How Can I Expand and Collimate a Laser Pointer Beam Using Basic Optics?

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Hop-AC8NS
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I have a small Chinese green laser pointer. It produces a very bright collimated beam, roughly 2mm diameter with its existing optics. I would like to know two things: (1) how to expand the laser pointer beam while maintaining collimation, (2) how to produce a collimated beam of any arbitrary size from the bare laser diode chip, for example from a Nichia NDG7H75E.

These are multi-transverse mode laser diodes. Should their emissions be spatially filtered before collimating?
 
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Hop-AC8NS said:
how to expand the laser pointer beam while maintaining collimation
Build a telescope with two lenses. The resulting collimation quality (divergence, really) depends on the beam quality from the source.

Hop-AC8NS said:
how to produce a collimated beam of any arbitrary size from the bare laser diode chip, for example from a Nichia NDG7H75E.
Most all laser diodes (edge emitters) have different divergence in the two axes (called the fast or slow axis). So good beam collimation usually uses something like a cylindrical or aspheric lens to get everything in synch. The size change is the magnification of your telescope.

Hop-AC8NS said:
These are multi-transverse mode laser diodes. Should their emissions be spatially filtered before collimating?
IDK, that depends on what you want. Spatial filters are located at the focal plane, aren't they? So maybe in the middle of your collimator.

Ultimately if you are going to do this, you'll have to study a bit about classical optics and laser diodes. We can't choose optics for you. There should be a ton of information on the web about this subject.

I will note that cheap Chinese green laser pointers have remarkably crappy beam characteristics. Still they will have collimated it as best they can/want. But then my experience was all with really, really good (and expensive) lasers. The physics world always assumes you have perfect beams, so some fiddling will be required.
 
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Thank you for your response. I'll go back and review some basic optics.

I used to be able to get by with some simple ray tracing and trigonometry, but there is probably an easier softer way, a design app perhaps. Edmunds has always been my "go to" source for optical information, and occasionally optical components before I retired. Nowadays its drug store junk, discarded cameras from flea market sales, and Amazon. Oh, well...