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Simultaneous reconstruction of space-dependent optical and thermophysical parameter fields based on a laser irradiation technique

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Abstract

A secondary reconstruction technique based on multi-section reconstruction is proposed to simultaneously reconstruct the space-dependent absorption coefficient, scattering coefficient, and thermal conductivity fields without any priori information in the participating medium. In the forward model, the finite volume method (FVM) is used to solve the coupled radiative–conductive problem. The radiative and temperature signals on one side of the medium boundary induced by laser irradiation heating are served as input measurements for the inverse analysis. In the inverse model, the sequential quadratic programming (SQP) algorithm is employed to solve the optimization problems. By this technique, more measurement signals can be obtained, which is necessary for exactly reconstructing the space-dependent optical and thermophysical parameters fields. All the retrieval results show that the proposed secondary reconstruction technique based on multi-section reconstruction can be adopted to reconstruct the complex space-dependent absorption coefficient, scattering coefficient, and thermal conductivity fields accurately and efficiently. This proposed technique will play an important role in practical application, such as non-destructive testing of materials, biology imaging in clinical medicine and optimization and design of composites.

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Abbreviations

B k :

The approximate hessian matrix

c i(x):

The restriction

c p :

Specific heat, J/(kg K)

F obj(x):

Objective function

h :

Convective heat transfer coefficient, W/(m2 K)

I :

Radiative intensity, W/(m2 sr)

L(x :

λ), The lagrangian function

L :

The geometric thickness, m

m :

The amount of equality and inequality constraints

m e :

The amount of equality restrictions

N :

The total number of the reconstruction parameters

n w :

Outward normal vector on the boundary

q laser :

Laser power density, W/m2

q r :

Radiative heat flux, W/m2

t :

Time, s

T :

Temperature, K

Ts :

Ambient temperature, K

Tw :

Boundary temperature, K

x :

The parameters to be estimated

α w :

The boundary absorptivity

γ w :

The boundary transmissivity

ε w :

The wall emissivity

κ a :

The absorption coefficient, m−1

κ s :

The scattering coefficient, m−1

λ :

Thermal conductivity, W/(m K)

ρ :

Density, kg/m3

σ :

Stefan–Boltzmann constant, W/(m2 K4)

Φ:

Scattering phase function

Ω :

Scattering direction

Ω ′ :

Incident direction

cd :

Conduction heat transfer

cv :

Convective heat transfer

est :

The estimated value

exa :

The exact value

mea :

The measured value

r :

Radiative heat transfer

w:

Boundary value

w1 :

The left boundary

w2 :

The right boundary

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Acknowledgements

This work was supported by the project of National Natural Science Foundation of China (grant numbers 51776053). A special thanks goes out to the editors and referees who contributed valuable feedback that helped improve this work. In addition, our sincere gratitude goes to Dr. David Ezekoye from Harbin Institute of Technology for proofreading this paper.

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  1. Key Laboratory of Aerospace Thermophysics of MIIT, School of Energy Science and Engineering, Harbin Institute of Technology, No. 92, West Dazhi Street, Harbin, 150001, Heilongjiang, China

    Pei Zhang, Chuang Sun, **n-Lin **a & Fei Wang

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  1. Pei Zhang
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  2. Chuang Sun
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Correspondence to **n-Lin **a.

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Zhang, P., Sun, C., **a, XL. et al. Simultaneous reconstruction of space-dependent optical and thermophysical parameter fields based on a laser irradiation technique. Appl. Phys. A 128, 514 (2022). https://doi.org/10.1007/s00339-022-05616-8

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