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Research on Modulated Thermal Wave Radar Imaging Technique for Photothermal Properties of Semi-transparent Materials

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Abstract

The photothermal characteristics of semi-transparent medium are the basis for describing the transmission process of photothermal radiation. Therefore, the related measurement researches have important application value for the non-destructive testing of high-tech module. In the present work, an infrared thermal wave radar imaging (TWRI) technique combined with sequential quadratic programming (SQP) algorithm was proposed for simultaneous reconstruction of the photothermal property distributions in 2D semi-transparent materials containing defects. The Fourier transform, Hilbert transform, and the Chirp lock-in correlation algorithm were applied and the results of the amplitude and phase information of the temperature signals were compared, so as to identify the position of internal defects, which reduced the number of parameters needed to reconstruct. Then, the SQP algorithm was introduced to simultaneously reconstruct the absorption coefficient and thermal conductivity coefficient distributions in the medium. The TWRI-SQP technique absorbs the advantages of fast identification of defects by TWRI technique and the accurate reconstruction of the photothermal properties of the semi-transparent materials by SQP algorithm. The number of internal defects, geometric dimensioning, shape, and photothermal properties can be reconstructed accurately. The results show that this method is practical and robust to detect the photothermal properties of 2D semi-transparent materials with defects.

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Abbreviations

A :

Amplitude of temperature signal, K

B k :

Approximation of Hession matrix

c p :

Specific heat capacity at constant pressure, J·(kg·K)−1

D 0 :

Reference in-phase function

D -90 :

Reference orthogonal function

E :

Reconstruction value

f 0 :

Initial frequency, Hz

f 1 :

End frequency, Hz

f :

Sampling frequency, Hz

F :

Objective function

g :

Gradient matrix of the objective function

h w :

Convective heat transfer coefficient, W·m−2·K−1

I :

Radiative intensity, W·m−2·sr−1

L :

Lagrangian function or size of medium, m

k :

Sampling time, s

M :

Measurement value

M s :

Modulation period

n :

Outward normal vector

N k :

The number of sampling points

N s :

The number of modulation periods

q :

Heat flux, W·m−2

r :

Penalty factor

s :

Spacial position

s :

Transmission direction

S 0 :

In-phase reference output

S -90 :

Orthogonal reference output

T :

Temperature, K

β e :

Extinction coefficient, m−1

β i :

Lagrangian multiplier

γ :

Reflectivity

ε :

Emissivity

κ a :

Absorption coefficient, m−1

κ s :

Scattering coefficient, m−1

λ :

Thermal conductivity, W·(m·K)−1

ρ :

Density, kg·m−3

σ :

Stefan–Boltzmann constant, W·(m−2·K−4)

τ :

Transmissivity

φ :

Phase angle of temperature signal

Φ:

Scattering phase function

a:

Amplitude

c:

Conduction heat transfer

e :

Ambient

r:

Radiative heat transfer

w :

Boundary value

exa:

Exact value

mea:

Measurement value

recon:

Reconstructed value

i :

ith value

s :

Sampling value

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Acknowledgments

The supports of this work by the National Natural Science Foundation of China (Nos. 51976044, 51806047), and National Science and Technology Major Project (2017-V-0016-0069) are gratefully acknowledged. A very special acknowledgment is also made to the editors and referees who make important comments to improve this paper.

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Authors and Affiliations

  1. School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Ju-Qi Zhang, Hong Qi, Shao-Bin Liu, Zhi-Tian Niu, Xiao-Ying Yu & Ya-Tao Ren

  2. Key Laboratory of Aerospace Thermophysics, Ministry of Industry and Information Technology, Harbin, 150001, People’s Republic of China

    Ju-Qi Zhang, Hong Qi, Shao-Bin Liu, Zhi-Tian Niu, Xiao-Ying Yu & Ya-Tao Ren

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Zhang, JQ., Qi, H., Liu, SB. et al. Research on Modulated Thermal Wave Radar Imaging Technique for Photothermal Properties of Semi-transparent Materials. Int J Thermophys 41, 63 (2020). https://doi.org/10.1007/s10765-020-02645-4

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