Atmospheric Attenuation
Beam attenuation along an outdoor path from Rayleigh scattering and visibility-based aerosol extinction (Beer-Lambert). Molecular absorption is left out, the conservative side for laser safety NOHD estimates.
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.
Transmission
93.42 %
at 1000 m
Attenuation
0.296 dB
Total extinction α
0.0681 km⁻¹
0.296 dB/km
Rayleigh
7.97e-4 km⁻¹
standard air, 15 °C, 1013 hPa
Aerosol (visibility)
0.0673 km⁻¹
Kim q = 1.30
Model
T = exp(−α L), α = α_Rayleigh + α_aerosol, attenuation (dB) = 4.343 α L
α_aerosol = [3.912/V − α_Rayleigh(550 nm)] · (λ/550 nm)^(−q)
Rayleigh scattering of standard sea-level air from its refractive index (Bucholtz, Appl. Opt. 34, 2765, 1995): 0.0115 km⁻¹ at 550 nm, falling as ≈ λ⁻⁴. The visibility V fixes the total extinction at 550 nm (Koschmieder); the aerosol part scales with Kim's exponent q(V) (Kim et al., Proc. SPIE 4214, 26, 2001), fitted in the visible and near IR. For mid-IR wavelengths it is only indicative.
Molecular absorption (water vapour, CO₂) is not included: real attenuation is higher in absorption bands and, at 10.6 µm, from the water-vapour continuum. Ignoring it overestimates the transmitted power, which is the conservative side for a hazard distance. Rain, snow and turbulence are not modelled either.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Rayleigh plus an empirical aerosol law from the visibility, only a rough guide beyond 1.55 µm. Molecular absorption, rain and snow are not modelled, so transmission is overestimated (conservative for hazard distances).
- Bucholtz A. (1995). Rayleigh-scattering calculations for the terrestrial atmosphere. Appl. Opt. 34, 2765. Rayleigh scattering of standard sea-level air, eqs. (2)–(4). doi:10.1364/ao.34.002765
- Kim I. I., McArthur B., Korevaar E. (2001). Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze for optical wireless communications. Proc. SPIE 4214, 26–37. Visibility-based aerosol exponent q. doi:10.1117/12.417512
- Peck E. R., Reeder K. (1972). Dispersion of Air. J. Opt. Soc. Am. 62, 958. Refractive index of standard air, fitted 0.23–1.69 µm. doi:10.1364/josa.62.000958
- Hansen J. E., Travis L. D. (1974). Light scattering in planetary atmospheres. Space Sci. Rev. 16, 527–610. Cross-check of the Rayleigh coefficient (0.46 % difference). doi:10.1007/bf00168069