I don't know what info you are looking for but, looking at the block diagram I see a few things of note.
1.) TR4 it the power transistor that charges the coil
2.) The clock frequency device that feeds TR4 could be replaced by your Arduino clocked output.
3.) The received or "bounced" signal that would come back from the coil will be AC therefor part of the circuit amplifies it and then biases it to a DC signal to facilitate measuring.
I am just a hobbyist so, I could be in error on somethings,
Mark