I think the reason you are getting a big number is because your standard deviation is including all the zero values.
Is it enough for you to simply ignore all zero values? (This will be okay, providing that no or very few pixels in the circle have value 0.) If so
np.std([x for x in ds.pixel_array if x > 0])
should do the trick. If this isn't good enough, then you can reverse the condition in your mask to be
mask = (X - lx/2)**2 + (Y - ly/2)**2 < lx*ly/8 # defining mask, < instead of >
and do
mp.std(ds.pixel_array[mask])