Beam Expander Safety
Irradiance of a beam before and after an M× expander: it falls by M², while the divergence falls by M, so far from it the hazard distance grows.
Educational only — not compliance-grade
These pages implement the published exposure limits for the cases each one states, but they are educational tools: no laser safety officer has signed them off.
- Do not use these results alone for PPE selection, NHZ / NOHD approval, controlled-area sign-off, enclosure/interlock approval, or formal classification.
- Always verify against ANSI Z136.1, IEC 60825-1, your local procedures, and the responsible laser safety officer / CLSO.
Output Diameter
10.00 mm
Input Irradiance
31.83 W/cm²
Output Irradiance
1.273 W/cm²
Reduction Factor (M²)
25.00×
E = 4P / (π d²), Eout = Ein / M², θout = θin / M
The diameter d is taken as the 1/e diameter (the ANSI Z136.1 / IEC 60825-1 convention, 63 % of the power), for which 4P/(πd²) is the peak irradiance of a Gaussian beam. If you have the 1/e² diameter instead, the peak irradiance is twice this value.
This is the irradiance at the expander. The expander also cuts the divergence by M, so far from it the beam is smaller than it would be without the expander, and the distance at which it falls to a given limit (the hazard distance) grows by about the factor M.
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Irradiance 4P/(πd²) before and after an ideal M× expander, no losses; with the 1/e diameter d it is the Gaussian peak. Not modelled: aperture averaging and the far-field NOHD, which grows about M-fold.
- Saleh B. E. A., Teich M. C. (1991). Fundamentals of Photonics, ch. 3 (Beam Optics): Gaussian beam intensity and power. Wiley. doi:10.1002/0471213748