A quick search for ‘laser cutter mirror alignment’ yields tons of resources, so I just offer a quick summary here: The laser beam needs to travel vertically through the center of the lens in order to cut through the material vertically, and to do this in all parts of the workspace, the laser beam needs to be parallel to the X and Y axes. In practice, this involves clipping a little U-shaped sheet metal piece (I used aluminum flashing) with masking tape to the mirror downstream of the one you are aligning, then pulsing the laser twice – once close and once far from the mirror being aligned – and adjusting until both pulses hit the same spot.
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