Question about highdivergent diodes like the NUBM44

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Unfortunately that's how life is with these diodes (and in fact, all lasers), they can only be improved so much and you must always make a trade-off somewhere else for those improvements.

Exactly, right--as has been stated/told many times over by many LPF members in many ways only to fall on overactive imaginations and deaf ears for whatever non-laser related reasons
This horse has been beaten to death so many times over already and the problem tackled in so many diferent ways by different members that people seem to think the basic reality/real answer is not a real answer, it seems --is like they think must be something missing/wrong-- not comprehending for whatever reasons. Asked, answered, and revealed another thousand times isn't going to make it any different.

As the saying goes: "You can't make a silk purse out of a sow's ear"

I'm resetting all of the lenses one lens at a time, Dang to get the beam dead center means moving the lens ever so small from side to side !!!
Thank you very much diachi for taking the time to explain that, Now I understand what's going on much better ....

Unfortunately,an NUBM44 while high output when pushed has very poor beam quality- low wavefront quality, high astigmatism and high divergence ---nothing is going to transform that into something it is not--there is no modern Alchemy that can do that.
Lens systems do not transform a source they just modify what is--garbage in, modified garbage out--may be acceptable may not be depending upon requirements.
Similarly, a lens system can't change Rosie O'Donnel into Melania Trump, except in imagination or with an imaginary lens system that doesn't exist.

Why don't you call or contact Edmond Optics and ask them what the best solution they can come up with for less than $1000 for iwhat you want to do. With all the optics they make and can supply they will be happy to adivise in hopes of a sale, I am sure. Call or e-mail them of both.
https://www.edmundoptics.com/contact-support/
Phone: 1-800-363-1992 Email: https://www.edmundoptics.com/contact-support/email-support/

Maybe buy a good book on the subject --study and learn what it teaches like "A Practical Guide to Handling Laser Diode Beams" by Haiyin Sun--"The only book completely devoted to laser diode beam control and handling. Provides systematically organized information about how to manipulate and characterise laser diode beams" . see: A Practical Guide to Handling Laser Diode Beams | Haiyin Sun | Springer

You can probably download it for free see: https://www.youtube.com/watch?v=qOIucyggyUc

Might be easier to get rid of the low/poor quality ouput diode and get one with better quality output/beam--maybe the new N450 diode--would save a lot of time and money for naught trying to reinvent the as good as optics get, wheel. Just a thought.

You've asked some interesting questions. If I were you I'd look for a used opitical board with lens holders and experiment. Something such as what this engineer is using in this demonstration. https://youtu.be/ac-vVNbQt2I

Good comment/idea.