The refractive index and absorption coefficient fields in participating media are reconstructed simultaneously in this work. In the direct model, the coupled radiation–conduction heat transfer in participating media exposed to a pulse laser irradiation is solved by finite volume method (FVM). In the inverse model, the sequential quadratic programming (SQP) algorithm combined with the generalized Gaussian Markov random field (GGMRF) model is employed to solve the reconstruction problem. It is found that the refractive index and absorption coefficient fields cannot be reconstructed simultaneously. A secondary reconstruction technique based on different regularization parameters is proposed to reconstruct the refractive index and absorption coefficient fields simultaneously. All the retrieval results indicate that the proposed secondary reconstruction technique performs accurately and effectively.

References

References
1.
Asrar
,
G.
,
Myneni
,
R. B.
, and
Choudhury
,
B. J.
,
1992
, “
Spatial Heterogeneity in Vegetation Canopies and Remote Sensing of Absorbed Photosynthetically Active Radiation: A Modeling Study
,”
Remote Sensing Environ.
,
41
(
2–3
), pp.
85
103
.
2.
Tyshchenko
,
V. A.
,
Shabalina
,
T. N.
,
Sheikina
,
N. A.
, and
Diskina
,
D. E.
,
2003
, “
Radiation Stability of Low-Viscosity Base Oils for Aerospace Engineering Control Systems
,”
Chem. Technol. Fuels Oils
,
39
(
3
), pp.
141
144
.
3.
Felske
,
J. D.
, and
Ku
,
J. C.
,
1992
, “
A Technique for Determining the Spectral Refractive Indices, Size, and Number Density of Soot Particles From Light Scattering and Spectral Extinction Measurements in Flames
,”
Combust. Flame
,
91
(
1
), pp.
1
20
.
4.
Suzuki
,
M.
,
Nishiura
,
K.
,
Masunaka
,
S.
,
Muroi
,
N.
, and
Namura
,
K.
,
2016
, “
Application of High Refractive Index and/or Chromogenic Layers to Control Solar and Thermal Radiations Nanostructured Thin Films IX
,”
Proc. SPIE
,
9929
, p.
99290G
.
5.
Ren
,
Y. T.
,
Chen
,
Q.
,
Qi
,
H.
, and
Ruan
,
L. M.
,
2017
, “
Experimental Comparison of Photothermal Conversion Efficiency of Gold Nanotriangle and Nanorod in Laser Induced Thermal Therapy
,”
Nanomaterials
,
7
(
12
), pp. 1–14.
6.
Siegel
,
R.
, and
Spuckler
,
C. M.
,
1993
, “
Variable Refractive Index Effects on Radiation in Semitransparent Scattering Multilayered Regions
,”
J. Thermophys. Heat Transfer
,
7
(
4
), pp.
624
630
.
7.
Huang
,
Y.
,
Liang
,
X. G.
, and
Xia
,
X. L.
,
2005
, “
Monte Carlo Simulation of Radiative Transfer in Scattering, Emitting, Absorbing Slab With Gradient Index
,”
J. Quant. Spectrosc. Radiat. Transfer
,
92
(
1
), pp.
111
120
.
8.
Huang
,
Y.
,
Xia
,
X. L.
, and
Tan
,
H. P.
,
2003
, “
Radiation Equilibrium Temperature Field in a Gradient Index Medium With Specular Surfaces
,”
Heat Mass Transfer
,
39
(
10
), pp.
835
842
.
9.
Liu
,
L. H.
,
2006
, “
Finite Volume Method for Radiation Heat Transfer in Graded Index Medium
,”
J. Thermophys. Heat Transfer
,
20
(
1
), pp.
59
66
.
10.
Zhao
,
J. M.
, and
Liu
,
L. H.
,
2007
, “
Solution of Radiative Heat Transfer in Graded Index Media by Least Square Spectral Element Method
,”
Int. J. Heat Mass Transfer
,
50
(
13–14
), pp.
2634
2642
.
11.
Zhang
,
Y.
,
Yi
,
H. L.
, and
Tan
,
H. P.
,
2015
, “
Analysis of Transient Radiative Transfer in Two-Dimensional Scattering Graded Index Medium With Diffuse Energy Pulse Irradiation
,”
Int. J. Therm. Sci.
,
87
(
87
), pp.
187
198
.
12.
Zhang
,
Y.
,
Yi
,
H. L.
, and
Tan
,
H. P.
,
2014
, “
The Lattice Boltzmann Method for One-Dimensional Transient Radiative Transfer in Graded Index Gray Medium
,”
J. Quant. Spectrosc. Radiat. Transfer
,
137
(
4
), pp.
1
12
.
13.
Hao
,
J. B.
,
Dong
,
S. K.
, and
Tan
,
H. P.
,
2003
, “
Numerical Simulation of Infrared Radiation Properties of Solid Rocket Engine Exhaust Plume
,”
J. Infrared Millimeter Waves
,
22
(
4
), pp.
246
250
.http://en.cnki.com.cn/Article_en/CJFDTOTAL-HWYH200304001.htm
14.
Sun
,
Y. P.
,
Lou
,
C.
, and
Zhou
,
H. C.
,
2011
, “
Estimating Soot Volume Fraction and Temperature in Flames Using Stochastic Particle Swarm Optimization Algorithm
,”
Int. J. Heat Mass Transfer
,
54
(
1–3
), pp.
217
224
.
15.
Affonce
,
D. A.
, and
Fowler
,
A. J.
,
2002
, “
The Effect of Thermal Lensing During Selective Photothermolysis
,”
J. Quant. Spectrosc. Radiat. Transfer
,
73
(
2–5
), pp.
473
479
.
16.
Namjoo
,
A.
,
Sarvari
,
S. M. H.
,
Lemonier
,
D.
, and
Dez
,
V. L.
,
2010
, “
Estimation of Arbitrary Refractive Index Distribution in a One Dimensional Semitransparent Graded Index Medium
,”
International Symposium on Radiative Transfer
, Antalya, Turkey, June 13–19.
17.
Henke
,
L.
,
Piunno
,
P. A. E.
,
Nagy
,
N.
,
Wust
,
C. C.
, and
Krull
,
U. J.
,
2001
, “
Rapid and Simple Technique for the Determination of the Refractive Index of Ultra-Thin Organic Films on Planar Transparent Substrates Using Forward Light Scatter
,”
Anal. Chim. Acta
,
433
(
1
), pp.
31
45
.
18.
Nihei
,
E.
, and
Shimizu
,
S.
,
2007
, “
Determination of the Refractive Index Profile of Polymer Optical Fiber Preform by the Transverse Ray Tracing Method
,”
Opt. Commun.
,
275
(
1
), pp.
14
21
.
19.
Wei
,
L. Y.
,
Qi
,
H.
,
Ren
,
Y. T.
, and
Ruan
,
L. M.
,
2016
, “
Application of Stochastic Particle Swarm Optimization Algorithm to Determine the Graded Refractive Index Distribution in Participating Media
,”
Infrared Phys. Technol.
,
79
, pp.
74
84
.
20.
Verma
,
S.
, and
Balaji
,
C.
,
2007
, “
Multi-Parameter Estimation in Combined Conduction–Radiation From a Plane Parallel Participating Medium Using Genetic Algorithms
,”
Int. J. Heat Mass Transfer
,
50
(
9–10
), pp.
1706
1714
.
21.
Chopade
,
R.
,
Agnihotri
,
E.
,
Singh
,
A. K.
,
Kumar
,
A.
,
Uppaluri
,
R.
,
Mishra
,
S.
, and
Mahanta
,
P.
,
2011
, “
Application of a Particle Swarm Algorithm for Parameter Retrieval in a Transient Conduction-Radiation Problem
,”
Numer. Heat Transfer, Part A: Appl.
,
59
(
9
), pp.
672
692
.
22.
Zhang
,
B.
,
Qi
,
H.
,
Ren
,
Y. T.
,
Sun
,
S. C.
, and
Ruan
,
L. M.
,
2014
, “
Inverse Transient Radiation Analysis in One-Dimensional Participating Slab Using Improved Ant Colony Optimization Algorithms
,”
J. Quant. Spectrosc. Radiat. Transfer
,
133
(
2
), pp.
351
363
.
23.
Sun
,
S. C.
,
Qi
,
H.
,
Sun
,
J. P.
,
Ren
,
Y. T.
, and
Ruan
,
L. M.
,
2017
, “
Estimation of Thermophysical Properties of Phase Change Material by the Hybrid SSO Algorithms
,”
Int. J. Therm. Sci.
,
120
, pp.
121
135
.
24.
Boggs
,
P. T.
, and
Tolle
,
J. W.
,
1995
, “
Sequential Quadratic Programming
,”
Acta Numer.
,
4
(
4
), pp.
1
51
.
25.
Hu
,
J. L.
,
Wu
,
Z.
,
Mccann
,
H.
,
Davis
,
L. E.
, and
Xie
,
C. G.
,
2005
, “
Sequential Quadratic Programming Method for Solution of Electromagnetic Inverse Problems
,”
IEEE Trans. Antennas Propag.
,
53
(
8
), pp.
2680
2687
.
26.
Kim
,
H. K.
, and
Hielscher
,
A. H.
,
2009
, “
A PDE-Constrained SQP Algorithm for Optical Tomography Based on the Frequency-Domain Equation of Radiative Transfer
,”
Inverse Probl.
,
25
(
1
), p.
015010
.
27.
Feng
,
D.
, and
Pulliam
,
T. H.
,
1995
, “
An All-at-Once Reduced Hessian SQP Scheme for Aerodynamic Design Optimization
,” NASA Ames Research Center, Mountain View, CA, Report Nos. NASA-CR-201068, NAS 1.26:201068, RIACS-95-19.
28.
Qi
,
H.
,
Qiao
,
Y. B.
,
Ren
,
Y. T.
,
Shi
,
J. W.
,
Zhang
,
Z. Y.
, and
Ruan
,
L. M.
,
2016
, “
Application of the Sequential Quadratic Programming Algorithm for Reconstructing the Distribution of Optical Parameters Based on the Time-Domain Radiative Transfer Equation
,”
Opt. Express
,
24
(
21
), p.
24297
.
29.
Scott
,
E. P.
, and
Beck
,
J. V.
,
1989
, “
Analysis of Order of the Sequential Regularization Solutions of Inverse Heat Conduction Problems
,”
ASME J. Heat Transfer
,
111
(
2
), pp.
218
224
.
30.
Dowding
,
K. J.
, and
Beck
,
J. V.
,
1999
, “
A Sequential Gradient Method for the Inverse Heat Conduction Problem (IHCP)
,”
ASME J. Heat Transfer
,
121
(
2
), pp.
300
306
.
31.
Dennis
,
B. H.
,
Dulikravich
,
G. S.
, and
Yoshimura
,
S.
,
2004
, “
A Finite Element Formulation for the Determination of Unknown Boundary Conditions for Three-Dimensional Steady Thermoelastic Problems
,”
ASME J. Heat Transfer
,
126
(
1
), pp.
110
118
.
32.
Pun
,
W. H.
, and
Jeffs
,
B. D.
,
1995
, “
Shape Parameter Estimation for Generalized Gaussian Markov Random Field Models Used in MAP Image Restoration
,”
Conference on Signals, Systems and Computers
, Pacific Grove, CA, Oct. 30–Nov. 1, pp.
1472
1476
.
33.
Dumont
,
D.
,
Palmeri
,
M.
,
Eyerly
,
S.
, and
Wolf
,
P.
,
2014
, “
Feasibility of Using a generalized-Gaussian Markov Random Field Prior for Bayesian Speckle Tracking of Small Displacements
,”
Ultrasonics Symposium
, Chicago, IL, Sept.3–6, pp.
1845
1848
.
34.
Babacan
,
S. D.
,
Molina
,
R.
, and
Katsaggelos
,
A. K.
,
2008
, “
Generalized Gaussian Markov Random Field Image Restoration Using Variational Distribution Approximation
,”
IEEE International Conference on Acoustics
, pp.
1265
1268
.
35.
Chai
,
J. C.
,
Lee
,
H. O. S.
, and
Patankar
,
S. V.
,
1994
, “
Finite Volume Method for Radiation Heat Transfer
,”
J. Thermophys. Heat Transfer
,
8
(
3
), pp.
419
425
.
36.
Liu
,
L. H.
, and
Tan
,
H. P.
,
2004
, “
Transient Temperature Response in Semitransparent Variable Refractive Index Medium Subjected to a Pulse Irradiation
,”
J. Quant. Spectrosc. Radiat. Transfer
,
83
(
3–4
), pp.
333
344
.
37.
Qiao
,
Y. B.
,
Qi
,
H.
,
Zhao
,
F. Z.
, and
Ruan
,
L. M.
,
2016
, “
Accurate Reconstruction of the Optical Parameter Distribution in Participating Medium Based on the Frequency-Domain Radiative Transfer Equation
,”
Chin. Phys. B
,
25
(
12
), pp.
144
152
.http://iopscience.iop.org/article/10.1088/1674-1056/25/12/120201/meta
38.
Hansen
,
P. C.
,
1999
, “
The L-Curve and Its Use in the Numerical Treatment of Inverse Problems
,”
Computational Inverse Problems in Electrocardiology
, WIT Press, Ashurst, UK, pp.
119
142
.
You do not currently have access to this content.