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Re: [Phys-l] question on averaging.



curtis osterhoudt wrote:
Doppler sonar can be fantastically accurate (*and* precise!). In air, of course, one generally has to work with lower frequencies than in, say, water, but still, several hundreds of kHz is a common carrier frequency.

It is certainly the case that acoustic microscopes can use ultrasonic frequencies in air of a hundred MHz or more. I suspect that your 'Fantastic accuracy" boast is not what one would get from the sort of doppler approach used - for example -
in single emitter, single sensor once round speed sensors. I think of depth finders. I rather got a sense that you had dual emitter dual sensor rigs with heterodyne mixing to eliminate the variable carrier frequency issue. Or perhaps the acoustic equivalent of the Michelson-Morley interferometer by using a split beam to a fixed reference target? (Come to think of it, these days one could easily use a laser diode MM interferometer and count fringes directly...)
For water/solids-based measurements, I routinely get into the 0.1 mm / second velocity regime (this with a homemade mixer/envelope unit); using a commercial medical Doppler unit (Parks Electronics), sub-mm /sec velocities are commonly measured. I'm sure you can get to mm/sec accuracy with some air-coupled transducers set side-by-side. My homemade units consist of an analog multiplier (MLT-04s work well, and you can get them cheaply or even for free if you order samples) and then a low-pass LRC filter (Chebyshev if a strict bandwidth is needed, designed using QUCS; simply LC if a gradual roll-off is sufficient). These multipliers work just fine even without pre-amplifying the mixed signals. Let the chip do the processing for you; it's much easier than capturing raw signals and post-processing (though in my lab we've shown that it can be done in efficient software, even in real-time, with multi-MHz carriers). With good curve-fitting software (rather than a windowed Fourier-based method) a *clean* one-cycle signal is more than enough to figure out its frequency to perhaps 0.1%; several cycles will easily get you another order of magnitude precision. One of the big advantages of the technique is that it doesn't really care about the air sound speed (within reason). The signal is generally much faster than the sound-speed changes (over laboratory length scales) and in a monostatic setup, even if there's a constant air flow, the frequency shifts due to air flow cancel each other.

Your microwave idea is a good one, and MiniCircuits used to sell little microwave horns and the associated mixers for a low-power setup. They have the advantages that if students point them at walls, they can see movements of people on the other side of the walls; hooking up the output to an audio amp and speaker is a dramatic demonstration.
This brings to mind the popular conception of the IR spy phone transducing window glass vibrations into (not so) confidential audio transcripts, not to mention that cold-war strategem used against (was it ) the Moscow embassy, whereby a judicious microwave beam trained on a copper diaphragm embodied on The US Eagle logo re-radiated a detectable audio modulated return....

Brian W