47-PTN Template v1.0 | Chapter 6 — Experiment/Observation Design & Sampling

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Chapter 6 — Experiment/Observation Design & Sampling

I. Geometry & Timebase

1. Observation geometry
   • Frames: {RA, Dec} or {x, y, z}; attitude quaternion q_att; field of view FOV; pointing r_hat (unit vector).
   • Explicit path: paired gamma(ell) and measure d ell; step Δell, path length L = ∑ d ell.
   • Coherence windows: temporal T_coh, spatial L_coh, spectral B_coh; require |∇ n_eff| · L_coh ≪ 1.
2. Sampling timebase
   • Sampling rate f_s, exposure/dwell t_exp, cadence; Nyquist: f_s ≥ 2 f_max.
   • Arrival-time sampling: ensure Δell ≤ ( c_ref / f_s ) / max(n_eff); phase sampling: Δt ≤ λ_ref / (2 c_ref).
3. Bands & references
   Reference wavelength λ_ref, wavenumber k_ref = 2π/λ_ref; bandwidth B; windowing (rectangular/Hann/Blackman).
4. Geometric bounds & occlusion
   Occlusion mask M_occ(x,y); effective FOV FOV_eff = FOV \ M_occ; boundary conditions (reflecting/absorbing/periodic).
5. Data structures
   Trajectory: {t_i, r_hat_i, gamma(ell)_i, d_ell_i}; phase: {t_i, Phi_i, λ_ref}; arrivals: {t_i, T_arr_i}.

II. Instrument & Calibration

1. Instrument lineage
   • instrument.id, instrument.mode ∈ {imaging|spectral|timing|mixed}, channels channels[].
   • Key specs: time resolution δt_clk, readout noise σ_ro, gain g, ADC bits N_bits, dynamic range DR.
2. Calibration tiers & freshness
   • Tiers: primary (traceable), transfer (lab), in-situ (field); parameter set θ = {bias, dark, flat, gain, PSF, delay}.
   • Freshness gate: |ts_start − calib.timestamp| ≤ τ_calib; otherwise trigger recalibrate/reject.
3. Metrological closure
   Run check_dim; unit table (m, s, rad, 1); expose units and uncertainties u(θ_k) for all θ.
4. Delays & dispersion
   System/link delay τ_sys, inter-channel skew Δτ_ch; if dispersion exists, provide n_eff(λ) or dispersion coefficients.
5. In-situ calibration (summary)
   • Timing: GNSS/PPS lock → PTP/NTP fallback;
   • Imaging: Bias/Dark/Flat → PSF scan → distortion → stamp calib.version;
   • Spectral: lamp line fit → wavelength solution → linearity;
   • Timing: pulser/loopback → channel align Δτ_ch → absolute time δt_abs.

III. Synchronization & Drift

1. Time sync
   • Primary: GNSS 1PPS + 10 MHz; fallback: PTP (preferred) → NTP.
   • Timestamps: ts = TAI/UTC, record leap-second policy; log clock_state ∈ {locked, holdover, free}.
2. Drift modeling
   • Clock offset δt(t), jitter, Allan deviation σ_y(τ); thermal drift α_T · ΔT; attitude drift Δq_att.
   • Slow medium drift: n_eff = n_0 + ε n_1(t, r), ε ≪ 1; treat first order within coherence windows.
3. Path correction & alignment
   • Geometric correction: distortion D(x,y); path correction: gamma(ell) ← gamma(ell) + δγ(ell).
   • Phase alignment: maximize correlation in reference window argmax_τ corr(Phi_ref, Phi_obs(·−τ)).
4. Monitoring & alerts
   • Thresholds: σ_y(1s) ≤ σ_target, |δt_abs| ≤ τ_abs, |Δτ_ch| ≤ τ_ch.
   • Exceedance actions: degraded mode, resync, recalibrate, mark quality.flags += {"sync_alert"}.

IV. Switching & Fallback Strategy

1. Mode switching
   • Conditions: SNR < SNR_min or σ_y(τ) out of bounds → increase timebase / reduce bandwidth;
   • Paraxial violation: |θ| > θ_max → exit S31-1, switch to full-wave/numerical propagation;
   • Sparse pathing: |Δell| > Δell_max → trigger densify or reject.
2. Coherence-window adaptation
   Adapt T_coh, L_coh, B_coh: if |∇ n_eff| rises, shorten T_coh/L_coh, increase spectral resolution B_coh.
3. Degradation & fallback
   • Time: GNSS loss → PTP → NTP → local free-run (raise reported uncertainty accordingly).
   • Calibration: τ_calib expired → restricted mode (low-risk tasks only) and forced recalibration schedule.
4. Triggers & logging
   • Triggers: sync_alert, drift_alert, geom_alert.
   • Log: in audit.jsonl record switch time, reason, pre/post parameter snapshots, and gate statuses.

V. Protocol Card (machine-readable template)

version: "1.0.0"

protocol:

id: "ptn-exp-0001"

title: "Baseline PTN Observation"

geometry:

frame: "RA-Dec"

r_hat: [<unit_vector>]

FOV_deg: 1.0

path:

gamma_ell: "<array-of-meters>"

d_ell: "<array-of-meters>"

L_min: 10.0

timebase:

fs_hz: 2000

t_exp_s: 0.01

cadence_s: 0.05

nyquist_guard: true

band:

lambda_ref_m: 1.55e-6

bandwidth_hz: 2.0e9

window: "hann"

instrument:

id: "INS-001"

mode: "timing"

specs: { dt_clk_ns: 5, readout_noise_e: 2.1, bits: 14 }

calibration:

version: "1.2.0"

timestamp: "2025-09-24T10:00:00Z"

freshness_s: 86400

theta:

bias_e: 0.3

dark_e_s: 0.01

delay_sys_ns: 25.0

sync:

ref: "GNSS_PPS"

fallback: ["PTP","NTP"]

thresholds: { allan_1s: 1e-11, abs_ns: 50, skew_ns: 5 }

coherence:

T_coh_s: 1.0

L_coh_m: 50.0

B_coh_hz: 1.0e6

gates: ["G1","G2","G3","G4","G5","G6","G7","G8"]

see:

- "EFT.WP.Core.Equations v1.1:S20-1"

- "EFT.WP.Core.Metrology v1.0:check_dim"

- "EFT.WP.Core.DataSpec v1.0:TARR"

exports:

manifest: "PTN_EXPORT/manifest.yaml"

reports: ["reports/check_dim_report.json","reports/quality_report.json","reports/audit.jsonl"]

VI. Sampling Plan (execution essentials)

• Sampling matrix: cover {time × channel × position}; mark missing values as null and record reasons in quality.flags.
• Stratified sampling: stratify by batch/device/sky-region; guarantee per-stratum minimum size and balance.
• Self-monitoring metrics: compute rolling SNR, σ_y(τ), Q_res, p_dim; out-of-bounds triggers Section IV switching.
• Revisit & remeasure: keep ≥ 10% revisit budget for robustness and drift assessment.

VII. Calibration & Sync Scripts (interface bindings)

• I60-calibrate(theta_in) -> theta_out: outputs θ and u(θ), updates calib.version and timestamp.
• I61-sync_lock(source) -> {clock_state, δt_abs, σ_y}: state machine and thresholding.
• I62-path_resample(gamma_ell, d_ell, Δell_max) -> {gamma_ell', d_ell'}: densify/resample path.
• I63-coherence_adapt(metrics) -> {T_coh, L_coh, B_coh}: adapt using |∇ n_eff|, SNR, and σ_y.

VIII. Required Items on Results Page (aligned with Chapter 5)

• Geometry & timebase summary (FOV_eff, cadence, T_coh/L_coh/B_coh).
• Instrument & calibration summary (calib.version, θ with u(θ), compliance with τ_calib).
• Sync & drift (clock_state, δt_abs, σ_y(τ), alerts and switching log).
• Quality-gate pass rates and key thresholds (G1–G8).