convert 1-d radial profile to a 2-d circular matrix

Hi,

I'm struggling to convert a 1-d radial profile to a 2-d circular matrix, my current process yields a rectangular matrix instead. So i guess i'm close, but i'm not sure how to convert the rectangular matrix into a circular one.

v_theta = cd(radiusc{3});
radius_r = radiusc{k};
theta = linspace(0,2*pi(),length(radiusc{k}));
theta_y = sin(v_theta)';
theta_x = cos(v_theta)';

v_y = cd(radiusc{k}).*theta_y; v_x = cd(radiusc{k}).*theta_x;

v_theta = sqrt(v_y.^2+v_x.^2);

imagesc(v_theta);

I get the following image (See attachment).

Answer 1

[Karan Singh]

HI @Optical_Stress,

It looks like your approach is generating a rectangular image rather than a circular one because imagesc(v_theta) is treating your matrix as a Cartesian grid rather than a polar one. To correctly convert your 1D radial profile into a 2D circular matrix, you need to interpolate your radial profile onto a polar coordinate grid and then transform it into Cartesian coordinates.

1. You can use "meshgrid" which creates a 2D representation of your r and theta values. https://in.mathworks.com/help/matlab/ref/meshgrid.html
2. Then "interp1" function ensures that the radial profile values are properly mapped onto the polar grid. https://www.mathworks.com/help/matlab/ref/double.interp1.html

I have taken some dummy data and wrote some code.

clc; clear; close all;

% Generate synthetic radial profile data
num_points = 100; % Number of radial points
r_max = 50; % Maximum radius
radius_r = linspace(0, r_max, num_points); % Radial positions
v_theta = exp(-radius_r / 20) + 0.1 * rand(1, num_points); % Sample radial profile

% Create a polar grid
theta = linspace(0, 2 * pi, num_points); % Angular positions
[R, Theta] = meshgrid(radius_r, theta); % 2D polar grid

% Convert polar coordinates to Cartesian
X = R .* cos(Theta);
Y = R .* sin(Theta);

% Interpolate the radial profile onto the 2D grid
V = interp1(radius_r, v_theta, R, 'linear', 'extrap');

% Plot the data as an image
figure;
pcolor(X, Y, V); % Ensures circular representation
shading interp;
axis equal; % Keeps it circular
colormap(jet);
colorbar;
title('2D Circular Representation of 1D Radial Profile');

●

Karan