Thanks, that makes the layout of the data clear.

Now that I've thought about it, I've never seen a polar plot distorted in a way you describe. The polar axis is in decibels, so it already uses logarithmic scale - by "making the outer donuts larger", as you say, you actually want to undo the logarithmic scaling, at least partially. In any case, I see this as a cosmetic alteration that may be harmful, because it changes the shape of the curve you want to show, without good reason.

With that in mind, here is a gnuplot script that produces a graph close to what you want:

set polar
set rr [-40:10]
set rtics 10
unset border
unset xtics 
unset ytics
set grid lt 1 lc rgb "blue"

f(x) = (x+50)**2
g(x) = sqrt(x)-50
set nonlinear r via f(r) inverse g(r)

plot  '/tmp/foo.n2p' u ($0>0&&$0<=361 ? $0*pi/180. : 1/0):1 w l lw 2 n
+otit
[download]

The scaling function (that determines the spacing of the grid circles) is a square function (f(x) in the script) as opposed to exponential. You could use this function in your script if you prefer to stay with your pure perl solution.