I just looked up standard procedures. I've seen both pulsed solid state lasers as well as CO2 lasers. Everything is extremely fast. It engraves a meter or so width instantaneously.
That gives you a good idea about what you're up against.
Now you want to use a laser diode.
You're going to get a VERY poor beam shape with the 445nm diodes. The only way you'd want to get around that is probably by focusing the laser (also compensating for the lesser power than the system I linked)
These diodes have poor beam shape vs CO2 and YAG lasers because of the way the light is emited. The diodes will emit a line --- vs the round dots the other two will produce.
The diodes have line shaped beams because there are two axes of divergence. The one diverges faster than the other.
Because you'll need to focus the laser, you must have the diode at a fixed distance from the fabric... meaning simply rotating from a distance back and forth will
NOT work. You can thank the divergence of the diode. You won't get a small focal point from a distance.
The system you plan to make using one of these diodes would require the diode assembly to rapidly move across the fabric with high precision.
I don't know how to calculate the speed you'll need to do nor the focal distance you'd want...
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Bottom line
I think there better options than diodes for this project. Look into Nd:YAG lasers or CO2 lasers for this application, more specifically ones with modulation. The beam shape on those is not a hindrance. You'll need to point the laser at a mirror galvanometer in order to redirect the beam... bringing back the safety goggles... and more importantly a self-contained system.