27-EFT.WP.Packets.Light v1.0 | Chapter 7 — Free-Space Optical Links (Turbulence / Pointing / Weather)

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Chapter 7 — Free-Space Optical Links (Turbulence / Pointing / Weather)

One-sentence goal: Establish an integrated channel convention and compensation baseline for Free-Space Optical (FSO) links that covers turbulence, pointing, and weather; provide configured vs measured dual-form link budgeting and availability assessment; and ensure traceable publication via contracts and manifests.

I. Scope & Objects

1. Inputs
   • Geometry & attitude: endpoint coordinates r_tx, r_rx (unit = "[m]"), link length L = | r_rx − r_tx |, divergence θ_div, TX/RX apertures D_tx / D_rx, pointing/tracking spectrum S_θ(f) or statistics σ_θ.
   • Atmosphere & weather: refractive-index structure profile Cn2(z), visibility V (km), rain rate R_r, aerosol class & extinction σ_ext(λ), temperature / humidity / pressure (RefCond).
   • Optical parameters: wavelength λ, center frequency f0 = c_ref/λ, pulse/symbol rate R_s, optical power P_tx.
   • Framing / timebase & metrology: frame_spec (Chapter 3), OSNR / Q / EVM metrology channels (Chapter 11), unified clocks tau_mono / ts.
2. Outputs
   • Link budget: atmospheric attenuation A_atm(λ), pointing loss L_point, turbulence scintillation index σ_I^2, aperture-averaging gain G_ap, equivalent SNR / OSNR.
   • Statistical availability: Avail = 1 − P_outage (scenarios: freshwater / urban / desert), fade-distribution parameters (lognormal / gamma-gamma).
   • Dual-form gap: configured (model- and weather-based) vs measured (received power / OSNR / error rate) discrepancy delta_form_fso.
3. Boundary
   Focus on first-order engineering models of intensity fluctuations plus pointing and weather; dispersion and arrival-time harmonization are treated in Chapters 2 and 8; eye-safety is out of scope.

II. Terms & Variables

• Geometry / beam: Rayleigh range z_R = π w_0^2 / λ, beam radius w(z) (Gaussian approx.), receiver geometrical coupling η_geo.
• Turbulence: Rytov log-amplitude variance σ_X^2; scintillation index σ_I^2 = exp(4 σ_X^2) − 1 (weak turbulence); Fried parameter r0; coherence time τ0.
• Pointing error: angular std. σ_θ, receive-plane displacement σ_p ≈ L * σ_θ, pointing loss L_point.
• Weather extinction: visibility V, Kim/Kruse exponent q(V, λ), specific attenuation γ_atm(λ) [dB/km].
• Statistical models: normalized intensity I, I ~ Lognormal(μ, σ^2) or I ~ GammaGamma(α, β); P_outage = P( I < I_th ).
• Dimensional examples: unit(A_atm) = "dB", unit(σ_I^2) = "1", unit(σ_θ) = "rad", unit(L_point) = "dB".

III. Postulates P607-*

• P607-1 (Two forms in parallel): FSO releases must publish both the configured (model budget) and measured (received power / OSNR / error / availability) results, and record delta_form_fso.
• P607-2 (Explicit measures & domains): Any path or statistical integral declares its measure ( ∫_{z∈[0,L]} • dz ), ( ∫_{I} • p(I) dI ), and frequency integral ( ∫_{f} • df ); record the spatial/temporal averaging windows.
• P607-3 (Dimensional compliance): Power / attenuation / angle / length / time fields must pass check_dim; logarithmic (dB) quantities note the reference for conversions.
• P607-4 (Aperture averaging & pointing guardrails): If aperture-averaging gain G_ap or pointing suppression is applied, co-publish the aperture/pointing parameters and bandwidth limits.
• P607-5 (Traceable environment): Weather/meteorology source, sampling time and location (RefCond) must be persisted for replay.

IV. Minimal Equations S607-*

1. Atmospheric attenuation (fog / haze / rain / snow)
   • Kim model (fog/haze, V in km):
     γ_atm(λ)[dB/km] = ( 3.91 / V ) * ( λ / 550 nm )^{−q},
     q = { 1.6, V>50; 1.3, 6<V≤50; 0.16V + 0.34, 1<V≤6; V − 0.5, 0.5<V≤1; 0, V≤0.5 }.
   • Total atmospheric loss:
     A_atm(dB) = γ_atm(λ) * L_km + A_rain/snow + A_aerosol (persist add-ons per service model).
2. Turbulence scintillation & aperture averaging
   • Rytov variance (flat terrain):
     σ_X^2 ≈ 1.23 * Cn2 * k0^{7/6} * L^{11/6} (weak turbulence; or path integral ∫ Cn2(z) z^{5/6} dz).
   • Scintillation index (weak): σ_I^2 ≈ exp(4σ_X^2) − 1.
   • Aperture averaging (empirical):
     G_ap ≈ 1 / ( 1 + ( D_rx / r0 )^{7/3} ), with r0 ≈ [ 0.423 k0^2 ∫ Cn2(z) dz ]^{−3/5 }.
   • Effective scintillation: σ_{I,eff}^2 = G_ap * σ_I^2.
3. Pointing error & geometric coupling
   • Receive-plane drift: σ_p ≈ L * σ_θ.
   • Gaussian-beam coupling:
     η_geo ≈ exp( − ( r_off^2 / w_e^2 ) ), with r_off^2 = σ_p^2 + r_bias^2, w_e^2 = w(L)^2 + D_rx^2/8 (approx.).
   • Pointing loss (dB): L_point = −10 log10(η_geo).
4. Fading statistics & availability
   • Lognormal: I = exp( X ), X ~ N( μ_X, σ_X^2 ), P_outage = Φ( ( ln(I_th) − μ_X ) / σ_X ).
   • Gamma-Gamma (weak→strong turbulence): shape α, β (inferred from σ_I^2 or Cn2), P_outage = F_{ΓΓ}(I_th; α, β).
   • Fade margin & availability: FM_dB = P_rx,med(dB) − P_th(dB); Avail = 1 − P_outage.
5. Link budget & OSNR/SNR
   • Expected received power:
     P_rx(dBm) = P_tx(dBm) − A_geo(dB) − A_atm(dB) − L_point(dB) − A_misc(dB) + G_amp(dB).
   • Map to OSNR_lin / SNR_lin per Chapters 4 and 11, then to BER / EVM predictions.
6. Dual-form gap
   delta_form_fso = | P_rx,config(dBm) − P_rx,meas(dBm) | + w_σ * | σ_{I,eff,config}^2 − σ_{I,eff,meas}^2 |.

V. Metrology Pipeline M60-7 (Ready → Model → Budget → Verify → Persist)

1. Ready: ingest RefCond (met station / visibility / rain / Cn2), geometry & optics, pointing and tracking bandwidth; unify units (m, km, dB, rad).
2. Model:
   • Weather extinction: Kim/Kruse or local regression for γ_atm(λ);
   • Turbulence: build Cn2(z) and σ_X^2 / σ_I^2, compute G_ap and σ_{I,eff}^2;
   • Pointing: from σ_θ / σ_p with w(L), D_rx obtain L_point.
3. Budget: compute A_atm, L_point, P_rx, OSNR/SNR, and Avail (lognormal / ΓΓ); report fade margin.
4. Verify: compare with OSA/ADC/power-meter measurements to get delta_form_fso; assert Avail ≥ Avail_min, FM_dB ≥ FM_min, σ_{I,eff}^2 ≤ σ_I,max; if not, re-provision (rate down / power adjust / reroute).
5. Persist:
   manifest.packet.fso.* = { geo.hash, optics, weather.hash, Cn2.hash, A_atm, L_point, σ_I^2, G_ap, P_rx, OSNR/SNR, Avail, delta_form_fso, RefCond, contracts.*, signature }.

VI. Contracts & Assertions C60-7x (Suggested Thresholds)

• C60-701 (Two-form gap): delta_form_fso_p95 ≤ tol_fso (recommend tol_fso = 1 dB or per device accuracy).
• C60-702 (Availability): Avail ≥ Avail_min (e.g., ≥ 99.9% for metro/short-haul; long-haul scenario-dependent).
• C60-703 (Scintillation bound): σ_{I,eff}^2 ≤ σ_I,max or P_outage ≤ P_out_max.
• C60-704 (Pointing jitter): σ_θ ≤ σ_θ,max (or σ_p ≤ σ_p,max); tracking bandwidth BW_track ≥ dominant pointing-disturbance band.
• C60-705 (Power / OSNR): P_rx(dBm) ≥ P_min + FM_min, OSNR_dB ≥ OSNR_min_dB.
• C60-706 (Dimensional compliance): all fields pass check_dim; dB↔linear conversions recorded in the manifest.

VII. Implementation Bindings I60-7* (interfaces, I/O, invariants)

• I60-71 fso_attenuation(weather, λ) -> γ_atm[dB/km] ( weather ∈ { V, R_r, aerosol }; persist model version )
• I60-72 scintillation(Cn2, λ, L, D_rx) -> { σ_X2, σ_I2, G_ap }
• I60-73 pointing_loss(L, θ_div, D_rx, σ_θ, r_bias) -> L_point[dB]
• I60-74 availability(stats, P_rx, P_th, model ∈ { lognormal, gammagamma }) -> { Avail, P_outage }
• I60-75 link_budget_fso(params) -> { A_atm, L_point, P_rx, OSNR/SNR, FM_dB }
• I60-76 compare_config_meas(cfg_metrics, meas_metrics) -> delta_form_fso
• I60-77 emit_fso_manifest(results, policy) -> manifest.packet.fso
  Invariants: two_forms_present = true; RefCond consistent with weather/Cn2 sampling; check_dim(*) passes; geometry/device hashes traceable.

VIII. Cross-References

• Physical baselines & arrival time: Chapter 2; compensation: Chapter 6; modulation & OSNR/SNR: Chs. 4 / 11; arrival-time harmonization: Chapter 8; routing & power equalization: Chapter 5.
• Timebase & framing: Chapter 3 (R_s and T_guard); panels & runtime: Chapter 14.

IX. Quality & Risk Control

• SLI / SLO: delta_form_fso_p95, Avail, FM_dB, σ_{I,eff}^2, P_rx_p50/p95, OSNR_dB_p95.
• Fallback strategies: sudden visibility drop → lower rate / reroute / switch to backup wired link; increased pointing jitter → stronger aperture averaging / higher tracking bandwidth; stronger scintillation → larger RX aperture / site diversity / time interleaving.
• Audit: weather/Cn2 data sources & timestamps, link-budget vs measurements, threshold evolution, manifest signature chain & replay consistency.

Summary

• This chapter unifies weather extinction, turbulence scintillation, and pointing error for FSO into a single budgeting and statistical-availability framework, with configured vs measured dual-form validation.
• Through P607 / S607 / M60-7 / C60-7x / I60-7* and the manifest.packet.fso.* schema, FSO link modeling, release, and rollback are traceable, auditable, and operational.