# Radar: frequency and target size

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.

• Possibly more expertise on the aviation site? aviation.stackexchange.com – Farcher Nov 29 '16 at 11:00
• 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 – user108787 Nov 29 '16 at 11:54
• Thanks for your replies and links. CountTo10, it's not clear to me why though - that's why I asked! – RH_data_maths Nov 30 '16 at 11:34

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 $\sigma = \frac{2\,\pi\,a}{\lambda}$.