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What happens to a ToF LiDAR in fog?

You Li, Pierre Duthon, Michèle Colomb, Javier Ibanez-Guzman

arXiv:2003.06660v4eess.SPcs.RO

TL;DR

ToF LiDAR performance under fog has limited prior evidence, despite the importance of adverse-weather effects for full self-driving deployment. The paper tests a Velodyne UltraPuck in controlled fog and models disappear visibility from collected data. Its Gaussian Process predictions show distance- and reflectivity-related differences in prediction performance.

  • Problem

    Prior LiDAR applications often assumed ideal environments, while research on fog, rain, and snow impacts was insufficient despite their relevance to full self-driving deployment.

    Source: §I · p. 1

  • Method

    The authors test a Velodyne UltraPuck in controlled artificial fog and use Gaussian Process modeling to predict disappear visibility from collected measurements.

    Source: §I · p. 1, 1) Artificial fog and visibility data · p. 3, §VI · p. 10

  • Results

    The Gaussian Process model’s overall failure rate is 6%, with higher failure rates for diffuse targets as distance increases and prediction errors around 2 meters for retro-reflective targets.

    Source: 3) Results · pp. 9–10

  • Takeaways & Limitations

    Disappear visibility provides an evaluation of LiDAR operational feasibility by comparison with measured visibility in natural fog.

    Source: 2) Disappear visibility · p. 8, §VI · p. 10

    Future tests should cover more targets, especially reflectivities between 50 and 100 at distances beyond 100 meters, and consider additional factors such as incident angle.

    Source: §VI · p. 10

Abstract

from arXiv · show

This article focuses on analyzing the performance of a typical time-of-flight (ToF) LiDAR under fog environment. By controlling the fog density within CEREMA Adverse Weather Facility 1 , the relations between the ranging performance and fogs are both qualitatively and quantitatively investigated. Furthermore, based on the collected data, a machine learning based model is trained to predict the minimum fog visibility that allows successful ranging for this type of LiDAR. The revealed experimental results and methods are helpful for ToF LiDAR specifications from automotive industry.

I. INTRODUCTION

The paper examines a ToF LiDAR under controlled fog, addressing limited empirical evidence on adverse-weather performance. It combines detailed performance analysis with a data-driven model of fog-related ranging failure.

I. INTRODUCTION

  • Adverse-weather LiDAR research was considered insufficient, while weather impacts were becoming non-negligible for full self-driving deployment.The paper identifies fog, rain, and snow as adverse conditions commonly overlooked in prior application assumptions.Source: §I · p. 1
  • The study analyzes a Velodyne UltraPuck2 in well-controlled artificial fog and trains a model to predict when ranging fails.The authors describe this as the first data-driven quantitative analysis and modeling of a ToF LiDAR’s performance under fog.Source: §I · p. 1

II. LITERATURE REVIEW

  • Prior theoretical studies modeled adverse-weather effects, but some lacked real-experiment verification and another tested only a few visibility levels.The cited studies include comparisons of 905 nm and 1050 nm ToF LiDARs, a rain model, and a Mie-scattering model.Source: §II · p. 2
  • Empirical studies covered varied sensors and weather, but identified gaps include coarse weather measurement, short test distances, and limited quantitative analysis.CEREMA-based work benchmarked range sensors, including two 905 nm Velodyne and IBEO LiDARs.Source: §II · p. 2

III. THEORETICAL MODEL OF TOF LIDAR AND ADVERSE WEATHER IMPACTS

The theoretical model links ToF ranging to pulse travel time and received return power. It identifies distance, target reflectivity, and transmission-medium losses as factors shaping the return.

A. Principle of a ToF LiDAR

  • ToF LiDAR measures range from the time difference between emitted and returned laser pulses.The range equation uses light speed and propagation-medium refractive index; the index is approximately 1 for air.Source: A. Principle of a ToF LiDAR · p. 2

1) Power model:

  • The received-power model relates return power to pulse energy, receiver aperture, system efficiency, target reflectivity, distance, and transmission loss.Target reflectivity depends on surface properties and incident angle.Source: 1) Power model · p. 2
  • Transmission loss represents propagation through the medium, where particles scatter and absorb the laser according to the extinction coefficient.The model’s transmission term is described as T(R).Source: 1) Power model · p. 3

2) Pulse detection:

The paper describes how return-signal detection produces range measurements and how adverse weather affects the return. Experiments use a Velodyne UltraPuck in a controlled fog facility with targets at varied distances.

2) Pulse detection:

  • The sensor detects returns against background noise, estimates pulse time difference, and calculates range; received energy falls quadratically with distance.Transmitted power cannot simply be increased because of eye-safety restrictions, so signal processing must detect returns at low signal-to-noise ratios.Source: 2) Pulse detection · p. 3

B. Influences of Adverse Weather

  • Fog and rain increase transmission loss through absorption or scattering, while wet surfaces can reduce reflectivity and maximum detection range.The weather-related extinction depends on water content and droplet size distribution; a liquid surface film weakens diffuse reflection.Source: B. Influences of Adverse Weather · p. 3

IV. EXPERIMENTS

  • Tests place a Velodyne UltraPuck and varied targets at different distances in CEREMA’s controlled adverse-weather facility.The sensor was selected for its wide applications in autonomous vehicles.Source: §IV · p. 3

A. CEREMA’s Adverse Weather Facility

CEREMA’s platform supports controlled adverse-weather tests over a 30-meter length, with instruments for characterizing fog and rain. The fog tests begin at 10 m visibility and let the fog dissipate while visibility is monitored.

A. CEREMA’s Adverse Weather Facility

  • The platform reproduces clear, night, fog, and rain scenarios over a total length of 30 m.It is used to investigate transport systems affected by adverse conditions.Source: A. CEREMA’s Adverse Weather Facility · p. 3
  • A transmissometer records fog visibility from 5 to 1000 m at 1 Hz, alongside instruments for droplet-size and rainfall measurements.The optical granulometer measures droplets from 0.4 to 40 µm; the rain gauge and spectro-pluviometer record rainfall rate from 0.001 to 1200 mm/h at 1 Hz.Source: A. CEREMA’s Adverse Weather Facility · p. 3

1) Artificial fog and visibility data:

  • High-pressure nozzles generate droplets similar in size to natural fog, and real-time monitoring of injected water regulates visibility.Tests start at the facility’s minimum available visibility of 10 m, then let the fog dissipate as droplets evaporate.Source: 1) Artificial fog and visibility data · p. 3
  • During dissipation, visibility increases until the air becomes clear; a sample test records visibility rising from almost 10 m to over 300 m.The paper notes that meteorological and French road standards use different visibility thresholds for defining the absence of fog.Source: Figure 4 · p. 4, 1) Artificial fog and visibility data · p. 4

2) Targets:

The experiments use calibrated boards and other typical road targets at varying distances, logging LiDAR measurements alongside visibility. The recorded data are restricted to manually selected laser regions of interest on the targets.

2) Targets:

  • The target set includes calibrated boards with 5%, 50%, and 90% reflectivity, a dummy, a car, and two traffic signs.The Velodyne UltraPuck operates at 10 Hz in strongest-return mode and reports a calibrated reflectivity byte for each range measure.Source: 2) Targets · p. 4
  • The dummy and car without a plate have similar measured reflectivities, ranging from 0 to 35.The calibrated boards distinguish from one another, while the car plate and traffic signs are treated as retro-reflectors.Source: 2) Targets · p. 4

C. LiDAR Recordings

  • Tests place one or more targets 5–30 m from the LiDAR and log fog-free ground truth before generating controlled fog.Range, azimuth, ring number, reflectivity, and timestamp are recorded until targets are stably detected, synchronized with meteorological visibility.Source: C. LiDAR Recordings · p. 4
  • The paper summarizes the tested scenarios in Table II, while the target measurements are represented in Fig. 5.The passage identifies the table as a summary of scenarios but provides no cell values.Source: Table II · p. 4, Figure 5 · p. 5
  • Manual regions of interest retain only measurements from lasers hitting the targets, indexed by ring number and azimuth angle.The ring number ranges from 0 to 31, and at 10 Hz azimuth is encoded from 0 to 1800.Source: C. LiDAR Recordings · p. 5

V. ANALYSIS OF EXPERIMENTAL RESULTS

The model relates ToF LiDAR ranging under fog to distance, target reflectivity, and fog severity, but the sensor’s black-box signal processing prevents an analytical form for the ranging function. Qualitative observations show better ranging with greater visibility and reflectivity, and at shorter distances.

A. Modeling ranging process impacted by fog

  • The ranging model identifies distance, target reflectivity, and fog severity as factors, but the black-box signal processing prevents deriving an analytical form for its function.The model assumes fog is evenly distributed through the ranging space, with visibility characterizing extinction and fog-influenced reflectivity.Source: A. Modeling ranging process impacted… · pp. 5–6

B. Qualitative analysis

  • At a fixed distance, higher visibility and target reflectivity correspond to smaller range error, while greater distance corresponds to larger error.These are the three qualitative relationships stated for ranging capability under fog.Source: B. Qualitative analysis · p. 6
  • At 15 m, boards and parts of the dummy model barely visible at 40 m visibility are all detected at 80 m visibility.The figure comparison also shows clutter points from fog and that higher-reflectivity objects are more robust under fog.Source: B. Qualitative analysis · p. 6, Figure 6 · p. 6
  • At the same visibility, the 90%-reflectivity board is detected before the other boards, while lower-reflectivity parts appear at shorter distance.Traffic signs are fully detected at 15 m visibility, whereas low-reflectivity car tires and windows remain invisible when other car parts are detected.Source: B. Qualitative analysis · p. 7

C. Quantitative analysis

Individual laser ranges within target regions of interest are synchronized with visibility measurements and averaged each second. The examples show ranges approaching the fog-free true distance as visibility increases, then generally remaining stable.

1) Individual ranging process:

  • Because the LiDAR records at 10 Hz and visibility at 1 Hz, the analysis uses average range measures for each second.The ranges are synchronized with meteorological visibility data.Source: 1) Individual ranging process · p. 7
  • As fog dissipates, sampled laser ranges move from false values below the true distance toward that distance, then are generally stable.This trend is observed for a board at 15 m and similarly across the other sampled targets.Source: 1) Individual ranging process · p. 7

2) Disappear visibility:

The paper defines disappear visibility as the minimum fog visibility at which a target at a given distance and reflectivity yields a true range measurement. It uses this measure to characterize LiDAR functionality in fog and finds that stronger reflectivity generally corresponds to lower disappear visibility.

2) Disappear visibility:

  • Disappear visibility is the minimum visibility that allows a target at a given distance and reflectivity to return its true distance measure.For an individual laser in the region of interest, a small threshold determines whether its measured range counts as the true distance.Source: 2) Disappear visibility · p. 8
  • A LiDAR’s disappear visibility can be compared with natural-fog visibility to assess operational feasibility for an autonomous vehicle.The measure also supports benchmarking different LiDARs for the same obstacle and distance; lower values indicate better anti-interference capability in fog.Source: 2) Disappear visibility · p. 8
  • The tests group car and dummy-model reflectivities into similar clusters, while treating the boards and traffic signs as homogeneous surfaces.At 15 m, reported average reflectivities range from 1.17 for the car’s weak part to 209.2 for traffic sign 2.Source: 2) Disappear visibility · p. 8
  • Stronger target reflectivity generally corresponds to lower disappear visibility, a pattern repeated across the tested model, car, and traffic signs.Traffic sign 2, the most reflective target, has the lowest disappear visibility.Source: 2) Disappear visibility · p. 8

D. Modeling disappear visibility by machine learning

Because an analytical expression for disappear visibility at a specific distance and target reflectivity is too complicated, the paper models it from the CEREMA test dataset. It represents the relationship as a two-input Gaussian process regression.

D. Modeling disappear visibility by machine learning

1) Gaussian Process Regression (GPR):

2) Training GP model:

The GP training data comprise 3,853 range-reflectivity samples, with 565 manually selected training samples and separate models for diffuse and retro-reflective targets.

2) Training GP model:

  • Average range measurements for each second from all lasers in the region of interest were used to remove jitter.Source: 2) Training GP model · p. 9
  • 3,853 distinctive samples were collected, and 565 training samples were manually selected from ranges of 10–30 m and reflectivities of 0–255.The dataset is unevenly distributed, with more samples at short ranges and low reflectivities, and insufficient samples for reflectivities from 60 to 100.Source: 2) Training GP model · p. 9
  • The authors trained two Gaussian processes separately: GPdiffuse for diffuse objects with β ∈ [0,100) and GPretro for retro-reflected objects with β ∈ [100,255].Range and reflectivity were normalized to [0,1] for training. Both models used Matérn 3/2 kernels, chosen for finite differentiability to match physical processes more realistically.Source: 2) Training GP model · p. 9

3) Results:

The trained GP predicts disappear visibility across reflectivities from 0 to 255 and distances from 10 to 30 m. Its overall failure rate is 6%, while prediction errors rise with distance, especially for low-reflectivity targets.

3) Results:

  • 6% is the overall GP prediction failure rate across the 3,853-sample dataset.A prediction is counted as failed when the measured disappear visibility falls outside the predicted 95% confidence region; failure rates increase with distance for diffuse targets but remain stable for retro-reflective targets.Source: 3) Results · p. 9, Table IV · p. 9
  • The trained GP predicts disappear visibility for reflectivities from 0 to 255 at distances from 10 to 30 m.The prediction surface is shown in Fig. 10, with typical predictions also reported in Table III.Source: 3) Results · p. 9, Table III · p. 9, Figure 10 · p. 10
  • Prediction errors increase with distance, particularly for targets with β < 10, while errors for retro-reflective targets (β > 100) remain stable at around 2 meters.The authors attribute worse performance at long range and low reflectivity to noisier ranging.Source: 3) Results · p. 10, Table V · p. 10

VI. CONCLUSION

  • The paper investigates factors affecting ToF LiDAR fog performance and proposes disappear visibility and GP modeling as tools for evaluating LiDAR safety in fog.Future tests are proposed for more targets, longer distances beyond 100 m, and additional factors such as laser-target incident angle.Source: §VI · p. 10
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