Scintillation event imaging with a single photon avalanche diode camera

A single photon avalanche diode (SPAD) detects individual photons with high temporal resolution, and SPAD arrays fabricated in CMOS offer high spatial resolution and low cost, enabling adoption in various imaging applications. Scintillators convert ionizing radiation energy depositions into visible photons; measurements of interaction location, time, energy deposition, and fluorescence decay are crucial for modalities such as Compton cameras and PET. Thick monolithic scintillators are desirable for gamma rays but make interaction localization challenging. Existing sensors typically trade spatial for temporal resolution: SiPM arrays provide high timing but few large readout channels (low spatial resolution), while high-resolution cameras such as EMCCD have low temporal resolution and readout rates, limiting discrimination of individual interactions. This motivates using a sensor with both high spatial and temporal resolution and a lens to focus light. The authors introduce MOSSC (monolithic scintillator–SPAD camera), a lens-coupled SPAD camera system that images individual scintillation events and estimates their 3D positions from defocus, leveraging SPAD arrays’ spatial and temporal denoising capabilities. They outline a hardware configuration and a depth-from-defocus algorithm, noting that ultimate measurement resolution depends on light collection, PDE, optical geometry, and lens f-number.

Prior SPAD-scintillator works generally used lensless, surface-coupled SPAD arrays, focusing on PET modeling and low-resolution arrays; e.g., Tétrault et al. built a low-resolution (6-channel) SPAD readout tested on monolithic LYSO, and Franks et al. tracked electrons in scintillating fibers with a high-resolution SPAD (SwissSPAD2), where spatial resolution is limited by fiber diameter and no depth is estimated. SiPM-based monolithic designs (lensless) infer 3D position from unfocused light distribution but are limited by channel count; pixelated scintillators improve spatial resolution at higher cost and complexity and often need dual-ended readout for depth. As SPAD/SiPM resolutions grow, their features may converge, but lens-based focusing remains essential to exploit high-resolution sensors due to the low spatial-frequency nature of isotropic scintillation emission. Camera-based radiography with CCD/CMOS integrates long exposures and thin scintillators; defocus from thick scintillators is typically mitigated computationally. EMCCD systems have been used for event imaging and particle tracking in thin plates or with fiber tapers but lack frame rate/temporal resolution for individual interactions at high rates. Flat-panel TFT arrays provide large-area, high pixel count for radiography but with low readout rates (~60 fps). Timepix-based hybrid pixel cameras achieve single-photon sensitivity via external intensification with high spatial/temporal resolution but are specialized and temporally limited by phosphor decay; SPAD cameras achieve internal avalanche gain and are more compact. LAPPD microchannel plate detectors provide excellent timing (~50 ps) and mm-scale spatial resolution over large areas; while competitive, they are low-volume and lower spatial resolution than modern SPAD arrays. Unlike most prior works that minimize defocus, this work exploits defocus for depth estimation and demonstrates 3D localization capability.

Overview: Interactions are modeled as point sources whose images on the SPAD array form disks described by the circle of confusion (CoC). A lens focuses scintillation light; defocus diameter c increases with distance from the focal plane and is used to infer depth. The full MOSSC pipeline: capture binary frames, detect frames containing an interaction, denoise via spatial clustering, fit a Gaussian to localize centroid and estimate diameter, and compute 3D position via calibrated diameter–depth mapping and perspective projection. Optical setup and CoC model: A thin ideal lens approximation relates spot diameter c to the interaction’s apparent distance S3 from the lens: c = A |(S3 S1 − S1 f)/S3| with f = 1/(1/S1 + 1/S2), rearranged to S3 = 1/(1/S1 + c/(A S2)). The focal plane is set at or below the scintillator’s apparent bottom so |·| is dropped. The interaction’s depth is Z_int = S_d + (S3 − d) n, correcting for refractive index n. Lateral world coordinates (X_int, Y_int) follow perspective: X_image = −S2 X_int/S3, Y_image = −S2 Y_int/S3, converting pixel to metric units using pixel pitch. Optical calibration (thick lens, non-idealities): Because the experiment uses a thick, low-f-number lens close to the scintillator, a direct calibration replaces the thin-lens model. A 50 μm pinhole is placed at the apparent bottom of the scintillator (accounting for n), illuminated in darkness, and imaged while translating along z in 2.54 ± 0.1 mm steps over −5.08 to +15.24 mm from the reference. The image diameter is measured visually to build a diameter–depth correspondence; given measured c, S3 is obtained by lookup/interpolation and then used for solving X_int, Y_int, Z_int as above. Interaction detection (experimental data): Frames are binary (per-pixel single-event) and contain scintillation photons or dark counts (DCR). The top 5% highest-DCR pixels are masked. Dark frames (9,175,040) at the experiment temperature establish noise. For k in {31, 51, 71, 91, 111, 131, 151, 191, 231}, the distribution of the maximum counts in any k×k region over dark frames is computed; thresholds T_k are set to the 10th-highest observed value + 1. A frame with the source present is flagged a detection if any k×k region meets or exceeds its T_k. Interaction localization and denoising: Nonzero pixels form nodes of a minimum spanning tree (MST) in pixel space. Edges longer than T_edge are removed; the largest connected component is retained as the photon cluster; others are discarded as noise. If counts after denoising are less than the smallest T_k, the frame is discarded. A spherical 2D Gaussian is fit by EM to the cluster’s coordinates, yielding centroid μ and σ; the diameter estimate is c = s σ with scale s chosen empirically (s = 3.7). For m interactions, retain m largest components and fit a Gaussian mixture with m components. Experimental hardware/configuration: Scintillator: CsI(Tl), 50×50×70 mm, n = 1.79, decay constant 1 μs, light yield 54,000 photons/MeV (polished faces). Source: 1 μCi Co-60 (1.17, 1.33 MeV), active pellet ~3.1 mm diameter, center 2.8 mm from disk surface. Lens: plano-convex Thorlabs LA1951-A, f = 25 mm, Ø25.4 mm. Camera: SwissSPAD2, 256×496 ROI, 7 V excess bias, peak PDP ~50% at 520 nm, fill factor 10.5% → peak PDE ~5.25%. Single-bit frames, global shutter, frame period 65 μs (15.4 kfps) with 10 μs gate; apparatus in a light-tight enclosure at 0–3°C. The lens’s plano surface is 58 ± 5 mm from the SPAD array; an air gap 2.7 ± 0.5 mm separates lens and scintillator. World origin is at the intersection of the lens optical axis and the scintillator bottom (opposite the lens); x along camera major axis (496 px), y along minor (256 px), z depth toward the camera. Detection thresholds: as above, with the lowest T_k = 5 at k = 31. Parameter choices: Localization scale s = 3.7 from visual inspection. The MST cut T_edge is tuned by making the mean estimated z across all detected interactions closest to 10 mm when the source is at z = 10 mm in the z-sensitivity experiment; T_edge = 46 pixels is used. Experiments: Two experiments assess sensitivity to shifts in interaction distributions. (i) x–y sensitivity: source shifted along x at the scintillator bottom: positions (−12.7,0,0), (0,0,0), (12.7,0,0) mm (±2). For each position, 27,525,120 frames are captured. (ii) z sensitivity: source moved along a side parallel to z, with lens edge protruding 3.7 ± 3 mm over scintillator edge (center 9 ± 3 mm inwards): source at (9,0,0), (9,0,10), (9,0,20) mm (±2). For each position, 18,350,080 frames are captured. Simulations: Geant4 models interactions in 10×10×70 mm CsI (n=1.79). A thin lens (7 mm diameter, f=25 mm) is centered at (0,0,72.7) mm; sensor at z=126.4 mm, focusing ~5 mm beyond the apparent bottom. Photon propagation through the thin lens to the nearest sensor pixel is simulated; binary images are generated. High-PDE MS-500 (Canon) and SwissSPAD2 are modeled by pixel pitch, array size, and count scaling to match experimental count statistics; MS-500 PDE is approximated 10× SwissSPAD2. Bias sources studied include refraction blur (n=1.79 vs 1), low-counts bias (photon downscaling), denoising/localization (GMM-Loc vs Exact-Loc), and dark counts (Poisson mean 2). Spatial resolution (FWHM = 2.355σ) and accuracy are computed per-axis over 0.5 mm x-intervals for depths z ∈ {5,10,15,20} mm. Compton camera feasibility is evaluated using GMM-Loc (m=2), depth-bias correction, and assumed energy resolutions corresponding to n counts (FWHM ≈ 2.355√n/n).

- Experimental sensitivity to 3D shifts: Moving the Co-60 source produces measurable shifts in the mean positions of detected interactions. • x–y sensitivity (27,525,120 frames per position): mean interaction locations and counts: (−0.57, 0.04, 9.88) mm, 430; (−0.02, −0.06, 9.14) mm, 1455; (0.48, 0.05, 9.70) mm, 384, for source at (−12.7,0,0), (0,0,0), (12.7,0,0) mm, respectively. • z sensitivity (18,350,080 frames per position): means and counts: (0.30, −0.10, 9.64) mm, 472; (0.47, −0.06, 9.76) mm, 1012; (0.38, −0.08, 11.35) mm, 1346, for source at (9,0,0), (9,0,10), (9,0,20) mm, respectively. • Simulated statistical uncertainty of the estimated mean: σ_mean ≈ 0.012 mm (x) and 0.278 mm (z). Experimental mean shifts (x: 1.05 mm; z: 1.71 mm) are ≫ uncertainties, confirming sensitivity. - Sensor operation: SwissSPAD2 operated at peak PDP ~50% (520 nm), fill factor 10.5% (peak PDE ~5.25%), with 10 μs gate and 65 μs frame period. Detection thresholds set from 9,175,040 dark frames (lowest T_k = 5 at k=31). - Algorithmic outcomes: MST denoising with T_edge=46 and Gaussian fit with s=3.7 enable centroid and diameter estimation from sparse counts; denoising can bias diameter depending on T_edge. - Simulation biases (SwissSPAD2): • Refraction + high counts, Exact-Loc: depth-independent median bias ≈ 0.91 mm; low counts reduce median bias to ≈ 0.19 mm but increase variance. • No refraction (n=1) vs refraction (n=1.79): refraction blur introduces ~0.3 mm additional bias. • Denoising + GMM-Loc with dark counts produces depth-dependent negative bias (increasing underestimation with larger z). - Localization performance: • Noise-free, experimentally adjusted counts (SwissSPAD2): lateral (x) resolution and error better than depth (z); performance degrades with larger defocus (higher z). A constant depth bias (e.g., 0.19 mm) can be subtracted. • With experimental-like noise and algorithms: z performance worsens; depth bias becomes depth-dependent, dominated by T_edge. - Compton camera feasibility: With SwissSPAD2-like counts and assumed 74.5% FWHM energy resolution (n≈10 counts), source reconstruction fails. With MS-500-like counts (≈10× PDE, 23.6% FWHM energy resolution, n≈100 counts), reconstruction succeeds, demonstrating feasibility of a monolithic single-crystal Compton camera using next-generation SPAD arrays. - Practical observations: Depth sensitivity is nonuniform; higher z interactions produce more detected photons (inverse square law), raising detection likelihood and causing mean z to skew higher when the source is nearer the lens. The observed FOV of interactions is ~3×6×23 mm.

The study addresses whether a lens-coupled SPAD camera can image individual scintillation events in a thick monolithic scintillator and extract 3D information from single-event images. Experiments show that the distribution of measured interaction locations shifts consistently with source movement in both lateral and depth directions, confirming 3D sensitivity. Simulations with ground truth quantify achievable accuracy and resolution and identify dominant biases. Depth estimation via defocus is sensitive to photon statistics, refraction blur at the scintillator–air interface, and denoising/localization parameters (notably the MST edge threshold). Nonuniform depth sensitivity is observed due to proximity and inverse-square effects: interactions closer to the lens yield higher photon counts and are more likely to be detected, biasing mean depth upward when comparing shallow vs deeper source positions. The lens and optical configuration govern the depth-of-field versus depth-of-interaction (DOI) resolution trade-off; a steeper diameter–depth response improves DOI resolution at the cost of narrower measurable depth range and light collection. Simulation indicates lateral localization outperforms depth for the chosen optics and count levels; improved PDE and optics reduce low-counts bias and variance. Finally, a monolithic, lens-based SPAD system can, in principle, enable multi-interaction event imaging (e.g., Compton double scatters) without pixelation, with simulations showing successful backprojection using an advanced high-PDE SPAD array (MS-500), highlighting the potential for compact, versatile radiation cameras.

This work introduces MOSSC, a lens-coupled SPAD camera approach to image individual scintillation events in a thick monolithic scintillator and infer 3D interaction positions using defocus. Experiments with a commercial SPAD camera (SwissSPAD2) directly image gamma-ray events and demonstrate sensitivity to 3D shifts in interaction distributions. Calibrated simulations show that single-event 3D localization is feasible, quantify spatial resolution and biases, and demonstrate that a monolithic single-crystal Compton camera becomes practical with next-generation high-PDE SPAD sensors (e.g., Canon MS-500). Contributions include: (i) a defocus-based 3D localization algorithm with MST denoising and Gaussian localization (GMM-Loc), (ii) an optical calibration procedure for thick, fast lenses at short standoff, and (iii) an empirical and simulated assessment of biases and performance. Future work should improve light collection (higher PDE, microlenses, larger arrays, optimized scintillator geometries and reflectors), refine optics (to tune DOI resolution and FOV), incorporate time-of-arrival SPAD timing for enhanced denoising and Cherenkov identification, model the true PSF for more accurate diameter estimation, and explore electron-tracking from in-focus events toward electron-tracking Compton cameras.

- Low light collection: SwissSPAD2’s modest PDE (≈5.25% peak) and fill factor (10.5%) led to sparse counts, necessitating operation near 0–3°C and aggressive denoising; many interactions in the FOV were likely missed. - Optical constraints: Short working distances and a thick, low-f-number lens reduce PSF ideality, introduce aberrations, and limit FOV; the thin-lens CoC model is only approximate and required empirical calibration. - Algorithmic bias: The MST threshold (T_edge) and Gaussian scaling (s) bias estimated diameters and thus inferred depths, causing depth-dependent errors that worsen at larger z; denoising can remove true photons or retain dark counts. - Depth sensitivity nonuniformity: Proximity effects (inverse square law) make detection more likely for higher-z interactions, skewing distributions and limiting uniform DOI sensitivity. - Limited ground truth in experiments: True interaction positions are unknown due to scattering; only shifts in distributions can be validated experimentally; a collimated high-activity source would be needed for stronger validation. - Temporal constraints: 10 μs gate with 65 μs frame period introduces dead time and may truncate scintillation tails; photon arrival times are not recorded, limiting temporal denoising. - Generalizability: Results depend on specific optics, sensor PDE, gating, and thresholds; the observed experimental shifts in mean depth were small due to DOI resolution and count limitations.