resolution)); [theta, r] = meshgrid(linspace(0, 2*pi, NumberOfGridPoints), linspace(0, 1, NumberOfGridPoints));
% Calculate the Zernike polynomial for the given (n, m) % Calculate the Zernike polynomial for the given (n, m)
Z = computeZernikePolynomials(n, m, r, theta); Z = computeZernikePolynomials(n, m, r, theta);
@ -79,16 +94,19 @@ function plotZernike(n, m, resolution)
shading interp; shading interp;
end end
function [theta, r, PSF] = modelPSF(C, pupil_radius, resolution) function [X, Y, PSF] = generateAberratedPSF(C, PupilRadius, NumberOfGridPoints, GridSpacing)
% C is the vector of Zernike coefficients [C_defocus, C_astigmatism, C_coma, C_spherical, ...] % C is the vector of Zernike coefficients [C_defocus, C_astigmatism, C_coma, C_spherical, ...]
% resolution is the number of points for the grid (NxN grid) % NumberOfGridPoints is the number of points for the grid (NxN grid)
% pupil_radius is the radius of the pupil aperture % PupilRadius is the radius of the pupil aperture
% Create a grid of (r, theta) coordinates % Create a grid of (x, y) of pupil-plane coordinates in Cartesian space
[theta, r] = meshgrid(linspace(0, 2*pi, resolution), linspace(0, 1, resolution)); [X, Y] = meshgrid((-NumberOfGridPoints/2 : NumberOfGridPoints/2-1) * GridSpacing);
% Convert (x, y) to polar coordinates (r, theta)
[theta, r] = cart2pol(X, Y);
% Pupil function: 1 inside the pupil radius, 0 outside % Pupil function: 1 inside the pupil radius, 0 outside
P = double(r <= pupil_radius); % 2D mask P = generateCircularMask(X, Y, 2 * PupilRadius); % 2D mask
% Wavefront error from Zernike polynomials % Wavefront error from Zernike polynomials
W = C(1) * computeZernikePolynomials(2, 0, r, theta) + ... % Defocus (Z2^0) W = C(1) * computeZernikePolynomials(2, 0, r, theta) + ... % Defocus (Z2^0)
@ -98,26 +116,22 @@ function [theta, r, PSF] = modelPSF(C, pupil_radius, resolution)
C(5) * computeZernikePolynomials(4, 0, r, theta); % Spherical Aberration (Z4^0) C(5) * computeZernikePolynomials(4, 0, r, theta); % Spherical Aberration (Z4^0)
% Fourier transform of the pupil function with aberrations % Fourier transform of the pupil function with aberrations
PSF = abs(fftshift(fft2(P .* exp(1i * W)))).^2; % Intensity distribution PSF = abs(calculateExtendedFFT2(P .* exp(-1i * 2*pi * W), GridSpacing)).^2;
end end
function plotAberratedPSF(C, pupil_radius, resolution) function plotAberratedPSF(X, Y, PSF)
% C: Zernike coefficients [C_defocus, C_astigmatism, C_coma_x, C_coma_y, C_spherical] % C: Zernike coefficients [C_defocus, C_astigmatism, C_coma_x, C_coma_y, C_spherical]
% pupil_radius: Radius of the pupil aperture % PupilRadius: Radius of the pupil aperture
% resolution: Number of points for plotting % NumberOfGridPoints: Number of points for plotting
% Generate PSF using the updated modelPSF function % Generate PSF using the updated modelPSF function
[theta, r, PSF] = modelPSF(C, pupil_radius, resolution); PSF = PSF / max(PSF(:));
% Convert polar to Cartesian coordinates for plotting
[X, Y] = pol2cart(theta, r);
figure(1) figure(1)
clf clf
set(gcf,'Position',[50 50 950 750]) set(gcf,'Position',[50 50 950 750])
surf(X, Y, PSF, 'EdgeColor', 'none'); surf(X, Y, PSF, 'EdgeColor', 'none');
xlim([-0.05 0.05])
ylim([-0.05 0.05])
view(2); % 2D view view(2); % 2D view
axis equal tight;
shading interp; shading interp;
colorbar; colorbar;
colormap jet; colormap jet;
@ -125,3 +139,36 @@ function plotAberratedPSF(C, pupil_radius, resolution)
xlabel('X', 'FontSize', 16); xlabel('X', 'FontSize', 16);
ylabel('Y', 'FontSize', 16); ylabel('Y', 'FontSize', 16);
end end
function C = convolveObjectWithPSF(A, B, GridSpacing)
N = size(A, 1);
C = calculateExtendedInverseFFT2(calculateExtendedFFT2(A, GridSpacing) .* calculateExtendedFFT2(B, GridSpacing), 1/(N*GridSpacing));
end
function z = generateCircularMask(x, y, D)
r = sqrt(x.^2+y.^2);
z = double(r<D/2);
z(r==D/2) = 0.5;
end
function G = calculateExtendedFFT2(g, Delta)
G = fftshift(fft2(fftshift(g))) * Delta^2;
end
function g = calculateExtendedInverseFFT2(G, Delta_f)
N = size(G, 1);
g = ifftshift(ifft2(ifftshift(G))) * (N * Delta_f)^2;
end
function ret = generateRectangle(x, D)
if nargin == 1, D = 1; end
x = abs(x);
ret = double(x<D/2);
ret(x == D/2) = 0.5;
end
function obj = generateObject(Wavelength, ImageDistance, NumberOfGridPoints, GridSpacing)
% Image-plane coordinates
[U, V] = meshgrid((-NumberOfGridPoints/2 : NumberOfGridPoints/2-1) * ((Wavelength * ImageDistance) / (NumberOfGridPoints * GridSpacing)));
obj = (generateRectangle((U-1.4e-4)/5e-5) + generateRectangle(U/5e-5)+ generateRectangle((U+1.4e-4)/5e-5)) .* generateRectangle(V/2e-4);
end