FSO Atmospheric Loss
Visibility-based aerosol (Kim) and Rayleigh scattering: attenuation in dB/km, total path loss and transmittance of a free-space optical link.
Attenuation α
0.180 dB/km
β = 0.0414 km⁻¹
Path loss
0.180 dB
over 1 km
Transmittance
95.94 %
Aerosol (Kim)
0.179 dB/km
q = 1.30
Rayleigh (molecular)
7.64e-4 dB/km
Spectral attenuation at V = 23 km
Model
β(λ) = β_R(λ) + [3.912/V − β_R(550 nm)] · (λ/550 nm)^(−q), α [dB/km] = 4.343 · β [km⁻¹]
The visibility V (Koschmieder, 2 % contrast) fixes the total extinction at 550 nm. Rayleigh scattering of standard air is computed from its refractive index (Bucholtz, Appl. Opt. 34, 2765, 1995); the rest is aerosol and scales with Kim's exponent q: 1.6 (V > 50 km), 1.3 (6–50 km), 0.16V + 0.34 (1–6 km), V − 0.5 (0.5–1 km) and 0 in fog, where scattering no longer depends on wavelength (Kim, McArthur & Korevaar, Proc. SPIE 4214, 26, 2001). β is the power extinction coefficient in km⁻¹; the loss in dB/km is 4.343 times larger.
Not modelled: molecular absorption (water-vapour bands near 940, 1130, 1380 and 1870 nm; choose a wavelength in a transmission window), rain and snow, turbulence and geometric loss. Kim's law was fitted in the visible and near IR.
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 scattering of standard sea-level air plus an empirical aerosol law scaled from the visibility, fitted up to 1.55 µm. Not modelled: molecular absorption bands, rain and snow, turbulence, geometric loss.
- 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