How this calculator works
The measured mode fits a conical envelope between two planes and can return a negative signed angle for a converging beam. It estimates far-field divergence only when the measured region is sufficiently far from a focus. The Gaussian mode uses the 1/e2 intensity waist diameter and an M² beam quality factor. Its angle is paraxial and its propagation curve uses an effective Gaussian envelope.
Formula
Measured Θ = 2 atan[(Df-Di)/(2L)]. Gaussian half-angle θ = M²λ/(πw0); zR = πw0²/(M²λ), where w0 is waist radius.
Worked example
A measured diameter increase from 1 mm to 3 mm over 10 m gives about 0.2 mrad full-angle divergence. At 500 nm and 1 mm waist diameter with M² = 1, the Gaussian half-angle is 0.31831 mrad.
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Frequently asked questions
Which diameter definition should I use?
Use the same definition at both planes. Gaussian mode expects the 1/e2 intensity diameter.
Is full divergence twice half divergence?
Yes. Mixing the two conventions causes a factor-of-two error.
Does a larger waist reduce divergence?
At the same wavelength and beam quality, the Gaussian divergence is inversely proportional to waist radius.