# How to Efficiently Determine the Range Precision of 3D Terrestrial Laser Scanners

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## Abstract

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## 1. Motivation

- An efficient approach will be presented which allows qualified users to determine the range precision of their terrestrial laser scanners from 3D points. The setup should be cheap and easy to replicate. So, it can be easily performed for several scanner settings (Section 5).
- As not every manufacturer provides raw intensity values, the second goal of this study is to find out whether raw as well as scaled intensity values, such as those from Leica Cyclone, can be utilized for determining the range precision of the given examples (Section 6).

## 2. Previous Work

## 3. Methodology to Model the Range Precision with 3D Points

#### 3.1. Determination of the Range Precision of 3D TLS

#### 3.2. Modeling the Intensity-Based Range Precision

**l**. The residuals of the observations are described by the variable

**v**.

## 4. Experiments

#### 4.1. Data Collection with Spectralon Targets

#### 4.2. Data Collection with Paperboards

- Firstly, it needs to be built with little effort and it should be cheap.
- Secondly, the precision still has to be determinable.
- Lastly, a wide range of intensity values needs to be obtainable.

#### 4.3. Data Collection to Analyze Scaled Intensities

## 5. Efficient Modeling of the Range Precision with 3D Points

#### 5.1. Determination of Intensity-Based Range Precision with Sepctralon Targets

#### 5.2. Determination of Intensity-Based Range Precision from Paperboards

## 6. Investigations of Raw and Scaled Intensities

#### 6.1. Relation between Intensity, Distance and Incidence Angle

#### 6.2. Estimated Function with Scaled Intensities

#### 6.3. Reproducibility of Intensity Values

#### 6.4. Influence of the Distance on Scaled Intensities

## 7. Discussion

## 8. Conclusions and Outlook

- This study introduced the estimation of the range precision by considering the range residuals of a plane adjustment and their standard deviation. As different observation groups are not weighted equally, the function can be properly estimated from samples with higher incidence angles. Thus, it is easier to get a wider range of intensity values and hence, this leads to a much quicker determination of the function. Furthermore, the proposed setup uses cheap cardboards, which are easy to install. Consequently, this simplifies the determination of the range precision of terrestrial laser scanners and makes it more efficient.
- It is demonstrated that the function, which models the relation between range precision and intensity, is applicable with raw intensity values, and likewise with scaled intensity values from Cyclone. However, this is only valid for shorter distances up to about 20 m. As the manufacturers modify the scaled intensities, this also influences the relation between range precision and intensity.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Two examples from practice [3].

**Left**: Wooden Panel;

**Middle**: water dam;

**Right**: Point clouds with intensity values.

**Figure 2.**Spectralon targets (26 cm × 26 cm) with high reflectivity (

**left**) and low reflectivity (

**right**).

**Figure 5.**

**Left**: Estimated function for HDS6100 and scan rate of 508 kHz;

**Right**: Corresponding histogram of the residuals of the function.

**Figure 7.**

**Left**: Relation between raw intensity and range;

**Right**: Relation between raw intensity and incidence angle for the Leica HDS6100.

**Figure 8.**

**Left**: Relation between scaled intensity and range;

**Right**: Relation between scaled intensity and incidence angle for the Leica HDS6100.

**Figure 9.**

**Left**: Estimated function for Leica HDS6100 with a scan rate of 508 kHz;

**Right**: Corresponding histogram of the residuals of the function.

**Figure 10.**

**Left**: Estimated function for Leica ScanStation P20 and resolution of 0.8 mm @ 10 m;

**Right**: Corresponding histogram of the residuals of the function.

**Figure 11.**Comparison of the range precision calculated with the raw and scaled intensity values by inserting these values in the estimated function.

**Figure 12.**

**Left**: Difference between intensity values of measurement one and those from the other measurements at a distance of 15 m;

**Right**: Percentage of the corresponding differences of the range precision. M1-M5: Measurements, that were taken one by one; A1, A2: Measurements after restarting the instrument; B1: Measurement after changing the battery.

**Figure 13.**Comparison of functions estimated with Spectralon targets and with the paperboard setup using scaled intensity values.

**Figure 15.**Corresponding range precision of the examples of Figure 1.

**Table 1.**Estimated parameters of Equation (5) with standard deviation.

Scanner | a (STD) | b (STD) | c (STD) | ${\mathit{\rho}}_{\mathit{ab}}$ | ${\mathit{\rho}}_{\mathit{ac}}$ | ${\mathit{\rho}}_{\mathit{bc}}$ |
---|---|---|---|---|---|---|

(Intensity—Scan Rate/Resolution) | [mm/inc] | [–] | [mm] | [–] | [–] | [–] |

Leica HDS6100(raw—508 kHz) | 1970.32 (141.96) | −0.65 (0.02) | 0.22 (0.02) | −0.99 | 0.92 | −0.93 |

Leica HDS6100(scaled—508 kHz) | 56.68 (3.27) | −0.69 (0.01) | 0.27 (0.02) | −0.99 | 0.88 | −0.92 |

Leica ScanStation P20(scaled—0.8 mm @ 10 m) | 46.82 (2.21) | −0.55 (0.01) | – | −0.97 | ||

Leica ScanStation P20(scaled—1.6 mm @ 10 m) | 60.34 (3.67) | −0.61 (0.01) | – | −0.98 | ||

Leica ScanStation P20(scaled—3.1 mm @ 10 m) | 64.04 (5.06) | −0.64 (0.02) | – | −0.98 |

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**MDPI and ACS Style**

Schmitz, B.; Holst, C.; Medic, T.; Lichti, D.D.; Kuhlmann, H. How to Efficiently Determine the Range Precision of 3D Terrestrial Laser Scanners. *Sensors* **2019**, *19*, 1466.
https://doi.org/10.3390/s19061466

**AMA Style**

Schmitz B, Holst C, Medic T, Lichti DD, Kuhlmann H. How to Efficiently Determine the Range Precision of 3D Terrestrial Laser Scanners. *Sensors*. 2019; 19(6):1466.
https://doi.org/10.3390/s19061466

**Chicago/Turabian Style**

Schmitz, Berit, Christoph Holst, Tomislav Medic, Derek D. Lichti, and Heiner Kuhlmann. 2019. "How to Efficiently Determine the Range Precision of 3D Terrestrial Laser Scanners" *Sensors* 19, no. 6: 1466.
https://doi.org/10.3390/s19061466