FSO Background Noise
Background power, photon rate and photoelectrons per bit from clear sky, clouds or the Sun for a given field of view, aperture, filter passband and wavelength (850–1550 nm).
Spectral radiance L_λ
0.0250 W m⁻² sr⁻¹ nm⁻¹
Giggenbach (2022), Table 1
Solid angle used Ω
7.85e-7 sr
π sin²(FOV/2)
Background power at the detector
-69.5 dBm
1.11e-10 W
Photon rate at the detector
8.66e+8 s⁻¹
Photoelectron rate
6.93e+8 s⁻¹
Background photoelectrons per bit
0.693
photoelectron rate / bit rate
Background power vs full FOV
Spectral radiance vs wavelength
Model
P_bg = L_λ · A · Ω · Δλ · T_f · η_opt, Ω = π sin²(FOV/2)
The filter passband Δλ sets the collected band and T_f is its in-band transmission; out-of-band light is assumed fully blocked. Sky and cloud radiances are typical values with the Sun high in the sky (Giggenbach, Sensors 22, 6773, 2022, Table 1, at 850, 1064 and 1550 nm, interpolated log-log). Real skies vary by about ×10 with haze, sun angle and pointing, and between the table wavelengths the interpolation ignores the 1.13 and 1.38 µm water-vapour bands, where the sky is much darker. The Sun is a 5772 K blackbody disc of 6.79×10⁻⁵ sr above the atmosphere (the real disc is within about ±20 %; the atmosphere lowers it at the ground); it fills only its own disc once the FOV is wider. The Sun scene counts the solar disc only: sky and aureole radiance outside the 9.3 mrad disc are not added when the FOV is wider. A clear night sky is several orders of magnitude darker.
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
P = L·A·Ω·Δλ·T·η with Ω = π sin²(FOV/2). Sky and cloud radiances are typical daytime values at 850–1550 nm (real skies vary ≈ ×10; no night sky or Moon); the Sun is a 5772 K disc above the atmosphere (±20 %). Out-of-band light is fully blocked.
- Giggenbach D. (2022). Free-space optical data receivers with avalanche detectors for satellite downlinks regarding background light. Sensors 22(18), 6773. Table 1: sky, cloud and sun radiances at 850, 1064 and 1550 nm; eq. (22). doi:10.3390/s22186773
- Prša A. et al. (2016). Nominal values for selected solar and planetary quantities: IAU 2015 Resolution B3. Astron. J. 152(2), 41. T_eff = 5772 K, R = 6.957×10⁸ m. doi:10.3847/0004-6256/152/2/41