Q:

Omni to Cardioid for ambisonics

Some friends and I are trying to build a DIY ambisonic mic using mems mic. The capsules say that the polar response is omni but in order to get the directionality we need to capture 4 cardioid signals. (first order) Does anyone have ideas for turning the omni into a cardioid response. We are basing our design on this http://www.core-sound.com/TetraMic/1.php 
Thanks
Edit: The enclosure that we designed was printed three dimensionally using a Mojo. As you can see from the design the back side of the capsules have gaps. We are not sure if this is something that would help with the phase cancellation or if we need to close this off and push the boards far inside the cylinder. Not sure what model the capsules are but they are about 2mm by 3mm and omni in response. 

A:

An omnidirectional capsule is a pressure receiver whereas all directional capsules are pressure gradient receivers.  That means that you would need to drill the right amount of holes/sound paths behind the membrane to get a proper cardioid capsule.  Going the other way is much more realistic (namely closing the sound paths to the back of the membrane).
You can try working with sound shields, but the resulting directivity will have sharp changes in the polar pattern rather than the gradual change of an actual directional capsule.
So in short: I don't think your proposed material is suitable for the task.

