I'm afraid that I'm still confused and there seems to be not much
thing I can help..

You're considering a circle, but you already have your function in a
cartesian coordinate. I'm not sure why you can't just plot in a
cartesian coordinate? (in other words, what is wrong with your
original script?)

There is an "set_image_extent" call in your original script (although
commented out). Maybe what you're trying to do is simply

 im = imshow(Z, cmap=cm.jet, extent=(-3, 3, -3, 3))

I'm not sure it would be relevant, but if you have your function or
data in  (r, theta) coordinate, one simple way is just to use the
polar axes with pcolormesh method.

 n_theta, n_r = 100, 50
 theta = np.linspace(0, 2*np.pi, n_theta+1)
 r = np.linspace(0., 1., n_r + 1)
 data = np.arange(0., n_theta*n_r).reshape(n_r, n_theta)
 ax=subplot(1,1,1, projection="polar", aspect=1.)
 ax.pcolormesh(theta, r, data)



-JJ

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