OPTICAL REVIEW Vol. 12, No. 3 (2005) 202–206

Multiple-Scattering-Free Optical Glucose Monitoring
Based on Femtosecond Pulse Interferometry
Yasuaki H ORI, Takeshi Y ASUI and Tsutomu A RAKI
Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science,
Osaka University, Toyonaka, Osaka 560-8531, Japan(Received September 30, 2004; Accepted February 15, 2005)

We have designed a novel multiple-scattering-free optical glucose monitoring system based on femtosecond pulseinterferometry. The glucose concentration is determined by a time-of-ﬂight method, while multiple-scattering light isrejected by a coherence gate. The resultant accuracy and precision were 94.7 and 24.5 mg/dl, respectively, forphysiological-equivalent glucose concentrations in a scattering medium of 1.0% intralipid solution, while the accuracy
and precision for a reference sample containing no scattering medium were 65.3 and 23.8 mg/dl, respectively.
Comparing these results, we conclude that the proposed method is eﬀective for glucose measurement in a scattering
medium. # 2005 The Optical Society of Japan
Key words: glucose, femtosecond pulse light, multiple scattering, coherence gate, interferometry, time-of-ﬂight, group refractive index

1.

and a coherence gate,7) the latter being attractive because of its
simplicity. It extracts only the ballistic light as an interference signal using the coherence remaining in the ballistic
light. Use of such a coherence gate oﬀers the possibility ofmultiple-scattering-free optical glucose monitoring.8,9)
Optical coherence tomography (OCT), which is one
attractive application of the coherence gate technique, canbe eﬀectively applied to in vivo glucose monitoring.10) OCTbased glucose monitoring uses the change of scattering
coeﬃcient depending on the glucose concentration in
biological tissue. Although there is a correlation between
glucose concentration and the scattering coeﬃcient in tissue,
the precision of the measurement does not meet thenecessary requirements, even in in vitro measurement,
because of the insensitive change of the scattering coefﬁcient. To improve the measurement precision, we havedesigned a novel time-of-ﬂight coherence gate system incombination with femtosecond pulse interferometry. Determination of the glucose concentration is based on themeasurement of a group refractive index (ng ) of the glucose
solution. Although measurement of the refractive index,
using an Abbe refractometer, is one attractive method todetermine the sugar content in fruits and drinks, it cannot be
simply applied to optical glucose monitoring because of thepoor resolution in the concentrations, necessity for blood
drops, and the multiple scattering. To apply refractive index
measurement to optical glucose monitoring, we propose
determination of the glucose concentration via precise
measurement of ng by an interferometric technique. Moreprecisely, the ng value of the glucose sample is extracted as atime delay of femtosecond order by a time-of-ﬂight methodwith femtosecond pulse interferometry. Simultaneously,
multiple-scattered light, which disturbs the precise measurement of ng , is rejected by the coherence gate.
After describing the principle and basic examination of
our method, we will evaluate its ability to eliminate
multiple-scattered light using a scattering medium. We will
also demonstrate in vitro multiple-scattering-free optical
glucose monitoring using a mixture of glucose and thescattering medium.

Introduction

There are today a considerable number of diabetes
mellitus patients worldwide. Among them, those suﬀeringfrom serious diabetes must draw their own blood several
times a day by puncturing their ﬁnger to monitor the glucose
concentration. This blood drawing results in mental andphysical stress for the patients. Furthermore, to carry out
clinical diagnosis, medical staﬀ members are subjected to
the risk of blood infection when collecting blood.
Optical glucose monitoring is an attractive technique toachieve noninvasive and pain-free monitoring; however, its
application to in vivo measurement has been limited. In in
vitro measurement, studies using various techniques havebeen reported: (a) near-infrared absorption spectroscopy,1)(b) polarimetry of optical rotatory power,2) and (c) Raman
spectroscopy.3) However, the sensitivity and quantitativenessof these methods do not meet the requirements necessary forclinical examinations. One reason for the limited sensitivity
and quantitativeness is the coexistence of multiple-scattered
light caused by particles present in blood, such as cells,
lipids, and proteins. For example, it is diﬃcult to distinguishbetween absorption by the glucose and scattering by theparticles in near-infrared absorption spectroscopy. In polarimetry, the multiple-scattering events depolarize the linear
polarization of the incident light, resulting in reduced
measurement precision. In Raman spectroscopy, multiplescattering and reabsorption in biological tissue weaken theanalytical Raman spectrum.4) The weak Raman signal
increases the measurement time required to gain a satisfactory signal-to-noise ratio (SNR) to at least a few minutes,
resulting in limited potential for practical use in real-time
glucose monitoring.
In optical glucose monitoring, because only non-multiplescattered, ballistic light in the blood oﬀers direct informationon the glucose concentration, elimination of multiplescattered light is essential to improve the reliability of themeasurement. Several techniques for elimination of themultiple-scattered light in biological tissues have beenreported, for example, using an ultrafast time-resolved gate5,6)202

OPTICAL REVIEW Vol. 12, No. 3 (2005)

Y. HORI et al.

sample depends on the group refractive index of the sample,
assuming a known geometric path length. Here, we consider
a temporal shift t of the femtosecond pulse light caused by
glucose addition, where the time origin is deﬁned as the time
to pass through a sample of pure water. The t value isdeﬁned as follows:

Pure water

Femtosecond
pulse light∆t0

Glucose solution

t ¼

d

(a)
Multiple-scatteedr light(coherent – lost)t ¼

Ballistic light

Femtosecond
pulse light

Incoherent

kCd
;
vc

ð2Þ

where C is the glucose concentration and k is a proportionality factor. If the k, d, and vc values are known, we candetermine the C value through precise measurement of t
by time-of-ﬂight measurement with femtosecond interferometry.
Coherent

Pulse interferometry(b)
Scattering medium
Pure water

t
0

∆t

Glucose solution

t
0

(c)
Fig. 1. (a) Principle of glucose concentration measurement. The
temporal shift of femtosecond pulse light is caused by glucose
addition, which is proportional to glucose concentration under aknown geometric path length. (b) Principle of elimination ofmultiple-scattered light. Unscattered ballistic light is coherent withincident pulse light, resulting in generation of the interference
signal in pulse interferometry. The coherent-lost, multiple-scattered
light is rejected by the coherence gate with pulse interferometry. (c)Principle of multiple-scattering-free optical glucose monitoring.
Temporal shift of ballistic light extracted by coherence gate gives
glucose concentration.

2.

ð1Þ

(coherent - kept)t

Femtosecond
pulse lightng  d;vc

where d is the geometric path length of the sample, vc is thevelocity of light in vacuum, and ng is the change of grouprefractive index caused by the glucose addition. Since theng value is proportional to the glucose concentration, we
can express t as follows:

0

Scattering medium

203

Principle

2.1 Glucose concentration measurement
The principle of the glucose concentration measurement isshown in Fig. 1(a). When femtosecond pulse light is incident
on an aqueous solution sample, the time to pass through the

2.2 Elimination of multiple-scattered light
The principle of elimination of the multiple-scattered lightis shown in Fig. 1(b). We consider the temporal behavior ofultrashort-pulse light propagation in the scattering medium.
When ultrashort pulse light passes through the scattering
medium, multiple-scattering events cause diﬀerent eﬀective
optical path lengths between multiple-scattered light andunscattered light. As a result, the unscattered ballistic lightarrives ﬁrst while the multiple-scattered light is delayed.
Hence, the ballistic light can be extracted by an ultrafast
time-resolved gate, such as an optical Kerr gate.5) In
practice, however, the multiple-scattered light and ballistic
light cannot be completely separated from each other, as
shown in Fig. 1(b), resulting in limited extraction of theballistic light.
Regarding the coherency of light in the scattering
medium, the ballistic light maintains the coherency of theincident pulse light, whereas the multiple-scattered light
loses the coherency during the scattering events. Hence, one
can extract the ballistic light from the scattering medium as
an interference signal by the coherence gate.
2.3 Multiple-scattering-free optical glucose monitoring
Combined use of the two ideas above provides a scheme
for multiple-scattering-free optical glucose monitoring, asshown in Fig. 1(c). Here, we consider a mixture of glucose
and scattering medium as the sample. Since the temporalcharacteristics of the ballistic light extracted by thecoherence gate are directly related to the glucose concentration, one can determine the glucose concentration fromthe t value obtained by the time-of-ﬂight measurement.
The t value in Fig. 1(c) is determined by temporal shift ofthe maximum on the interference signal envelope of ballistic
light with respect to glucose concentration. In this way, thefemtosecond pulse interferometry provides the ability toachieve multiple-scattering-free optical glucose monitoring.

OPTICAL REVIEW Vol. 12, No. 3 (2005)

Y. HORI et al.
160

CR

PC
Envelope signal

Temporal shift ∆t [fs]204

Ref. path

Fringe signal

L
Demodula-tor

Amp

Sample CR

PD

Kerr-lens modelocked Ti:Al2O3
laser

BS

100
80
60

d = 1 mm
∆t = 0.0049C
R2 = 0.9968

40

0

PZT
stage

0

500

1000

1500

2000

2500

3000

Glucose concentration C [mg/dl]

M

Fig. 2. Experimental setup of femtosecond pulse interferometry.
M: mirror, BS: beam splitter, CR: corner reﬂector, PZT stage:
piezoelectric stage, L: lens, PD: photodetector, Amp: ampliﬁer, PC:personal computer.

Fig. 3. Relationship between the glucose concentration and thetemporal shift in 10-mm cell and 1-mm cell. Measurements wererepeated 10 times at each concentration. Solid lines are correlation
curve obtained by a linear ﬁtting.

4.
3.

d = 10 mm∆t = 0.0435C
R2 = 0.99994

120

20

Meas. path
(λ=800 nm, 200 mW,
100 fs, 87 MHz )140

Experimental Setup

Figure 2 shows the experimental setup of the femtosecond
pulse interferometry system. The laser source is a Kerr-lensmode-locked Ti:Al2 O3 laser (Avesta Project, Ltd., TiF-Kit100, central wavelength = 800 nm, pulse width = 100 fs,
average power = 200 mW, repetition rate = 87 MHz). The
laser light is divided into a reference path and a measuring
path with a beamsplitter (BS). A sample cuvette is set in themeasuring path. The two beams from both corner reﬂectors(CRs) are combined again by the BS. A PZT stage(Piezosystem Jena PX400CAP, stroke = 320 mm, with aircapacitive sensor) scans the measuring CR with a 1-Hz
triangular wave. At the moment the two optical path lengths
are equal to each other, a pulse interference signal(coherence time = 133 fs, full width at half maximum) is
observed during the scanning procedure. The generated
interference fringe signal is detected with a photodetector(PD). After ampliﬁcation, the envelope signal of the fringe
signal is electrically extracted using a demodulator. The
temporal shift of the maximum on the envelope signal isdetermined by the PZT stage displacement.
Before demonstration of the optical glucose monitoring,
we estimated the linearity and resettability of the PZT stage
displacement using a Michelson interferometer equippedwith a frequency-stabilized Zeeman laser. Here, the linearity
is deﬁned as the standard deviation of error between themeasured displacement and the ideal value within a range
used in the actual glucose measurement. The resettability isdeﬁned as the standard deviation of time origin ﬂuctuation
without the sample. To obtain the resettability value, wemeasured the ﬂuctuation of the time origin every 2 min for
1 h. The resulting linearity and resettability were estimatedas 5.3 and 35.1 nm, which correspondto a linearity of 0.04 fs
and a resettability of 0.23 fs in time delay, respectively.
These values limit accuracy and precision in glucose
concentration measurement.

Results

4.1 Glucose concentration measurement
We investigated the relationship between the glucose
concentration and the temporal shift of the envelope signal.
Sample cells with 10-mm and 1-mm thickness were used.
We prepared glucose solution samples with concentrationsof 0, 500, 1000, 1500, 2000, 2500, and 3000 mg/dl, which
covered the physiological range of blood glucose concentration (normal: 60–200 mg/dl, diabetic: 200–2000 mg/dl).
In the measurement with the 10-mm cell and 1-mm cell, thetemperatures of the glucose samples were stable within0:2 C. The measurements were repeated ten times at eachconcentration; Fig. 3 shows the results. The solid lines are
the correlation curves obtained by linear ﬁtting of the data
points, equivalent to kd=vc in eq. (2). As one can see, linear
correlations were observed in both the 10-mm cell and the
1-mm cell. The ratio of the correlation slopes between the
10-mm cell and the 1-mm cell (¼ 8:9) was not completely
consistent with the sample thickness ratio (¼ 10). The
resettability of the PZT stage (¼ 0:23 fs) inﬂuences themeasured value of time delay directly, resulting in variationsof slopes for the two cells. Furthermore, the concentration
error in the glucose sample also contributes to these slopes.
Precision in an electronic balance used in sample preparation(¼ 0:3 mg) causes concentration error of 37 mg/dl at
3000 mg/dl glucose concentration, resulting in variation of
the slopes within 0:0435  0:0005 for the 10-mm cell and
0:0049  0:00006 for the 1-mm cell. Considering botheﬀects, we estimate the minimum slope ratio is 8.76. Hence,
we can conclude that the present slope ratio of 8.9 is within
the range expected by resettability and concentration error.
Here, we introduce an accuracy and a precision for the
glucose measurement to evaluate the performance of the
proposed system. Accuracy is deﬁned as the standard
deviation of the diﬀerence of each measurement value fromthe value on the correlation curve. Precision corresponds tothe standard deviation of the ten repeated measurements ateach concentration. The measurement accuracy and precision in the 10-mm cell were 8.34 and 1.75 mg/dl, respectively. We consider that the accuracy is limited by theOPTICAL REVIEW Vol. 12, No. 3 (2005)

Y. HORI et al.

∆t = 0.0040C
R2 = 0.9907

14
12
10
8
6
4
2
0
0

500

1000

1500

2000

2500

3000

Glucose concentration C [mg/dl]

Fig. 5. Relationship between the glucose concentration and thetemporal shift in a mixture of a 1.0% intralipid solution andglucose. Thickness of a sample cell is 1 mm. Measurements wererepeated 10 times at each concentration. Solid line is a correlation
curve obtained by a linear ﬁtting.

multiple-scattered light collinear with the ballistic light
contaminates the analytical signal and appears as an oﬀset
signal, resulting in an increase in the background noise levelto 30 dB, though the shot noise level due to the detector
and the electronic equipment is as low as 80 dB. If the
background noise level is eﬀectively reduced to the shotnoise level (80 dB), thicker samples, up to 8-mm thick, canbe used.

1

Glucose concentration measurement in scattering
mediumWe demonstrated the measurement of the glucose
concentration in intralipid solutions using the proposedsystem. Mixtures of glucose and a 1.0% intralipid solution
were measured ten times at each concentration (¼ 0, 500,
1000, 1500, 2000, 2500, and 3000 mg/dl). The sample
thickness was 1 mm considering the clinical measurement.
Figure 5 shows the relationship between the glucose
concentration and the temporal shift. One can ﬁnd a linear
correlation between the concentration and the shift value
similar to that for the 1-mm thickness in Fig. 3. The
measurement accuracy and precision were 94.7 and 24.5
mg/dl, respectively. These values are in good agreementwith those of the 1-mm thick aqueous glucose solution. This
result indicates the possibility of multiple-scattering-free
optical glucose monitoring.

10-1

5.

4.2 Elimination of the multiple-scattered light
We evaluated the ability to eliminate the multiplescattered light using scattering solution samples of three
diﬀerent thicknesses. As the scattering samples, 1.0%
intralipid solution, whose scattering coeﬃcient is equivalent
to that of biological tissue (¼ 1:0 mm1 ), was prepared. To
examine the measurement dynamic range, we measured the
maximum intensity level of the envelope signal at eachsample thickness. Assuming that reliable glucose monitoring
can be carried out when the SNR of the measurement islarger than 2, this system enables samples up to 3-mm thick
to be used, as shown in Fig. 4. In the present system,

Intensity [normalized]

16

Temporal shift ∆t [fs]linearity of the PZT stage displacement, the concentration
error in the glucose sample and/or the ﬂuctuation of sample
temperature, while the precision depends on the resettabilityof the PZT stage. The linearity of the PZT stage displacement (¼ 5:3 nm) and the concentration error in the glucose
sample lead to the accuracy error of 0.79 and 4.78 mg/dl,
respectively. Here, we estimated the concentration error
using the standard deviation of sample concentration
variance that arises from precision of a pipet (¼ 8:0 ml) for
dilution of the glucose sample. On the other hand, thetemperature instability of 0:2 C causes an accuracy errorof 9.63 mg/dl. Hence, the accuracy is mainly aﬀected by the
instability of the sample temperature. The precision islimited by the resettability of the PZT stage displacement.
The resettability of the PZT stage (¼ 35:1 nm) is equivalent
to a precision of 5.19 mg/dl. However, the actual precision
value obtained (¼ 1:75 mg/dl) is better than the predictedvalue corresponding to the resettability of the PZT stage,
because the measurement time (¼ 10 s) in the actual glucose
monitoring was much shorter than that in the performance
testing of the PZT stage (¼ 1 h).
For clinical applications, an optical path length of 1 mm ismore realistic. The measurement accuracy and precision in
the 1-mm cell were 65.3 and 23.8 mg/dl, respectively. These
values are about 10 times larger than those in the 10-mm cellbecause of the lower dependence on glucose concentration
due to the reduced sample thickness (see Fig. 3). In this way,
there is an inherent trade-oﬀ between the optical path lengthand the measurement quantitativeness.

205

10-2

backgroundnoise level-30 dB

10-3
10-7

shot noise level-80 dB

10-8
0

1

2

3

4

Sample thickness [mm]Fig. 4. Maximum intensity of envelope signal detected at eachscattering sample thickness. A 1.0% intralipid solution was used asa scattering sample.

4.3

Discussion

We have accomplished a measurement accuracy inglucose concentrations of 8 and 65 mg/dl for the 10-mmcell and 1-mm cell, respectively. These values are satisfactory for in vitro glucose monitoring. However, several
problems for clinical application remain unresolved in oursystem. Since usual interferometric methods are very
sensitive to environmental disturbances (air turbulence,mechanical and sound vibrations, and changes in sample
temperature), the proposed method needs a very stable,
controlled environment, such as a laboratory. We are now
investigating an optical glucose monitoring method using

206

OPTICAL REVIEW Vol. 12, No. 3 (2005)

femtosecond two-color pulse interferometry as a commonpath interferometric method to overcome the problems
concerning environmental disturbances.11)
Although the present method was demonstrated under theassumption of known sample thickness, unknown sample
thickness is more realistic in clinical applications. In thatcase, the temporal shift t is dependent on both the glucose
concentration and the sample thickness. Simultaneous
measurement of two independent optical parameters sensitive to glucose concentration (for example, group refractive
index and optical rotatory power) can determine the glucose
concentration and sample thickness, respectively.
Selection of the measurement site is a troublesome
problem common to various optical glucose monitoring
methods. The power penetrating 3 mm into a scattering
medium is not necessarily suﬃcient for optical glucose
monitoring through skin. One possibility is to use anotherfemtosecond pulse laser, such as a mode-locked Cr:Forsterite laser (center wavelength = 1300 nm), which possesses
deeper penetration power into biological tissues. However,
optical glucose monitoring through the skin is strongly
inﬂuenced by the condition of the skin surface even if such alaser is applied. Another possibility is to use the aqueous
humor in the eye as a direct window for the optical glucose
monitoring; this technique is conventionally used in polarimetry of optical rotatory power12) and Raman spectroscopy.13)
6.

Conclusion

We proposed a multiple-scattering-free optical glucose
monitoring method based on femtosecond pulse interferometry. For determination of the glucose concentration, weused the temporal shift of femtosecond pulse light caused by
glucose concentration dependence of the group refractive
index. The resulting accuracy and precision of the glucose

Y. HORI et al.

concentration measurement were 8.34 and 1.75 mg/dl in a
10-mm cell, and 65.3 and 23.8 mg/dl in a 1-mm cell. The
ballistic light component was eﬀectively extracted in ascattering medium having a scattering coeﬃcient equivalent
to that of biological tissue (¼ 1:0 mm1 ) by the proposed
method. Furthermore, we demonstrated multiple-scatteringfree optical glucose measurement using a mixture of glucose
and scattering medium.
Acknowledgements
This work was supported by grants-in-aid for scientiﬁc research
13750045 and 15656069 from the Ministry of Education, Culture, Sports,
Science, and Technology of Japan, Tateishi Science and Technology
Foundation, and the Sasakawa Scientiﬁc Research Grant from The Japan
Science Society. We also thank Dr. M. Hashimoto at Osaka University formany insightful explanations of the measurement results.

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