Asimov's Corner

@Crashalot - I'll try to explain as best as I can. With radar (and sonar), you simultaneously transmit a pulse and start a timer. The timer continues to run... and then you receive an echo.

The time at which the echo was received is then used to calculate the distance between the transmitter and the object. This is a pretty straightforward calculation - distance is speed times time; x = vt.

You have the time, you want the distance, so the only thing you need to know is the speed at which the pulse travels. For radar, this is the speed of light; for sonar, it's the speed of sound through whichever medium you're using the sonar (air, water, skin, etc.)

So far, pretty straightforward. The thing now to understand is that the pulse is emitted like a cone. Very close to the transmitter, the area of the pulse is relatively small. As the pulse propagates away from the transmitter, the area of the pulse increases.

You can think of this like a flashlight. Close to the flashlight, the light may only cover an area the size of your hand. Very far from the flashlight, it may cover an entire wall.

So the radar (or sonar) wave front travels out until any part of the wave front hits any object. This causes (the first) reflection. That reflection is detected by the radar (or sonar) unit and converted to a distance.

Now, this is important because the reflected wave front does not give any information about the size of the object. All you can know is that you sent a pulse and got a return.

So, typically the way this is handled is to assume that whatever caused the reflection is at least as big as the cone is at that particular distance.

You may receive a weak reflection - was this because a very large object with poor reflectivity was in the path of the beam, or because a very small object with high reflectivity was in the path? You can't know.

So, any object, no matter how small, gets "smeared" to the width of the beam because you cannot know how large or small the object is or where exactly it's located within the beam based on the reflection alone.

All you can know is that the object was "somewhere" in the cone, at whatever distance you detected the object. Typically, for radar (or sonar) imaging, the way this is handled is to display the width of the cone at whatever distance, and then shade the display based on the return intensity.

This helps to visually interpret the data - darker objects are weaker returns, brighter objects are stronger returns, but again, there's no way to tell size/shape/reflectivity of the object based on the return signal.

So, back around to my original comment that you asked about, if you want to find the range of the golf ball, all you care about is getting the distance return signal. The cone can be as big as you want, because you don't care about where the ball is within that cone, you just care about how far the ball is from the transmittter.

If you want to track the golf ball, then you do care about where it is located within the cone. Unfortunately though, as discussed above, it is not possible to determine where within the cone an object exists. The only option is to make the cone narrower.

With a narrower cone, there exists the possibility that the golf ball could (almost certainly will) travel outside the cone, so now you need to move that cone around to "look" for the ball.

There are two ways that you can "move" the cone - physically, with a rotating or articulated radar (or sonar) transmitter, or electronically, with a phased array of transmitters. I'm not going to go any further into depth on the topic, though (unless you really want to).

I'll cut to the point about your radar question, though. In order to pinpoint a golf ball at 100m, you need a very, very narrow "pencil" beam. The size of the beam transmitted by a radar (or sonar) system depends on the physical size of the transmitter relative to the operating frequency of the transmitter.

In order to get the resolution you want, you need a "super high frequency" radar system. I say that with quotes because Super High Frequency is an actual term that refers to an actual radio band, like very high frequency (VHF) or ultra high frequency (UHF) does.

There's a lot of other information that goes into radar design, but suffice it to say that, to scan for a golf ball at the range you're talking about, you couldn't practically implement a radar (or sonar) system with a physically maneuvered transmitter. You'd have to use a phased array.

A K-band (SHF) phased radar array large enough to track a golf ball at 100m is the same kind of a phased radar array that could track an object 100x that size, say a missile, at 10km. This is how you get into defense/military applications. You technically might be able to purchase something like this, but you could almost certainly not afford it. This is the kind of equipment used for surface to air missile batteries, or missile defense systems, etc.

But again, if you don't care about tracking the golf ball and instead only want to know how far away it is, then you don't need any form of high-resolution radar.

I'm not sure how this is useful to you though, because as mentioned earlier the radar system detects a return from any object - you won't be able to differentiate the golf ball from the ground once it is "very close" to the ground. Golf balls roll/bounce a very long distance, so if you are thinking of using a system like this to help retrieve balls then the radar distance measurements aren't going to help.

What I would consider instead is using computer vision to track the golf balls. You mentioned that there would be difficulty using this in bright sunlight. This is true if you're using white golf balls and there's a bright or cloudy sky, but what about using black golf balls instead? Or any other color. Those should be easily distinguished from the sky.

There's also a computer vision (CV) technique called "background subtraction," where you essentially record a couple frames of video, average them, invert them, and then add them back to the current frame. If the current frame is the same as the previous couple frames, the result is a black screen.

Any object in the current frame frame (or any object in a different position) from the previous X frames then shows up clearly, dramatically reducing the amount of work required to locate "new" objects in the scene.

This would be the technique I would use to track golf balls. If you coupled that with a second camera, you could probably get a stereo vision system setup for relatively little money that would track objects with x/y/z coordinates over time. Now the only issue would be, like with radar, resolving an object the size of a golf ball from 100m. This was my comment about the limits of human vision.

A person can see objects as small as an arc of 0.2 degrees wide. A golf ball at the range you're talking about is about 0.28 degrees wide. Maybe a camera will detect it, maybe not. Maybe it just looks like one pixel (noise). But a stereo camera system should be so inexpensive that you could afford to put multiple stations in.

Final comment - I'm not sure what your application is. I understand that you want to measure or do something with sporting equipment; baseballs, golf balls, etc., but to what end? What are you trying to do with this information? Is this to aid recovery of the objects, or to provide feedback for proper form, or something else?

There are a lot of people that visit this site that have a problem, have already decided on an inappropriate solution, and then come asking for help on how to implement the inappropriate solution. An example might be someone that wants help building a cement extruder when all they really want is a bunch of cinder blocks. Maybe they didn't realize cinder blocks existed.

I'm not saying this to suggest your ideas are inappropriate, but instead to highlight the fact that we can best help you when you give us your problem statement along with your question. For the example, if the poster says, "I'm trying to generate concrete Lego. How can I build a cement extruder?" Then the answer is clearly - have you tried bricks?

So, I feel like maybe this was a flood of information, but hopefully it puts your project in perspective. If you'd like more advice or feedback, please ask!

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