Estimation of bulk optical properties of turbid
media from hyperspectral scatter imaging
measurements: Metamodeling approach
Ben Aernouts,1 Chyngyz Erkinbaev,1 Rodrigo Watté, Robbe Van Beers, Nghia Nguyen
Do Trong, Bart Nicolai, and Wouter Saeys*
KU Leuven, Department of Biosystems, MeBioS, Kasteelpark Arenberg 30, box 2456, 3001, Leuven, Belgium
1
These two authors contributed equally to this work
*Wouter.Saeys@kuleuven.be
Abstract: In many research areas and application domains, the bulk optical
properties of biological materials are of great interest. Unfortunately, these
properties cannot be obtained easily for complex turbid media. In this study,
a metamodeling approach has been proposed and applied for the fast and
accurate estimation of the bulk optical properties from contactless and nondestructive hyperspectral scatter imaging (HSI) measurements. A set of
liquid optical phantoms, based on intralipid, methylene blue and water, were
prepared and the Vis/NIR bulk optical properties were characterized with a
double integrating sphere and unscattered transmittance setup. Accordingly,
the phantoms were measured with the HSI technique and metamodels were
constructed, relating the Vis/NIR reflectance images to the reference bulk
optical properties of the samples. The independent inverse validation
showed good prediction performance for the absorption coefficient and the
reduced scattering coefficient, with RP2 values of 0.980 and 0.998, and
RMSEP values of 0.032 cm-1 and 0.197 cm-1. respectively. The results
clearly support the potential of this approach for fast and accurate estimation
of the bulk optical properties of turbid media from contactless HSI
measurements.
© 2015 Optical Society of America
OCIS codes: (170.0110) Imaging systems; (120.3150) Integrating spheres; (160.4760)
Optical properties; (300.1030) Absorption; (290.0290) Scattering.
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____________________________________________________________________
1 Introduction
The propagation of light through biological tissues is an important research topic in the
domain of biomedical optics, serving as a basis for non-destructive in-vivo medical
diagnostics e.g. cancer detection, etc. [1]. With recent advances in optical sensing and the
technology becoming more cost-efficient, these methods draw the attention of food and
agricultural industry for quality assessment of fruits and vegetables, determining moisture
content in food, fat content in meat, etc. [2–5]. Moreover, the development of innovative
optical sensors for rapid, non-destructive and non-contact food quality monitoring would be
promoted once the bulk optical properties (BOP) of such agri-food products can be accurately
measured on the production or sorting line.
When light travels through the sample tissue, two phenomena can occur: absorption of
light by the tissue’s molecules, and light scattering, caused by refractive index mismatches
inside the sample. Light absorption is related to the chemical constituents (e.g., water, protein,
fat, carbohydrates), whereas light scattering is associated with the physical characteristics of
the tissue (e.g., cellular structure, turgor, density) [1]. As these properties define light
propagation in the biological tissue, and accordingly the measured visible (Vis) and nearinfrared (NIR) signals, this could open opportunities for simultaneous extraction of chemical
(composition) and physical (microstructure) information from optical measurements.
However, in a single Vis/NIR spectroscopic measurement, usually reflectance or
transmittance, both the effect of absorption and scattering are indissolubly connected and
cannot be accurately separated. Consequently, a change in the scattering properties of the
measured sample might be misinterpreted as a change in the sample composition and vice
versa. On the other hand, multiple spectroscopic measurements in a slightly different
measurement configuration are influenced by absorption and scattering in a different way. The
combination of these multiple measurement series with an accurate model, which
mathematically describes the Vis/NIR light propagation as a function of the sample’s
absorption and scattering properties, could allow for separation of the BOP. These multiple
spectroscopic measurements can vary in space [6,7], time [8–10] and/or frequency [11,12].
Amongst them, spatially resolved spectroscopy (SRS) is fast, cost-efficient and simple
compared to the others. Moreover SRS can be easily adapted for routine laboratory
measurements [5].
Two types of SRS methods have already been reported: contact [6,7,13] and non-contact
measurements [14–16]. A contact SRS method uses a fiber probe comprised of one or
multiple light illumination fibers and several collection fibers. As the probe is positioned in
contact with the sample, this technique is less applicable for on-line industrial applications,
mainly due to the risk of cross-contamination and the additional time needed for positioning
the probe on the sample. Alternatively, non-contact SRS, which is also known as
hyperspectral scatter imaging (HSI), uses a hyperspectral line-scan camera to capture the
spatially resolved reflectance profile at the position where the sample is illuminated with a
focused white light beam [3,4,17]. Thanks to the contactless character of both the illumination
and the imaging, this technique has more potential for integration in sorting lines (e.g. fruits,
vegetables etc.) in an industrial environment. Therefore, the potential of this SRS technique
for contactless food quality control has recently become a relevant research topic [2,3,17].
In order to estimate the BOP from the acquired optical measurements, the relation between
both needs to be resolved. Light propagation in turbid media can be accurately described by
the radiative transfer theory (RTT) which neglects the wave properties and only considers the
energy transport [18]. However, due to the geometrical complexity of the microstructure and
the phenomenon of multiple light scattering in real biological media, an analytical solution of
the RTT is practically impossible. When the radiance in a homogeneous medium is considered
at a sufficient distance from the illumination point, where the assumption of isotropic radiance
holds, and when scattering is dominant over absorption, the RTT can be approximated with
the diffusion theory [19–21]. However, in the NIR, this last condition is rarely fulfilled for
biological tissues as the absorption by the water molecules generally dominates the scattering.
For these samples, the RTT can be solved numerically based on stochastic Monte Carlo (MC)
simulations. This method has been shown to provide high accuracy for many different sample
geometries and any range of absorption and scattering properties [22,23]. However, to reduce
stochastic noise, the Monte Carlo method requires to simulate the propagation of many
photons, which makes this method very time-consuming. The simulation speed can be further
increased by using modern computers with high computational power, employing parallel
computing approaches [24–26] and/or rescaling originally-simulated photons for each new set
of BOP [27–31]. Nevertheless, despite of these improvements, the required time to accurately
simulate the light propagation for a single set of BOP is still too high. Moreover, depending
on the BOP, and with that the number of simulated photons required for an accurate result, the
minimum time needed for a single forward simulation is still in the order of seconds to
minutes [29,31]. The inverse problem, which links a set of BOP to an optical measurement, is
typically ill-posed, leading to non-uniqueness and possible instability. Therefore, the inverse
problem is generally solved with an iteration over the forward model, independent of the
model type (e.g. MC method, diffusion theory, etc.). Generally, the nonlinear optimizer needs
to evaluate many sets of BOP before convergence is reached. As a result, the inverse MC
method is very time-consuming, taking several minutes for the estimation of each BOP set.
Therefore it is not suitable for fast and on-line practical applications [27,28,31]. Additionally,
following these theoretical light propagation models (e.g. MC methods, diffusion theory, etc.),
the geometric relationships between the detection system (e.g. imaging or probe) and the
sample still needs to be implemented separately. Generally, this relation is not straightforward
and approximations needs to be introduced [17].
To overcome the limitations of the above mentioned theoretical solutions, the use of
metamodels has been proposed to directly link a set of measured SRS profiles to their
respective BOP [13]. Moreover, the metamodels serve as a high-way bridge between the
design space (input parameters: BOP) and the performance space (output parameters: SRS
profiles). Following this approach, the estimation procedure is seriously simplified and more
robust, as both the light propagation characteristic as well as the measurement geometry is
correctly accounted for in a single forward model. Dam et al. [32] used polynomial regression
to relate SRS profiles measured with a contact probe to their respective BOP. Nevertheless,
due to the simplicity of the models, their methodology was only accurate for a very small
range of absorption and scattering properties, which translates into a small wavelengthwindow for samples with limited variability. Other researchers used neural network, trained
on the SRS profiles simulated with the MC method, to avoid the time-intensive MC
simulations in future calculations [27,33]. The major drawback of these computationally fast
neural networks is their incapability of correctly handling the stochastic noise present in
Monte Carlo results or the instrumental noise typical for SRS measurement. Moreover, as the
noise is incorporated into the neural network, it will influence the simulated output and
consequently the inverse estimation process. In contrast, stochastic data-based surrogate
models can handle noise which is typical for measurements or data simulated with stochastic
techniques. Moreover, they can solve non-linear, intensive design problems with minimal
computational effort, resulting into an efficient model which enables tasks such as
visualization, design space exploration, sensitivity analysis and optimization [34–38].
Therefore, this metamodeling approach can be used as a computationally efficient method to
estimate the BOP from SRS profiles [13]. Moreover, in a previous study, this approach has
been successfully tested to link the BOP of a designed set of optical phantoms to their
respective SRS profiles, measured with a reflectance probe which was in contact with the
samples [13].
The main objective of the current study is to evaluate the performance of the surrogate
metamodels if trained on hyperspectral scatter images. Due to the fundamentally different
measurement geometry (e.g. collection angle, etc.) compared to a contact probe, the SRS
profiles generated with this contactless technique are significantly different [17]. The
metamodels should take this into account, without resorting to approximations generally used.
The novelty of this research can be found in the use of (1) a contactless technique to measure
the SRS profiles, in combination with (2) stochastic data-based surrogate metamodels which
were trained on (3) a designed set of optical phantoms, to finally derive the BOP of turbid
samples. To the best of our knowledge, this research presents the first time a hyperspectral
imaging technique is used to estimate the BOP without resorting to the diffusion theory [2–
4,17].
The developed metamodels were evaluated with respect to the prediction of SRS profiles
from provided BOP (forward validation), as well as its performance in combination with an
iterative optimization routine (inverse validation). The latter allows for the estimation of the
sample’s BOP from contactless HSI measurements. Double integrating sphere (DIS) and
unscattered transmittance measurements, in combination with the inverse adding-doubling
(IAD) routine, were used to obtain the reference BOP needed for model construction and
validation.
2 Materials and methods
2.1 Liquid phantoms
Liquid optical phantoms were prepared as aqueous mixtures of a scattering component:
Intralipid 20% (Fresenius Kabi, Sweden), and a water-soluble absorbing dye: methylene blue
(Sigma Aldrich, Belgium). Methylene blue (MB) is a non-scattering dye which allows for
independent design of the scattering and absorption properties. Moreover, MB has a clear and
sharp absorption peak in the considered wavelength range, making it easier to interpret the
effects of scattering and absorption on the measured diffuse reflectance spectra.
In total, sixteen liquid phantoms were prepared by mixing four concentrations of the
absorber (0, 0.74, 1.48 and 2.22 ml of a 400 µM stock solution of MB) with four
concentrations of the scatterer (2, 4, 6 and 8 ml of the Intralipd 20% solution). The mixtures
were diluted with distilled water to obtain phantoms of 100 ml. Sixteen prepared phantoms
were labeled with a letter and a number, in which an increasing letter (A, B, C and D)
indicates an increasing scattering level, while an increasing number (1, 2, 3 and 4)
corresponds to an increasing absorption level. The phantoms were thoroughly mixed before
taking an aliquot of the sample for measuring in the DIS and unscattered transmittance
measurement system. The phantoms were carefully mixed and allowed to rest before scanning
by the HSI system.
2.2 Reference bulk optical properties of liquid phantoms
A pre-dispersive double integrating sphere (DIS) and unscattered transmittance setup was
used to acquire the diffuse reflectance and total and unscattered transmittance of the sample
slabs. These measurements are considered to be the ‘golden standard’ to estimate the BOP for
turbid media [39–41]. The sample was illuminated with a wavelength-tunable laser setup,
especially designed to obtain high signal-to-noise spectra in the 550 – 2250 nm wavelength
range [39,42]. Diffuse reflectance and total transmittance were measured simultaneously with
detectors mounted on the wall of two integrating spheres, positioned respectively in front and
behind the cuvette which was filled with the sample. An integrating spheres is a hollow
spherical cavity with its interior covered with a diffuse reflective coating to obtain the total
power coming from the sample in a single measurement, independent of the original direction
and spatial information of the light. The unscattered transmittance, on the other hand, was
measured in a separate path with the detector positioned 1.5 m behind the sample and a series
of slits placed in between to limit the fraction of scattered photons collected [41,43]. For a
more extensive description of the measurement setup, the calibration and measurement
procedure and a thorough validation, the reader is referred to Aernouts et al. [39]. Moreover,
this extensive validation study illustrates the high repeatability and signal-to-noise ratio (SNR)
of the system to obtain the Vis/NIR BOP for very turbid samples [39].
The liquid phantom samples were carefully pipetted into a custom made cuvette with
borosilicate glass walls of 1.1 mm thickness (Borofloat 33®, Schott, Germany) with 1 mm
path length and the cuvette was placed into the sample holder. Measurements were performed
only in the 550 – 950 nm spectral range with an interval step of 5 nm, because the HSI setup
is limited to this range. Each liquid phantom sample was measured in three random ordered
replicates and the cuvette was thoroughly cleaned after each measurement to avoid associated
errors.
The BOP (µa and µs’) were derived from the diffuse reflectance and total and unscattered
transmittance measurements, following the inverse adding-doubling (IAD) routine [41,44]. In
the adding-doubling (AD) method, the RTT is used to calculate the total reflectance and
transmittance for a single ‘infinitesimally’ thin sample layer for which the single scattering
assumption is fulfilled. This plane-parallel layer is then ‘doubled’ and the reflectance and
transmittance of the doubled layer are calculated. This process of doubling is repeated until
the desired thickness of the homogeneous sample is reached. Different layers (e.g., glass
slides, etc.) can be ‘added’, together with their contributions, taking into account internal
reflections at the boundaries [42]. The AD method allows to calculate the diffuse reflectance
and total and unscattered transmittance very accurately, while maintaining a high degree of
flexibility and time efficiency [44]. However, as the forward method calculates the reflectance
and transmittance for a tissue layer with known bulk optical properties, it has to be inverted to
allow extraction of the bulk absorption (μa) and reduced scattering coefficients (μs’) from the
measured spectra. Moreover, these BOP, which are the inputs for the AD method, are
iteratively changed until the simulated reflectance and transmittance values match with the
measured ones [42,44]. As the method needs to compensate for the specular reflectance at the
sample-cuvette and cuvette-air boundaries, the wavelength-dependent refractive indices of the
cuvette glass and sample are required. Refractive index information for the cuvette windows
was provided by the manufacturer (Schott, Germany), while the refractive index of the
intralipid phantoms was calculated with the formula for lipid particles in water [45]. The
reference BOP for the three replicates of each phantom, acquired with IAD from DIS and
unscattered transmittance measurements, were averaged and used as input for the metamodel
and for the validation.
2.3 Hyperspectral scatter imaging
A HSI setup was developed for contactless acquisition of spatially resolved reflectance
profiles in the wavelength range from 400 to 950 nm. The system has four main units: a
hyperspectral camera system, a sample presentation unit, a light source and a computer.
The hyperspectral camera system consists of a high performance 12-bit panchromatic
CCD camera (TXG14NIR, Baumer, Germany), a prism-grating-prism based imaging
spectrograph (ImSpector V10, Spectral Imaging Ltd., Oulu, Finland) and a 12.5 – 75 mm
focusing lens with f/1.8 (Cosmicar, Pentax, Japan). The camera has an optical sensitivity from
400 to 950 nm, 1392 by 1040 effective pixel image resolution and is based on GigE Vision®
fast Ethernet data transfer. The imaging spectrograph covers the spectral range from 400 to
1000 nm with a resolution of 9 nm, which is well-compatible with the sensitivity of the
camera.
Fig. 1 Schematic illustration of the hyperspectral scatter imaging system.
The light source unit consists of a quartz tungsten halogen lamp (Alphabright, East Sussex,
UK) generating broadband light (300 – 1550 nm) with 20 W electrical power and 280 lumen
flux. The light is coupled into a 200 μm optical fiber (FC-IR200-1.5, Avantes, Eerbeek, The
Netherlands) ending on a 74-VIS collimating lens (Ocean Optics, Duiven, The Netherlands)
with 350 – 2000 nm range. The lens focuses the light onto the sample surface as a spot of 1.0
mm diameter at 7.5 cm distance, under an angle of 15° with respect to the vertical axis to
avoid measuring the specular reflection of light. This angle was chosen as small as possible,
based on the design of the HSI system. Moreover, it was confirmed that the influence of this
angle on the symmetry of the captured images is negligible [46].
The sample presentation consists of an X-Y-Z axis metric stage (Edmund Industrial
Optics, NJ, USA) mounted on a breadboard (Thorlabs, NJ, USA). This unit allows to
precisely position the sample during each measurement to ensure an accurate height (13.5 cm)
distance between sample surface and the camera lens of the measurement system. A schematic
illustration of the entire HSI setup is presented in Fig. 1. The hyperspectral imaging system
was placed in a dark chamber to exclude the effects of ambient light during the measurements.
The HSI system was spectrally and spatially calibrated as described in [4]. Each phantom
was measured ones. For each pixel in the scanned line, the light diffusively reflected by the
sample is focused by the zoom lens onto the slit (80 µm width) of the spectrograph which
disperses it into its different wavelength components. This light is further projected onto a
pixel line of the CCD detector. The hyperspectral image of 696×520 pixels has a spectral
resolution of 1.15 nm/pixel and a spatial resolution of 0.052 mm/pixel. The scanning line was
taken 1.5 mm from the center [Fig. 1 top view] of the illumination spot to avoid saturation of
the CCD detector pixels due to high signal intensity close to the illumination point. In order to
limit the calculation time and to improve the signal-to-noise ratio, the images were binned by
reducing the number of wavelength bands to 81 (from 550 – 950 nm) with a step of 5 nm,
corresponding to the DIS and unscattered transmittance measurements. The region of interest
(ROI) of the image was then selected based on pre-defined area in the image order to reduce
the data size and speed up the computation time. The symmetric two sides in positive and
negative direction of the scanning line [Fig. 1 top view] were averaged and converted to
relative reflectance using the white and dark reference images, measured on a calibrated 99%
reflectance Spectralon® disk (Labsphere Inc., North Sutton, USA) and a black cap,
respectively [4]. At each single wavelength, the final SRS profile describes the diffuse
reflectance in function of the source-detector distance. The latter varied from 0 to 0.8 cm with
a 0.04 cm step, resulting in 21 source-detector distances. These SRS profiles were used as
input for training the metamodel (calibration phantoms) and for validation purposes.
2.4 Metamodeling
Metamodeling, also known as surrogate modeling, is defined as the construction of an
input/output function based on experimental measurements or simulations. A metamodel
based on Kriging regression uses an interpolation method which computes each new value
through a Gaussian process. Although the interpolation property of this method has certain
advantages, it is not desirable when dealing with measurements subject to noise, which can be
characterized by performing several (independent) measurements. In stochastic Kriging, on
the other hand, this variance is taken into account to avoid overfitting the model [13].
Therefore, a stochastic Kriging surrogate model was constructed in this study to link the
measured SRS values and the respective BOP. This was done by using the ooDACE toolbox,
which is a versatile Matlab toolbox that implements the Gaussian Process based Kriging
surrogate models [47–49]. First, the metamodels were trained on an accurate dataset of SRS
profiles, covering the relevant range of BOP. Such a dataset can be acquired by measuring
reference materials with pre-defined BOP, known as optical phantoms [1,39,45].
As the metamodels describe the SRS profile as a function of the BOP, the procedure
should be inverted in order to estimate the BOP from an SRS profile. Once the metamodels
were trained, the inverse problem is solved through an iterative optimization algorithm which
uses the forward model as a basis [13]. Moreover, it uses a Nelder-Mead simplex optimization
procedure, which adjusts the BOP estimates at a certain wavelength until the simulated SRS
profile matches with the measured one. To avoid that the high diffuse reflectance values
acquired close to the point of illumination would dominate the BOP estimation, the sum of the
squared relative errors was used as the cost function in the optimization procedure [13]. As
this optimization problem may not be convex, several combinations of BOP, evenly
distributed in the design space were used as starting points for the simplex algorithm. This
ensures that at least one of the starting points would lead to the global minimum
corresponding to the actual BOP.
2.5 Forward and inverse validation of metamodeling approach using liquid
phantoms
The sixteen liquid phantoms were divided into two groups: a calibration set of 12
phantoms and a validation set of 4 phantoms. The metamodels were built on the calibration
set, while their performance was evaluated on the phantoms which were not used for
calibration. The selection of phantoms for the calibration and validation sets is represented in
Table 1.
Table 1 Selection of calibration set (normal) and validation set (bold) of liquid phantoms.
A1 A2
B1 B2
C1 C2
D1 D2
A3
B3
C3
D3
A4
B4
C4
D4
In total, 21 metamodels were built, each one corresponding with a single source-detector
distance. Every single metamodel relates the diffuse reflectance values at a specific sourcedetector distance with the respective set of BOP. The metamodels were constructed by linking
the measured SRS profiles (output) of the calibration phantoms with the corresponding BOP
(input) in the 550 – 950 nm wavelength range. First, the metamodels themselves were
evaluated by comparing the diffuse reflectance values predicted by the metamodels with those
measured by the HSI setup. Moreover, the root mean squared error was calculated for the
calibration samples (RMSEC) and the validation samples (RMSEV).
After the forward validation, the performance of the inverse model for estimating the BOP
of the validation samples was also investigated. This evaluation step was done by comparing
the estimated BOP at all wavelengths for the four validation phantoms (A3, B1, C2 and D3)
with the corresponding values obtained from DIS measurements. The prediction performance
of the inverse model was then quantified in terms of the root mean squared error of prediction
(RMSEP), which was calculated as:
RMSE P 

n pred
i
( meas ,i   pred ,i ) 2
n pred
(1)
Where:
 meas ,i : Measured bulk optical properties (µa and µs’) of sample i
 pred ,i : Predicted bulk optical properties (µa and µs’) of sample i
n pred : Number of phantoms per wavelength used in the prediction set
3 Results and discussion
3.1 Reference bulk optical properties of the liquid phantoms
For each of the 16 liquid phantoms, the BOP in the wavelength range from 550 to 950 nm
were estimated with the inverse adding-doubling algorithm from the DIS and unscattered
transmittance measurements. The mean results for 3 replicates are presented in Fig. 2, where
the absorption coefficient (µa) spectra are grouped (same color) according to the four
absorption levels (1 – 4), while the reduced scattering coefficient spectra (µs’) are grouped
according to the four scattering levels (A – D).
In Fig. 2, the absorption coefficient and reduced scattering coefficient spectra are clearly
grouped according to the designed levels of scattering and absorption. This indicates that the
inverse adding-doubling algorithm was well able to separate the effects of scattering and
absorption from the reflectance and transmittance spectra acquired in the DIS and unscattered
transmittance setup.
(a)
(b)
22
1
2
3
4
1
18
16
-1
µs' (cm )
-1
µa (cm )
0.8
0.6
0.4
A
B
C
D
20
14
12
10
8
6
0.2
4
0
550
600
650
700
750
800
Wavelength (nm)
850
900
950
2
550
600
650
700
750
800
850
900
950
Wavelength (nm)
Fig. 2 Reference bulk optical properties estimated from DIS measurements for 16 liquid
phantoms: (a) absorption coefficients µa spectra grouped according to the absorption level (1 –
4) and (b) reduced scattering coefficients µs’ spectra grouped according to the scattering level
(A – D).
The absorption spectra corresponding to a given absorption level (1, 2, 3 and 4) are very
similar with clear absorption peaks at 615 and 670 nm for respectively the methylene blue
dimers and monomers [39], where the dimers are more pronounced for the higher
concentrations. The minimum and maximum values at the methylene blue peak were about
0.001 cm-1 (no methylene blue) and 1.2 cm-1 (2.2 ml of 400 µM methylene blue), respectively.
In Fig. 2(b), a clear decrease in the reduced scattering coefficient values with increasing
wavelength can be observed. This can be associated with the scattering properties of the fat
globules of the intralipid emulsion which have diameters ranging from 0.1 to 0.65 µm [50]. At
each designed scattering level, the reduced scattering coefficient spectra of the four liquid
phantoms with different absorption levels overlap very well. The reduced scattering
coefficient values range from about 5.0 cm-1 (2 ml of intralipid) until 17 cm-1 (8 ml of
intralipid) at 670 nm. Overall, the reference BOP were accurately estimated from the DIS and
unscattered transmittance measurements and were in good agreement with values found in
literature [39,45]. The use of methylene blue as a molecular absorbing agent (non-scattering)
resulted in a better (visual) separation of the absorption and scattering effects compared to
studies where indian ink was used. Moreover, the absorption spectrum of indian ink is rather
independent of the Vis/NIR spectral wavelength and not easily distinguishable from the effect
of scattering [13].
3.2 Hyperspectral scatter imaging SRS profiles of the liquid phantoms
A typical 2D hyperspectral image acquired for liquid phantom B3 is illustrated in Fig. 3. In
this figure, each horizontal line represents the reflectance spectrum for a particular sourcedetector distance on the scanning line [Fig. 1 top view], while the X-axis represents the
wavelength dimension. The intensity of the camera is expressed in digital counts (DC), which
ranges from 0 until maximum 4096 (12-bit), is given as a color bar.
-1.5
-1
2000
1500
0
x
Distance (cm)
-0.5
1000
0.5
1
500
1.5
400
500
600
700
800
Wavelength (nm)
900
0
Intensity (DC)
Fig. 3 Illustration of the 2D hyperspectral image of liquid phantom B3 (µa = 0.8 cm-1 and µs’ =
9 cm-1 at 670 nm). The X-axis represents the wavelength dimension, while each horizontal line
represents the reflectance spectrum for a particular source-detector distance on the scanning
line.
The extracted SRS profiles in the 550 – 960 nm range for the B* phantoms, with the same
scattering property, but different absorption levels, are illustrated in Fig. 4. A clear decrease of
the diffuse reflectance values with increasing distance can be observed at each wavelength.
This can be explained by the facts that the radial area increases with increasing distance from
the point of illumination. Furthermore, the photons exiting the sample at a further distance
from the point of illumination have travelled a longer path through the sample and thus have
had more chance to be scattered and/or absorbed. Also, for phantoms B2, B3 and B4 a dip in
reflectance around 670 nm can be observed. Moreover, the reflectance dip at 670 nm is more
significant if the dye concentration is increased as it relates to absorption by the methylene
blue dye. The reflectance decreased for wavelengths above 900 nm, indicating the presence of
water with an absorption peak at around 980 nm.
(b)
100
Relative reflectance (%)
Relative reflectance (%)
(a)
80
60
40
20
0
0
100
80
60
40
20
0
0
0.2
0.2
0.4
0.6
Distance (cm)
0.8
500
600
700
800
0.4
900
0.6
Wavelength (nm)
Distance (cm)
0.8
500
700
800
900
Wavelength (nm)
(d)
100
Relative reflectance (%)
Relative reflectance (%)
(c)
600
80
60
40
20
0
0
0.2
100
80
60
40
20
0
0
0.2
0.4
0.6
Distance (cm)
0.8
500
600
700
800
900
Wavelength (nm)
0.4
0.6
Distance (cm)
0.8
500
600
700
800
900
Wavelength (nm)
Fig. 4 Hyperspectral SRS profiles for the liquid phantoms of group B with the same scattering
coefficient level µs’ = 9 cm-1 and different levels of absorption: (a) B1: µa = 0 cm-1, (b) B2: µa =
0.4 cm-1, (c) B3: µa = 0.8 cm-1, (d) B4: µa = 1.2 cm-1 at 670 nm.
3.3 Bulk optical property estimation of the liquid phantoms
The performance of the forward metamodels is presented in Fig. 5 as scatter plots that
show the predicted versus measured diffuse reflectance values at four selected sourcedetection distances. The validation is done for all wavelengths of both the calibration (blue)
and validation phantoms (red). The reflectance values predicted by the metamodels are very
close to the measured reflectance values. This good performance can also be noticed from the
high R2 and low RMSE values for calibration ( RC2 = 0.969 – 0.999 and RMSEC = 0.089 –
0.596%) and validation ( RV2 = 0.944 – 0.999 and RMSEV = 0.123 – 0.581%). Moreover, for
the different source-detector distances, both the R2 and RMSE for calibration and validation
set are nearly similar, indicating the high robustness of the metamodels. The further the
distance from the illumination spot, the lower the prediction capability of the metamodel. This
is probably due to the decrease in signal-to-noise ratio (SNR) with increasing source-detection
distance. As a result, some deviation of the points was observed for the furthest distance [Fig.
5(d)], resulting in a slightly lower R2 value of 0.969 (calibration) and 0.944 (validation).
However, as the signal at that distance was relatively low and noisy, this is acceptable.
Therefore, it can be concluded that the forward metamodels was able to predict well the
measured SRS profiles for the liquid phantoms based on the corresponding BOP.
(a)
(b)
60
25
R2 = 0.999
R2 = 0.998
RMSEC = 0.596%
RMSEC = 0.186%
Predicted reflectance (%)
50
C
Predicted reflectance (%)
C
R2 = 0.999
V
RMSEV = 0.581%
40
30
20
10
0
0
10
20
30
40
50
20
V
RMSEV = 0.166%
15
10
5
0
60
R2 = 0.999
0
5
Measured reflectance (%)
10
(c)
25
3
R2C = 0.993
R2C = 0.969
RMSEC = 0.138%
8
RMSEC = 0.089%
2.5
Predicted reflectance (%)
Predicted reflectance (%)
20
(d)
10
R2V = 0.995
RMSEV = 0.123%
6
4
2
0
15
Measured reflectance (%)
R2V = 0.944
RMSEV = 0.129%
2
1.5
1
0.5
0
2
4
6
Measured reflectance (%)
8
10
0
0
0.5
1
1.5
2
2.5
3
Measured reflectance (%)
Fig. 5 Scatter plots of predicted versus measured reflectance values for 12 liquid calibration
phantoms (blue) and four validation phantoms (red) at four source-detector distances: (a) 0.1
cm, (b) 0.2 cm, (c) 0.4 cm, and (d) 0.8 cm.
The inverse model was validated by comparing the estimated BOP of the 4 validation
phantoms with the reference values obtained from DIS and unscattered transmittance
measurements. The SRS profiles were obtained from the measured hyperspectral scatter
images, while the BOP were estimated from the SRS profiles through the iterative inversion
of the forward metamodels. In Fig. 6, the predicted BOP for these validation phantoms are
plotted against the corresponding reference values. The obtained results (red and blue dots)
show that both the predicted absorption and reduced scattering coefficient values for the four
validation phantoms closely match the reference values [section 2.2] with RP2 values of 0.912
and 0.997, and RMSEP of 0.068 cm-1 and 0.226 cm-1 for µa and µs’, respectively. Moreover,
the relations between the measured and reference BOP are indicated by the blue lines in Fig.
6.
To get a better view on the prediction performance in function of the spectral dimension,
the predicted BOP spectra for the four validation phantoms (A3, B1, C2, and D4) are
illustrated in Fig. 7 as a function of the wavelength, together with the reference BOP spectra.
(a)
(b)
1.2
20
-1
Predicted µs' (cm )
-1
Predicted µa (cm )
1
0.8
0.6
0.4
2
R = 0.912
12
8
2
R = 0.997
RMSE = 0.226 cm-1
RMSE = 0.068 cm-1
0.2
R2 = 0.980
0
0.2
0.4
0.6
0.8
Measured µa (cm-1)
1
R2 = 0.998
RMSE = 0.197 cm-1
4
RMSE = 0.032 cm-1
0
16
1.2
4
8
12
16
20
Measured µs' (cm-1)
Fig. 6 Scatter plots of predicted versus measured bulk optical properties for the four validation
liquid phantoms: (a) absorption coefficients µa ; (b) reduced scattering coefficients µs’. The red
dots represent the data of the 570 – 900 nm range, while the blue dots represent the 550 – 570
nm and 900 – 950 nm range. The blue line is a linear fit to all the data (blue and red dots),
while the red line is the linear fit to the data of the reduced wavelength range (red dots).
Visual inspection of the curves in Fig. 7(a) shows a very good match between the
absorption coefficient spectra predicted from the hyperspectral scatter images and those
obtained from the DIS measurements. Especially, the absorption peak of methylene blue is
predicted very well for the different phantoms, without crosstalk between the reduced
scattering and bulk absorption coefficient spectra. However, the prediction of the µa values in
the 550 – 570 nm and 900 – 960 nm range was less reliable [Fig. 7(a)], while the µs’ of the
highest scattering level (phantom D) was slightly underestimated for the wavelengths below
570 nm [Fig. 7(b)]. This can be explained by the low SNR of the measured reflectance values,
mainly due to the low sensitivity of the camera at these wavelengths. Additionally, above 900
nm, the SNR is even further reduced due to high absorption by the sample’s water molecules.
To illustrate the effect of the wavelength range on the model performance, the data points
corresponding to the 570 – 900 nm range (higher SNR) were indicated in red [Fig. 6] and the
performance parameters were recalculated. Moreover, the red lines [Fig. 6] represent the
linear relation between the predicted and measured BOP, resulting in an RP2 of 0.980 and
0.998, and RMSEP of 0.032 cm-1 and 0.197 cm-1 for µa and µs’, respectively. This clearly
indicates that the model performs even better in the 570 – 900 nm, were the SNR of the SRS
profiles is sufficient.
(a)
(b)
22
A3 - measured
A3 - predicted
B1 - measured
B1 - predicted
C2 - measured
C2 - predicted
D4 - measured
D4 - predicted
0.6
18
16
-1
-1
µa (cm )
0.8
20
µs' (cm )
1
.
0.4
14
12
10
8
6
0.2
4
0
550
600
650
700
750
800
Wavelength (nm)
850
900
950
2
550
600
650
700
750
800
850
900
950
Wavelength (nm)
Fig. 7 Predicted and measured bulk optical properties spectra for the four liquid validation
phantoms: (a) absorption coefficients µa; (b) reduced scattering coefficients µs’.
Apart from the good prediction performance of the inverse modeling approach, also the
required computation time is important for practical usage. Training the metamodels is the
most computational intensive step, taking about 52 minutes on a standard desktop computer
(Intel® Core ™ i5-4570 CPU @ 3.2 GHz) for a single source-detector distance or single
metamodel. In total, as 21 metamodels were constructed, the entire calibration process took
approximately 18 hours to complete. Once the metamodels were constructed, it only required
9.4 milliseconds on the same computer to estimate the SRS profile (21 source-detector
distances) for a single set of BOP. Moreover, the calculation time is independent of the BOP
itself. This is substantially faster relative to the seconds or minutes which is required by the
optimized MC algorithms [29,31]. Nevertheless, as the used Nelder-Mead simplex
optimization is relatively simple, many sets of BOP (1305 on average) were evaluated to find
the BOP which correspond to a measured SRS profile. Therefore, the inverse estimation
required 12.5 seconds on average to complete, which is too still high for predicting the
sample’s BOP in an on-line application. Therefore, future research should focus on the
optimization of this inverse estimation. For instance, the BOP estimate at a neighboring
wavelength can be used as a starting point for the optimizer since the BOP of neighboring
wavelengths are highly correlated. This could reduce the number of required starting points to
find the global minimum corresponding to the actual BOP.
Finally, it should also be noted that the applicability of the approach followed in this study
is limited to turbid media which are homogeneous on a scale which can be visualized with the
imaging system (± 50 µm) [51]. Nevertheless, this approach could be further extended to
cases of multi-layered sample structures. However, to train the extended model, a significantly
larger set of calibration phantoms would be required to cover all the possible variability (BOP
and thickness of each layer).
4 Conclusions
In this study, a metamodeling approach based on the stochastic Kriging concept has been
elaborated and combined with an iterative inversion to estimate the bulk optical properties
from spatially resolved reflectance profiles obtained with contactless hyperspectral scatter
imaging. Forward validation of these models showed that the predicted reflectance values
matched well with the measured ones (R2 ≥ 0.944). Next, these metamodels were incorporated
in an to estimate bulk optical properties from the measured reflectance profiles. Validation of
the iterative inversion scheme showed accurate and fast prediction of the absorption
coefficient and reduced scattering coefficient for an independent set of validation phantoms,
with RP2 values of respectively 0.980 and 0.998, and RMSEP values of 0.032 cm-1 and 0.197
cm-1. This confirms the potential of the inverse metamodeling approach for rapid and accurate
bulk optical property estimation of turbid media. Future research should be focused on
validating this approach for actual biological tissues and samples.
Acknowledgments
This publication has been produced with the financial support of the European Union
(project FP7-226783 - InsideFood). The authors gratefully acknowledge IWT-Flanders for the
financial support through the GlucoSens (SB-090053) and Chameleon (SB-100021) projects.
Ben Aernouts has been funded as PhD fellow of the Research Foundation-Flanders (FWO,
grant 11A4813N). Rodrigo Watté and Robbe Van Beers are funded by the Institute for the
Promotion of Innovation through Science and Technology in Flanders (IWT-Flanders,
respectively grants 101552 and 131777). Nghia Nguyen Do Trong has been funded by the
Interfaculty Council for Development Cooperation, KU Leuven (IRO scholarship). The
provision of the ooDACE toolbox from the Department of Information Technology (INTEC),
Ghent University, Belgium is greatly acknowledged.