numerous cheap battery boxes/small preamps can power the DPA microdots, like coresound, soundprofessionals, church audio. they are pretty easy on power consumption, 5V@1mA
Yeah, it isn't a difficult one, but the use case seems to be that it should all up be significantly smaller than the MK600, and an external power box is eating into that difference, and adding an additional box. No free lunch.
This is an interesting idea, but not offered by manufacturers of these devices as far as I can see. It's a shame as, in photography, many good photo editors now include lens correction profiles. It would be nice to have correction profiles for recorders like this as, in my opinion, the on-board microphones are the weak link in their capabilities.
I wonder if it would be worthwhile DIY calibrating a unit like this. Use some flat on-axis response speakers and record a tone sweep to determine corrective EQ/convolution.
Lens correction has the advantage that you have a clear and complete target to correct to. A microphone is dire in comparison. The problem is that off axis response can vary wildly. A pixel has no off axis response. What you see is what you get. correction is in the first part geometric in nature, moving the field about. Chromatic aberration is harder, and in general is not exactly reversible, but things can be improved. A microphone is like a single pixel.
With a mic your sound depends as strongly on the off axis vagaries as the direct on axis. Turning the mic axis is often a useful tone control. Ambient sounds come from all directions and each angle has a different response. It is intrinsically impossible to correct this. If you had a single source and only direct sound, and if you knew the position of the source you could correct it. But add diffuse field, unknown positions and multiple sources and you are screwed. A pure omni can be corrected, but most people will be starting with some form of cardioid. For video probably a hypercardioid.
Audio is just plain hard to manage.