mathematical expression of am

Hello All,
I am doing a experiment in reflector feed design where I am looking for mathematical expression for its radiation pattern.
Now let me descibe in detail.I am currently finding the System Temperature of a Parabolic Dish+Receiver etc assembly.I am using feed pattern of (cos(theta/2)^n) which is body of revolution pattern and rotaionally symmetric one.But now my estimate of Tsys with this pattern is very differnt from that of ideal or expected value of Tsys.
I want to use some other mathematical expression like cos(theta)^n or sin(theta)^n or so.I was looking for radiation pattern of corrugated horn or array of conical horn.Patterns seems to be fine but I need a mathematical formula which feats to radiation pattern of corrugated horn or horns or log pereodics etc.
I want a -10 to -20 db taper at the edge of dish.
Anyone has anyidea of mathematical expressions of horn antennas other than which I mentioned above.
Thank you.

I suspect that you will want to include sidelobe energy in your analysis. The approximations you mention are typically used to model the main beam.

I wonder if (sin(x)/x)2 would be more useful because it produces sidelobes. You could weight it with cos(x) to some power the adjust the sidelobes to what you need for your model.

The software SABOR might be useful (w*w.gr.ssr.upm.es/sabor.htm). TICRA is another commercial tool.

Hi Azulykit,
Thank for reply.
Actually,yes there will some side lobes and back lobes ,so I have taken into account the ground and sky temperature for that..
I want trying with Gaussian Beam,then cos(theta/2)^2n etc...I got worst number for Gaussian beam but improved result for last one..
OKay..I will try the patten u said...but may I know what is that pattern exactly..? Horn is generating it or what....?
Basically I know both the simulator..but I think SABOR dosen't have the flexibity of giving feed pattern of our choice and TICRA GRASP has limited facilities in trial version...
I am doing all this in C...so I need mathematical expression to get answers..

Added after 45 minutes:

Hi Azulykit,
I guess you have suggested me that I should multiply my feed pattern for cos(theta/2)^n with some kind of Pattern factor as we do in antenna array radiation pattern finding.Thats good,but right now I am not getting results with that kind of mathematical formula.
Anymore suggestion pls...

You caught the idea in that suggestion. A uniform rectangular aperture radiates with a sinc pattern.

Silver and Kraus both have additional information and are references you might want to spend some time studying.

Another simple approach might be to model a dense array where you can model various amplitude and phase distributions to replicate your reflector. An amplitude taper would simulate the effect of edge directed tapering on a reflector. You could also kill the center elements to model feed blockage. Let the computer do the work calculating your pattern.