Horn antenna Radiation pattern

Question

Ok This might sound dumb but I am trying to get an equation for the radiation intensity of a pyramidal horn antenna in spherical coordinates. I got a whole bunch of books and they all have the same equation: $$ \mathbf{E}_\theta = \frac{j\, e^{-j k r}\, E_0\, A\, B\, (1 + \cos(\theta))\, \sin(\phi) ...}{8\, \lambda\, r} $$ $$ \mathbf{E}_\phi = \frac{j e^{-j k r} E_0\, A\, B\, (1 + \cos(\theta)) \cos(\phi) ...}{8\, \lambda\, r} $$

Ive got like 4 different text books about the subject and the all of them have those exact same equations. But not a single one says what \$r\$ is anywhere. Anybody know what this is?

Sorry to ask but I've been searching for hours. Can't find a single source that explicitly says what \$r\$ is.

Answer 1

For a compound box antenna the formula is similar and this might be useful: -

Obviously they are not using A and B to denote the aperture dimensions but, I suspect that "r" is going to be exactly the same i.e. distance between centre of aperture and measurement point.

Answer 2

Spherical coordinates are normally denoted by r, Θ, and φ. Your equation is in terms of those coordinates. r is the distance from the source origin (horn antenna) to the point given by the values of r, Θ, and φ. Thus you already have the answer to your question.