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Performance Bounds of Ranging Precision in SPAD-Based dToF LiDAR.

Hao Wu1,2, Yingyu Wang1, Shiyi Sun1

  • 1Hikvision Research Institute, Hangzhou 310051, China.

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|October 16, 2025
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Summary
This summary is machine-generated.

This study derives the Cramér-Rao lower bound for direct time-of-flight (dToF) LiDAR, revealing how system dead time and photon pile-up degrade ranging precision. It provides optimal operating parameters for SPAD-based dToF systems.

Keywords:
Cramér–Rao lower bounddirect time-of-flightsingle-photon avalanche diode

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Area of Science:

  • Photonics and Optical Engineering
  • LiDAR Technology
  • Signal Processing

Background:

  • Single-photon avalanche diode (SPAD) detectors are crucial for direct time-of-flight (dToF) LiDAR systems.
  • Existing theoretical frameworks lack a comprehensive understanding of ranging performance bounds, especially concerning dead time and pile-up effects.

Purpose of the Study:

  • To theoretically derive the Cramér-Rao lower bound (CRLB) for dToF systems, incorporating dead time effects.
  • To generalize the analysis for SPADs with photon-number-resolving capabilities.
  • To establish a unified theoretical framework for SPAD-based dToF LiDAR performance limits.

Main Methods:

  • Theoretical derivation of the CRLB for dToF systems with dead time.
  • Generalization of the CRLB for photon-number-resolving SPADs.
  • Validation through Monte Carlo simulations and maximum likelihood estimation.

Main Results:

  • Pile-up effects introduce a statistical coupling between distance and photon flux rate, degrading ranging precision.
  • Optimal optical photon flux, laser pulse width (≈0.56τ FWHM), and ToF quantization resolution were determined.
  • An optimal precision of ≈0.53τ/N is theoretically achievable, where τ is TDC resolution and N is the number of laser pulses.
  • Photon-number resolution offers limited performance improvement with diminishing returns.

Conclusions:

  • The study establishes a unified theoretical framework for SPAD-based dToF LiDAR fundamental limits.
  • Findings provide concrete design guidelines for optimizing operating points in dToF LiDAR systems.
  • The work addresses gaps in prior research regarding dead time and pile-up effects in dToF LiDAR.