How can I mathematically show the similarity between these 3 plots?

Question

I have 3 3D plots of field strength measured around an antenna.

I want to calculate the mathematical similarity between the points of the field patterns. How can I do this?

thanks

Answer 1

There is more than one way to measure similarity. Here are three. They all start with $f(x,y)=|a(x,y)-b(x,y)|$, the function that measures the distance between plot $a$ and plot $b$, at every point.

Method 1: Take the maximum of $f(x,y)$ over the region.

Method 2: Take the integral of $f(x,y)$ over the region, i.e. the area underneath the surface.

Method 3: Take the integral of $f(x,y)^2$ over the region, and take the square root of the answer.

These are called $L^p$ norms, specifically the $\infty$, $1$ and $2$ norms respectively.