Ang2Gist Unit in Radiation Detection

• Ang2Gist Unit is an integrated simulation and reconstruction platform that models photon and particle propagation along with photosensor responses in Anger camera-type detectors.
• It employs a ROOT-based 3D simulation, CUDA-accelerated event reconstruction, and B-spline parameterized LRFs to enable high-throughput and precise event localization.
• The system supports adaptive iterative calibration and multiple reconstruction algorithms, including statistical, ANN, and k-NN methods, to optimize detector performance.

The Ang2Gist Unit, a term reflecting the functional core of advanced Anger camera-type detectors, denotes the integrated system enabling simulation, data processing, and event reconstruction in position-sensitive detection. Represented by the ANTS2 package, the Ang2Gist Unit encapsulates a comprehensive toolkit for simulating the full detection chain—including photon and particle generation, photon tracing, photosensor response modeling, and sophisticated event reconstruction—optimized for both synthetic and experimental scenarios. Deployed primarily in nuclear instrumentation and imaging applications, it embodies adaptive parameterization and reconstruction algorithms, exploiting modern computational methods and tailored graphical user interfaces.

1. Simulation Architecture and Photon/Particle Propagation

The Ang2Gist Unit's simulation module is architected atop the ROOT 3D geometry and navigation framework, capturing detector structure and performing detailed event-level modeling. It operates in two principal simulation modes:

• Photon source mode: Isotropic emission of optical photons from specified spatial nodes, with user-selectable photon count statistics (fixed, uniform, normal, or custom distributions).
• Particle source mode: Initiation with user-defined particles, tracked through the full detector volume. Charged particle energy depositions rely on externally supplied stopping power tables; gamma and neutron propagation is parametrized by mean free paths.

Energy depositions are mapped to scintillation photon yields. For primary scintillation, photon emission is isotropic from the deposition site. Secondary scintillation yields are computed as $N = k \cdot E / W$, where $k$ is user-defined (photons per electron) and $W$ is the mean electron-ion pair creation energy. Photons from secondary scintillation are distributed uniformly in the z-dimension within the relevant region, fixing $x$ and $y$ coordinates.

Photon tracking proceeds on a cycle-by-cycle basis across the complete detector geometry, accounting for absorption, Rayleigh scattering, and interface phenomena—implementing either custom-defined rules or applying Fresnel equations and Snell’s law for realistic optical boundary behavior.

2. Event Reconstruction Algorithms

The reconstruction module aggregates several complementary approaches, each targeting accurate spatial (and optionally energetic) reconstruction of detected events from observed sensor signals:

• Statistical (LRF-based) reconstruction: Event locations are derived by minimizing the residuals between actual sensor signals and those forecast by Light Response Functions (LRFs). This module offers two main optimization strategies:
  • Minuit2-based minimization using Migrad and Simplex algorithms from the ROOT suite.
  • Contracting grids method, an inherently parallelizable approach that iteratively refines spatial grids around preliminary positions. A CUDA-accelerated GPU implementation achieves up to $10^6$ events per second.
• Artificial Neural Network (ANN) reconstruction: Integrates the FANN library for multilayer perceptron training and inference, supporting a broad range of architectures and training schemes (standard/adaptive back-propagation, SARPROP, CASCADE2).
• k-Nearest Neighbour (k-NN) reconstruction: Employs the FLANN library to locate $k$ nearest calibration events in signal space, computing event position as the centroid of their true locations.

The reconstruction suite is equally applicable to simulated or imported (experimental) photosensor data, supporting real-world validation and iterative improvement.

3. Photosensor Response Modeling and Signal Synthesis

Photo-detection is modeled as a composite probability: $$P_{\text{det}} = Q(\lambda) \cdot P_t(\theta) \cdot P_A(x, y)$$ where

• $Q(\lambda)$: Quantum efficiency at the specific photon wavelength
• $P_t(\theta)$: Angular sensitivity (normalized to unity at normal incidence)
• $P_A(x, y)$: Local variation over the sensor’s XY surface

For silicon photomultipliers (SiPMs), the simulation tracks individual microcells to capture saturation effects, and provides options for simulating dark counts, electronic (Gaussian) noise, and digitization artifacts (ADC/digital noise). Output can be configured as raw photon counts or full photodetector signal emulation, with user-selectable statistical response distributions (normal, Gamma, or custom).

4. B-spline Parameterization and Light Response Functions (LRFs)

The spatial response of each photosensor is encoded using a bespoke B-spline parameterization library. Supported schemes include:

• Axial LRF: For sensors exhibiting axial symmetry, as a function of radial distance in the XY plane.
• XY LRF: For asymmetric cases, modeled directly in the XY domain.
• Composite LRF: Axial response computed first; residuals parameterized by XY splines.

For three-dimensional detectors, “Axial+Z” or “Sliced LRF” paradigms are implemented, further enabling compact, efficiently interpolated parameter sets suited for accelerated computation. This B-spline infrastructure not only assures flexible model fitting but also underpins the iterative LRF update cycles central to adaptive reconstruction.

5. Graphical User Interface and Analytical Tools

The Ang2Gist Unit features a graphical user interface facilitating comprehensive workflow management:

• Configuration: Visual geometry editing, detector assembly, and real-time feedback. Supports format export/import via JSON or GDML.
• Visualization: Depicts geometry, tracking, and reconstructed event clouds; enables overlay of LRF surfaces and measured scatter plots.
• Analysis: Delivers 2D/3D histograms for position, energy, and chi-squared metrics; event filtering tools; and real-time evaluation via ROOT Tree-based queries.

This integrated GUI accelerates prototyping and supports rapid iterative experimentation.

6. Iterative (Adaptive) Reconstruction and Flood Field Calibration

A key methodological innovation is iterative refinement of detector response functions (LRFs) from calibration using flood field irradiation data. The process entails:

1. Initial LRF guess (simulation or centroid estimate).
2. Bulk reconstruction using statistical methods.
3. LRF recalculation from reconstructed positions and sensor signals (utilizing B-splines).
4. Iterative repetition until convergence.

Accuracy and convergence are enhanced by:

• Sensor grouping (peripheral and central),
• Event filtering (e.g., chi-squared thresholds) to exclude outliers,
• Scripting tools for automated iterative cycles with real-time feedback, minimizing bias from poorly reconstructed events.

A plausible implication is that robust convergence properties render this approach tolerant to imperfect initial models, streamlining empirical calibration workflows.

7. Implementation, Extensibility, and Applications

ANTS2, the reference implementation of the Ang2Gist Unit, is written in C++, is multiplatform, and open source. Key internal and external dependencies are presented below:

Functionality	Library / Toolkit	Notes
3D geometry, minimization, I/O	ROOT	Foundation for geometry, navigation, plotting
GPU-based reconstruction	CUDA toolkit	Optional for high throughput processing
Artificial neural networks (ANN)	FANN	Multilayer, customizable networks
k-NN search	FLANN	Fast search in high-dimensional spaces

The design’s modularity eases adaptation to a variety of Anger camera-type detector architectures. The system supports both simulation studies (including for clinical gamma cameras) and experimental pipelines (e.g., for thermal neutron detectors), facilitating both instrument development and operational calibration.

In summary, the Ang2Gist Unit, as realized in ANTS2, constitutes a comprehensive, extensible framework for the simulation and reconstruction requirements of position-sensitive radiation detectors with Anger camera-type readouts, integrating advanced parameterization, high-performance computation, and adaptive calibration methodologies (Morozov et al., 2016).