How this calculator works
A collimated beam focused by a lens exchanges a large entrance diameter for a small waist. This paraxial approximation assumes the waist is near the focal plane and the incoming Rayleigh range is large compared with focal length. Both input and spot diameters use the 1/e2 intensity convention. Aberrations, truncation and imperfect beam quality enlarge a real spot. The reported depth is the confocal parameter, not a universal machining tolerance.
Formula
S = 4M²λf/(πD); zR = π(S/2)²/(M²λ); confocal depth = 2zR.
Worked example
At 500 nm, a 10 mm beam focused by a 100 mm lens with M² = 1 has a spot diameter of about 0.0063662 mm. Doubling focal length doubles this diameter.
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Frequently asked questions
Is this the Airy disc diameter?
No. This is a Gaussian 1/e2 intensity diameter; a uniformly filled circular aperture has a different diffraction pattern.
What does M² mean?
It compares the beam parameter product with an ideal Gaussian beam. Values are at least one in this model.
Where does the diameter grow by sqrt(2)?
At one Rayleigh range on either side of the waist, giving a total confocal length of 2zR.