Configuration of optics

I’ve been talking to the guys over at laser mechanisms and it looks like I could get into a new, better quality laser cutting head for around $1200. I’ve been wanting a new laser head for a while because I am pretty sure if I go with a better focal length I’ll be able to cut thicker metal. There is a good chance I may be able to double the thickness of the sheet metal in fact.

Life is all about power density. As in, if you want to blow a hole in metal you need to focus the beam of the laser to pack as much possible power into a really tight spot. There are couple of formulae that govern what happens with the spot size. The formula for the size of the spot is:

spot size = .013 * M^2 * (fl/D)

where M^2 is equal to 1.5 (comes from the laser specs),
fl is the focal length of the cutting head, and
D is diameter of incoming beam.

So there are two things I can change that impact the spot size, focal length and the incoming beam size.

Take a look at this picture. This shows the idea. The spot size (called beam waist in the pic) changes depending on focal length from the lens. The picture shows another important element to the process — focus depth. The focus depth is the distance range that an object can be placed in front of the lens and still get cut. The focus depth is a volume (shaped like an hour glass) that is packing a reasonable amount of energy that can actually get through the metal. The larger the depth, the thicker the metal is that I can cut.

So: small spot size good, big focus depth good.

The focus depth is governed by focal length and beam diameter in this equation, where:

depth = 2.5 x wavelength x ( focal_length / beam_diameter )^2

Have a look at this chart:

It calculates various spots sizes and focus depths – called “DOF” (depth of field) in the chart. The main factors that are varied in the chart are focal length and beam diameter. So my current arrangement is shown on the third line down. I have a 1.5 inch focal length and 10.5mm beam. This creates a tight tight little spot size of 76 micron.

small spot size: good, not big focus depth: not good.

The focus depth is only 0.36 mm. It is this short little number that explains why I can only cut 0.032 inch thick metal.

Lets change this. How much energy do I actually need to pack into a little spot in order to cut metal?

This book has an offhand statement “The power density is raised above 10^6w/cm^2 levels, at which most metals can be vaporized.”

The last column of my table also shows the power density for various configurations. What you can see is for my current set up, I have 61,000 W/mm^2, and in theory I only need 10,000. Wow. Have I been wasting major energy while not even maximizing my laser?

Crazy. I made a graph of showing power densities for different beam size and focal lengths…

what it shows is that its easy to get up over the 10,000 W/mm^2 range with pretty much any focal length.

So going back to the chart, there’s a row marked in red that looks pretty promising. The beam diameter is 10mm which is good for me because that’s the current beam size — I wouldnt have to make any changes to my optics in that case.

Conclusion: If I get a new cutting head with focal length of 3 inches and use my current beam diameter I can be well over beyond my power density and get a depth of field of 1.57 mm. This has the potential of tripling the thickness of metal I am currently cutting.


3 Responses to “Configuration of optics”

  1. Anonymous Says:

    thanks 😛

  2. Anonymous Says:

    great work 😀

  3. Luis Says:

    You did really a good job with your calculations. I am exactly in the same point you where at the moment of writing your post: trying to get a deeper cut by optimizing my optics. I ve got one quetion for you: would you also share the spreadsheet you used for your table?


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