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I am wondering if there is a general rule of thumb in the radar world for what frequency you should pick to detect targets of a certain size.

For instance, if one had two radars set up - one for detecting targets of 5cm and one for detecting targets of 500m - what frequencies would be best?

I understand that many more factors will go into this like surface roughness, etc but I would like to understand the rough relationship between carrier frequency and target size.

I found by Knott (The Radar Handbook, chapter 11)- "The echo characteristics depend in strong measure on the size and nature of the target surfaces exposed to the radar beam. The variation is small for electrically small targets (targets less than a wavelength in size) because the incident wavelength is too long to resolve target details."

So from this I understand that the more detail you want, the smaller the frequency should be. If anyone could elaborate I would be most grateful.

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  • $\begingroup$ Possibly more expertise on the aviation site? aviation.stackexchange.com $\endgroup$ – Farcher Nov 29 '16 at 11:00
  • $\begingroup$ To me, as with optical systems and their microwave analogs, it would seem clear that the shorter the wavelength the better the resolution. The main drawback being the increase in power required. This site has a lot of detail radartutorial.eu/08.transmitters/!tx01.en.html $\endgroup$ – user108787 Nov 29 '16 at 11:54
  • $\begingroup$ Thanks for your replies and links. CountTo10, it's not clear to me why though - that's why I asked! $\endgroup$ – RH_data_maths Nov 30 '16 at 11:34
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A good, ballpark physically realistic answer will be given by the theory of Mie scattering. Basically, your wavelength needs to be smaller than the smallest features that you wish to detect by radar. Aside from this, you need to choose a frequency which will propagate well in the atmosphere without absorption, and a frequency at which you can readily generate powerful signals at. Some radars are bounced off the ionosphere; if this is your application, you also need to choose a frequency that will be reflected from the ionosphere.

Below is a plot I made some years ago to check that some software I was working with would reproduce Figure 13-14 in Born and Wolf, "Principles of Optics". It is a plot of the effective cross-section of a scatterer as a function of its physical size. The vertical axis is twice the ratio of power scattered from a homogeneous sphere of water to the power one calculates assuming ray theory. The horizontal axis is the size factor $\sigma = \frac{2\,\pi\,a}{\lambda}$.

Mie Scattering Curve Born and Wolf Fig 13-14

The curve is saying that for size factors of 2 or greater, the scattered power can be calculated by ray theory, by thinking of light as little pellets that bounce off a macroscopic object blocking them. That is, the scattering cross section roughly equals the cross sectional area of the target. For much lower size factors, the scattering cross section is much smaller than the "physical" target cross sectional area, and indeed as the object gets very small, the scattering is proportional to the inverse fourth power of the wavelength - much smaller than the linear decrease you would expect from ray theory.

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