SNO+ Optical Instrumentation — Event Spatial Calibration & Recovery
Overview
The SNO+ detector is a massive neutrino observatory utilizing an array of over 9,000 Photomultiplier Tubes (PMTs) to capture faint optical signals in a 12-meter liquid scintillator volume. During an optical upgrade phase, incomplete liquid mixing created severe spatial stratification across the medium. This introduced non-linear, position-dependent optical attenuation, distorting pulse energy reconstruction and obscuring time-coincident events known as inverse beta decays (IBDs).
Since global detector-wide optical re-modeling was nearly impossible, the data in this period was initially considered unusable. To recover this, I developed a spatial calibration and event recovery engine in C++ and Python. By utilizing known monoenergetic reference pulses (specifically from $^{210}\text{Po}$ decay events), the algorithm dynamically equalizes local sensor response across the 3D volume.
Key Engineering Outcomes:
- 81% Signal Recovery Efficiency: Salvaged 345 coincident pulse pairs that were previously lost beneath noise and distortion thresholds.
- Spatial Calibration Algorithm: Designed a 7-probe 3D Cartesian gradient filter ($R = 1.5\text{ m}$) that measures and compensates for local attenuation without corrupting global baseline calibration.
- Massive Statistical Verification: Validated calibration stability across ~18,000 stochastically chosen spatial probe vertices.
The Engineering & Signal Processing Challenge
- Non-Uniform Sensor Transmission: Optical stratification altered photon yield and propagation non-linearly, causing monoenergetic pulses to scatter into multi-peaked distributions.
- Time-Coincident Pulse Extraction: Detecting target events requires resolving a strict dual-pulse time signature (a prompt pulse followed by a delayed capture pulse $50\text{–}200\,\mu\text{s}$ later). While timing channels remained sharp, degraded energy reconstruction caused valid pulse pairs to fail acceptance thresholds.
- SNR vs. Spatial Resolution Tradeoff: Global energy filters discarded degraded signals, whereas overly tight spatial windows lacked sufficient sample statistics for reliable curve fitting.
Calibration Architecture & Methodology
- Reference Signal Normalization: Tracked a monoenergetic reference standard ($E_{\text{ref}} = 0.4734 \pm 0.0003\text{ MeV}$) across time to establish baseline gain.
- Spatial Probe Optimization: Swept spatial boundary cuts from $1.0\text{ m}$ to $2.5\text{ m}$ to identify the optimal probe radius ($R = 1.5\text{ m}$) that maximized peak energy resolution while maintaining statistically robust sample sizes (~1,500–3,000 pulses/fit).
- 3D Gradient Filter: Deployed a 7-sphere Cartesian geometry (1 central probe + 6 tangent peripheral probes along $\pm X, \pm Y, \pm Z$) to detect and filter out local optical divergence.
- Maximum Likelihood Correction: Applied event-by-event energy equalization $E_{\text{corr}} = E_{\text{raw}} \times \left(\frac{E_{\text{ref}}}{E_{\text{local}}}\right)$ with rigorous Gaussian variance propagation ($\sigma_R$).
Key Performance Metrics
| Metric | Result | Engineering Significance |
|---|---|---|
| Signal Recovery Rate | ~81.0% | Successfully recovered 345 out of 426 distorted candidate pulse pairs |
| Stochastic Verification | 60.26% ± 0.75% | Baseline efficiency across 4,300 randomized spatial test vertices |
| Reference Energy ($E_{\text{ref}}$) | 0.4734 ± 0.0003 MeV | High-precision baseline established in stable detector operational phase |
| Residual Acceptance Window | ±0.06 MeV | Defined $\sim1.8\sigma$ acceptance cut to reject uncalibratable noisy regions |
Technical Report
The complete 13-page engineering report detailing the mathematical derivations, RAT/ROOT C++ analysis pipelines, and recovery catalogs is embedded below: