GAP9Shield: Histogram-less LiDAR SPAD Method

• GAP9Shield is a histogram-less direct Time-of-Flight approach for SPAD-based LiDAR sensors that uses linearized photon statistics to eliminate conventional histogram construction.
• The method employs both acquire-or-discard and time-gated schemes to mitigate SPAD dead-time and avoid pile-up, ensuring accurate depth extraction at high photon fluxes.
• Experimental validation demonstrates high depth precision with minimal per-pixel memory, outperforming traditional histogram-based systems in efficiency and scalability.

GAP9Shield refers to a “histogram-less” direct-Time-of-Flight (d-ToF) acquisition and estimation methodology for arrays of SPAD-based (single-photon avalanche diode) LiDAR sensors, specifically as implemented in 5×5 VL53L1-style ToF block arrays. This method eliminates the need for on-chip construction of timestamp histograms—historically required to overcome SPAD non-linearity—in favor of a scalable, resource-efficient approach based on linearized photon statistics and simple accumulations. The approach emulates dead-time-free SPAD behavior, enabling accurate ToF extraction at photon fluxes far beyond conventional pile-up limits while maintaining minimal per-pixel memory and robust depth precision under high ambient and background flux. This system architecture and methodology is detailed and mathematically analyzed in Tontini et al. ("Histogram-less LiDAR through SPAD response linearization" (Tontini et al., 2023)).

1. System Architecture and Acquisition Flow

The system repurposes each VL53L1 “block” (single pixel) to directly expose first-photon timestamps, eschewing conventional on-chip histogramming. Four on-chip registers per pixel are used: $N_{bg}$ (background event count), $S_{bg}$ (sum of background timestamps), $N_{tot}$ (event count, laser on), and $S_{tot}$ (sum, laser on). Acquisition consists of alternating laser OFF and ON phases, with both phases performed over an acquisition window $T_{acq}$, and repeated $M$ times per frame to ensure statistical robustness.

Within each phase, the incident Poisson photons are recorded such that systematic selection bias, typically due to SPAD dead-time ($\tau_d$), is eliminated. Two hardware-level approaches achieve this:

• Acquire-or-Discard scheme: A simple comparator and register logic accept only one photon per enable window, discarding subsequent events until the next run, thereby ensuring each SPAD event is sampled after full reset.
• Time-Gated scheme: A programmable per-pixel enable delay line triggers SPAD activation, maintaining only the first arrival after each enable, with the absolute delay incremented post-detection, eliminating the possibility of event pile-up.

At the end of all $M$ runs, only the four per-pixel registers are needed for ToF computation, ensuring both memory and computational efficiency (Tontini et al., 2023).

2. SPAD Dead-Time Linearization Model

The theoretical analysis models the incident photon flux as $\lambda_B$ (background) and $\lambda_S(t)$ (signal, laser-echo), with combined flux

$$\lambda(t) = \begin{cases} \lambda_B & t \notin [\text{ToF}, \text{ToF}+T_W] \ \lambda_B+\lambda_S(t) & t \in [\text{ToF}, \text{ToF}+T_W] \end{cases}$$

For a dead-time-free SPAD, detected timestamps $T_i$ over $[0,T_{acq}]$ are i.i.d., drawn from the normalized rate function $f(t) = \lambda(t)/\int_0^{T_{acq}} \lambda(u)\,du$. The mean timestamp is thus $$\mu = (\int_0^{T_{acq}} u \lambda(u)\,du) / (\int_0^{T_{acq}} \lambda(u)\,du)$$. Real SPAD dead-time introduces histogram distortion, biasing the earliest bins (pile-up). The described acquisition logic reforms the statistical process so every trigger samples a "fresh" detector, eliminating systematic undercounting and ensuring accurate photon statistics at high flux (Tontini et al., 2023).

3. ToF Extraction via Average-Timestamp Estimator

Once accumulation is complete, ToF is extracted using a closed-form average estimator: $$\widehat{\text{ToF}} = \frac{S_{tot} - S_{bg}}{N_{tot} - N_{bg}} - \bar{t}_l$$ where $\bar{t}_l$ is the intrinsic average laser-pulse time with respect to emission. Under uniform background, $S_{bg} \approx N_{bg} (T_{acq}/2)$, enabling further storage reductions.

The variance of this estimator across frames is

$$\operatorname{Var}(\widehat{\text{ToF}}) \approx \frac{\sigma^2}{N_{tot} - N_{bg}}$$

with $\sigma^2 = \int_0^{T_{acq}} (t-\mu)^2 f(t) dt$ reflecting the spread in photon arrival times. This formula applies directly due to the linearization schemes, rendering dead-time effects negligible in the extraction, and ensures Cramer–Rao efficiency in the large-count limit (Tontini et al., 2023).

4. Multi-Pixel Array-Level Integration, Data Pipeline, and Calibration

The architecture assigns each VL53L1 pixel to route first-photon timestamps to a central controller (FPGA or ASIC). The controller manages the four registers per pixel, orchestrates the M-run acquisition phase, and computes per-pixel ToF values. Laser firing can be simultaneous for all 25 pixels, or temporally multiplexed depending on optical constraints.

Readout involves resetting counters, collecting statistics in alternating background/total (laser-off/on) modes, and streaming the 100-word register set ($4\times25$) once per frame. Synchronization is achieved by distributing a global reference clock and a laser synchronization pulse to all blocks. Per-pixel time-skew and laser-pulse shape bias are calibrated by targeting a known planar reflector and recording measured ToFs. Residual calibration constants $\Delta_i$ and $\bar{t}_{l,i}$ are then updated to correct for systematic offsets.

Regular background-only acquisitions monitor and adjust for non-stationary background rates $\lambda_B$, ensuring consistent estimation fidelity across environmental conditions (Tontini et al., 2023).

5. Performance Metrics and Experimental Validation

Key performance metrics established by Tontini et al. for the GAP9Shield method include:

• Range up to 3.8 m (optical test setup constraint)
• Resilience to pile-up: linear operation up to 90% detection rate per bin, exceeding the classical 5% pile-up threshold by 18×
• Ambient tolerance to ~85 klux (142 Mph/s per chip)
• Per-pixel memory requirement: ~80 bits (2×16b counters, 1×32b accumulator), compared to ~8–10 kbits for a standard 1D histogram
• Accuracy: <0.5% of measured range with negligible background; <2% with moderate background; rising to ~10% at 75 klux
• Precision (1σ): <0.25% of range with no background; <6% at 15 klux; <21% at 75 klux (Tontini et al., 2023)

A mapping to commercial VL53L1 arrays (100 ps TDC resolution) predicts linear performance up to 1.5×10⁹ ph/s. With $M \approx 3×10^4$ runs and typical $N_S ≈ 10^4$, single-frame depth precision approaches 3 ps (∼0.5 mm at 3 m), though practical reflectivity and background elevate measurement variance to ∼1–2 cm at 3 m.

6. Implementation Recipe and Resource Comparison

Implementation involves (1) firmware modification to expose first-photon timestamps, (2) add-on of four small accumulators/counters per pixel, (3) global clock and laser synchronization distribution, and (4) choice of acquire-or-discard or time-gated logic per pixel. The FPGA-based controller manages run orchestration, register readout, ToF computation, and calibration. Systematic validation is performed against planar targets at controlled ranges and illumination. Parameter tuning of $M$ and $T_{acq}$ allows tradeoffs between precision, frame rate, power, and laser duty-cycle.

The primary system-level advantage is the complete elimination of per-pixel histograms (∼kilobytes per pixel), replaced by compact registers (<100 bits per pixel), enabling support for high photon rates while maintaining depth precision and accuracy matching or exceeding conventional approaches (Tontini et al., 2023).