Re: [CAD_CAM_EDM_DRO] Re: added laser cutter to my mill (pics)

Hello Rick,

> Excellent post Tom, thanks! (Are you an optics guy? You sound like
> it!)

Yes. See my recent (Wed 4 Aug) post titled "Newbie Intro"

> I am seeing pretty much exactly what you described. A focused spot
> of about 0.012 inches and a depth of focus of at least 1/4 inch. I
> am not sure the Synrad laser M^2 value is 1...might be 1.1 or
> something.
>
> The formula I found for focus spot size is:
>
> spot dia. = 1.27 * f * wavelength * M2 / D
>
> Or for CO2 lasers in particular:
>
> spot dia. (in mm) = 0.013 x M2 x f / D
>
> Where f is the focal length of the lens and D is the diameter of the
> beam entering the lens.
>
> So, for my 3 inch focal length lens if the beam is about 4mm, then
> the spot dia = 0.25mm = 0.0098 inches, assuming M^2 = 1, which it
> probably doesn't. The only thing I can control with my existing
> parts is the Diameter of the laser beam by moving it farther from the
> lens, right? Increasing D will decrease my spot size.

D is the diameter of the laser beam waist...not the diameter as it
enters the lens.

ideal beam divergence = (4/pi) * (lambda/D) = 1.27 * lambda / D

actual beam divergence = M2 * ideal beam divergence

focused spot diameter = f * actual beeam divergence

where:

pi = 3.14159

D = Gaussian waist diameter = 3.5mm (see
http://www.synrad.com/48series/48_10.htm)

lambda = 10.6 microns for most CO2 lasers

M2 = fudge factor for not quite Gaussian = 1.2 (see
http://www.synrad.com/48series/48_10.htm)

The three equations above combined will give you the first of your two
equations.

Moving the lens farther from the laser results in a larger diameter beam
at the lens but does little to reduce focused spot size. There is a
subtle reduction in focused spot size and a slight change in spot
distance from the lens, but this is mostly academic.

Accurate propogation of a Gaussian beam through optics is computed a
little differently than geometric optics. But, you can still use
geometric optics very effectively to predict the beam shape on the
output side of the lens if you know the beam shape on the input side of
the lens.

Tom Hubin
thubin@...