Single-photon avalanche diodes (SPADs) are becoming popular in time-of-flight depth-ranging due to their unique ability to capture individual photons with picosecond timing resolution. However, ambient light (e.g., sunlight) incident on a SPAD-based 3D camera leads to severe non-linear distortions (pileup) in the measured waveform, resulting in large depth errors. The authors propose asynchronous acquisition schemes that temporally misalign SPAD measurement windows and the laser cycles through deterministically predefined or randomized offsets. Their approach demonstrates "improvement in depth accuracy of up to an order of magnitude" compared to existing methods across a wide range of imaging scenarios with high ambient flux.

Single-photon avalanche diodes (SPADs) offer unprecedented photon detection sensitivity and picosecond timing precision, yet remain "restricted to a limited set of niche applications" primarily due to performance degradation under ambient light conditions. The fundamental problem is photon pileup: in conventional synchronous acquisition, "early arriving ambient photons prevent the SPAD from measuring the signal (laser) photons that may arrive at a later time bin." This creates a systematic bias toward shorter depth estimates, which worsens as ambient light intensity increases.

Prior approaches include optical attenuation (reducing incident photon count), computational pileup correction (post-processing algorithms), temporally-shifted gated acquisition, and photon-driven acquisition modes. Optical attenuation sacrifices signal photons along with ambient photons, reducing the signal-to-background ratio. Computational correction relies on accurate noise models that may not hold in practice. The authors distinguish their contribution by focusing on acquisition strategy design that fundamentally prevents rather than corrects pileup effects.

The paper establishes mathematical foundations using Poisson-distributed photon arrival models, defining the incident photon flux waveform and describing how synchronous acquisition fails under ambient illumination. In conventional operation, the SPAD measurement window is synchronized with each laser pulse. When ambient flux is high, photons from background illumination trigger the SPAD before the signal photon arrives, causing the measured histogram to be distorted toward earlier time bins. This distortion is fundamentally non-linear and cannot be removed by simple averaging.

The core theoretical contribution is the derivation of a Poisson-Multinomial Distribution for measured histograms under asynchronous acquisition, and the generalization of Coates's estimator for arbitrary temporal offsets. The formulation introduces the "denominator sequence" concept representing photon detection opportunities per bin. Two foundational results establish that uniform shifting strategies minimize depth estimation error bounds by achieving constant expected denominator sequences across all histogram bins, thereby distributing ambient light effects uniformly rather than concentrating them in early bins.

Three practical implementations are presented. SPAD Active Time Optimization derives the optimal active window duration, achieving RMSE improvements up to six-fold. Photon-Driven Shifting uses a free-running mode where cycle lengths vary stochastically based on photon detection timing, automatically achieving uniform shift distributions and providing adaptive per-pixel flux utilization. Combination with Flux Attenuation yields higher optimal attenuation fractions than synchronous methods. The photon-driven approach is particularly elegant as it requires no external synchronization hardware.

Hardware implementation uses a 405 nm pulsed laser, TCSPC module, and fast-gated SPAD operating at 10 MHz repetition frequency with 1000 histogram bins covering 15-meter unambiguous range. Results demonstrate sub-centimeter depth accuracy on test scenes under high ambient illumination (11 photons background per cycle at signal-to-background ratio of 0.02), with successful adaptation to varying surface reflectivities. The asynchronous schemes achieve depth accuracy improvements of up to an order of magnitude compared to synchronous baselines under identical ambient conditions.

This work demonstrates that asynchronous acquisition strategies can fundamentally mitigate photon pileup in SPAD-based 3D imaging, achieving up to an order of magnitude improvement in depth accuracy under high ambient light. The generalized image formation model and denominator sequence framework provide theoretical tools for analyzing and optimizing any acquisition scheme. Future extensions to non-uniform shifting schemes for time-domain fluorescence imaging and non-line-of-sight applications are noted as promising directions.