# A Raspberry Pi Based Portable Endoscopic 3D Measurement System

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## Abstract

**:**

## 1. Introduction

## 2. The Measurement System

#### 2.1. Image Acquisition

#### 2.2. Calibration

#### 2.3. Pattern Projection and Reconstruction

## 3. Results

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

GUM | Guide to the expression of uncertainty in measurement |

HDMI | High-definition multimedia interface |

CSI | Camera serial interface |

LED | Light emitting diode |

## References

- Kästner, M. Optische Geometrieüberprüfung präzisionsgeschmiedeter Hochleistungsbauteile. Ph.D Thesis, Leibniz Universität Hannover, Hannover, Germany, 2008. [Google Scholar]
- Chen, L.; Huang, C. Miniaturized 3D surface profilometer using digital fringe projection. Meas. Sci. Technol.
**2005**, 16, 1061. [Google Scholar] [CrossRef] - Karlstorz, MULTIPOINT, webpage. Available online: https://www.karlstorz.com/be/en/neues-multipoint-mess-videoendoskop.htm (accessed on 20 June 2016).
- General Electric, XLG3, webpage. Available online: https://www.gemeasurement.com/download/xlg3-videoprobe-brochure (accessed on 20 June 2016).
- Matthias, S.; Loderer, A.; Koch, S.; Gröne, M.; Kästner, M.; Hübner, S.; Krimm, R.; Reithmeier, E.; Hausotte, T.; Behrens, B.-A. Metrological solutions for an adapted inspection of parts and tools of a sheet-bulk metal forming process. Product. Eng.
**2016**, 10, 51–61. [Google Scholar] [CrossRef] - Zhang, Z. A flexible new technique for camera calibration. IEEE Trans. Pattern Anal. Mach. Intell.
**2000**, 22, 1330–1334. [Google Scholar] [CrossRef] - Peng, T. Algorithms and Models for 3-D Shape Measurement Using Digital Fringe Projections. Ph.D Thesis, University of Maryland, College Park, MD, USA, 2006. [Google Scholar]

**Figure 2.**Rendering of the measurements system. The system is mounted on a goniometer. The following parts are labeled: (a) projector; (b) camera adapter; (c) Raspberry Pi 2; (d) borescope shaft; (e) camera (f) fields of view of the projector (green) and the camera (blue).

**Figure 3.**Photograph of the measurement system from the top. The labels are consistent with Figure 2.

**Figure 4.**Example sequence of fringe patterns. Three frequencies (waves per pattern) are used: 1, 6, 36. Only one pattern per frequency is shown.

**Figure 5.**Distances of the sample measurements points to the nominal geometry of the gap (top left), the cylinder with radius 1 $\mathrm{m}\mathrm{m}$.

**Figure 6.**Sample measurements of the cylinder with a radius of 10 $\mathrm{m}\mathrm{m}$ in pose 1 (left), pose 2 (middle) and pose 3 (right).

**Table 1.**Evaluation of a gap with a depth of 1 $\mathrm{m}\mathrm{m}$ and the cylinder with a radius of 1 $\mathrm{m}\mathrm{m}$.

Gap with Depth 1 $\mathrm{m}\mathrm{m}$ | Cylinder with Radius 1 $\mathrm{m}\mathrm{m}$ | |
---|---|---|

calibrated value | 1000.5 ± 0.4 μ$\mathrm{m}$ | 1001.5 ± 0.7 μ$\mathrm{m}$ |

measured value | 992.6 ± 0.5 μ$\mathrm{m}$ | 935.4 ± 1.1 μ$\mathrm{m}$ |

deviation | 7.9 μ$\mathrm{m}$ | 66.1 μ$\mathrm{m}$ |

single point distance (σ) | 16.7 μ$\mathrm{m}$ | 18.6 μ$\mathrm{m}$ |

**Table 2.**Evaluation of two cylinders with a radius of 6 $\mathrm{m}\mathrm{m}$ and 10 $\mathrm{m}\mathrm{m}$.

Cylinder with Radius 6 $\mathrm{m}\mathrm{m}$ | Cylinder with Radius 10 $\mathrm{m}\mathrm{m}$ | |
---|---|---|

calibrated value | 5994.0 ± 1.2 μ$\mathrm{m}$ | 10002.1 ± 0.9 μ$\mathrm{m}$ |

pose one | ||

measured value | 6037.4 ± 1.6 μ$\mathrm{m}$ | 9945.1 ± 1.1 μ$\mathrm{m}$ |

deviation | 43.4 μ$\mathrm{m}$ | 57.0 μ$\mathrm{m}$ |

single point distance (σ) | 83.4 μ$\mathrm{m}$ | 100.0 μ$\mathrm{m}$ |

pose two | ||

measured value | 5971.5 ± 4.4 μ$\mathrm{m}$ | 9851.0 ± 4.0 μ$\mathrm{m}$ |

deviation | 22.4 μ$\mathrm{m}$ | 151.1 μ$\mathrm{m}$ |

single point distance (σ) | 29.3 μ$\mathrm{m}$ | 23.1 μ$\mathrm{m}$ |

pose three | ||

measured value | 5911.7 ± 2.8 μ$\mathrm{m}$ | 9905.1 ± 4.3 μ$\mathrm{m}$ |

deviation | 82.3 μ$\mathrm{m}$ | 97.0 μ$\mathrm{m}$ |

single point distance (σ) | 71.0 μ$\mathrm{m}$ | 35.0 μ$\mathrm{m}$ |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Schlobohm, J.; Pösch, A.; Reithmeier, E.
A Raspberry Pi Based Portable Endoscopic 3D Measurement System. *Electronics* **2016**, *5*, 43.
https://doi.org/10.3390/electronics5030043

**AMA Style**

Schlobohm J, Pösch A, Reithmeier E.
A Raspberry Pi Based Portable Endoscopic 3D Measurement System. *Electronics*. 2016; 5(3):43.
https://doi.org/10.3390/electronics5030043

**Chicago/Turabian Style**

Schlobohm, Jochen, Andreas Pösch, and Eduard Reithmeier.
2016. "A Raspberry Pi Based Portable Endoscopic 3D Measurement System" *Electronics* 5, no. 3: 43.
https://doi.org/10.3390/electronics5030043