Not sure there is such a thing as an Eye safe Q switched laser, but megawatt class peak pulses are easy if you go there, and narrow band filters are not that problematic for the common laser wavelengths.
I seem to remember a short ranged synthetic aperture experimental design being published as part of a course on radar systems somewhere (MIT?).
If I wanted to play, I would probably ignore the transmit side, there are plenty of transmitters having well defined pulsed signals (DAB has lovely convenient guard bands around each symbol, GSM has possibilities, Tetra...), a phased array of aerials and an accurate timebase would probably let you build an image by looking for correlation peaks between the transmitted signal and each of your beams, and modern graphics cards are good at that kind of maths.
Point one fairly narrow TX aerial at whichever transmitter you are using as your source, and point your phased array away from it so the transmitter is in a null, then digitize (A Rack full of those cheap dongles butchered to have a common reference clock), and get your math on.
Not everything interesting needs to be boring monostatic affairs, and the nice thing about bistatic is that sometimes other people have set up transmitters for you....
73, Dan.