The current proof of concept module uses the programmable real time unit of the Beaglebone. This is a device similar to a microprocessor and runs at 200 MHz.
In my next iteration, I plan to use a FPGA. FPGA can be faster and offer more tight control. The current model has a vendor lock to the AM355X ARM core of Texas instruments.
I just finished routing the hat for the Raspberry Pi with uses the ICE40HX4K. This chip comes in a TQ144 package so is easy to solder. The chip is also quite cheap, around 5 euro's. I was able to reuse a lot of the design of the beaglewire and icecore. Information for the laser controller is streamed to the chip via SPI. Maybe in a later stage, I will use the SDIO connector which is faster.
Schematic is shown below, full design available here.