Pointing Loss
Interactive FSO pointing-loss calculator with jitter, misalignment, beam waist, and aperture coupling.
Beam radius @ 1 km
3.19 cm
far-field divergence λ/(πw₀) = 19.7 µrad
Pointing offset / jitter at RX
0 / 0.100 cm
static offset b, jitter s per axis
Aligned capture η₀
99.28 %
geometric loss 0.0315 dB
Mean capture ⟨η⟩
99.26 %
with offset and jitter
Pointing loss
6.19e-4 dB
−10 log₁₀(⟨η⟩/η₀)
Geometric + pointing loss
0.0322 dB
−10 log₁₀⟨η⟩
Loss vs jitter at 1 km
- Pointing loss
- Geometric + pointing
- Current jitter
Model
w(z) = w₀√(1 + (z/z_R)²), z_R = πw₀²/λ, η₀ = 1 − exp(−2a²/w²)
⟨η⟩ = 1 − Q₁(b/σ_t, a/σ_t), σ_t² = w²/4 + s², b = θ_b z, s = σ_θ z
A Gaussian beam with its waist at the transmitter reaches the receiver with radius w(z). Its intensity is a 2-D Gaussian (σ = w/2 per axis); random jitter of σ_θ per axis moves its centre by a Gaussian amount, so the time-averaged power on the aperture of radius a is the fraction of a wider Gaussian (σ_t) offset by the static error b, a Marcum Q-function. For a small aperture this reduces to η₀ · w²/(w² + 4s²) · exp(−2b²/(w² + 4s²)) (Farid & Hranilovic, J. Lightwave Technol. 25, 1702 (2007)). Jitter is a fading process: this is the mean, not the outage probability.
Not modelled: atmospheric attenuation, turbulence (beam wander, spreading, scintillation) and truncation of the transmitted beam by the TX 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
Exact for a Gaussian beam in vacuum with a static offset and isotropic Gaussian jitter, averaged over the jitter. Not modelled: atmospheric loss, turbulence (beam wander, spreading, scintillation), TX truncation.
- Farid A. A., Hranilovic S. (2007). Outage Capacity Optimization for Free-Space Optical Links With Pointing Errors. J. Lightwave Technol. 25, 1702–1710. The small-aperture jitter result, which the exact mean capture reduces to for an aperture much smaller than the beam. doi:10.1109/jlt.2007.899174
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