As video as the reference,
Requirement understood.
The laser will be mounted on a head that moves on X and Y position freely with x resolution. An image will be given as an input to the software which needed to be designed. Depending on the image the laser will be turned ON(time till the material is etched) or OFF.
For example:
Assumption, Laser should be turned ON for 500ms to etch on a surface.
A dot should be made on a material at (Xn,Yn):
The gear motors should be driven to go Xn and Yn location. After the laser reaches the destination, turn on the LASER for 500ms.
Incase of etching an image on the material, the laser should be moved to different X and Y location and should turn on LASER for X seconds(X depends on material) with respect to the image.
Software should be designed in such a way that the Laser movement and Laser activation should be controlled, in layered approach. The software could be designed in C programming or python, which ever is ok.
To start working on this, the customer has to provide the hardware and proper requirements.