# A Correction Method for Heat Wave Distortion in Digital Image Correlation Measurements Based on Background-Oriented Schlieren

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. The Principle of the Influence of Heat Waves on DIC Measurement

#### 2.2. Principle of Background-Oriented Schlieren

#### 2.3. Correlation Algorithm Flow

## 3. Experimental System

## 4. Experiments and Results

#### 4.1. Baseline Noise of the Experimental Setup

#### 4.2. Characteristics of Distortions due to Heat Waves

#### 4.3. Influence of Heat Waves on DIC Measurement Results

#### 4.4. Verification of the Correction Algorithm

## 5. Conclusions

- The distortion on the images caused by heat waves can be divided into the main distortion and a random distortion. In the experiments performed in this paper, the main distortion reached 0.05 pixels, and the most significant swing amplitude of the random distortion reached 0.2 pixels. The effect of this distortion on the measurement results of digital image correlation is not negligible.
- Spot patterns used in digital image correlation measurements can also be used in the background-oriented schlieren technique. The background schlieren method can be used to obtain the vector displacement fields of the main distortion caused by heat waves.
- The main distortion vector obtained by the background-oriented schlieren technique remap the deformed images to eliminate the main distortion. Then, the time-average method should be used to eliminate the random distortion. The experimental results showed that the proposed correction method can effectively remove the disturbance of heat waves and obtain high precision DIC measurement results.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 6.**Experimental device diagram: (

**a**) The camera is facing vertically to the measured object; (

**b**) Temperature control box; (

**c**) Hot plate in front of the measured object.

**Figure 8.**Representative contour plots of the displacements and strains computed in the DIC measurement without the introduction of a heat source: (

**a**) Displacement in U direction; (

**b**) displacement in V direction; (

**c**) strain ε

_{xx}; (

**d**) strain ε

_{xy}; (

**e**) strain ε

_{yy}.

**Figure 9.**Representative contour plots of the displacements and strains computed in DIC measurement affected by heat waves: (

**a**) Displacement in U direction; (

**b**) displacement in V direction; (

**c**) strain ε

_{xx}; (

**d**) strain ε

_{xy}; (

**e**) strain ε

_{yy}.

**Figure 10.**Displacement of the center subset as a function of time: (

**a**) U direction; (

**b**) V direction.

**Figure 13.**Displacement fields obtained from the DIC measurement without the influence of heat waves: (

**a**) Component in U direction; (

**b**) component in V direction.

**Figure 15.**Displacement fields obtained from DIC measurement with the influence of heat waves: (

**a**) Component in U direction; (

**b**) component in V direction.

**Figure 16.**Displacement field after time average: (

**a**) Component in U direction; (

**b**) Component in V direction.

**Figure 17.**Main distortion measured by the BOS technique: (

**a**) Displacement vector distribution (the box represents local amplification results); (

**b**) resultant displacement vector distribution.

**Figure 18.**Corrected image obtained by the proposed method (The blue box is the region where the DIC calculation is performed).

**Figure 20.**Displacement fields obtained from DIC measurement using the corrected image: (

**a**) Component in U direction; (

**b**) component in V direction.

**Figure 21.**Plots of displacement in U vs. Y and in V vs. X: (

**a**) Displacement component in U direction vs. Y (X = 226); (

**b**) displacement component in V direction vs. X (Y = 226).

**Table 1.**Baseline noise floor for the experimental setup, without the purposeful introduction of a heat source, quantified by spatial and temporal standard deviations (STD) of the data.

Component | Spatial STD | Temporal STD |
---|---|---|

U (pixels) | 0.0037 | 0.0023 |

V (pixels) | 0.0040 | 0.0024 |

ε_{xx} (%) | 0.0077 | 0.0040 |

ε_{xy} (%) | 0.0047 | 0.0027 |

ε_{yy} (%) | 0.0076 | 0.0039 |

**Table 2.**Mean error of displacements and strains caused by imaging through heat waves, quantified by spatial and temporal standard deviations (STD) of the data.

Component | Spatial STD | Temporal STD |
---|---|---|

U (pixels) | 0.0516 | 0.0108 |

V (pixels) | 0.0365 | 0.0069 |

ε_{xx} (%) | 0.1100 | 0.0336 |

ε_{xy} (%) | 0.0490 | 0.0139 |

ε_{yy} (%) | 0.0590 | 0.0149 |

© 2019 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**

Ma, C.; Zeng, Z.; Zhang, H.; Rui, X.
A Correction Method for Heat Wave Distortion in Digital Image Correlation Measurements Based on Background-Oriented Schlieren. *Appl. Sci.* **2019**, *9*, 3851.
https://doi.org/10.3390/app9183851

**AMA Style**

Ma C, Zeng Z, Zhang H, Rui X.
A Correction Method for Heat Wave Distortion in Digital Image Correlation Measurements Based on Background-Oriented Schlieren. *Applied Sciences*. 2019; 9(18):3851.
https://doi.org/10.3390/app9183851

**Chicago/Turabian Style**

Ma, Chang, Zhoumo Zeng, Hui Zhang, and Xiaobo Rui.
2019. "A Correction Method for Heat Wave Distortion in Digital Image Correlation Measurements Based on Background-Oriented Schlieren" *Applied Sciences* 9, no. 18: 3851.
https://doi.org/10.3390/app9183851