# Why does a sonar or radar's frequency correlate with its resolution?

A sonar's (or radar's) frequency determines its limit on the smallest size that it can detect and its resolution. I've heard that it's due to aliasing, if so, please explain the reason behind it a little more.

EDIT: My own understading: Lower frequencies don't reflect well off small objects, thus the reflected wave has a smaller amplitude and this increases the inaccuracy, but this is a practical rather than a physical limit as devices with more precision can also detect smaller amplitudes better. Is this correct?

• Too often overlooked in introductory instruction is the correspondence between this fact of wave-optics and the Heisenberg uncertainty principle of quantum mechanics (which after all relies on exactly the same math). – dmckee --- ex-moderator kitten Mar 1 '19 at 3:06

I’ll confine my answer to pulsed radars. Longer wavelengths reflect just fine from large targets, unless the targets have been specially shaped to minimize back-scatter by diverting reflections, as in the design of stealthy aircraft.

The range resolution is roughly $$c/2B$$, where B denotes signal bandwidth, which is limited in practice to roughly 10% of the frequency. The cross-range angular resolution is roughly $$\lambda /d$$, where d denotes the diameter of the antenna.

(Remember that the terminology of resolution is topsy-turvy. A small value for resolution is called high resolution. More is less.)

Consider the case where you use a pencil to draw a coastline. The finest detail of the coastline that you can put down would be the size of the pencils tip, right? The comparison is not exact, but the principle is the same for radar and sonar.

There are many aspects that would characterize a radar system, I'd say that for the purpose of your question the receiver and frequency in this case might answer it for you.

The frequency of the sent signal does indeed reflect differently for differently sized objects, and this is why we can't observe some objects with radars. If they're small enough their radar cross section is below what the receiver would require or they are simply too transparent at the frequency we're operating at.

The receiver puts other limitations on the systems, with, as you've mentioned in your post, the lowest distinguishable power. The noise floor in a receiver is highly dependent on the type of amplifiers used and the antenna. Narrow beams pick up less RFI for example. With a lower noise floor, weaker signals can be detected, which means that for a fixed range, objects with a smaller radar cross section may be observed. Keep in mind however, that radar cross section is not the same as physical cross section, but is the term used when dealing with radars.

• Not a scientific explaination, you have to agree :) – shah.shah Feb 28 '19 at 12:33
• We are not drawing anything, we are recieving a reflected pulse, and even within a wavelength, different parts of a wave have different phases and thus are distinguishable. – shah.shah Feb 28 '19 at 12:35
• I do agree, but i believe the comparison still makes a point. @shah.shah You don't have to explain to me how a radar works, I am very well aware with my degree, thank you. Due to the way the question was asked I don't believe throwing equations in his/her face will ease learning. – DakkVader Feb 28 '19 at 12:54
• I didn't mean to be rude at all, sorry if you were offended. I was just explaining why I didn't think this was a good analogy – shah.shah Feb 28 '19 at 13:01
• @shah.shah We've a difference of opinion then, i believe it gets the point through. I've updated my answer nonetheless, let's hope it answers his/hers question – DakkVader Feb 28 '19 at 13:02