# Using a Slit to Suppress Optical Aberrations in Laser Triangulation Sensors

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## Abstract

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## 1. Introduction

## 2. Hypotheses

## 3. Methods

## 4. Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**The proposed camera obscura. In (

**a**), the parts labeled. In (

**b**), the diffraction pattern. (

**a**) The proposed camera obscura. ① Casing. ② Band-pass optical filter. ③ Slit mask. ④ Protective glass. ⑤ Image sensor. Axis indicates the x direction relative to the schematic. (

**b**) Diffraction pattern created by incident monochromatic light.

**Figure 6.**A simple high-precision position table. Useful range: 150 cm. ① Step motor, ② worm gear, ③ target carriage, and ④ limit switch. On a metal plate (dashed): ⑤ laser, ⑥ camera with lens or slit.

**Figure 8.**Analysis of a laser spot through a lens. (

**a**) Image cropped around detected reflected laser spot. (

**b**) Reflected laser spot modeled as a Gaussian. (

**c**) Reflected laser spot with center superimposed.

**Figure 9.**Error in center estimations from both methods. The material measured in this figure is the brushed metal. (

**a**) Error in center estimation from using a lens. (

**b**) Error in center estimation from using a slit.

**Figure 10.**Reflected laser spot through a slit. (

**a**) Image cropped around detected reflected laser spot. (

**b**) Reflected laser spot with centers, line-by-line. (

**c**) Reflected laser spot with center superimposed.

**Figure 12.**Geometric model, fit, and positions. (

**a**) Geometric model fitted on slit data. Dots are estimated centers from image analysis, and the straight line is Equation (1) fitted to the data. (

**b**) Known positions vs. fitted geometric model. The dots are known (discrete) positions, and the line is the prediction from the geometric model.

**Figure 13.**Violin plots of errors for the lens compared to the slit. The x-axis shows the magnitude of errors (dashed line is zero), and the y-axis is the normalized probability.

Lens | Slit with Gaussian Fit | Slit with Fraunhofer Fit | ||||
---|---|---|---|---|---|---|

Material | MAX μm | MAE μm | MAX μm | MAE μm | MAX μm | MAE μm |

Brushed Metal | 851 | 182 | 520 | 115 | 527 | 155 |

Rusty Metal | 860 | 164 | 640 | 158 | 638 | 158 |

Light Wood Plank | 651 | 151 | 429 | 72 | 476 | 81 |

Printer Paper | 812 | 144 | 468 | 81 | 437 | 72 |

Black Electric Tape | 1098 | 280 | 735 | 134 | 743 | 134 |

Microfiber Fabric | 677 | 154 | 602 | 118 | 600 | 119 |

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**MDPI and ACS Style**

Pigeon, S.; Lapointe-Pinel, B.
Using a Slit to Suppress Optical Aberrations in Laser Triangulation Sensors. *Sensors* **2024**, *24*, 2662.
https://doi.org/10.3390/s24082662

**AMA Style**

Pigeon S, Lapointe-Pinel B.
Using a Slit to Suppress Optical Aberrations in Laser Triangulation Sensors. *Sensors*. 2024; 24(8):2662.
https://doi.org/10.3390/s24082662

**Chicago/Turabian Style**

Pigeon, Steven, and Benjamin Lapointe-Pinel.
2024. "Using a Slit to Suppress Optical Aberrations in Laser Triangulation Sensors" *Sensors* 24, no. 8: 2662.
https://doi.org/10.3390/s24082662