Measuring Horn Directivity using Dimensions

Hi I need to calculate the directivity of some horns based on their dimensions. I'm using a program wrote by Constatine Balanis which is based on the equation 13-52 in his textbook Antenna Theory Analysis and Design 3rd Edition .

In this program I needed to find the dimensions rho1, rho2, a, b, a1 and b1.

I'm having trouble distinguishing between rho1 and rho2, because it seems to me in the diagram from his text book that they would be the same length. and I also included a picture of the horn that I am measuring. Can anyone help me on how I can get the values rho1 and rho2? Thanks

Diagram from his textbook

Image of a horn

I gather that you want to use the Balanis formulation to calculate the directivity of your horn.

a and b are the inside dimensions of the waveguide feed of your horn. It would be easier to remove the transition to measure the wg. You will probably find that it matches one of the standard sizes and have a 2:1 ratio. It looks like it might be S band. The height of the flared section you can measure. Pe and Ph are the same else the sides of the flare will not mate to the waveguide properly. The aperture dimensions you can also measure.

I see a similar triangle argument to calculate the rho lengths for each plane. Stare at the figures a bit and you will probably see the relation too.

I suspect that the gain is on the order of 18 dBi or so but that is just a guess.

You might look at the horn carefully to see if you can determine the manufacturer and if so the gain is probably published. It looks like it might be a "standard gain" horn.