Applied Physics B

, 124:55 | Cite as

Non-destructive testing of ceramic materials using mid-infrared ultrashort-pulse laser

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  1. Mid-infrared and THz Laser Sources and Applications

Abstract

The non-destructive testing (NDT) of ceramic materials using mid-infrared ultrashort-pulse laser is investigated in this study. The discrete ordinate method is applied to solve the transient radiative transfer equation in 2D semitransparent medium and the emerging radiative intensity on boundary serves as input for the inverse analysis. The sequential quadratic programming algorithm is employed as the inverse technique to optimize objective function, in which the gradient of objective function with respect to reconstruction parameters is calculated using the adjoint model. Two reticulated porous ceramics including partially stabilized zirconia and oxide-bonded silicon carbide are tested. The retrieval results show that the main characteristics of defects such as optical properties, geometric shapes and positions can be accurately reconstructed by the present model. The proposed technique is effective and robust in NDT of ceramics even with measurement errors.

List of symbols

A

Set of all restriction

b

Weight coefficient

c

Speed of light (m/s)

ci

Restriction

d

Search direction

f

Parameter of DRIFD phase function

E

Set of equality restriction

F

Objective function

g

Parameter of H–G phase function

H

Heaviside step function or approximation of the Hessian

I

Radiative intensity, W/(m2 sr)

k

Iteration number

L

Size of medium

m

Number of restriction

me

Number of equality restriction

min

Minimize

n

Refractive index

\({\mathbf{n}}\)

Normal vector

N

Number of grid or set of all neighboring pixel pairs

NN

Total number of the parameter to be reconstructed

Number of discretized direction

p

Sharpness parameter

r

Penalty factor

\({\mathbf{r}}\)

Position

R

Emerging radiative intensity

s0

Transmission distance of the collimated intensity

s.t.

Subject to

S

Source term (W/m3)

t

Time (s)

tp

Pulse width of laser (s)

ui

Lagrangian multiplier in SQP

w

Directional weight

x

Parameter to be reconstructed or coordinate in x direction (m)

y

Coordinate in y direction (m)

Greeks symbols

α

Search step size

β

A positive value

βe

Extinction coefficient (m−1)

δ

Dirac’s delta function

ε

Convergence accuracy

Δt

Time step (s)

Δx

Grid size in x direction

Δy

Grid size in y direction

η

Directional cosines of y direction

ϑ

Scale parameter

κa

Absorption coefficient (m−1)

κs

Scattering coefficient (m−1)

λi

Lagrangian multiplier in adjoint model

\(\varvec{\Omega}\)

Scattering direction

\({\varvec{\Omega}^\prime }\)

Incident direction

υ

A small positive value

ξ

Directional cosines in x direction

\(\Re\)

Regularization term

Subscripts

bck

Back scattering

est

Estimated value

exa

Exact value

c

Collimated value or central point

d

Diffused value

D

Computational domain

DIFF

Diffraction-dominated

DIF RER

Diffusely reflective

hg

Henyey–Greenstein

is

Isotropically scattering

l

lth discretized direction

∂D

Boundary of computational domain

m

mth discretized direction

max

The maximum value

p

Penalty function

t

Time

u

Neighboring position

v

Neighboring position

x

x direction

y

y direction

xu

Upstream position in x direction

yu

Upstream position in y direction

Notes

Acknowledgements

The supports of this work by the National Natural Science Foundation of China (No. 51576053) is gratefully acknowledged. A very special acknowledgement also to the editors and referees who made important comments to improve this paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Energy Science and EngineeringHarbin Institute of TechnologyHarbinPeople’s Republic of China

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