# Measuring the distance to an object with RF resonance

Assume I put an RF antenna in front of an object (typically the face of someone sitting in a chair, so able to move about +/- 10cm in all directions) at a typical distance of 1m. If I consider the system antenna/face as a resonant cavity, I'd get a fundamental resonant frequency of about 150MHz.

I have a general physics education but no experience at all with RF antennas and resonators, so I have no orders of magnitude in mind. I realize such a 'resonant' cavity would be extremely poor, but how poor? My question is: is it conceivable to have enough resonance with basic antenna and processing electronics to be able to measure the mean distance to the face with a precision of say 1cm (i.e. measure the mean resonance frequency with about 1.5MHz precision), or is it an obvious and complete no go?

If it were conceivable, how 'clean' would the background need to be? Assuming there could be many unconstrained background objects (typically at a distance twice larger) all in a small room, could I just pick up the main resonance frequency around 150MHz for my measurement or would all the reflections / interferences with the other objects + room walls mess the signals completely up?

Note: I'm not expecting a detailed solution to my problem (although I'll happily take it if it comes :) I'm more looking for an "expert's feeling" like "yes, people have done that for decades", "maybe, you'd have to try" or "No way dude, you're completely dreaming".

In any case, if anyone sees any other (as cheap as possible, and most importantly automated and non intrusive) way to get such a measurement (+/- 1cm at 1m distance) please let me know.

• What you're describing may or may not be possible, but I would suggest looking into ultrasonic rangefineders - they definitely have the accuracy you are looking for, if you can focus them reliably on a certain part of the face. There may also be an answer with two cameras and visible light. – Ethan48 Oct 11 '15 at 15:40
• The dual camera solution was already our first idea, but we'd like a simpler one if possible... I quickly thought about ultrasounds a while ago and somehow guessed it would be too complex / expensive. But after you mentioned it again, I discovered how cheap of the shelve units can be, pretty amazing! I guess this will be my first solution to try. Thanks! – Julien Oct 12 '15 at 3:46

I do not believe this will be an effective scheme. The $Q$ of a resonator, a number which describes the strength of the resonant peak, is given by $$Q=\frac{f_0}{\delta f}\approx f_0\frac{2\pi\ t_{RT}}{\ell},$$ where $f_0$ is the resonant frequency, $\delta f$ is the FWHM of the resonance, $t_{RT}$ is the round-trip time, and $\ell$ is the round-trip loss. The approximation is for $\ell\ll1$, but it actually overestimates the $Q$ value for $\ell\sim1$ so it will be useful for this case.
The biggest problem for your application are the losses. I don't know exactly how much power a human face will reflect back towards the RF antenna, but I would think 5% is a relatively high value. Putting $\ell=0.95$ in the above equation gives $Q\sim3,$ which is a very low value. Good resonators have $Q$ values between 100 and 10,000. Using the other definition of the $Q$ parameter given above you can see that the width of the resonant peak will be $$\delta f=\frac{f_0}{Q}\simeq50\ \text{MHz}.$$