I've designed various types of autofocus systems for machine vision systems and microscopes. Contrast focus is inherently slower because you have to scan the lens through focus, and read out the sensor many times. Theoretically you can change the focus in discrete steps (step focus, read sensor, step focus, read sensor, etc) or scan the motor continuously while reading out the sensor (in that case the two have to be well synchronized (usually with an encoder) so you know which frame corresponds to which focus position). I'm pretty sure Oly uses the stepping method simply because you can hear it. Either way, once you have the data (multiple frames vs focus), you simply look for where the edges are sharpest (mathematically, you calculate a derivative). Then you tell the lens to go to that focus position. Often you will have a two step process - scan a large range to roughly find focus, then scan a smaller range to get it more precisely. If the light level is low, then the noise level is high, and you may have to try again - which is when the "hunting" begins.
A phase system has separate, discrete, sensors to measure where the focus is. It's faster for two reasons: 1) The lens doesn't have to scan through focus because the different sensors are themselves focused so that the combined signals from them tell you where best focus is. That's the most common way to set up a phase system - details vary, and there are many tradeoffs to be made when designing such a system. 2) These discrete sensors respond MUCH faster than the time it takes to read a bunch of frames from the CCD.
Contrast systems have a hard time getting below 1 sec. Phase systems can be 5 to 10x faster.
The battery isn't the limiting factor. Even an AA could supply enough power to move these motors quickly - just not for very long. But the circuitry on the EM5 may not be designed to supply enough power to move the big 4/3 lenses quickly. Maybe the problem is something in the MMF adapter?
Anyway, I can't see any good engineering reason for the problem. Whatever the problem is, I think Olympus missed it, and it's really a shame. I'm hoping that it's NOT a motor power issue, because then there's a chance it can be fixed in firmware.
