A negative lens act opening the slow axis (from here SAC, slow axis correction), making the whole beam from the diode almost square ..... if the assembly include a good aspherical lens, it can also be used for burn, but the more common use for this is in nightvision illuminators, cause it permit to focus better the beam in an almost uniform circle (a bit like a torch reflector do), so the effect is better in focusing the beam for long distance throwing ..... also, expanding the beam, it require lenses more large than the usual ones used, as example, in aixiz or other similar modules (cause, for the presence of the cylindrical lens, the focusing one cannot be too much near the diode, so a small lens lost part of the beam)
A positive, instead, act closing the fast axis (fast axis correction), so the beam become (until certain point) more close, and can be focused from a more small lens in a more "almost round shaped" point at closed distance, as example for engrave ..... also this correction can be used, ofcourse, also for refocus it for distance ..... only, the FAC one produces a more small and short distance point (and can also be focused more easily in a little more "deep shape" area)
But let me draw it, is always more clear with a draw
Done, it's a bit schematic, but i think it can be understood the same (hope, at least
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