Bit of a note on control theory:
Yes, you can constant current drive them, and yes, current is what makes it move.
But with regards to motion, voltage is king.
But current is force (and position).
So, what gives?
You almost never want an ideal anything source when it comes to transducers, antennas, amplifiers*, etc. You want it matched.
(*Audio amps are bad, so they get an exception. But where SNR and power efficiency reign supreme, like RF amps, it's vital.)
So, what's a good match here? It's not DCR of the coil -- that's almost always too low, as for example electric motors are usually designed to present an impedance 10-20 times higher than DCR. This gives good stability and efficiency. The same is probably true here: a voice coil is simply a short range reciprocating (rather than continuously rotating) AC motor.
One way you can figure it out: wire up a signal generator to the coil. Make sure to apply enough DC bias so it's not resting against an end-stop or something like that. (I haven't looked at a lens assembly real close, so I don't know if they're normally sprung to the middle of the range or what; just make sure it's in the usable range is all.) Apply a square wave from a relatively high resistance source (relative to a few-ohms coil, a 50 ohm function generator will probably do a fine job) and observe the amplitude of the ringing (if any). Also, make sure it's not banging into the limits, use a small enough amplitude to avoid that. Now, measure the peak amplitude of the ringing, and compare that to the height of the step: the ratio is effectively the voltage divider ratio between source resistance and equivalent motional impedance. This is the impedance you want to match to. Also, measure the frequency of the resonance while you're looking.
The coil and lens have mass, which means your control system will probably have to apply overshoot to get it to move. If you have good positional feedback in your system (the original purpose does, since it's continuously monitoring a laser beam!), you can simply apply a suitable compensator (pole-zero or lead-lag probably) and tune it for critical damping.
If your application has slower feedback, or you want it open loop altogether, you may want to apply some pre-shoot to compensate: what you'd do is, use an amplifier with an output impedance matched to the equivalent motional impedance, and put a filter in front of it. You want, not a high-pass filter, but a high-"boost" filter. This gives you the gain you need at DC to control position accurately, but gives it just a little kick in the pants at high frequencies to move it as fast as possible. Design it so the gain starts rising around the cutoff / resonant frequency of the lens system (which you measured from the step response), then drops off again at a somewhat higher frequency. The amount of boost you need depends on how much rise time you need, and how accurately you need it (needless to say, without a control loop, your motion is only as accurate as your calibration, so.. have fun with that).
The ultimate cutoff frequency is dominated by coil L and R. You'll generally want amplifier bandwidth, and the filter cutoff, around the same frequency (maybe 1-3x above?), so 1. you aren't buying more amp BW than you need, 2. you aren't trying to push it faster than it can move, and 3. you aren't accidentally cooking the coil with frequencies (or accidental parasitic oscillations...) that don't do any good.
Ok, so a little more than a note I guess...
Tim
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