1. May 19, 2010

### erkokite

I am trying to write a program to numerically calculate RCS using geometrical optics (or some form of it). Basically my idea was to cast a bunch of rays from an emitting object (in my code it is a 1 m^2 plate), find where they intersect a surface, reflect the rays off of this surface and see if they intersect the emitter again (monostatic RCS).

The rays take the form:
$$u=\vec{A}e^{iks}$$, where $$k=\lambda/c$$, and is a vector amplitude representing the electric field, and s is path length.

Basically I sum all outgoing rays:

$$E_{transmit}=\sum{u_{transmit}}$$

and
incoming rays:

$$E_{receive}=\sum{u_{receive}}$$

Basically I have a Monte Carlo integrator spit out rays randomly, which are added to $$E_{transmit}$$, specularly reflected over geometry and added to $$E_{receive}$$ if they bounce back and hit the emitter/detector geometry. This iterates until $$E_{receive}$$ converges (also at least 1000 runs are performed). Now, I know it converges because I can run the program over and over again and get roughly the same answers with less and less variation depending upon my acceptable error value.

After I have a value for $$E_{receive}$$, I then take:

$$RCS=(|E_{receive}|^2/|E_{transmit}|^2)$$

Now, when all outgoing rays are reflected back to the transmitter, I get a value of 1.0. This was my test case for a 1 m^2 flat plate parallel to the emitter, with all rays traveling along the z axis- basically perfect directivity in a sense. If I let rays scatter along a hemisphere and attenuate them based on pointing error, I get a lesser value, but still a sane value. This makes sense to me. However, I have yet to figure out how exactly to convert this square meters.

Aerospaceweb.org gives an RCS equation of:

$$4\pi a^2b^2/\lambda^2$$

This of course, does not match my results, but I think that's because I am quantifying my RCS much differently.

So in short, my questions are:

Does my method seem to make any sort of rational sense? (My training was in aerospace engineering, not electrical engineering, so I don't know these things)

How do I go from received E field magnitude to an RCS in square meters?

Thanks.

2. May 20, 2010

### Antiphon

You are attempting to use ray tracing to compute an integral by Monte Carlo. This is a really bad way to compute radar cross section unless you capture the rays and use the radiation equation to integrate the ray field. Even then the answers will be terribly inacurate. You want to use Physical Optics, not geometrical optics. If you really insist on using GO, look into using GTD/UTD (geometrical theory of diffraction/uniform theory of diffraction). There are good programs for this developed at Ohio state.

3. May 20, 2010

### Ken Freeman

One problem in predicting RCS is the irregularity and complexity of real objects. In my previous job we obtained measurements of the RCS of several different cars on a turntable, full circle at 1 degree increments. The variation in RCS was in some cases more than 10 dB in adjacent bins.

With this in mind you should consider the utility of your results, if you intend to detect complex real-world objects.

My basic point is, is there really any benefit to having a tool for estimating RCS, compared to measuring it?

4. May 20, 2010

### erkokite

I am looking at switching to GTD/UTD, and eventually figuring out a way to add traveling/creeping waves, but first I want to get the basics working. So I wanted to get pure specular reflection working first, then adding diffuse scattering due to surface roughness and edge diffraction then corner diffraction.

You are right that it is terribly inaccurate and inefficient and a poor way of going about things, but I figure, Monte Carlo is easily parallelizable and also this seemed like a rather intuitive way of going about things for me, so this is just the way I coded it. I'm mainly doing it purely as a learning process to learn about RCS physics as well as Monte Carlo techniques, not as a practical tool.

I thought about using PO, but the problem with this is that doesn't handle curved surfaces well, but I suppose if I am using GO, accuracy is probably not my main concern anyway. :D

What is this radiation equation you speak of?

I just want to predict simple objects, as a learning exercise, like spheres, and plates, perhaps some very approximate simple aircraft shapes. I would like to estimate these things as I don't have access to an RCS range or fabrication equipment or the money or time to fabricate and measure these things.

5. Feb 2, 2011

### antoine170

Hello Freeman,

I know this is a old post, but I'm looking on the web for results for measurements for RCS of cars (up to have an idea on the range on various angles, mainly for perpendicular incident wave).

Have you an idea of where could I find such information ?

Thanks a lot !

Antoine