### Laser Optics 101 – Lenses

The useful power of a laser comes down to power density.  The more power per unit of area (power density) you have, the more cutting power you have.   The beam that comes out of a laser has a rather large diameter.  It is much cheaper to increase power density by focusing the beam to a small spot than to increase the laser tube power.   To do this you need a lens.  “OK”, you say, “what lens should I use?”.  Unfortunately the answer is not that simple.  When it comes down to real world cutting, a lot of the desired qualities conflict with each other.

Cutting actual materials differs from ideal conditions because the material has a thickness and the smoke and spattering that come from cutting needs to be a reasonable distance from the lens to protect the it.  Material thickness comes into play because if the beam is focused at a sharp angle, the beam quickly diverges on either side of the focal point.  This is know as depth of field.  Basically this means how far away from the beam focal point does it still have a useful power density.  “OK, so it is best to have a long focal length?”  A long focal length addresses depth of field and safe distance from the cutting affects, but it turns out that works against ideal spot size.

The spot size can be calculate with the following formula.

$\fn_phv \120dpi \large \fn_phv \120dpi \large SpotDia. = \frac{1.27\cdot f\cdot wavelength \cdot M^{2}}{D}$

• f = focal length
• wavelength = wavelength of beam
• M = Beam quality.  A TEM00 beam has a value of 1.
• D = Diameter of the beam at the lens.

The only thing most of us will have control over is the focal length (f), because you can buy lens with different focal lengths.  Above we determined that a long focal length is desirable for depth of field and preserving the lens, but it is directly proportional to the spot size.  A focal length of 100mm will have a spot size twice as big as a 50mm lens.  Some of the really high power cutters actually use a beam expander to increase the diameter (D) of the beam at the lens.  As you can see, this will directly decrease the spot size.

OK, so now it looks like a short focal length is better, but what about that depth of field thing.  Depth of field is basically the useful thickness of the spot  Per the Parallax Technology, Inc FAQ, depth of field has been arbitrarily determined as the region where the beam diameter is less than 1.4X the spot size on both sides of the focal point.

The 1.4x Depth of field can be determined with the following formula.

$\fn_phv \120dpi \large DOF = 2.5 \cdot wavelength \cdot \left ( \frac{f}{D} \right )^{2}$

• wavelength = wavelength of beam
• f = focal length
• D = beam diameter at lens

Note:  All these formulas (formulae) are on my automated Laser Optics Calculator Page.

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