NIR remission spectroscopy of turbid media

NIR remission spectroscopy of turbid media
Philipp Krauter
Institut für Lasertechnologien in der Medizin und Meßtechnik, Helmholtzstr. 12, D-89081 Ulm, Germany
Tel.: 0049 731 1429886; E-mail: philipp.krauter@uni-ulm.de
1. Introduction
In process control the knowledge of the quantitative concentration of the ingredients is important. This can
be achieved by measuring the remission spectrum and by comparison with calibration spectra. However, this
method cannot separate the reduced scattering coefficient µ ′ s from the absorption coefficient µ a , e.g. an unnoticed
change of µ ′ s is interpreted as a change in µ a . In contrast, a combination of the spatially resolved
reflectance and the total reflectance enables the determination of µ a undisturbed by scattering. At the same
time, it delivers a high wavelength resolution. 1
In the following, µ ′ s was determined using the spatially resolved reflectance 2 in the VIS. An empirical description
of the wavelength dependence of µ ′ s is given by the power law µ ′ s(λ) = k 0 λ k1 . In the NIR µ ′ s is obtained by
extrapolating this law. Compared to our recent work 1 the focus of this work is the enhancement of the spectral
range of the total reflectance to 450 nm ≤ λ ≤ 1700 nm. An optimized data analysis allows fast interpretation
of the measured remission spectrum by use of a lookup table. The distribution of light is calculated numerically
with the radiative transfer equation. For these calculations, the detection geometry is taken into account. Verification
of the method is done by determination of the absorption coefficient of an optical phantom, consisting
of a known concentration of polystyrene spheres in water. Finally, the absorption spectrum of butter is shown,
representing a possible application of the method. Even though only the total reflectance is regarded here, it
is important to remember, that the knowledge of µ ′ s(λ) is needed for proper evaluation of µ a . (Since there is
already a publication for the VIS, 1 spectra are only shown in the NIR.)
2. Total reflectance
shutter
aperture
0.07
0.06
0.05
f lens
θ light
source
ρ
d spot sample /
reflectance
standard
NIR
VIS
remission / a.u.
0.04
0.03
0.02
a)
PC
scattering disks
h
0
b)
0.01
0
10
2,5
1
0,4
µ s
/ mm −1
0,1
10 −1 10 1 10 3 10 5
µ s
/ µ a
Figure 1. a) The setup to measure the total reflectance with two spectrometers. b) Remission values R for
the grid of reduced scattering coefficients µ ′ s and different fractions of µ ′ s/µ a are stored in the lookup table.
In order to measure the total reflectance of a sample (see Figure 1a), the end of a liquid light guide (Ø= 5 mm),
transferring the broadband light of a halogen bulb, is imaged by a lens onto the surface of the sample. Because
of the magnification, the diameter of the spot is d = 16 mm. One part of the light is remitted by the sample
and falls on one of the scattering disks and is then transferred to a spectrometer. Since the ratio of remitted

light to incident light is needed, also a reflectance standard is measured.
There is no explicit function µ a = µ a (R, µ ′ s), so the implicit one R = R(µ a , µ ′ s) has to be inverted. This so-called
inverse problem is solved by means of the following procedure: In the first step one has to calculate R(µ a , µ ′ s)
for pairs of (µ ′ s, µ a ). The distance in the optical parameter space should be small, so linear interpolation can
be applied (see Figure 1b). The second step is the interpolation of R(µ a , µ ′ s) for the given reduced scattering
coefficient µ ′ s. The result is a monotonically increasing curve R µ ′ s
(µ a ), therefore, it can be inverted numerically.
In the last step, the absorption coefficient µ a is given by interpolation of the inverted curve µ a (R µ ′ s
) at the
measured remission R.
The calculation of R(µ a , µ ′ s) for the pairs of (µ ′ s, µ a ) is done by means of the radiative transfer equation, which is
solved numerically by Monte Carlo simulations taking into account the geometry of the detection. The Henyey-
Greenstein phase function with the anisotropy factor g = 0.7 was assumed. Since some of the parameters are
not known exactly, the influence of their deviation was evaluated for the phase function p(θ), the anisotropy
factor g, the refractive index n and the z-position of the surface of the sample. The error in the determination
of µ a caused by a deviation in the assumption of the optical parameters can be limited to 10% for relevant cases
except for the z-position. For small absorption (e.g. µ a = 10 −3 mm −1 ) the error in µ a is higher than 50% for
the sample being 1 mm away from the assumed value z = 0. Thus, one has to adjust the sample with great
care to minimize this error.
3. Results
polystyrene phantom
water [Kou]
butter (Landliebe)
fitted curve
water [Kou]
fat
µ a
/ mm −1
10 0 wavelength / nm
10 −1
µ a
/ mm −1
10 0 wavelength / nm
10 −1
10 −2
10 −2
a)
900 1000 1100 1200 1300 1400 1500 1600 1700
b)
10 −3
900 1000 1100 1200 1300 1400 1500 1600 1700
Figure 2. a) Measured absorption spectrum of the optical phantom compared to the absorption of water. b)
Measured absorption spectrum of butter and fitted absorption curve of water and fat (see text).
a) Polystyrene
For verification of the method, a phantom of polystyrene microspheres (c W = 1.93%) in water was prepared
having 1.65 mm −1 ≤ µ ′ s ≤ 1.95 mm −1 in the shown range of wavelengths. The measured absorption spectrum
as well as the absorption of water measured by Kou et al. 3 using collimated transmission can be found in Figure
2a. Both curves show good agreement. However, systematic deviations seem to occur at wavelengths around
λ = 1080 nm and above λ = 1450 nm. A small sample container (compared to the penetration depth at the
considered wavelengths) could be the reason for the former. The reason for the latter could not be clarified.
The absorption of polystyrene is not relevant in this wavelength range.
b) Butter
With respect to practical applications, it is desirable to determine the concentration of water and fat in butter
without calibration measurements. To do so, the absorption spectra of water and fat are needed. While the first
can be found in literature, 4,3 the latter had to be determined on our own by using total and spatially resolved
reflectance. Fat absorption was assumed to be the mean of the measurements of three different commercial sorts

of fat. Assuming the measured absorption of butter to be the sum of the weighted absorption by the volume
concentration c fat and c water , both parameters can be obtained by a fit.
The sample was prepared as follows: The package of a commercial butter (”mildgesäuerte Butter”, Landliebe)
was unwrapped. In order to clear the influence of longterm contact with air, the upper layer was removed.
After that, the new surface was flatted, so it meets the requirements for measurements of the total and spatially
resolved reflectance.
The measurement of butter is presented in Figure 2b together with the fitted curve for c fat = 89% and c water =
11%. For comparison, the applied absorption spectra of water and fat can be found in grey.
Both the measured and the fitted curve show good agreement with a systematic deviation above λ = 1450 nm
which is comparable to the systematic deviation of the phantom (see above). Furthermore, the approach of
equalizing different sorts of fat is a first step and not very accurate.
The manufacturer lists the mass concentration of fat as 82%, which is a relative deviation of about 7% compared
to the determined value of 88%.
4. Conclusion
We presented a method for determination of the absorption spectra, using the reduced scattering coefficient,
which was obtained by spatially resolved reflectance. Light propagation is described by the radiative transfer
equation, taking into account the illumination and detection geometry. Comparing measured absorption spectra
of an optical phantom based on water with literature values, we found good agreement. Furthermore we
presented a measurement of butter to determine the concentration of fat and water without calibration. Not
shown are measurements in the VIS where less absorption can be found in most cases. Absorption in the
range of 10 −3 mm −1 ≤ µ a ≤ 10 mm −1 can be measured, while this range is valid for µ ′ s = 1 mm −1 and scales
approximately proportional to µ ′ s.
REFERENCES
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method,” Journal of Biomedical Optics 17(3), pp. 037009–1, 2012.
2. F. Foschum, M. Jäger, and A. Kienle, “Fully automated spatially resolved reflectance spectrometer for the
determination of the absorption and scattering in turbid media,” Review of Scientific Instruments 82(10),
pp. 103104–103104, 2011.
3. L. Kou, D. Labrie, and P. Chylek, “Refractive indices of water and ice in the 0.65-to 2.5-µm spectral range,”
Applied Optics 32(19), pp. 3531–3540, 1993.
4. R. Pope, E. Fry, et al., “Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements,”
Applied Optics 36(33), pp. 8710–8723, 1997.