horn antenna radiation pattern cos(theta)^q approximation

In reflector antenna, usually we use horn as the feed. It has been checked that the radiation patterns of the horn can be simulated as a function:

^q (

) .

The power q has been chosen at each frequency to fit the horn patterns.

I already have the radiation gain pattern of one horn, I am wondering how to approx it to

^q (

) ? By using 10*log10(

^q (

))? I want to know how to calculate the number of q.

Thanks so much!
Any discussion will be appreciated!


Regards,
Panou