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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
Wouter.saeys@kuleuven.be
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
Introduction
Light propagation in turbid media
4
Absorption
Scattering
Incident light
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
Anisotropy factor g
Particle << wavelengthAnisotropy = 0Isotrope scattering
Particle ≈ wavelengthAnisotropy ≈ 0.6
Particle > wavelengthAnisotropy → 1
6
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
Research hypothesis
Composition
Microstructure
Absorptionµa
Scatteringµs & g
Light propagation
R(t,r)
T(t,r)
Inverse light
propagationmodels
Chemometrics
Inverse microscale
light propagation
models
Bulk optical propertiesFrom optical measurements to BOP
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
Double integrating spheres set-upMonochromator
550 – 2250 nm
Aernouts et al., Opt. Express 21 (2013)
Total reflection
Total transmission
Unscatteredtransmission
11
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
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
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)
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)
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
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)
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
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
Particle size distribution estimationFrom scattering spectra to PSD
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]
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
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
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
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
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+
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
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
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
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
Applications• Link to product properties and quality attributes
o Viscosity, creaming, mouth feeling/creaminess perception, nutrient uptake...
• Quality monitoring during production and storage
31
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
32
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
Questions?Contact:www.biophotonics.beWouter.saeys@kuleuven.be
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