MAJOR UPDATE: Corrected script to extract lattice properties and improved plotting routines.

This commit is contained in:
Karthik 2025-02-07 17:58:19 +01:00
parent 897743531e
commit 0647b032d0
5 changed files with 176 additions and 69 deletions

View File

@ -56,7 +56,7 @@ function [contrast, periodX, periodY] = analyzeGSWavefunction(folder_path, run_i
%------------------ Lattice Properties ------------------ %
[kx, ky, fftMagnitude, lattice_type, periodX, periodY, freq_x, freq_y, rotation_angle] = Scripts.extractLatticeProperties(nxyScaled, x, y);
[kx, ky, fftMagnitude, lattice_type, periodX, periodY, freq_x, freq_y] = Scripts.extractLatticeProperties(nxyScaled, x, y);
%------------------ Plotting ------------------ %
@ -72,10 +72,31 @@ function [contrast, periodX, periodY] = analyzeGSWavefunction(folder_path, run_i
cbar1.Label.Interpreter = 'latex';
colormap(gca, Helper.Colormaps.plasma())
% clim(ax1,[0.00,0.3]);
% Define normalized positions (relative to axis limits)
x_offset = 0.025; % 5% offset from the edges
y_offset = 0.025; % 5% offset from the edges
% Top-left corner (normalized axis coordinates)
text(0 + x_offset, 1 - y_offset, lattice_type, ...
'Color', 'white', 'FontWeight', 'bold', 'Interpreter', 'tex', 'FontSize', 30, 'Units', 'normalized', 'HorizontalAlignment', 'left', 'VerticalAlignment', 'top');
% Top-right corner (normalized axis coordinates)
text(1 - x_offset, 1 - y_offset, ['C: ', num2str(contrast, '%.3f')], ...
'Color', 'white', 'FontWeight', 'bold', 'Interpreter', 'tex', 'FontSize', 30, 'Units', 'normalized', 'HorizontalAlignment', 'right', 'VerticalAlignment', 'top');
% Bottom-left corner (normalized axis coordinates)
text(0 + x_offset, 0 + y_offset, ['dx: ', num2str(periodX, '%.2f'), ' \mum'], ...
'Color', 'white', 'FontWeight', 'bold', 'Interpreter', 'tex', 'FontSize', 30, 'Units', 'normalized', 'HorizontalAlignment', 'left', 'VerticalAlignment', 'bottom');
% Bottom-right corner (normalized axis coordinates)
text(1 - x_offset, 0 + y_offset, ['dy: ', num2str(periodY, '%.2f'), ' \mum'], ...
'Color', 'white', 'FontWeight', 'bold', 'Interpreter', 'tex', 'FontSize', 30, 'Units', 'normalized', 'HorizontalAlignment', 'right', 'VerticalAlignment', 'bottom');
ylabel(cbar1,'$na_{dd}^2$','FontSize',16,'Rotation',270)
xlabel('$x$ ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14)
ylabel('$y$ ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14)
title(['$|\Psi(x,y)|^2$ - Contrast: ', num2str(contrast, '%.3f'), '; Period X = ', num2str(periodX, '%.2f'), '$ \mu$m', '; Period Y = ', num2str(periodY, '%.2f'), '$ \mu$m'], 'Interpreter', 'latex', 'FontSize', 14)
title('$|\Psi(x,y)|^2$ ', 'Interpreter', 'latex', 'FontSize', 14)
% Plot 2-D FFT with detected peaks
nexttile; % Equivalent to subplot('Position', [0.05, 0.55, 0.28, 0.4]);
@ -90,6 +111,6 @@ function [contrast, periodX, periodY] = analyzeGSWavefunction(folder_path, run_i
ylabel('$k_y l_o$', 'Interpreter', 'latex', 'FontSize', 14)
title('$\mathcal{F}\{|\Psi(x,y)|^2\}$', 'Interpreter', 'latex', 'FontSize', 16);
sgtitle(['$\omega_z = 2 \pi \times$', num2str(round(Params.wz/(2*pi)), '%.2f'), ' Hz; $\theta = $', num2str(rad2deg(Params.theta), '%.2f'), '$^\circ$; ', sprintf('Detected Lattice Type: %s\n', lattice_type)], 'Interpreter', 'latex', 'FontSize', 18, 'FontWeight', 'bold')
sgtitle(['$\omega_z = 2 \pi \times$', num2str(round(Params.wz/(2*pi)), '%.2f'), ' Hz; $\theta = $', num2str(rad2deg(Params.theta), '%.2f'), '$^\circ$'], 'Interpreter', 'latex', 'FontSize', 18, 'FontWeight', 'bold')
end

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@ -1,6 +1,6 @@
function [kx, ky, fftMagnitude, lattice_type, dx_um, dy_um, freq_x, freq_y, rotation_angle] = extractLatticeProperties(I, x, y)
function [kx, ky, fftMagnitude, lattice_type, dx_um, dy_um, freq_x, freq_y] = extractLatticeProperties(I, x, y)
% Detects lattice geometry, extracts periodic spacings, and reconstructs real-space lattice vectors.
% Handles arbitrary lattice geometries with rotation correction.
% Handles arbitrary lattice geometries
%
% Inputs:
% I - Grayscale image with periodic structures.
@ -12,7 +12,7 @@ function [kx, ky, fftMagnitude, lattice_type, dx_um, dy_um, freq_x, freq_y, rota
% dx_um - Spacing along x-axis in micrometers.
% dy_um - Spacing along y-axis in micrometers.
% real_lattice_vectors - [2x2] matrix of lattice vectors in micrometers.
% rotation_angle - Angle of rotation of the lattice in degrees.
% angle_in_reciprocal_space - Angle of the reciprocal lattice primitive vectors in degrees.
% Compute 2D Fourier Transform
F = fft2(double(I));
@ -64,7 +64,7 @@ function [kx, ky, fftMagnitude, lattice_type, dx_um, dy_um, freq_x, freq_y, rota
dy_um = NaN;
freq_x = NaN;
freq_y = NaN;
rotation_angle = NaN;
angle_in_reciprocal_space = NaN;
else
% Select two shortest independent lattice vectors - Reciprocal lattice vectors
@ -72,7 +72,7 @@ function [kx, ky, fftMagnitude, lattice_type, dx_um, dy_um, freq_x, freq_y, rota
G1 = unique_vectors(1, :); % Reciprocal lattice vector 1
G2 = unique_vectors(3, :); % Reciprocal lattice vector 2
reciprocal_lattice_vectors = vertcat(G1, G2);
reciprocal_lattice_vectors = abs(vertcat(G1, G2));
% Calculate the angle between the reciprocal lattice vectors using dot product
dotProduct = dot(G1, G2); % Dot product of G1 and G2
@ -80,7 +80,7 @@ function [kx, ky, fftMagnitude, lattice_type, dx_um, dy_um, freq_x, freq_y, rota
magnitudeG2 = norm(G2); % Magnitude of G2
% Angle between the reciprocal lattice vectors (in degrees)
rotation_angle = rad2deg(acos(dotProduct / (magnitudeG1 * magnitudeG2)));
angle_in_reciprocal_space = rad2deg(acos(dotProduct / (magnitudeG1 * magnitudeG2)));
% Convert to real-space lattice vectors
@ -88,67 +88,153 @@ function [kx, ky, fftMagnitude, lattice_type, dx_um, dy_um, freq_x, freq_y, rota
detG = G1(1) * G2(2) - G1(2) * G2(1); % Determinant of the matrix formed by G1 and G2
if detG == 0
% Handle the case of collinear reciprocal lattice vectors
disp('Reciprocal lattice vectors are collinear.');
% Handle the case of reciprocal lattice vector matrix being singular
% If both G1, G2 or just G1 are along x-direction
if G1(1) ~= 0 && G1(2) == 0
a1 = [1 / norm(G1), 0]; % Real-space lattice vector along x
a2 = [0, 0]; % No periodicity in the y-direction (1D lattice)
% If G2 is along x-direction or if G1 is zero.
elseif G2(1) ~= 0 && G2(2) == 0
a1 = [1 / norm(G2), 0]; % Real-space lattice vector along x
a2 = [0, 0]; % No periodicity in the y-direction
% If G1 and G2 are both in the y-direction (i.e., [0, non-zero])
elseif G1(1) == 0 && G2(1) == 0
a1 = [0, 1 / norm(G1)]; % Real-space lattice vector along y
a2 = [0, 0]; % No periodicity in the x-direction
% If both vectors are zero (no periodicity)
else
a1 = [0, 0];
a2 = [0, 0];
v1 = reciprocal_lattice_vectors(1, :);
v2 = reciprocal_lattice_vectors(2, :);
% Check if either vector is the zero vector
if all(v1 == 0) && all(v2 == 0)
% If both vectors are zero, return the same zero matrix
real_lattice_vectors = [0, 0; 0, 0];
end
% Compute the norms of the vectors
norm_v1 = norm(v1);
norm_v2 = norm(v2);
% Find the vector with the smallest norm
if norm_v2 < norm_v1
% If v2 has the smaller norm, set v1 to zero and keep v2
reciprocal_lattice_vectors = [0, 0; v2];
if v2(1) == 0
real_lattice_vectors = [0, 0; 0, 1/v2(2)];
elseif v2(2) == 0
real_lattice_vectors = [0, 0; 1/v2(1), 0];
else
real_lattice_vectors = [1/v2(1), 1/v2(2); 0, 0];
end
else
% If v1 has the smaller norm, set v2 to zero and keep v1
reciprocal_lattice_vectors = [v1; 0, 0];
if v1(1) == 0
real_lattice_vectors = [0, 1/v1(2); 0, 0];
elseif v1(2) == 0
real_lattice_vectors = [1/v1(1), 0; 0, 0];
else
real_lattice_vectors = [1/v1(1), 1/v1(2); 0, 0];
end
end
else
% If reciprocal vectors are not collinear, compute the 2D real-space lattice
a1 = [G2(2), -G1(2)] / detG;
a2 = [-G2(1), G1(1)] / detG;
real_lattice_vectors = inv(reciprocal_lattice_vectors');
end
real_lattice_vectors = vertcat(a1, a2);
% Ensure correct orientation
real_lattice_vectors(isinf(real_lattice_vectors) | isnan(real_lattice_vectors)) = 0;
% Compute lattice spacings
dx_um = (1/norm(G2)) * 1E6;
dy_um = (1/norm(G1)) * 1E6;
% Separate the components of real space vectors
real_x = real_lattice_vectors(:, 1);
real_y = real_lattice_vectors(:, 2);
% Correct for rotation by applying inverse rotation matrix
theta_rad = deg2rad(-rotation_angle); % Convert to radians
R = [cos(theta_rad), -sin(theta_rad); sin(theta_rad), cos(theta_rad)]; % Rotation matrix
real_lattice_vectors = (R * real_lattice_vectors')'; % Apply rotation correction
% Compute projections
proj_real_x = real_lattice_vectors * [1; 0]; % Projections onto x-axis
[smaller_value, idx] = min(proj_real_x);
proj_real_x(idx) = []; % Remove the element
proj_real_y = real_lattice_vectors * [0; 1]; % Projections onto y-axis
[smaller_value, idx] = min(proj_real_y);
proj_real_y(idx) = []; % Remove the element
% Separate the components of reciprocal space vectors
reciprocal_x = reciprocal_lattice_vectors(:, 1);
reciprocal_y = reciprocal_lattice_vectors(:, 2);
% Compute projections
proj_reciprocal_x = reciprocal_lattice_vectors * [1; 0]; % Projections onto x-axis
[smaller_value, idx] = min(proj_reciprocal_x);
proj_reciprocal_x(idx) = []; % Remove the element
proj_reciprocal_y = reciprocal_lattice_vectors * [0; 1]; % Projections onto y-axis
[smaller_value, idx] = min(proj_reciprocal_y);
proj_reciprocal_y(idx) = []; % Remove the element
%{
% Create a figure for side-by-side subplots
figure('Position', [100, 100, 1600, 800]);
clf
t = tiledlayout(1, 2, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x3 grid
% Plot real space vectors in the first subplot (2D case)
nexttile; % 1 row, 2 columns, first plot
quiver(0, 0, real_x(1) * 1E6, real_y(1) * 1E6, 'r', 'LineWidth', 2, 'MaxHeadSize', 0.5);
hold on;
quiver(0, 0, real_x(2) * 1E6, real_y(2) * 1E6, 'b', 'LineWidth', 2, 'MaxHeadSize', 0.5);
% Plot projections of the real space vectors
quiver(0, 0, proj_real_x * 1E6, 0, 'k--', 'LineWidth', 2, 'MaxHeadSize', 0.5); % Projection on X-axis (horizontal dotted line)
quiver(0, 0, 0, proj_real_y * 1E6, 'k--', 'LineWidth', 2, 'MaxHeadSize', 0.5); % Projection on Y-axis (vertical dotted line)
hold off;
xlabel('X');
ylabel('Y');
title('Real Space Primitive Vectors', 'FontSize', 14);
grid on;
axis equal;
% Plot reciprocal space vectors in the second subplot (2D case)
nexttile; % 1 row, 2 columns, second plot
quiver(0, 0, reciprocal_x(1) * 1E-6, reciprocal_y(1) * 1E-6, 'r', 'LineWidth', 2, 'MaxHeadSize', 0.5);
hold on;
quiver(0, 0, reciprocal_x(2) * 1E-6, reciprocal_y(2) * 1E-6, 'b', 'LineWidth', 2, 'MaxHeadSize', 0.5);
% Plot projections of the real space vectors
quiver(0, 0, proj_reciprocal_x * 1E-6, 0, 'k--', 'LineWidth', 2, 'MaxHeadSize', 0.5); % Projection on X-axis (horizontal dotted line)
quiver(0, 0, 0, proj_reciprocal_y * 1E-6, 'k--', 'LineWidth', 2, 'MaxHeadSize', 0.5); % Projection on Y-axis (vertical dotted line)
hold off;
xlabel('X');
ylabel('Y');
title('Reciprocal Space Primitive Vectors', 'FontSize', 14);
grid on;
axis equal;
%}
% Compute lattice spacings
dx_um = proj_real_x * 1E6;
dy_um = proj_real_y * 1E6;
% Classify lattice type based on angle symmetry
angle_between_vectors = atan2d(real_lattice_vectors(2,2), real_lattice_vectors(2,1)) - ...
atan2d(real_lattice_vectors(1,2), real_lattice_vectors(1,1));
angle_between_vectors = mod(angle_between_vectors, 180);
angle_in_real_space = abs(atan2d(real_lattice_vectors(2,2), real_lattice_vectors(2,1)) - ...
atan2d(real_lattice_vectors(1,2), real_lattice_vectors(1,1)));
angle_in_real_space_mod180 = mod(angle_in_real_space, 180);
if abs(angle_between_vectors - 60) < 5 || abs(angle_between_vectors - 120) < 5
lattice_type = 'Hexagonal';
elseif abs(angle_between_vectors - 90) < 5
lattice_type = 'Square';
elseif abs(angle_between_vectors - 90) > 5 && abs(angle_between_vectors - 120) > 5
lattice_type = 'Oblique';
if all(real_lattice_vectors(1, :) == 0) || all(real_lattice_vectors(2, :) == 0)
lattice_type = 'Stripe';
angle_in_real_space = NaN;
angle_in_reciprocal_space = NaN;
else
lattice_type = 'Undetermined';
if abs(angle_in_real_space_mod180 - 60) < 5 || abs(angle_in_real_space_mod180 - 120) < 5
if abs(dx_um - dy_um) < 1E-6
lattice_type = 'Triangular';
else
lattice_type = 'Sheared Triangular';
end
elseif abs(angle_in_real_space_mod180 - 90) < 5
lattice_type = 'Square';
elseif abs(angle_in_real_space_mod180 - 90) > 5 && abs(angle_in_real_space_mod180 - 120) > 5
lattice_type = 'Sheared';
else
lattice_type = 'Undetermined';
end
end
% Display results
% fprintf('Detected Lattice Type: %s\n', lattice_type);
% fprintf('Estimated Spacing (dx): %.2f µm\n', dx_um);
% fprintf('Estimated Spacing (dy): %.2f µm\n', dy_um);
% fprintf('Rotation Angle: %.2f°\n', rotation_angle);
% fprintf('Lattice Vectors:\n');
% disp(real_lattice_vectors);
fprintf('Detected Lattice Type: %s\n', lattice_type);
fprintf('Estimated Spacing (dx): %.2f µm\n', dx_um);
fprintf('Estimated Spacing (dy): %.2f µm\n', dy_um);
fprintf('Angle between real space lattice primitve vectors: %.2f°\n', angle_in_real_space);
fprintf('Angle between reciprocal lattice primitve vectors: %.2f°\n', angle_in_reciprocal_space);
fprintf('Real Space Primitive Vectors:\n');
disp(real_lattice_vectors);
end
end

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@ -251,7 +251,7 @@ Plotter.visualizeGSWavefunction2D(SaveDirectory, JobNumber)
%% - Analysis
SaveDirectory = './Results/Data_TiltingOfDipoles/AdjustedSystemSize/Hz500';
JobNumber = 1;
JobNumber = 2;
% Plotter.visualizeGSWavefunction2D(SaveDirectory, JobNumber)
[contrast, period_X, period_Y] = Scripts.analyzeGSWavefunction(SaveDirectory, JobNumber);
@ -270,7 +270,7 @@ JobNumber = 2;
%% - Analysis
SaveDirectory = './Results/Data_TiltingOfDipoles/AdjustedSystemSize/Hz2000';
JobNumber = 2;
Plotter.visualizeGSWavefunction2D(SaveDirectory, JobNumber)
% Plotter.visualizeGSWavefunction2D(SaveDirectory, JobNumber)
[contrast, period_X, period_Y] = Scripts.analyzeGSWavefunction(SaveDirectory, JobNumber);
%% - Analysis
@ -298,6 +298,6 @@ SaveOption = 'images';
[contrast_array, periodX_array, periodY_array] = Scripts.analyzeGSWavefunction_multipleruns(SaveDirectory, NumberOfJobs, SaveOption);
%% - Analysis
SaveDirectory = './Results/Data_TiltingOfDipoles/HarmonicTrap/Hz500';
JobNumber = 0;
JobNumber = 1;
% Plotter.visualizeGSWavefunction2D(SaveDirectory, JobNumber)
[contrast, period_X, period_Y] = Scripts.analyzeGSWavefunction(SaveDirectory, JobNumber);

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@ -1,5 +1,5 @@
%% Tilting of the dipoles
% Atom Number = 1250 ppum
% With an in-plane harmonic trap
%% v_z = 500, theta = 0
@ -17,13 +17,13 @@ OptionsStruct.NumberOfGridPoints = [256, 256];
OptionsStruct.Dimensions = [35, 35];
OptionsStruct.TimeStepSize = 0.005; % in s
OptionsStruct.MinimumTimeStepSize = 1E-5; % in s
OptionsStruct.TimeCutOff = 5E5; % in s
OptionsStruct.TimeCutOff = 1E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.05;
OptionsStruct.MaxIterations = 10;
OptionsStruct.VariationalWidth = 1.3;
OptionsStruct.VariationalWidth = 1.5;
OptionsStruct.WidthLowerBound = 0.01;
OptionsStruct.WidthUpperBound = 12;
OptionsStruct.WidthCutoff = 5e-3;
@ -50,7 +50,7 @@ OptionsStruct = struct;
OptionsStruct.NumberOfAtoms = 101250;
OptionsStruct.DipolarPolarAngle = deg2rad(15);
OptionsStruct.DipolarAzimuthAngle = 0;
OptionsStruct.ScatteringLength = 65.00;
OptionsStruct.ScatteringLength = 71.00;
OptionsStruct.TrapFrequencies = [50, 50, 500];
OptionsStruct.TrapPotentialType = 'Harmonic';
@ -59,13 +59,13 @@ OptionsStruct.NumberOfGridPoints = [256, 256];
OptionsStruct.Dimensions = [35, 35];
OptionsStruct.TimeStepSize = 0.005; % in s
OptionsStruct.MinimumTimeStepSize = 1E-5; % in s
OptionsStruct.TimeCutOff = 5E5; % in s
OptionsStruct.TimeCutOff = 1E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.05;
OptionsStruct.MaxIterations = 10;
OptionsStruct.VariationalWidth = 1.3;
OptionsStruct.VariationalWidth = 1.5;
OptionsStruct.WidthLowerBound = 0.01;
OptionsStruct.WidthUpperBound = 12;
OptionsStruct.WidthCutoff = 5e-3;

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@ -1,5 +1,5 @@
%% Tilting of the dipoles
% Atom Number = 1250 ppum
% With an in-plane harmonic trap
%% v_z = 500, theta = 0
@ -17,7 +17,7 @@ OptionsStruct.NumberOfGridPoints = [256, 256];
OptionsStruct.Dimensions = [35, 35];
OptionsStruct.TimeStepSize = 0.005; % in s
OptionsStruct.MinimumTimeStepSize = 1E-5; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.TimeCutOff = 1E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.05;
@ -59,7 +59,7 @@ OptionsStruct.NumberOfGridPoints = [256, 256];
OptionsStruct.Dimensions = [35, 35];
OptionsStruct.TimeStepSize = 0.005; % in s
OptionsStruct.MinimumTimeStepSize = 1E-5; % in s
OptionsStruct.TimeCutOff = 2E6; % in s
OptionsStruct.TimeCutOff = 1E6; % in s
OptionsStruct.EnergyTolerance = 5E-10;
OptionsStruct.ResidualTolerance = 1E-05;
OptionsStruct.NoiseScaleFactor = 0.05;