Background réaliste CsI(Tl) + hybridation mesuré/synthétique + dashboard continuum

- Remplace le continuum exponentiel par un modèle réaliste CsI(Tl) dans
  l'entraînement (bosse asymétrique ~110 keV + queue Compton)
- Ajoute l'injection de background mesuré (70% mesuré / 30% synthétique)
  via --measured_background et MEASURED_BACKGROUND_PATH
- Ajoute l'endpoint /api/background/continuum et le toggle "Continuum CsI"
  sur le dashboard background
- Exclut le canal 1023 (overflow bin) de l'affichage web (NUM_CHANNELS=1023)
- Corrige le lissage Gaussien du background (normalisation locale aux bords)
- Met à jour README.md, CLAUDE.md, TUTORIEL.md, TOTO.md, vega_ml/README.md

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

web/app/theoretical_bg.py

@@ -0,0 +1,139 @@
+"""
+Theoretical natural background spectrum for CsI(Tl) detectors (Radiacode 103).
+
+Shape calibrated against real Radiacode 103 background measurements.
+The CsI(Tl) crystal (1 cm³, 8.4% FWHM) produces a spectrum with:
+- A dominant low-energy hump peaking around 100-120 keV
+- Exponential decay at higher energies
+- Subtle photopeaks from natural isotopes
+"""
+
+import numpy as np
+from app.config import ENERGY_OFFSET, ENERGY_SLOPE, NUM_CHANNELS
+
+
+# Photopeak lines: (energy_keV, relative_weight)
+# Weights tuned so peaks are visible above local continuum at typical CPS
+NATURAL_BG_LINES = [
+    (295.22, 0.10),   # Pb-214
+    (351.93, 0.18),   # Pb-214
+    (609.31, 0.15),   # Bi-214
+    (911.20, 0.08),   # Ac-228
+    (968.97, 0.05),   # Ac-228
+    (1120.29, 0.06),  # Bi-214
+    (1460.83, 0.12),  # K-40
+    (1764.49, 0.08),  # Bi-214
+    (2614.51, 0.18),  # Tl-208
+]
+
+
+def _gaussian(x, center, sigma, amplitude):
+    return amplitude * np.exp(-0.5 * ((x - center) / sigma) ** 2)
+
+
+def generate_theoretical_bg(cps: float = 6.0, live_time_s: float = 3600.0):
+    channels = np.arange(NUM_CHANNELS, dtype=np.float64)
+    energy_axis = ENERGY_OFFSET + ENERGY_SLOPE * channels
+    total_counts = cps * live_time_s
+
+    # ── 1. Main hump: asymmetric peak at ~105 keV ──
+    # Real data: rises from ~60 at 10keV to ~280 at 100-120keV, then falls
+    hump_center = 110.0
+    hump = np.zeros(NUM_CHANNELS, dtype=np.float64)
+    low_mask = energy_axis <= hump_center
+    hump[low_mask] = _gaussian(energy_axis[low_mask], hump_center, 55.0, 1.0)
+    hump[~low_mask] = _gaussian(energy_axis[~low_mask], hump_center, 50.0, 1.0)
+
+    # ── 2. Compton continuum tail ──
+    # Real data: ~136@200, ~80@250, ~44@295, ~14@400, ~5@600
+    tail = 0.45 * np.exp(-energy_axis / 240) + 0.04 * np.exp(-energy_axis / 700)
+
+    # ── 3. Low-energy noise floor ──
+    noise_floor = 0.008
+
+    # ── 4. Combine continuum ──
+    continuum = hump + tail + noise_floor
+
+    # ── 5. Photopeaks ──
+    # CsI(Tl) 8.4% FWHM at 662 keV, scaling as sqrt(E)
+    # sigma(E) = FWHM(E) / 2.355 = 0.084 * sqrt(E * 662) / 662 / 2.355
+    # Simplified: sigma = 23.6 * sqrt(E/662) keV
+    def sigma_keV(E):
+        return max(12.0, 23.6 * np.sqrt(max(E, 1.0) / 662.0))
+
+    peak_frac = 0.08  # 8% of total counts in resolved photopeaks
+    total_weight = sum(w for _, w in NATURAL_BG_LINES)
+
+    peaks = np.zeros(NUM_CHANNELS, dtype=np.float64)
+    for line_energy, weight in NATURAL_BG_LINES:
+        sig = sigma_keV(line_energy)
+        peak_counts = total_counts * peak_frac * (weight / total_weight)
+        amplitude = peak_counts / (sig * np.sqrt(2 * np.pi))
+        peaks += _gaussian(energy_axis, line_energy, sig, amplitude)
+
+    # ── 6. Combine and normalize ──
+    raw = continuum + peaks / total_counts  # peaks normalized later
+    raw *= total_counts / raw.sum()
+
+    # ── 7. Poisson-like noise ──
+    rng = np.random.default_rng(42)
+    noise = rng.normal(0, 1, NUM_CHANNELS) * np.sqrt(np.maximum(raw, 1.0)) * 0.25
+    raw += noise
+
+    # Floor at 0.9 for log scale
+    spectrum = np.clip(raw, 0.9, None)
+
+    key_lines = [
+        (295.22, "Pb-214"), (351.93, "Pb-214"),
+        (609.31, "Bi-214"), (911.20, "Ac-228"),
+        (1120.29, "Bi-214"), (1460.83, "K-40"),
+        (1764.49, "Bi-214"), (2614.51, "Tl-208"),
+    ]
+
+    return {
+        "energy_kev": [round(float(E), 2) for E in energy_axis],
+        "counts": [round(float(c), 1) for c in spectrum],
+        "cps": round(cps, 2),
+        "live_time_s": round(live_time_s, 1),
+        "lines": [
+            {"energy_keV": E, "name": name} for E, name in key_lines
+        ],
+    }
+
+
+def generate_continuum_only(cps: float = 6.0, live_time_s: float = 3600.0):
+    """Generate only the CsI(Tl) continuum shape (no photopeaks, no noise).
+
+    This matches the model used in training (generate_realistic_continuum in
+    spectrum_physics.py) for direct comparison with measured backgrounds.
+    """
+    channels = np.arange(NUM_CHANNELS, dtype=np.float64)
+    energy_axis = ENERGY_OFFSET + ENERGY_SLOPE * channels
+    total_counts = cps * live_time_s
+
+    # Asymmetric hump at ~110 keV
+    hump_center = 110.0
+    hump = np.where(
+        energy_axis <= hump_center,
+        np.exp(-0.5 * ((energy_axis - hump_center) / 55.0) ** 2),
+        np.exp(-0.5 * ((energy_axis - hump_center) / 50.0) ** 2),
+    )
+
+    # Compton continuum tail
+    tail = 0.45 * np.exp(-energy_axis / 240.0) + 0.04 * np.exp(-energy_axis / 700.0)
+
+    # Noise floor
+    noise_floor = 0.008
+
+    continuum = hump + tail + noise_floor
+
+    # Normalize to target total counts
+    if continuum.sum() > 0 and total_counts > 0:
+        continuum *= total_counts / continuum.sum()
+
+    return {
+        "energy_kev": [round(float(E), 2) for E in energy_axis],
+        "counts": [round(float(c), 1) for c in continuum],
+        "cps": round(cps, 2),
+        "live_time_s": round(live_time_s, 1),
+    }