Focal length, spot size and depth of field

Quick answer

A 50.8 mm lens on a CO2 laser with an 8 mm beam focuses to about 0.086 mm, with a depth of field near 0.87 mm. A shorter lens gives a finer spot over a shorter usable depth, which is why fine engraving and thick cutting want different lenses.

The Gaussian beam relationship is standard optics. Real desktop diode lasers use compound lenses on a non circular beam, so treat the absolute figures as indicative and the comparison between lenses as sound.

Focal length, spot size and depth of field Standard formula, convention inputs
Raw beam width entering the lens. CO2 tubes are typically 6 to 9 mm.
Focused spot diameter 0.086 mm
Depth of field1.09 mm
Wavelength10.6 um
f numberf/6.3
Power density multiplier136 per mm2

A shorter focal length concentrates the same power into a smaller spot, which cuts and engraves more finely, but the usable depth over which the beam stays that small falls away quickly.

This is why thick stock wants a longer lens: the beam stays acceptably small through the full thickness instead of diverging halfway down the cut.

Desktop diode lasers use compound lenses on a rectangular emitter, so their real spot is not circular and these figures are indicative rather than exact.

Formula: spot = 4 x lambda x f / (pi x D) ; depth_of_field = 2 x pi x (spot/2)^2 / lambda

Machines by laser type

Common questions

Which lens should I use for cutting thick material?

A longer focal length, typically 2.5 or 4 inch. The spot is larger so the cut is slightly wider and less fine, but the beam stays close to that size through a much greater depth, which is what lets it cut cleanly through 6 mm or more. A short lens focused at the surface has already diverged significantly by the time it reaches the bottom of thick stock.

Why is my engraving blurry at the edges of the bed?

On a gantry machine the distance from the lens to the work changes slightly across the bed if the rails are not parallel to the bed surface, and the depth of field is small enough that a fraction of a millimetre shows. Check that the bed is level relative to the gantry rather than to the floor, since it is the relationship between them that matters.

Does a smaller spot mean more cutting power?

It means more power density, which is what actually does the cutting. The same watts concentrated into half the spot diameter gives four times the power per unit area, which is why a well focused beam cuts material that a slightly defocused one only scorches. It is also why focus is the first thing to check when a machine that used to cut suddenly does not.

What is depth of field in a laser?

It is the distance along the beam over which the spot stays close enough to its minimum size to work properly. Inside that range the cut quality is consistent; outside it the beam widens and the cut degrades. Short lenses have a shallow depth of field measured in fractions of a millimetre, which is why they demand a flat workpiece and accurate focus.