In other words with more:
For laser diodes, a large single lens with a long enough focal length (without any other lens/expander in front of it) can produce a lower divergence beam than a fancy multi-element/lens beam expander, if the lenses used in said beam expander is producing a smaller beam diameter output than the single lens collimator produces.
If using a laser diode and you want to build a cheap large beam diameter low divergence pointer, just find a large single PCX lens with a long enough focal length so the diameter of the beam from the laser diode fills 80% of its diameter at its focal length and adjust to infinity focus. Only problem is without correction, the beam from most laser diodes is a rectangle, so half of the lens diameter won't be used, wasted glass, but far less expensive than using cylinder or prism pair lenses to square the shape of the beam.
PDF: How to build a classic multi-element beam expander
https://photos.imageevent.com/qdf_f...beamexpander/How-to-Build-a-Beam-Expander.pdf