OPTICAL REVIEW Vol. 13, No. 1 (2006) 29–33

Optical Glucose Monitoring
Based on Femtosecond Two-Color 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 April 27, 2005; Accepted October 5, 2005)
We demonstrate the potential of femtosecond two-color pulse interferometry for in vitro optical glucose monitoring, bydispersion of the group refractive index in a glucose solution sample with respect to a red-color light and a blue-color
light. By comparison with femtosecond one-color pulse interferometry, the basic performance of the present systemwith regard to sensitivity, quantitativeness, and tolerance to surrounding disturbances, is evaluated. The resulting
accuracy and precision of glucose determination are 77 and 118 mg/dl for 10-mm-sample-thickness, respectively. This
near-common-path conﬁguration of the two-color pulse light provides good stability to ﬂuctuations of sample
temperature, which is important in clinical applications. Considering the performance of femtosecond two-color pulseinterferometry as an optical glucose sensor, a suitable measurement site for in vivo optical glucose monitoring is
discussed. # 2006 The Optical Society of Japan
Key words: glucose, femtosecond two-color pulse light, multiple scattering, coherence gate, interferometry, time-ofﬂight, group refractive index

1.

temperature ﬂuctuation of the sample, because they disturb
the interference signal and hence decrease the measurement
quantitativeness.
One attractive method to suppress such eﬀects is use ofcommon-path-conﬁguration in interferometry. Combined
use of an optical nonlinear eﬀect [second-harmonic-generation (SHG)] induced by femtosecond pulse light withinterferometry provides unique near-common-path pulseinterferometry consisting of a red pulse light and a blue
pulse light, namely femtosecond two-color pulse interferometry (FTPI).7) The FTPI generates an interference signal
arising from the diﬀerence of group refractive index between
the two-color pulse lights and derives good stability to thesurrounding disturbances described above.
In this paper, we apply the FTPI to optical glucose
monitoring and evaluate its potential as an optical glucose
sensor through comparison with the FOPI. We ﬁrst evaluate
its sensitivity to glucose concentration and quantitativenessof the glucose concentration measurement using an aqueous
glucose solution sample. Next, we determine the stability totemperature change of sample in the glucose concentration
measurement to evaluate tolerance to surrounding disturbances. Finally, based on the resulting performance of FTPI,
suitable measurement sites for in vivo optical glucose
monitoring are discussed.

Introduction

One of the most challenging and valuable subjects inbiomedical optics is optical glucose monitoring, which frees
not only diabetic patients from the physical and mental
burden accompanying ﬁnger puncture but also the medical
staﬀ from risk of a blood infection accident. Such the optical
glucose monitoring also oﬀers continuous and/or sensitive
monitoring of glucose concentration in the blood. There areseveral reports on optical glucose monitoring: infraredabsorption spectroscopy,1) polarimetry of optical rotatory
power,2) Raman spectroscopy,3) and so on. When thesemethods are applied for clinical examinations, selection of ameasurement site is crucial. Considering direct measurementof blood glucose in blood vessel across the skin, thesensitivity, and quantitativeness of these methods do notsatisfactorily meet the requirements for clinical examinations. One reason for the low sensitivity and quantitativenessis the coexistence of multiple-scattered light caused by theundesirable particles in blood such as cells, lipids, andproteins. Recent advance in optical technology, however
provides eﬀective techniques to extract the desired opticalproperty from heavily-scattering biological tissue, such as
coherence gate4) or ultrafast time-resolved gate.5) These
techniques can detect the weak ballistic light while theyreject the multiple-scattered light. We previously proposed
the application of femtosecond one-color pulse interferometry (FOPI) to optical glucose monitoring.6) The combined
use of time-of-ﬂight measurement and coherence gateachieved by FOPI gives quantitativeness to glucose concentration measurement even in a scattering medium similar toblood, resulting in the achievement of in vitro multiplescattering-free optical glucose monitoring. To extend suchan interferometry method to in vivo glucose monitoring, it isnecessary to suppress the eﬀects of surrounding disturbances: air turbulence, sound and mechanical vibrations, and2.

Principle

2.1 Glucose concentration measurement
The principle of glucose concentration measurement isshown in Fig. 1. In general, when an ultrashort pulse light isincident to a glucose solution sample, the time required topass through the sample depends on the group refractive
index of the sample on the assumption of a ﬁxed geometricpath length. Since the group refractive index is proportional
to the sample concentration, one can determine the glucose
concentration by time delay of the interference signal based
29

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OPTICAL REVIEW Vol. 13, No. 1 (2006)
two-color
pulse light pure water
red
blue
blue

Y. HORI et al.
(a)ng

fs-Ti:S laser∆nwaterblue

redTime delay

λ(b)

Glucose sample(a)Variabletime delay

time delay unit

ng

(c)

glucose solution

increase

BBO

denser∆nglucose+∆nwater∆tglucosedM( λ = 800 nm, 200 mW,
LBO
100 fs, 87 MHz)∆ twaterd

PZT stage
HS

BS

red

Red pulse lightBlue pulse light

BPF
(d)
blue

red

λ
Demodulator

PC

(b)

PMT

Fig. 1. Glucose concentration measurement based on FTPI: (a)pure water sample and (b) glucose solution sample. When
temporally and spatially overlapped two-color (red and blue) pulse
is incident to a glucose solution sample, the time delay between thetwo-color pulse varies depending on the glucose concentration.

Fig. 2. Experimental setup of FTPI. LBO: frequency-doubling
LiB3 O5 crystal, BS: beam splitter, HS: harmonic separator, M:
mirror, PZT stage: piezoelectric stage, BBO: frequency-doubling BaB2 O4 crystal, BPF: blue-pass ﬁlter, PMT: photomultiplier, PC:personal computer.

on a time-of-ﬂight method with femtosecond pulse interferometry.6)
Let us consider that spatially and temporally overlapped
red and blue pulse light (namely, two-color pulse light) are
incident to a glucose solution at the same time. First, we
assume the sample is pure water without glucose [Fig. 1(a)].
After passing through the sample, the blue pulse light isdelayed by twater relative to the red pulse light because of
positive dispersion of the group refractive index in the water.
The value of twater is given as follows:twater ¼

nwater  d
;
c

ð1Þ

where nwater is the diﬀerence of group refractive index
between red and blue pulse light in the water, d is thegeometric path length of the sample, and c is the light
velocity in vacuum. Second, we consider a glucose solution
as a sample [Fig. 1(b)]. The time delay in this sample(tsample ) is given as follows:tsample ¼

ðnglucose þ nwater Þd
;
c

ð2Þ

where nglucose is the diﬀerence of group refractive index
between red and blue pulse light in the glucose. Using
eqs. (1) and (2), the nglucose value is determined as follows:tsample  twater
nglucose ¼ nwater;
ð3Þ
twater
where nwater and twater are known values. The grouprefractive index at each wavelength increases proportionallywith the glucose concentration, and the increment of thegroup refractive index at the shorter wavelength is larger
than at the longer wavelength. Hence, the nglucose value
proportionally increases with the concentration of glucose
solution. We determine the glucose concentration throughprecise measurement of the tsample value by the time-ofﬂight measurement using FTPI.

3.

Experimental Setup

Figure 2 shows an experimental setup of FTPI. The laser
source is a Kerr-lens mode-locked Ti:Al2 O3 laser (Avesta
Project, TiF-Kit-100, central wavelength = 800 nm, pulse
width = 80 fs, average power = 200 mW, repetition rate =87 MHz). The SHG light is produced from the fundamental
laser light by a frequency-doubling LiB3 O5 crystal (LBO,
thickness = 1 mm). The SHG light (blue pulse light, wavelength = 400 nm) and remaining fundamental light (redpulse light, wavelength = 800 nm) are introduced to theinterferometer as two-color pulse light maintaining atemporal and spatial overlap [(a) in Fig. 2]. The red pulse
light is separated and delayed compared to the blue pulse
light by a time delay unit consisting of a ﬁxed harmonic
separator (HS; reﬂected wavelength = 400 nm) and a
movable mirror mounted on a piezoelectric (PZT) stage(variable time delay, displacement stroke = 320 mm) with acapacitive positioning sensor [(b) in Fig. 2]. After adjusting
the time delay between them, the two-color pulse light isincident to the glucose solution sample. The SHG light isagain generated from the red pulse light by anotherfrequency-doubling -BaB2 O4 crystal (BBO, thickness =1 mm). The remaining red pulse light is eliminated by ablue-pass ﬁlter (BPF). The resulting two blue pulses are
spatially superimposed and ﬁnally detected with a photomultiplier (PMT). Because dispersion of group refractive
index of the sample results in diﬀerent optical path lengths
for the two-color pulse light, the interference between red
and blue pulse light is extinguished without adjusting thetime delay of the red pulse. However, when the time delay inthe sample is well compensated by the time delay unit [(c) in
Fig. 2], the blue interference fringe appears [(d) in Fig. 2].
The envelope component is electrically extracted from theinterference fringe by a demodulator. A fringe signal andextracted envelope signal are shown in Fig. 3. The resulting
envelope of the interference signal has 300 fs full-width at

1.0

1.0

0.5

0.8

Intensity [a.u.]

Intensity [a.u.]

OPTICAL REVIEW Vol. 13, No. 1 (2006)

0.0
-0.5

Y. HORI et al.

0.6
0.4
0.2

-1.0
0.0

0

200

400

600

800

1000

0

200

Time delay [fs]

400

600

800

1000

Time delay [fs]Fig. 3. Interference signal in FTPI: (a) interference fringe signal
and (b) extracted envelope signal.

half-maximum (FWHM) width. The temporal shift of the
maximum on the envelope signal is determined by displacement of the PZT stage in the time delay unit, which is readfrom the precise capacitive positioning sensor equipped withthe stage (linearity = 5.3 nm, resettability = 35.1 nm).
4.

Results

4.1 Glucose concentration measurement
Before demonstration of optical glucose monitoring using
FTPI, we evaluated the dependence of group refractive index
on glucose concentration for a red pulse light (wavelength =800 nm) and a blue pulse light (wavelength = 400 nm) using
FOPI. A sample cell of 10-mm-thickness was used. We
prepared glucose solution samples with concentrations of 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).
The temperatures of these samples were stable within0:2 C and the measurements were repeated ten times at
each concentration. The resulting relationships between
glucose concentration and time delay for red and blue pulse
lights are shown in Fig. 4, respectively. The solid lines are
the slopes obtained by linear ﬁtting of the data points. The
slopes for red and blue pulse lights are 0.0435 and 0.0493
fsdl/mg, respectively. This diﬀerence in slope between
them is due to a positive dispersion of group refractive index
in the glucose solution sample. Here, we deﬁned accuracy as

140Time delay [fs]120Blue-FOPI
y = 0.0493 x

100
80

Red-FOPIy = 0.0435 x

60
40

0
0

500

1000

1500

2000

the standard deviation of the diﬀerence of each measurement
value from the value on the slope, and precision as thestandard deviation of ten repetitive measurements at eachconcentration. For optical glucose measurement using redFOPI, the accuracy and precision were 8.3 and 1.8 mg/dl,
respectively;6) the former was mainly due to temperatureﬂuctuation of sample (¼ 0:2 C, corresponding error = 9.6
mg/dl), concentration precision in sample preparation(¼ 0:32%, corresponding error = 4.8 mg/dl), and/or linearity of PZT stage displacement (¼ 5:3 nm, corresponding
error = 0.80 mg/dl) while the latter depended on resettability of PZT stage displacement (¼ 35:1 nm, corresponding
error = 5.2 mg/dl).
Next, we examined the relationship between time delay of
two-color pulse light (tsample ) and glucose concentration in
optical glucose measurement using FTPI as also shown in
Fig. 4. In this experiment, we used the same glucose samples
as those used in FOPI measurement. The resulting slope of
0.0045 fsdl/mg for FTPI was about 10 times smaller thanthose for FOPI because of reduced sensitivity due to use ofdispersion of group refractive index. Although this value isin approximate agreement with diﬀerence of the gradient
between red-FOPI and blue-FOPI (¼ 0:0058 fsdl/mg),
there is an error of 28.9% between them. The slope for
red-FOPI and blue-FOPI may ﬂuctuate within a range of
0:0435  0:001 and 0:0493  0:001 fsdl/mg, respectively,
depending on the resettability of the PZT stage displacement(¼ 35:1 nm) and the concentration precision of each glucose
sample (¼ 37 mg/dl at 3000 mg/dl). As a result, thediﬀerence of the two slopes in FOPI is expected to range
from 0.0037 to 0.0079 fsdl/mg. On the other hand, similar
ﬂuctuation in FTPI is estimated to be within a range of
0:0045  0:0001 fsdl/mg, in which the eﬀect of theconcentration precision compensated as a result of thenear-common-path conﬁguration. Therefore, the slope of
0.0045 fsdl/mg for FTPI exists within tolerance limits. The
accuracy and precision of the glucose determination withFTPI were 77 and 118 mg/dl, respectively. The accuracy isinﬂuenced by linearity of PZT stage displacement (estimatederror = 7.9 mg/dl), and/or ﬂuctuation of sample temperature (estimated error = 10.2 mg/dl), while the precision ismainly due to resettability of PZT stage displacement(estimated = 52 mg/dl). Furthermore, the actual accuracy
and precision may be inﬂuenced by individual ﬂuctuation ofpulse width and its intensity in two-color pulse light.
Here, we consider a signal-to-noise ratio (SNR) in FOPI
and FTPI. Intensity of the interference signal in FOPI (IFOPI )is expressed as follows:
IFOPI ¼ 2ðI0 þ I0 Þ þ 2ðI0 þ I0 Þð1 Þ1 cos 1 ;FTPI
y = 0.0045 x

20

2500

3000

Glucose concentration [mg/dl]
Fig. 4. Relationship between glucose concentration and timedelay with respect to red-FOPI, blue-FOPI, and FTPI. Sample
thickness is 10 mm. Solid lines are correlation curves obtained by alinear ﬁtting.

31

ð4Þ

where I0 and I0 is an average and a ﬂuctuation in intensityof laser pulse light, ð1 Þ is the degree of temporal overlap
between the two pulse lights when a phase diﬀerence
between a reference and a signal light is 1 , and 1 is thedegree of spatial overlap between the two lights. 2ðI0 þ
I0 Þð1 Þ and cos 1 in the second term of eq. (4),respectively give an envelope component and a fringe
component in the interference signal whereas the ﬁrst term

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OPTICAL REVIEW Vol. 13, No. 1 (2006)

Y. HORI et al.

IFOPI ¼ 2I0 þ 2ðI0 þ I0 Þð1 Þ1 :Glucose concentration [mg/dl]

indicates an oﬀset component. In the present setup, since abias component and high-frequency component in theinterference signal are electrically eliminated by the demodulator, eq. (4) is modiﬁed as follows:ð5Þ

When we deﬁne SNR as a ratio of the second term to the ﬁrst
term in eq. (5), SNR in FOPI (SNRFOPI ) is expressed asfollows:
ðI0 þ I0 Þð1 Þ1
SNRFOPI ¼
:
I0

ð6Þ

In contrast, intensity of interference signal in FTPI (IFTPI ) is
given as follows:
2

IFTPI ¼ ð1 þ 2 ÞðI0 þ I0 Þ
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
þ 2 1 2 ðI0 þ I0 Þ2 ð2 Þ2 cos 2 ;

ð7Þ

where 1 and 2 respectively indicate SHG conversion
eﬃciency in the ﬁrst and the second SHG crystals (LBO andBBO in Fig. 2), 2 is the phase diﬀerence between the redand blue pulse light and 2 is the degree of spatial overlap
between the two pulse light. In eq. (7), we neglect loss of ared pulse light caused by the SHG process. After demodulation, the interference signal is modiﬁed as follows:
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
IFTPI ¼ 2ð1 þ 2 ÞI0 I0 þ 2 1 2 ðI0 þ I0 Þ2 ð2 Þ2 ; ð8Þ
here we made the approximation that I0 2  0. The SNR in
FTPI (SNRFTPI ) is determined by the following equation:pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
1 2 ðI0 þ I0 Þ2 ð2 Þ2SNRFTPI ¼
ð9Þð1 þ 2 ÞI0 I0The actual SNR in the present FOPI and FTPI were bothnearly 2:0  103 .
4.2 Dependence of temperature change in sample
Because of very high sensitivity for change of therefractive index and/or optical path length, usual interferometry is easily inﬂuenced by surrounding disturbances suchas air turbulence, sound and mechanical vibrations, or
temperature change. This results in a limitation of applications to the measurement under unstable environments suchas clinical examination. For example, temperature of thehuman body ﬂuctuates within 0:5 C during a day,physiologically. Such temperature change in a sample
causes changes of refractive index (or time delay) even if
the glucose concentration is constant. Stability to thetemperature change can be gained by FTPI because nearcommon-path conﬁguration of the two-color pulse light cancompensates the eﬀect in the interferometer. Here, we
compare stability to the change in sample temperature in
FTPI to that in red-FOPI. The sample is pure water with athickness of 10 mm, and the sample temperature is continuously changed from 24 to 40 C. Figure 5 shows dependence of glucose concentration on the sample temperature in
FTPI, which is compared with that in red-FOPI. The glucose
concentration value is calculated from the slopes (see Fig. 4)
and ﬂuctuation of time delay with respect to the sample
temperature. In Fig. 5, the value at 40 C is shown as the

3000

Red-FOPI
y = -228 x + 9135

2000

FTPI

1000

y = -1.3 × 102 x + 5.3 × 103
0
24

26

28

30

32

34

36

38

40

Temperature [°C]Fig. 5. Dependence of glucose concentration on sample temperature for red-FOPI and FTPI. Sample is pure water with 10 mmthickness. Time delay at 40 C is deﬁned as origin of time delay
ﬂuctuation.

origin of ﬂuctuation in glucose concentration. The resulting
temperature-dependent slope is 1:3  102 mg/(dl C) for
FTPI and 228 mg/(dl C) for red-FOPI, respectively. For
example, temperature ﬂuctuation of 0:5 C, which is thephysiological value in the human body in a day, leads toinstability of 114 and 65 mg/dl in glucose concentration
for red-FOPI and FTPI, respectively. One can conﬁrm thatthe eﬀect of temperature ﬂuctuation in the sample is reduced
to 57% by FTPI, although there is still ﬂuctuation of timedelay due to temperature change in FTPI. The remaining
ﬂuctuation results from diﬀerent temperature dependence ofthe group refractive index for red and blue pulse lights. Fromthe comparison, we can conclude that the FTPI is eﬀective
for glucose measurement of a temperature-ﬂuctuant sample
such as the human body.
5.

Discussion

From the comparison of performance between the FTPI
and FOPI for optical glucose monitoring in vitro, the nearcommon-path FTPI shows superiority in tolerance toﬂuctuations in sample temperature. Besides the temperatureﬂuctuations in a sample, the near-common-path conﬁguration is inherently tolerant of surrounding disturbance of air,mechanical vibration, or sound vibration. Good stability inthese disturbances in FTPI will provide a powerful tool toachieve clinical application. For application of the optical
glucose monitoring to clinical use, selection of a measurement site to which transdermal measurement at a transmittance conﬁguration can be achieved is most important.
Skin and vessel are heavily scattering media to visible andinfrared lights. Although the FTPI possesses the elimination
power of multiple-scattering light using the coherence gate,7)
the power is rather smaller than that in red-FOPI because of
double scattering of the two-color pulse lights, severe
scattering of a blue light, and decreased detection sensitivity
due to the two SHG processes. Hence, it is diﬃcult to ﬁnd atransdermal measurement site possible for the optical beam
to pass through the skin and vessel overall. Use of deeppenetrative femtosecond laser with longer wavelength, such

OPTICAL REVIEW Vol. 13, No. 1 (2006)

as a mode-locked Cr:Forsterite laser (fundamental wavelength = 1250 nm, SHG wavelength = 625 nm) or a modelocked ﬁber laser (fundamental wavelength = 1500 nm,
SHG wavelength = 750 nm), may improve the elimination
power of multiple scattering in FTPI because the scattering
is less eﬃcient at these wavelengths. However, the sensitivity of FTPI to glucose concentration is reduced because ofa gradual decrease in the dispersion of group refractive index
in the longer wavelength region. Furthermore, such transdermal glucose monitoring is often aﬀected by the conditionof skin surface such as drying and sunburn. On the other
hand, the aqueous humor in the eye at which multiple
scattering hardly occurs is interesting as a measurement
window for the optical glucose monitoring because there ishigh correlation between the blood glucose and the aqueous
glucose.8) In general, the blood is comprised of glucose andother components (cells, lipids, and proteins). In optical
glucose measurement based on the group refractive index
and its dispersion in such a multi-component system,
ﬂuctuation of the concentration of other components
interferes with that of the glucose, resulting in diﬃculty ofquantitativeness in the glucose concentration measurement.
Another advantage in using the aqueous humor as themeasurement site is to suppress the interference caused byother components because the aqueous protein has very low
concentration (0.013 g/dl) in aqueous humor.9) The sensitivity of FTPI to glucose concentration can be gained byincreased optical thickness of the aqueous humor. Considering in vivo optical glucose monitoring via the eye, use ofan eye-safe laser has to be considered although there are few
femtosecond lasers which generate a femtosecond two-color
pulse light in the eye-safe region (wavelength = 1.4 –2.6 mm). From these considerations, we expect FTPI to besuitable for in vivo optical glucose monitoring of anterior
humor.
6.

Conclusion

We propose optical glucose monitoring using FTPI andevaluate its performance through comparison with FOPI.
Linear dependence of glucose concentration on dispersion of
the group refractive index gives quantitativeness in the invitro optical glucose monitoring. Accuracy and precision in
the glucose concentration measurement is seriously aﬀectedby the performance of the PZT stage positioning for timedelay because of the gentle dependence on dispersion of theY. HORI et al.

33group refractive index. The precision of this measurement isalso limited by lengthy coherent time (¼ 300 fs) of thepresent FTPI signal as compared with the temporal shift(< 10 fs) caused by the glucose concentration. Near-common-path conﬁguration of the two-color pulse light in FTPI
provides good stability to ﬂuctuations of the sample temperature. This feature is signiﬁcant of reproducability in in vivo
optical glucose monitoring based on the interferometricmethod because the temperature of the human body
ﬂuctuates within 0:5 C during a day. Furthermore, thenear-common-path FTPI will eﬀectively suppress the inﬂuence of air disturbance or vibrations on the interferometry,
which is encountered in unstable environments such as aclinic. This tolerance to surrounding disturbances allows the
FTPI to be used in a clinical setting. Based on the present
investigations of performance of the FTPI as an optical
glucose sensor, the aqueous humor is proposed as a nontransdermal measurement site for in vivo optical glucose
monitoring based on the FTPI. The proposed FTPI will be a
powerful tool for stable optical glucose monitoring in vivo inclinical applications.
Acknowledgements
This work was supported by a Grants-in-Aid for scientiﬁc
research Nos. 16300155 and 17200032 from the Ministry of
Education, Culture, Sports, Science and Technology of Japan, andthe Tateishi Science and Technology Foundation. We also thankDr. M. Hashimoto at Osaka University for many insightful
explanations of the measurement results.
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