How to "circularize" a 1-D plot into a 2-D image

I have written a script that generates a 1-D plot of modulation trasnfer function (MTF) vs. frequency. I want to use this to create a 2-D image of the MTF by "circularizing" the 1-D plot about the center of an image.

I want to go from this:

to something that looks like this:

Answer 1

[DGM]

Depending on what you need, this may be a start.

% define TF curve
tfr = [0 1.3 4];
tfz = [1 1 0.2];
% array setup
maxxy = 4;
npoints = 101;

% calculate x,y,z
x = linspace(-maxxy,maxxy,npoints);
y = x.';
[th r] = cart2pol(x,y);
z = interp1(tfr,tfz,r,'linear','extrap');

% plot it
pcolor(x,y,z);
shading flat
colormap(gray)
colorbar

Depending on your needs, you may want to adjust how the extrapolation is handled. You can disable the extrapolation or specify a constant extrapolation value to use. Also, you may choose to clamp the extrapolated regions at some value (e.g. zero, using max(z,0)).