Light, I'm much more familiar with; I'm doing a lot of MRI work right now which utilizes that to an extent.
The math... does tend to be fairly complex, but the basics can be..well...basic. Think of a single ray of light. You hit it at something and it bounces. Your detector picks it up and tells you what angle it came at. Some simple geometry and you now know the angle the surface forms to produce the deflection you observed. Do the same with many rays of light and you have a coherent view of the object. Our eyes do this all the time (though only superman actually shoots the light beams). Light scattering would be a very good way of fulfilling your requirements. Any small particle can be used actually, though light may be easiest to think about.
I'm reluctant to respond to that second part. Yes, everything has a natural frequency it oscillates at, but that property is difficult to make use of in small particles like that. Resonance is explained through circuit theory, for the most part, and requires two particular typical elements: an inductor and capacitor. All things contain traits of these parts, but not necessarily to a noticeable extent. I can't say for sure, but what you say is theoretically possible, but practically very very very difficult.