Optical Density from a Known Exposure Limit
For when you already have the exposure limit: the beam's irradiance over its aperture, the target and the optical density that reaches it.
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.
A limit you supply
This page doesn't look up the exposure limit: enter one from a standard or a reviewed calculation, with the aperture it is averaged over. To get the limit from the wavelength and exposure time, use the optical density page.
The standards use 1/e values; 1/e² values are divided by √2. If unsure, pick 1/e²: it errs on the safe side.
Beam irradiance
1.30 W/cm²
Averaged over 7.00 mm
Target irradiance
2.50e-3 W/cm²
Limit / safety factor
Required OD
OD 2.72
Behind the filter
962 µW
Beam power at the required OD
OD = log₁₀(Ebeam / Etarget), Etarget = limit / safety factor
Ebeam = P(1 − exp(−2D²/d²)) / (πD²/4): a Gaussian beam of 1/e² diameter d averaged over the aperture D
Transmission = 10−OD
Irradiance behind the filter vs optical density
- Behind the filter
- Target
ICNIRP 2013 averages the eye limits over 7 mm for the retina (400–1400 nm), 3.5 mm for the anterior eye, and 1 mm growing to 3.5 mm at 10 s on the cornea in the UV and from 1.4 µm. A wide beam's average approaches its peak irradiance, 8P/(πd²) with the 1/e² diameter; a narrow beam puts all its power inside the aperture.
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
OD = log₁₀(E/E_limit) for an irradiance limit you supply; E is a round Gaussian beam averaged over the aperture you enter (7 mm by default). No wavelength, time or pulse logic is applied.
- ICNIRP (2013). Guidelines on limits of exposure to laser radiation of wavelengths between 180 nm and 1,000 µm. Health Phys. 105(3), 271–295. Table 8 (apertures). doi:10.1097/HP.0b013e3182983fd4
- ANSI Z136.1-2014, American National Standard for Safe Use of Lasers. Appendix B: optical density of protective eyewear.