Every laser data sheet I've ever read has the initial spot size and the divergence. Usually in milliradians, ie starting with a 1 mm beam at 1 mil means a 1 meter spot at 1000 meters.
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If you have the initial spot size, you use the formal Gaussian equation. This is further complicated by diode lasers usually having two divergences, as their beams are elliptical.
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If you have no other means of doing it, the arctangent based equation is the one to go with,
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Most hobbyists measure the beam divergence by taking an initial diameter measurement, then moving downrange and taking a second one. If you take it at the 10% and 90% power points, ie just inside the beam where the Gaussian function really starts to increase in intensity, its not a bad way, although pros will take the data at the 86% points. This works as long as you take the two diameters past the beam "waist" which is often near the exit point of the beam from the laser.
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You then take the two diameters and the distance and work out the angle.
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ie Theta is D2-D1/Z2-Z1 where D is the diameter and z is the distance.
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see:
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http://vlab.amrita.edu/?sub=1&brch=189&sim=342&cnt=1
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Steve
Qui habet Christos, habet Vitam!
I should have rented the space under my name for advertising.
When I still could have...