Arduino Uno: rectangular signal during other tasks

The MOSFET, the LMP91051 and the sensor reading should be controlled by the Arduino Uno.

Look it is no good trying to pull rabbits out of a hat. You know what you have but we have no idea. So please post a schematic and links to your sensors.

There is no synchronisation needed.

So I repeat you are happy to take a measurement with the IR source off?