Re: [DIYbio] Why does a beam expander allow a smaller focused spot size?

On 03/30/2012 11:19 AM, Nathan McCorkle wrote:
> does the smaller focal length allow less
> overall divergence to occur? As in, if the focal length were longer,
> the rays would have a longer time to diverge?

Yes, but you think of the focal length as negligibly short.

You take care of whatever divergence has happened by unmagnifying it
to a small spot with a short focal length lens system.

For the original question, You choose a fatter beam to get the near in
effects where divergence varies less, see http://en.wikipedia.org/wiki/File:GaussianBeamWaist.svg

You use the fat beam in the part of the sketch called Zr

"where the origin of the z-axis is defined, without loss of generality, to coincide with the beam waist, and where

http://upload.wikimedia.org/wikipedia/en/math/e/5/8/e58a707d1ccf4ed6cefac660633038a8.png

is called the Rayleigh range." http://en.wikipedia.org/wiki/Gaussian_beam

Then, for some light source, it might make sense to expand it to a collimated beam of a certain width,
then focus down to a spot. The advantage would be that over the different distances,
(as in the distances a laser cutter mirror moves to),
the spot size would be changing less because it is in the Rayleigh range.

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