optical characterization of the composition and ...€¦ · estimate bop from srs data • forward...
TRANSCRIPT
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Optical characterization of the composition and scatterer size distributions of turbid
liquids from Vis/NIR spectroscopy
W. Saeys, A. Postelmans, R. Watté, R. Van Beers, B. Aernouts
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Overview• Introduction
• From optical measurements to bulk optical propertieso Double integrating sphereso Spatially resolved spectroscopy
• From scattering spectra to particle size distributiono Shape dependento Shape independento Case study polystyrene particles
• Conclusions 2
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Introduction
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Light propagation in turbid media
4
Absorption
Scattering
Incident light
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Bulk scattering and absorption coefficient• Bulk absorption coefficient µa
o Probability of photon absorption per unit infinitesimal pathlength
• Bulk scattering coefficient µso Probability of photon scattering per unit infinitesimal pathlengtho Non-linear effect on light extinction
5
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Anisotropy factor g
Particle << wavelengthAnisotropy = 0Isotrope scattering
Particle ≈ wavelengthAnisotropy ≈ 0.6
Particle > wavelengthAnisotropy → 1
6
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Optical properties and product characteristics• Why interest in bulk optical properties? Related to emulsion/suspension characteristics
Bulk optical properties
Chemical
Physical
µa
µs
Chemical composition
Particle size distributionVolume fraction
7
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Research hypothesis
Composition
Microstructure
Absorptionµa
Scatteringµs & g
Light propagation
R(t,r)
T(t,r)
Inverse light
propagationmodels
Chemometrics
Inverse microscale
light propagation
models
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Bulk optical propertiesFrom optical measurements to BOP
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BOP from optical measurements• Calculate BOP from multiple (uncorrelated) measurements
Reflectance & transmittance
o Double integrating spheres (DIS)
o Unscattered transmission (UT)
Multiple distances from
light source
o Spatially resolved spectroscopy (SRS)
10
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Double integrating spheres set-upMonochromator
550 – 2250 nm
Aernouts et al., Opt. Express 21 (2013)
Total reflection
Total transmission
Unscatteredtransmission
11
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Inverse adding-doubling (IAD)• Find optical properties that correspond to measured
reflection and transmission
• 3 optical measurementso Diffuse reflectiono Diffuse transmissiono Unscattered transmission
• Iterative process
µaµsg
µaµs’
12
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Inverse adding-doubling (IAD)Initial guess
BOP
Calculate reflection + transmission
Update BOP
Calculated vs. measuredMatch?
BOP found
Thin slabKnown BOP, reflection, transmission
Adding or Doubling
Correct thickness?
Reflection + transmission found
Summing reflections and transmission contributions
ADDING-DOUBLING
13
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Example: optical phantoms
14
Intralipide concentratie
Met
hy
leen
bla
uw
co
nce
ntr
atie
A B C D E F G IL
8
7
6
5
4
3
2
1
Intralipid concentration
Met
hyle
nebl
ue c
once
ntra
tion
Aernouts et al., Opt. Express 21 (2013)
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15
IAD
500 1000 1500 20000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Wavelength (nm)
Dif
fuse
ref
lect
ance
M
R
(*1
00
%)
(a)
A*
G*
500 1000 1500 20000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Wavelength (nm)
Dif
fuse
ref
lect
ance
M
R
(*1
00
%)
(b)
A*
G*
500 1000 1500 20000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Wavelength (nm)
To
tal
tran
smit
tan
ce
MT
(*1
00
%)
(a)
A*
G*
500 1000 1500 20000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Wavelength (nm)
To
tal
tran
smit
tan
ce
MT
(*1
00
%)
(b)
A*
G*
500 1000 1500 20000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Wavelength (nm)
Un
scat
tere
d t
ran
smit
tan
ce
MU
(*
10
0%
)
(a)
A*
G*
500 1000 1500 20000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Wavelength (nm)
Un
scat
tere
d t
ran
smit
tan
ce
MU
(*
10
0%
)
(b)
A*
G*
500 550 600 650 700 7500
2
4
6
8
10
12
14
Wavelength (nm)
µa (
cm-1
)
(a)
*1
*2
*3
*4
*5
*6
*7
*8
500 550 600 650 700 7500
2
4
6
8
10
12
14
Wavelength (nm)
µa (
cm-1
)
(b)
*1
*2
*3
*4
*5
*6
*7
*8
500 1000 1500 20000
50
100
150
200
Wavelength (nm)
µs (
cm-1
)
(a)
A*
B*
C*
D*
E*
F*
G*
IL
500 1000 1500 20000
50
100
150
200
Wavelength (nm)
µs (
cm-1
)
(b)
A*
B*
C*
D*
E*
F*
G*
IL
500 1000 1500 20000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Wavelength (nm)
An
iso
tro
py
fac
tor
(a)
A*
B*
C*
D*
E*
F*
G*
IL
500 1000 1500 20000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Wavelength (nm)
An
iso
tro
py
fac
tor
(b)
A*
B*
C*
D*
E*
F*
G*
IL
Aernouts et al., Opt. Express 21 (2013)
0 50 100 1500
2
4
6
8
10
12
14
16
Concentration MB cMB
(M)
a (
cm-1
)
(a)
0.55 mm
1.1 mm
a = 0.1071c
MB
0.75 0.8 0.85 0.9 0.95 1
22
24
26
28
30
32
34
36
Volume concentration water w (m
3/m
3)
a (
cm-1
)
(b)
0.55 mm
1.1 mm
a = -15.75 + 48.76
w
R² = 0.996 (up to 70 µM)
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Spatially resolved spectroscopy (SRS)• Detectors at multiple distances from light source
• Interaction history is function of distance do Further from light source
• Lower signal• More interaction with tissue
• Intensity profile R(d)
• Possible for dense samples without dilution
d
16
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Estimate BOP from SRS data• Forward light propagation model
o Adding-doubling → no 2D informationo Diffusion approximation → assumptions not valido Monte Carlo simulations → computationally expensiveo Data-based metamodeling approach
• Stochastic Kriging• Train on set of liquid phantoms covering wide range of BOP
17
Watté et al., Opt. Express 21 (2013)
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Wavelength by wavelength
18
• Iterative optical properties estimationo Nelder-Mead optimizer for minimization
• Cost function = sum of squared relative errors
o No assumptions on scattering or absorption profiles used
Watté et al., Opt. Express 21 (2013)
600 800 1000 1200 1400 1600
101
102
Wavelength [nm]
µs' [c
m-1
]
Original µs' profile
Estimated µs' profile
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Constrained optimization• Include expert knowledge: µs’ as parametric function
o Trade-off smoothness - flexibility
• Minimising cost function over entire wavelength range• Construction of ‘information grid’ to select best combination
19
Watté et al., Opt. Express (2016)
𝜇𝑠′ 𝑊𝐿 = 𝑝1. 𝑒𝑥𝑝 𝑝2.𝑊𝐿 + 𝑝3 + 𝑝4.𝑊𝐿 + 𝑝5.𝑊𝐿
2 + 𝑝6.𝑊𝐿3
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Particle size distribution estimationFrom scattering spectra to PSD
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Forward problem• Calculate optical properties for known PSD
0 0.5 1 1.5 2 2.5 30
0.2
0.4
0.6
0.8
1
1.2
1.4
Radius a (µm)
Re
lative
we
igh
t
discrete
continuous
Mie theory
Discretise PSD
+
MICROSCALE
Physical information• Particle size distribution• Volume fraction scatterers• Refractive indices
MACROSCALE
Bulk optical properties• Bulk absorption coefficient• Bulk scattering coefficient• Anisotropy factor
21
0.4 0.6 0.8 1 1.2 1.4 1.6 1.80.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0.022
µs [
µm
-1]
wavelength [µm]
10-1
100
101
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
radius [µm]
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Inverse estimation PSD
Inverse estimation
polydispersePSD
RegularizationShape dependent Assume shape
Shape independent Smoothness condition
22
Scattering spectraµs, µs’ or g
0.4 0.6 0.8 1 1.2 1.4 1.6 1.80.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0.022
µs [
µm
-1]
wavelength [µm]
Particle Size Distribution (PSD)Volume fraction
10-1
100
101
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
radius [µm]
Mathematical solutions Non-negative
solutions Conform literature/ measurements
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Shape dependent PSD estimation
23
• Assume probability density functiono Monomodal: PSD = logn(μ1,σ1)
o Bimodal: PSD = scale . logn(μ1,σ1) + (1-scale) . logn(μ2,σ2)
• Robust against noise• Limited flexibility
10-2
10-1
100
101
0
0.1
0.2
0.3
0.4
0.5
0.6
radius [µm]
(vo
lum
e b
ase
d)
10-2
10-1
100
101
0
0.1
0.2
0.3
0.4
0.5
0.6
radius [µm]
(vo
lum
e b
ase
d)
Estimate parameter values and volume fraction
Minimize sum of relative least squared errors
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Shape independent PSD estimation• Approximate PSD by weighted sum of splines
• Find B-spline weights
o Calculate volume fraction from weights
B-spline basis
Weighted sum B-splines
24
10-2
10-1
100
101
0
0.1
0.2
0.3
0.4
0.5
0.6
radius [µm]
(vo
lum
e b
ase
d)
10-3
10-2
10-1
100
101
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
radius [µm]
𝜇𝑠 𝜆 =
𝑟𝑚𝑖𝑛
𝑟𝑚𝑎𝑥
𝑃𝑆𝐷 𝑟 . 𝜎𝑠 𝑟, 𝜆 𝑑𝑟 =
𝑟𝑚𝑖𝑛
𝑟𝑚𝑎𝑥
𝑗=1
𝑁𝐵
𝑤𝑗 . 𝐵𝑗 𝑟 . 𝜎𝑠 𝑟, 𝜆 𝑑𝑟 =
𝑗=1
𝑁𝐵
𝑤𝑗 . 𝜇𝑠,𝑗 𝜆
Number of splines
Particle radius range
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Shape independent PSD estimation• Tikhonov regularization
o Non-negative least squares
• Chahine algorithmo Iterative update spline weights
µs = ∑ wi . µs, spline i Non-smoothness penalty
γ: regularization parameter,strength of penalty
L: regularization matrix,discrete 2nd derivative
• More flexible• Less robust,
regularization needed
25
𝑤𝑗𝑝+1= 𝑤𝑗𝑝.𝜇𝑠, 𝑚𝑒𝑎𝑠 𝜆𝑗
𝜇𝑠, 𝑐𝑎𝑙𝑐𝑝𝜆𝑗
min 𝐴𝑤 − 𝜇𝑠2 𝑤 ≥ 0+𝛾 𝐿𝑤 2,
10-1
100
101
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
radius [µm]
(vo
lum
e b
ase
d)
reference
estimated
0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
0.005
0.01
0.015
0.02
0.025
wavelength [µm]
µs [
µm
-1]
input
estimated
spline 17
spline 22
spline 23
spline 24
spline 25
spline 28
spline 29
0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
0.005
0.01
0.015
0.02
0.025
wavelength [µm]
µs [
µm
-1]
input
estimated
spline 22
spline 23
spline 24
spline 25
10-1
100
101
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
radius [µm]
(vo
lum
e b
ase
d)
reference
estimated
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Case study polystyrene particles
26
Input PSD BOPForward
simulation Add noise
Input scattering spectrum Estimated PSD
Inverse estimation
Estimated BOP
DIS + UT500-1850 nm
IAD BOP
Laser diffractionDLS
Check
Check
Measured data
Simulated data
Reference PSD
Measured BOP+
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Results polystyreneMonomodal shape dependent
27
1 1.5 3 50
2
4
6
8
10
12
radius [µm]
(vo
lum
e b
ase
d)
3µm reference
= 1.5015 = 0.043472
6µm reference
= 3.1259 = 0.066031
10µm reference
= 4.9887 = 0.20495
0.5 0.6 0.7 0.8 0.9 12
3
4
5
6
7
8
9
10x 10
-3
µs [
µm
-1]
wavelength [µm]
3µm input, VF = 0.005
3µm estimated, VF = 0.0047072
6µm input, VF = 0.0075
6µm estimated, VF = 0.010936
10µm input, VF = 0.0075
10µm estimated, VF = 0.0070289
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Results polystyreneMonomodal shape dependent
0.6 0.8 1 1.2 1.4 1.6 1.80.65
0.7
0.75
0.8
0.85
0.9
0.95
1
g [
-]
wavelength [µm]
1µm input, VF = 0.75%
1µm estimated
10-1
100
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
radius [µm]
(vo
lum
e b
ase
d)
1µm reference
= 0.50673 = 0.083152
28
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Results simulated fat in waterBimodal shape dependent bimodal
29
0.5 1 1.5
4
5
6
7
8
9
10
11
x 10-4
µs' [
µm
-1]
wavelength [µm]
0.5 1 1.5
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0.022
0.024
µs [
µm
-1]
wavelength [µm]
60s input
60s estimated
bimod input
bimod estimated
10-2
10-1
100
101
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
radius [µm]
(vo
lum
e b
ase
d)
60s reference
60s estimated
bimod reference
bimod estimated
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Results simulated fat in waterShape independent
30
0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
0.005
0.01
0.015
0.02
0.025
wavelength [µm]
µs [
µm
-1]
Raw reference
Raw estimated
120s reference
120s estimated
480s reference
480s estimated
bimod reference
bimod estimated
10-3
10-2
10-1
100
101
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
radius [µm]
(vo
lum
e b
ase
d)
Raw reference
Raw estimated
120s reference
120s estimated
480s reference
480s estimated
bimod reference
bimod estimated
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Applications• Link to product properties and quality attributes
o Viscosity, creaming, mouth feeling/creaminess perception, nutrient uptake...
• Quality monitoring during production and storage
31
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Conclusions• Accurate determination of bulk optical properties from
o Reflectance & transmittance data• DIS + UT
o Multiple reflectance measurements• SRS
• Use of BOP for characterizing emulsions/suspensionso Absorption: chemical compositiono Scattering: PSD, volume fraction scatterers
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Conclusions
33
• PSD estimation from Vis/NIR bulk scattering spectra
• Shape dependent methodo Good estimation if correct choice of probability density
function
• Shape independent methodo Flexible, but more prone to artefactso Good estimation if good regularization and choice B-
spline basis
• Opportunities for (on-line) optical determination of microphysical emulsion/suspension quality
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Questions?Contact:[email protected]