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# Experimental Investigation of Emissivity Influence to Obtain Thermal Field by Near Infrared Thermography

Chao Zhang, Jérémy Marty, Anne Maynadier, Philippe Chaudet, Julien

Réthoré, Marie-Christine Baietto

► To cite this version:

Chao Zhang, Jérémy Marty, Anne Maynadier, Philippe Chaudet, Julien Réthoré, et al. Experimental Investigation of Emissivity Influence to Obtain Thermal Field by Near Infrared Thermography. 2018 Annual Conference on Experimental and Applied Mechanics, Jun 2018, Greenville, United States. pp.35-37, 10.1007/978-3-319-95074-7_6. hal-04670560

HAL Id: hal-04670560

https://hal.science/hal-04670560v1

Submitted on 22 May 2025

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Distributed under a Creative Commons Attribution 4.0 International License
# Experimental Investigation of Emissivity Influence to Obtain Thermal Field by Near Infrared Thermography

C. Zhang, J. Marty, A. Maynadier, P. Chaudet, J. Réthoré, and M.-C. Baietto

**Abstract** Thermal fields are usually obtained by infrared camera (operating in 3–12 µm). However, the infrared cameras are expensive, fragile and low resolution, thus the infrared camera is more used for laboratory researches. Nowadays, silicon-based sensor camera has been widely used to perform real-time observation of the kinematic fields, mainly thanks to digital image correlation or interferometry. Silicon-based camera is also sensitive in the near infrared spectral ranges (operating in 0.7–1.1 µm). An automatic prediction of the camera exposure time is developed and presented in this paper to follow the surface emissivity of the sample and avoid saturation of the gray level.

**Keywords** Thermography · Emissivity · Silicon camera · Radiometric model · Near infrared

Kinematic and thermal field measurements can provide rich information in the field of thermo-mechanics of materials and structures (e.g., constitutive model identification, fatigue behavior investigation, cracking detection, etc.). Up to now, silicon-based sensor cameras (CCD and CMOS) have been widely used to perform in situ observation of the kinematic field on the material surfaces, mainly thanks to digital image correlation or interferometry. Measuring temperature distribution of an object undergoing thermal cycle is also very important and meaningful in the field of thermo-mechanics of materials. To date, thermal fields are usually obtained by mid-wave infrared camera (operating in 3–12 µm), which can transform the thermal energy, emitted by objects in the infrared band of the electromagnetic spectrum (i.e. from 1 to 1000 µm), into an electronic video signal. However, the infrared camera is more used for laboratory researches because it is expensive, fragile, low resolution and difficult to use. The silicon-based camera is also sensitive in the near infrared spectral ranges (operating in 0.7–1.1 µm), thus it is possible and suitable for silicon-based camera to acquire the thermal fields at high temperature. Compared with infrared camera, silicon-based camera is low-cost, low noise, durable and high resolution, and can be widely used in industrial applications. In the near infrared spectral ranges, a small temperature variation readily cause a large modification in the image illumination (gray level), readily resulting in the acquired images with saturation or poor dynamic range of gray levels. The bad image acquired will make the thermal field measurement impossible.

In previous work we have proposed a method to precisely and automatically adjust the exposure time of the camera to control the image illumination whatever the temperature evolution is. The principle is to use the two last image to predict the next exposure time of the camera to keep the gray level constant when the camera frequency is maintained constant. In our study, the radiometric model of camera describing the relationship between intensity and temperature is given by [1]:

$$I_n(T) = \frac{gl}{\tau}(T) = k_w \exp\left(\frac{-C_2}{\lambda_x(T)T}\right) \qquad (6.1)$$

<footnote>C. Zhang (✉) · P. Chaudet · M.-C. Baietto</footnote>

<footnote>LaMCos, Université de Lyon/INSA Lyon/UMR CNRS 5259, Villeurbanne Cedex, France</footnote>

<footnote>e-mail: chao.zhang@insa-lyon.fr</footnote>

<footnote>J. Marty (✉)</footnote>

<footnote>LaMCos, Université de Lyon/INSA Lyon/UMR CNRS 5259, Villeurbanne Cedex, France</footnote>

<footnote>ESTA LAB, Belfort, France</footnote>

<footnote>e-mail: jeremy.marty@insa-lyon.fr</footnote>

<footnote>A. Maynadier</footnote>

<footnote>University of Bourgogne Franche-Comté, FEMTO-ST Institute, CNRS/UFC/ENSMM/UTBM, Department of Applied Mechanics, Chemin de L'épitaphe, Besançon, France</footnote>

<footnote>J. Réthoré</footnote>

<footnote>GeM, Ecole Centrale de Nantes/Université de Nantes/UMR CNRS 6183, Nantes, France</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 6.1 Experimental data and radiometric calibration curve</figcaption></figure>

where gl, τ and In are respectively the gray level, the exposure time and the intensity of the image and T the temperature. C2 is the Planck constant equal to 1.44 × 10⁻² m·K, λₓ(T) is the extended effective wavelength and is defined in the following Equation [2]:

$$ \frac{1}{\lambda_x(T)} = a_0 + \frac{a_1}{T} + \frac{a_2}{T^2} + \frac{a_3}{T^3} + \dots + \frac{a^n}{T^n}, (n = \infty) \qquad (6.2) $$

where a₀, a₁, a₂, a₃, ..., an and the parameter kᵥ of Eq. (6.1) are parameters of the camera which should be determined by radiometric calibration process. The radiometric model of our camera is plotted on the Fig. 6.1 and the parameters are given in the tabular.

The prediction of the exposure time is based on the Planck law (1) where the extended wavelength has only one parameter a₀. During the acquisition of two images, we suppose that the camera frequency is enough high to have a small difference of temperature (magnitude of 10° or 20°). So the extended wavelength is depending of only one parameter. Thus the prediction of the next intensity of image is equal to [3]:

$$ I_n(i) = \frac{\overline{gl(i)}}{\tau(i)} = \frac{I_n(i-1)^2}{I_n(i-2)} = \left[ \frac{\overline{gl(i-1)}}{\tau(i-1)} \right]^2 \times \frac{\tau(i-2)}{\overline{gl(i-2)}} \quad \text{with } i > 2 \qquad (6.3) $$

In order to make sure the gray level constant (i.e., that $\overline{gl(i)} = \overline{gl(1)}$), the next exposure time can be predicted as follows:

$$ \tau(i) = \overline{gl(1)} \times \left[ \frac{\tau(i-1)}{\overline{gl(i-1)}} \right]^2 \times \frac{\overline{gl(i-2)}}{\tau(i-2)} \qquad (6.4) $$

These experiments have been realized with a black body device which has a surface emissivity uniform and equal to one. The thermal field is easily obtained by inverting the radiometric model of the optic device.

However a specimen surface has heterogeneities of emissivity due to the material or even the coating if you add one on the surface. The Planck law presented before in Eq. (6.1) is only valid with an emissivity equal to one which is the case of a black body. In practical application, the specimen surface has heterogeneities of emissivity and the measurement of different surface emissivity is more difficult. In this study, we propose a novel method to measure the thermal fields of specimen surface with different emissivity by using silicon-based camera. Firstly, a specimen surface is sprayed with paint with different emissivities, which were made by mixing different proportions of white paint and black paint. Secondly, several thermocouples are welded to specimen surface to measure the temperature of various regions with different emissivities. Thirdly, the Planck's algorithm proposed above is used to predict new exposure time to control the mean image gray level
constant with temperature evolution from 873 to 1023 K. Fourthly, all radiometric models of various regions with different emissivities can be calibrated by experimental data. This method will give the evolution of emissivity on the radiometric model and will permit to perfectly understand the evolution of temperature in function of the emissivity of a specimen.

References

1. Orteu, J.J., Rotrou, Y., Sentenac, T., Robert, L.: An innovative method for 3-D shape, strain and temperature full-field measurement using a single type of camera: principle and preliminary results. Exp. Mech. **48**, 163–179 (2008)

2. Saunders, P.: General interpolation equations for the calibration of radiation thermometers. Metrologia. **34**, 201–210 (1997)

3. Zhang, C., Marty, J., Maynadier, A., Chaudet, P., Réthoré, J., Baietto, M.C.: A novel approach to control gray level of image invariant during near infrared thermography. 23ème Congrès Français de Mécanique-S04 Mesures de champs et mécanique expérimentale (2017)