# Photogrammetry for Concentrating Solar Collector Form Measurement, Validated Using a Coordinate Measuring Machine

^{*}

## Abstract

**:**

## 1. Introduction

#### Shape Measurement Methods

## 2. Methodology

#### 2.1. Equipment

#### 2.2. Camera Settings Optimisation

#### 2.3. Photogrammetry Validation against CMM

#### 2.4. Point Cloud Analysis

## 3. Results

#### 3.1. Camera Settings Optimisation

#### 3.2. Facet Measurements

#### 3.3. Photogrammetry Validation

#### 3.4. Onsite Measurements

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

CMM | Coordinate measuring machine |

CSP | Concentrating solar power |

CSY | Coordinate system |

MATS | Multipurpose application by thermodynamic solar |

RMS | Root mean square |

VSHOT | Video Scanning Hartmann Optical Testing |

X | Camera lens coordinate system |

Y | Camera lens coordinate system |

r | Distance from principal point of camera lens |

${K}_{1},{K}_{2},{K}_{3}$ | Radial distortion parameters |

${P}_{1},{P}_{2}$ | Decentring distortion parameters |

$d{p}_{X},d{p}_{Y}$ | Calculated correction factors |

f | Camera focal length |

x | Direction parallel to trough axis |

y | Direction along trough curve |

z | Direction perpendicular to x and y |

M | Measured point cloud |

${M}_{r}$ | Aligned point cloud |

R | Rotation transformation matrix |

T | Translation transformation matrix |

${z}_{err}$ | Surface error in z direction |

$Er{r}_{RMS}$ | RMS surface error |

n | Number of measured points |

${y}_{slope}$ | Slope in curved direction |

F | Focal length of parabola |

$SD$ | Vector standard deviation |

$SX$ | Standard deviation in x direction |

$SY$ | Standard deviation in y direction |

$SZ$ | Standard deviation in z direction |

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Shutter Speed (s) | Accuracy (μm) |
---|---|

1/60 | 84.6 |

1/60 | 73.3 |

1/125 | 40.7 |

1/125 | 40.6 |

Repeat Number | CSY Length (mm) | |||
---|---|---|---|---|

200 | 400 | 600 | 800 | |

1 | 94.6 | 96 | 44.3 | 41.1 |

2 | 78.9 | 80.7 | 38.9 | 40.6 |

3 | 107.8 | 84 | 38.3 | 40.5 |

4 | 78.9 | 82 | 39.5 | 40.9 |

Average | 89.9 | 85.7 | 40.3 | 40.8 |

Standard Deviation | 14.1 | 7.0 | 2.7 | 0.3 |

Name | RMS Form (mm) | RMS Slope (mrad) | RMS Defocus (mm) | Intercept Factor (%) |
---|---|---|---|---|

Mirror1-1 | 1.20 | 2.35 | 17.2 | 94.6 |

Mirror1-2 | 1.15 | 2.94 | 19.5 | 91.5 |

Mirror1-3 | 1.14 | 2.85 | 19.3 | 91.5 |

Average | 1.16 | 2.71 | 18.7 | 92.5 |

Mirror2-1 | 1.29 | 3.35 | 21.3 | 89.3 |

Mirror2-2 | 1.39 | 4.36 | 25.9 | 81.9 |

Mirror2-3 | 1.35 | 3.83 | 23.7 | 85.7 |

Average | 1.34 | 3.84 | 23.7 | 85.6 |

Mirror3-1 | 0.98 | 2.46 | 17.9 | 93.4 |

Mirror3-2 | 1.15 | 2.84 | 19.5 | 91.4 |

Mirror3-3 | 1.10 | 2.92 | 19.6 | 91.1 |

Average | 1.08 | 2.74 | 19.0 | 92.0 |

Mirror4-1 | 0.59 | 3.48 | 16.5 | 95.5 |

Mirror4-2 | 1.20 | 3.79 | 17.3 | 94.4 |

Average | 0.90 | 3.64 | 16.9 | 94.9 |

Overall Average | 1.12 | 3.23 | 19.6 | 91.3 |

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## Share and Cite

**MDPI and ACS Style**

King, P.; Sansom, C.; Comley, P.
Photogrammetry for Concentrating Solar Collector Form Measurement, Validated Using a Coordinate Measuring Machine. *Sustainability* **2020**, *12*, 196.
https://doi.org/10.3390/su12010196

**AMA Style**

King P, Sansom C, Comley P.
Photogrammetry for Concentrating Solar Collector Form Measurement, Validated Using a Coordinate Measuring Machine. *Sustainability*. 2020; 12(1):196.
https://doi.org/10.3390/su12010196

**Chicago/Turabian Style**

King, Peter, Christopher Sansom, and Paul Comley.
2020. "Photogrammetry for Concentrating Solar Collector Form Measurement, Validated Using a Coordinate Measuring Machine" *Sustainability* 12, no. 1: 196.
https://doi.org/10.3390/su12010196