Ahh, now I understand the purpose of the distorted graph. Still, I think it's a distortion, because the real difference between 10 dB and -40 dB is five orders of magnitude - if you plot that on a polar chart with linear (undone logarithmic) scaling, you get a spike, not a slightly altered, "real-world" shape (and you can forget about everything under 0 dB, not -20).

But I realize that for your application it is the kind of graph you and your users expect and understand. In that case it might be a good thing to provide an option to display either mode. To produce graphs that look like your PNG example (and like the examples I've found on the internet) you could use an exponential unscaling function with a very small exponent (something between 1.05 and 1.1 seemed to work for me).

(By the way, one advantage of gnuplot is that it has an interactive mode, which helps to rapidly prototype the kind of chart you want, and find the right parameters, and then you can go and reuse the commands in a script that produces a publication-ready graph from the same data.)