Here is my solution, whether it’s clever or not is up to you. It makes sense to this former math/science department of Chicago’s DESIGN school (Harrington College of Design, now closed), although I did raise the ire of those on Photon Lexicon and probably will here from those who like to whip out the integrals and differential equations, (usually to impress no one but themselves!), but it seems the solution for this geometrical optics problem simply relies on ray-tracing and trigonometry.
Everyone knows that parallel rays come to a focus one focal length away from a lens, and its inverse, a point source placed one focal length away from a lens will emerge collimated. So if a lens is placed at the appropriate position in front of a laser, the rays should emerge parallel.
The trick is in finding the position of the “point source” of a laser. Everyone has witnessed divergence with their lasers, and the manufacturers supply a divergence angle, along with a beam diameter in their spec sheets.
So to my high school trigonometry-teaching mind, if you know one of the sides of a right triangle and one of its angles, you can figure out the rest of the sides and angles. In the case of the laser spec’s, we know the base of a right triangle as the light exits the laser, half the given beam diameter, and the angle opposite it, one half of the divergence angle. The adjacent side is the distance from where the beam diameter is measured to the tip of the triangle, or the “virtual point source”. Here it is in pictures, with some solutions to the problems, He-Ne’s and DPSSes included.
- VPS.jpg (186.19 KiB) Viewed 3999 times
Doing the sums for the 315M yields the “virtual point source” to be 145.45 mm behind the output window of the laser. Which would mean putting a 150 mm lens less than 5 mm away from the output should yield a collimated beam, but more practical would be a 200 mm lens 54.55 mm away.
Moving the lens closer to the laser would diverge the beam, but not as quickly as the laser does on its own, and moving it further from the laser would start it converging. See something like Popular Optics by Sam Brown to understand why. http://edweslystudio.com/nlutie/Bookshe ... sponly.htm
The basic reason why laser beams diverge is the wave-like nature of light, and it does require heavier guns of mathematics to completely quantify the beam waist. But it can be extrapolated where the beam waist becomes zero using the above trigonometric relationships, which gives a first order approximation of what to buy and where to put it.