A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal

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Optics Communications 259 (2006) 40–48

A polarimetric glucose sensor using a liquid-crystal polarizationmodulator driven by a sinusoidal signal

Yu-Lung Lo *, Tsung-Chih Yu

Department of Mechanical Engineering, National Cheng Kung University, University Road, Tainan 701, Taiwan

Received 11 April 2005; received in revised form 19 August 2005; accepted 31 August 2005

Abstract

Rather than using a conventional Faraday modulator, this study adopts a liquid-crystal based rotator to modulate the azimuth of thelinear polarized light in a sinusoidal signal for the measurement of glucose concentrations. The tilt angle of the LC director would vary asa sinusoidal-like function; however the modulating frequency in the sensing system is the double of the driving signal. A new signaldemodulation algorithm, therefore, is developed that enables the polarization rotation angle corresponding to the glucose concentrationto be derived. The standard deviation in rotation angle level of 0.00551� has been obtained, with a 0.998773 correlation coefficientbetween the reference and the measured values. The proposed measurement method has a minimum resolvable concentration of0.2 g/dl. Compared to its conventional counterparts, the developed polarimeter potentially has a simpler structure, fewer opticalelements, and a cheaper modulator component.� 2005 Elsevier B.V. All rights reserved.

Keywords: Optical polarimetry; Glucose sensor; Liquid-crystal; Optical rotator

1. Introduction

Polarimetric glucose sensing involves measuring therotation of polarization caused by the optical activity ofthe glucose. Because a glucose solution rotates a polarizedlight beam�s polarization proportional to its concentration,various polarimetric glucose sensors have been developedby the use of Faraday rotators [1,2] or electro-optic modu-lator (Pockels and Kerr cells) [3] to modulate the beam�spolarization state or by the use a Zeeman laser in opticalheterodyne detection [4]. In addition, a surface microma-chined phase modulator [5] and a fiber-optic rotator [6]were recently proposed in the polarimetric glucose sensing.A Faraday rotator requires magnetic field, so it is inconve-nient and difficult to integrate into optical system. Themain problem with an electro-optic modulator is that ittends to be bulky and expensive and typically requires a

0030-4018/$ - see front matter � 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.optcom.2005.08.061

* Corresponding author. Tel.: +886 6 2757575x62123; fax: +886 62352973.

E-mail address: [email protected] (Y.-L. Lo).

high voltage for operation. These sensor constructions usedin past studies are actually pretty bulky, complicated, andnot flexible for setting. For a practical glucose sensor, amore compact and flexible sensor construction is required.

Liquid crystal (LC) was chosen in this study because ofits compact size and unique electro-optical effects, whichpermit a small electric field to change the retardation ofthe cell. The LC linear retarders (non-twisted nematic)are optically anisotropic media that act as a uniaxial retar-dation plate and exhibit optical birefringence [7]. They pro-duce different polarization states depending on the externalapplied voltage and therefore were used in the polarizationcontrol [8,9], imaging polariscope [10], interference micro-scope, and optical rotators [11,12].

As Jones predicted [13], a variable linear retarder placedbetween two orthogonal quarter-wave plates whose slowaxes form an angle of ±45� with that of the linear retarderacts as an azimuth optical rotator which can rotate thepolarization state. The rotation angle can be controlledby controlling the birefringence of the linear retarder.Recently, Ye [11] developed an optical rotator by the use

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Y.-L. Lo, T.-C. Yu / Optics Communications 259 (2006) 40–48 41

of a liquid crystal variable retarder (LCVR) as the variablelinear retarder. The amount of the azimuth rotation isdetermined by the retardation of the liquid-crystal cell,which can be controlled by the applied electric field. It isnoticed that the LCVR was conventionally controlled byhigh frequency square-wave ac voltage [8–12], and theretardation of the liquid crystal retarder was adjusted toa specific value by changing the voltage amplitude. Bymeans of this driving method, however, the LC rotatorcannot act as the Faraday modulator, which modulatesthe angle of linear polarization as a sinusoidal function.

In our study, the LC retarder was driven with a sinusoi-dal voltage and it was experimentally confirmed the LCrotator would act as a Faraday rotator. According to theauthors� knowledge, it is the first investigation in a LCrotator driven by a sinusoidal signal for a sensing systemapplication. It is proved that the LC rotator could be analternative modulator in the measurement system. A newsignal-processing algorithm is also developed to demodu-late the detected signal such that the polarization rotationangle of the light, which corresponds to the concentrationof the glucose, can be derived. The performance of the pro-posed LC modulator-based polarimeter is validated bothnumerically and experimentally.

Spacer

E

t

Asin(ωmt)

mθ

0θ

θ

θ

ITO glass

a

b

Fig. 2. (a) Application of sinusoidal driving signal to LC wave plate. (b)Time-based variation of LC molecule tilt angle.

2. Liquid-crystal polarization modulator

The polarization modulator is the key component of thepolarimetric glucose measurement system. This studyemploys a LC retarder as the rotation modulator andperforms modulation with a sinusoidal voltage. The Jonesmatrix, Rm , of the LC optical rotator arrangement pre-sented in Fig. 1 can be expressed as follows:

Rm ¼0 �1

1 0

� �e�ip=4 0

0 eip=4

" #0 1

�1 0

� �cos C

2�i sin C

2

�i sin C2

cos C2

" #

�1 0

0 1

� �e�ip=4 0

0 eip=4

" #1 0

0 1

� �

¼cos C

2sin C

2

� sin C2

cos C2

" #; ð1Þ

QWP Liquid Crystal Waveplate

y

x

Fig. 1. Schematic illustration of

where C is the retardance of the liquid-crystal wave plateand is given by C ¼ 2pðDnÞd

k , where Dn is the birefringenceof the LC wave plate, d is the path length of the light beampassing through the wave plate, and k is the wavelength ofthe light source.

The nematic liquid-crystal layer of the LC retarder issandwiched between two glass coated with a transparentelectrode and is homogeneous non-twisted alignment.As shown in Eq. (1), the rotation angle of the opticalrotator is equal to one-half of the phase retardance ofthe LC wave plate. A sinusoidal voltage, A sin(2pmmt), isapplied to the LC retarder. As a result, the tilt angle ofthe LC molecules would change periodically as illustratedin Fig. 2.

The software LCDMaster (Shintech Co.) was utilized tosimulate the variation of the LC molecule tilt angle. TheLC molecules in the LC retarder are nematic liquid crystalwith positive dielectric anisotropy. Two liquid crystal mate-rials were considered in the tilt angle simulations, namelyZOC-5044XX and ZLI4792 (Merck). In both cases, thethickness of the LC cell was assumed to be 6 lm. The sim-ulation results are presented in Fig. 3.

Figs. 3(a) and (b) present the simulation results forthe cases where a sinusoidal voltage with a 5 V amplitude

QWP

optical rotator arrangement.

1.25

1.3

1.35

1.4

1.45

x 10-5

n

74.5

75

75.5

76

76.5

77

77.5

78

78.5

400 405 410 415 420 425 430Time(ms)

Tilt

Ang

le(d

eg)

-5

-4

-3

-2

-1

0

1

2

3

4

5

Applied V

oltage (volts)

Tilt angle θ Applied voltage

71

71.5

72

72.5

73

73.5

74

74.5

120 124 128 132 136 140 144 148Time(ms)

Tilt

Ang

leθ

(deg

)

-5

-4

-3

-2

-1

0

1

2

3

4

5

Applied V

oltage (volts)

Tilt angle θ Applied voltage

a

b

Fig. 3. LCD master simulation results for tilt angle variation: (a) LC:ZOC-5044XX and (b) LC: ZLI4792.

42 Y.-L. Lo, T.-C. Yu / Optics Communications 259 (2006) 40–48

and a 100 Hz frequency was used to drive the ZOC-5044XX and ZLI-4792, respectively. In other cases (notshown), regardless of the driving frequency is higher orlower than 100 Hz, the tilt angle variation of the LCmolecules will be similar to Fig. 3. The results aboveindicate that if only the driving voltage amplitude exceedsthe liquid-crystal threshold voltage, the frequency of the tiltangle h of the LC director is twice that of the drivingvoltage, i.e.,

1.2

∆

h ¼ h0 þ hm cosð4pmmtÞ; ð2Þ

0.4 0.401 0.402 0.403 0.404 0.405 0.406

1.05

1.1

1.15

Time(sec)

Fig. 4. Simulation results for variation of birefringence (Dn) of LCwaveplate.

where h0 and hm are the DC and AC terms of the tilt anglein the LC molecule, respectively, and mm is the modulationfrequency of the driving voltage.

The LC waveplate is a uniaxially anisotropic media.When light propagates in this uniaxial crystal, the eigen-refractive indices associated with the ordinary (O) waveand the extraordinary (E) wave are given by [14]:

O wave : n ¼ no;

E wave :1

n2eðuÞ¼ cos2u

n2oþ sin2u

n2e;

ð3Þ

where u is the angle between the direction of propagationand the optic axis, and h + u = 90�.

Therefore, the refractive index of the E wave can be ex-pressed as

neðhÞ ¼noneffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðne sin hÞ2 þ ðno cos hÞ2q . ð4Þ

The simulation results for the LC molecule tilt angle varia-tion presented in Fig. 3(a) can be employed to calculatethe variation of birefringence, i.e., Dn = (ne(h) � no). Thecorresponding results are presented in Fig. 4. It can be seenthat the variation of birefringence, Dn, is also a sinusoidal-like function of time. Significantly, it is noted that thevariation of birefringence has double the frequency of thedriving signal. Hence, the phase retardation, C, betweenthe E wave and the O wave propagating normally throughthe LC wave plate also has a sinusoidal-like form. As shownin Eq. (1), when the phase retardance is time-dependent, therotation angle of the polarized light is also time-dependent.Consequently, the simulation results confirm that the appli-cation of a sinusoidal driving signal permits the LC rotatorto be used a polarization modulator.

In the above simulation, the LC waveplate is assumed asa perfect linear retarder. In order to demonstrate the line-arity of the commercial LC retarder (Meadowlark Optics,LRC-200-Vis), the LC retarder is placed between a pola-rizer and an analyzer. The axes of LC retarder and pola-rizer are parallel, and the analyzer is rotated from 0� to360� to verify the Malus law (I = Imaxcos

2/, where / isthe angle between the polarizer and analyzer). As shown

0 40 80 120 160 200 240 280 320 3600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Φ(deg)

norm

aliz

ed in

tens

ity

theoreticaldata

experimentalresult

Fig. 5. Experimental results for the verification of Malus law.

0.5 0.5004 0.5008 0.5012 0.5016 0.502

-4

-3

-2

-1

0

1

2

3

4

Time (sec)

Inte

nsity

(V

olts

)

Fig. 7. Signal detected experimentally with frequency of 3 kHz.


in Fig. 5, the detected signal is in a good agreement withthe theoretical value. Therefore, the LC retarder can beregarded as a linear retarder in the following experiment.

The simple optical system illustrated in Fig. 6 wasconstructed in order to verify the feasibility of driving theoptical LC rotation modulator with a sinusoidal signal.When the modulator is placed between crossed polarizers,the intensity, I, of the light incident upon the photo-detectorat any point in time can be expressed as:

I / sin2 C2

� �¼ 1

2� 1

2cosðCÞ. ð5Þ

As shown in Fig. 6, a He–Ne laser was employed as thelight source and two Glan–Thomson polarizers served asthe polarizer and the analyzer, respectively. Meanwhile,the optical rotator comprised a LC variable retarder andtwo 632.8 nm quarter-wave plates.

In the verification experiment, the LC wave plate wasdriven by a sinusoidal voltage with a 1.5 kHz frequencyand 6 V amplitude. The light intensity signal, I, detectedby the photo-detector was acquired using a DAQ card(PCI-6071E, National Instrument). The experimental

P(0˚) λ /4(0˚) λ/4(90˚) A(90˚)

Optical Rotator

He-Ne Laser

LC retarder(45˚)

Asin(ωmt)

I

Detector

Fig. 6. Schematic illustration of experimental verification system.

results for the detected intensity signal are illustrated inFig. 7.

The results confirm that the use of a sinusoidal drivingsignal enables the optical liquid-crystal rotator to operateas a polarization modulator. Fig. 7 reveals that the fre-quency of the detected signal (3 kHz) is double that ofthe driving signal (1.5 kHz). Hence, the optical rotatornot only has the ability to rotate the polarization of thelight to a specific angle, but can also modulate the polari-zation angle as a sinusoidal-like function.

The numerical and experimental results presented in thissection of the paper have confirmed the feasibility of mak-ing the LC rotator be a polarization modulator by drivinga sinusoidal signal. The LC polarization modulator is easilyproduced and integrated as compared with a traditionalFaraday modulator. Furthermore, compared with theelectro-optic modulator (Pockels or Kerr cell), the LCpolarization modulator has a low operational voltage, lowpower consumption, a compact size, and a large polariza-tion rotation angle due to the high birefringence of theLC molecules. On account of the above advantages, it isattractive to use the LC modulator to be an alternativemodulator in the glucose measurement system. However,the slow frequency response is the LC modulator�s draw-back. The following sections of this paper address the appli-cation of the developed LC polarization modulator to themeasurement of glucose concentrations.

3. Principles of polarimetry for measurement of glucose

concentration

The glucose concentration in a liquid solution, expressedin grams per deciliter of the solution, is given by:

C ¼ 100aL½a� ; ð6Þ

where a is the observed rotation in degrees, L is the layerthickness in decimeters, and [a] is the specific rotation

Sample

Polarization Modulator

I

Asin(ωmt)

QWP(0˚)

QWP(90˚) A(90˚)

LCVR(45˚)

P(0˚)

He-Ne Laser

PD

Fig. 8. Schematic diagram of glucose measurement system. P, polarizer;QWP, quarter-wave plate; LCVR, liquid-crystal variable retarder; A,analyzer; PD, photo-detector. Sample: glucose solution.

0 0.5 1 1.5 2 2.5 3 3.5 4-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Γm

JΓ(n

m)

0.5(J1-J3)J2

1.57

Fig. 10. Optimal value of Bessel functions.


depending on temperature, wavelength and pH level. InEq. (6), the concentration of the glucose, C, can be deter-mined by measuring the polarization rotation angle, a.

Fig. 8 presents a schematic illustration of the measure-ment system utilized to measure the glucose concentration.As shown, the LC rotator comprises two quarter-waveplates and a liquid-crystal retarder. As discussed previously,the LC retarder is driven by a sinusoidal signal, A sin 2pmmt.

Having passed through the glucose sample and the ana-lyzer, the polarized laser beam can be expressed as:

E*

¼ExðtÞEyðtÞ

� �¼

0 0

0 1

� �Analyzerð90�Þcos a sin a

� sin a cos a

� �Sample

�cos C

2

� �sin C

2

� �� sin C

2

� �cos C

2

� �" #LC rotator

1 0

0 0

� �Polarizerð0�Þ1

0

� �

¼0

� sin C2� a

� �� ; ð7Þ

where C ¼ Cm cosð4pmmtÞ is the phase retardance intro-duced by the LC waveplate, Cm is the modulation depth,and a is the rotation angle of the polarized light causedby the glucose sample. The output signal from the photo-detector is therefore given by:

I / E2 ¼ 1

2� 1

2cos½2aþ Cm cosð4pmmtÞ�. ð8Þ

As can be seen, the detected signal consists of a DC termand a modulated term. The present study utilizes the signalprocessing algorithm illustrated in Fig. 9 to extract therotation angle, a, induced by the optically active substance.

I Band Pass Filter (4νm)

cos8πνmt

I1 I1'

Band Pass Filter (4νm)

I2cos(4πνm)t

I2'I'

Fig. 9. Signal proce

As shown in Fig. 9, the detected signal, I, is mixed with asynchronous signal, cos 4pmmt, to generate a signal I 0. Hav-ing passed through two band-pass filters with pass-bandfrequencies of 4mm, the filtered signals (I and I 0) become:

I1 ¼ J 2ðCmÞ cosð8pmmtÞ cosð2aÞ; ð9Þ

I2 ¼1

2½J 1ðCmÞ � J 3ðCmÞ� cosð8pmmtÞ sinð2aÞ; ð10Þ

where J1, J2, and J3 are Bessel functions of the first kind ofthe 1st, 2nd, and 3rd order, respectively. The signals I1 andI2 are then mixed with a synchronous signal, cos(8pmmt) togenerate signals of:

I 01 ¼ J 2ðCmÞ1

2þ 1

2cosð16pmmtÞ

� �cosð2aÞ; ð11Þ

I 02 ¼1

4½J 1ðCmÞ � J 3ðCmÞ�½1þ cosð16pmmtÞ� sinð2aÞ. ð12Þ

The modulated terms in Eqs. (11) and (12) are then filteredout by two low-pass filters, each with an 8mm cutoff fre-quency. The two signals can then be expressed as:

I 001 ¼ 1

2J 2ðCmÞ cosð2aÞ; ð13Þ

I 002 ¼ 1

4½J 1ðCmÞ � J 3ðCmÞ� sinð2aÞ. ð14Þ

It is necessary to adjust the modulation depth such that theamplitudes of Eqs. (13) and (14) become equal. As illustrated

KLow PassFilter (8νm)

Arctangent 2α

Low PassFilter (8νm)

I1"

I2"

ssing algorithm.

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.2 0.4 0.6 0.8 1 1.2glucose concentration (g/dl)

rota

tion

angl

e α

(deg

)

Corre. Coef. = 0.998773Stan. Dev.= 0.00551 (deg)

Fig. 11. Experimental results with 20 Hz driving signal.


in Fig. 10, when Cm = 1.57, J 2ðCmÞ ¼ 12½J 1ðCmÞ �J 3ðCmÞ�

and the amplitudes of I 001 and I002 are equal. Therefore, the tan-

gent function of the polarization angle, a, can be obtained bydividing I 002 by I 001, i.e.,

I tanð2aÞ ¼I 002I 001

¼ tanð2aÞ. ð15Þ

The rotation angle, a, can then be derived from the arctan-gent algorithm of Eq. (15).

The signal processing method presented above allowsthe rotation angle induced by the optically active sampleto be extracted.

4. Experimental setup and results

As can be seen from the analytical model describedabove, the variation of the phase retardance of theliquid-crystal wave plate, C = Cm cos(4pmmt), has no initialphase. Hence, in order to achieve absolute measurements,the DC-bias birefringence of the LC retarder (MeadowlarkOptics, LRC-200-Vis) should be adjusted to comply withthe analytical results. Adjusting the initial phase such thatit equals zero is clearly an important procedure [15].

This study commenced the adjustment procedure byplacing de-ionized water only in the sample cell. Under thiscondition, the intensity of the signal detected by the photo-detector is given by:

Ino-glucose / sin2 C0

2

� �¼ 1

2� 1

2cosðC0Þ; ð16Þ

where C 0 is the practical phase retardance of the LC waveplate and is defined as C0 ¼ CDC þ Cm cosð4pmmtÞ, whereCDC is the initial phase. The signal Ino-glucose was thenpassed through a band-pass filter with a pass-band fre-quency of 2mm, mixed with a synchronous signal,cosð4pmmtÞ, and then passed through a low-pass filter withcutoff frequency, 4mm. Eq. (16) can therefore be rewrittenas:

I 0no-glucose /1

2J 1ðCmÞ sinðCDCÞ. ð17Þ

From Eq. (17), it is clear that provided the initial phaseretardance, IDC, is adjusted to zero, I 0no-glucose also equalszero, regardless of the value of the modulation depth. Inaddition to adjusting the initial phase to zero, the modula-tion depth, Cm, of the LC modulator must be set to 1.57 toensure that the amplitudes of I 001 and I 002 in Eqs. (13) and (14)are equal. Therefore, the analyzer was rotated to simulatethe rotation angles of the polarization plane for calibrationpurposes. Consequently, the detected signal received by thephoto-detector can be expressed as:

I / E2 ¼ 1

2þ 1

2cos½2/þ Cm cosð4pmmtÞ�; ð18Þ

where / is the rotation angle of the analyzer. When therotation angle of the analyzer is set to / = 22.5� , the valueof the gain, K, is given by:

K ¼ I tanð2/Þ ¼I 002I 001

¼ J 1ðCmÞ � J 3ðCmÞ2J 2ðCmÞ

tanð2� 22:5�Þ

¼ J 1ðCmÞ � J 3ðCmÞ2J 2ðCmÞ

. ð19Þ

Eq. (19) indicates that the signal I 001 can be multiplied by thegain, K, such that the amplitudes of I 001 and I 002 becomeequal. Having adjusted CDC = 0 and obtained the gain,K, the rotation angle associated with the glucose concentra-tion can then be extracted using the signal process illus-trated in Fig. 9.

The present study performed an experimental investiga-tion to confirm the ability of the proposed glucose sensorand signal-processing algorithm to detect various concen-trations of glucose. As shown in Fig. 8, the light from a sta-bilized He–Ne laser was passed through a Glan–Thompsonpolarizer, whose azimuth angle was set at 0�. Initially, theLC polarization modulator was driven by a sinusoidal sig-nal with a frequency of 20 Hz. The modulated light passedthrough the glucose solution and was detected by a photo-detector. The output signal of the photo-detector was ac-quired by a DAQ card and subsequently transmitted to aPC for signal processing. In the present experiment,50 mm long rectangular sample cells were used to hold glu-cose solution samples of differing concentrations

The present glucose solutions were prepared from a60-mg/ml stock glucose solution made by dissolving6.00 g of D-glucose (Merck Ltd) in a total volume of100 ml of de-ionized water. Individual glucose sampleswith concentrations ranging from 0 to 1.2 g/dl in 0.2 g/dlincrements were then prepared by diluting the stock solu-tion with an appropriate volume of de-ionized water.

Fig. 11 presents the experimental relationship betweenthe rotation angle and the glucose concentration for a driv-ing signal with a frequency of 20 Hz. A correlation coeffi-cient of 0.998773 indicates a good linear response, with ameasurement deviation of 0.00551�. However, it is notedthat the low SNR, possibly caused by the low driving fre-quency of 20 Hz, prevents the measurement of glucose con-centrations of less than 0.2 g/dl.

0.04

0.042

0.044

0.046

0.048

0.05

0.052

0.054

1 3 5 7 9 11Mesurement Times

Mea

sure

d R

otat

ion

Ang

les

(deg

)

Fig. 12. System repeatability. 20 40 60 80 100 120 140 160 180 200

-100

-90

-80

-70

-60

-50

-40

-30

-20

Frequency (Hz)

Mag

nitu

de(d

B)

Fig. 14. Power spectrum of 20 Hz driving signal.


To demonstrate the repeatability of the proposed sys-tem, the consecutive measurements are taken at the sameplace. A glucose sample of 0.2 g/dl at 633 nm wavelengthand 25� is measured 11 times in every 10 min for repeatabil-ity. In theory, the rotation angle of 0.2 g/dl glucose solu-tion is 0.05�. As illustrated in Fig. 12, the average valuein repeatability experiments is 0.049� and the standarddeviation is 0.002�. Therefore, the average relative erroris around 2%. From the experimental results, the thermaldrift of the LC modulator may cause the variation of themeasured value in Fig. 12.

In an attempt to improve the SNR of the detected sig-nal, the driving frequency was increased to 1 kHz. The cor-responding experimental results are illustrated in Fig. 13.From Fig. 13, the correlation coefficient, the measurementdeviation, and the minimum resolvable rotation angle areworse than when a 20 Hz driving signal is employed.Therefore, the performance of the system is not improvedby increasing the frequency of the driving signal. Thepower spectrum of the detected signals driven by 20 Hz fre-quency is shown in Fig. 14, the highest peak (80 Hz) is theinterested signal, and the signal (80 Hz) to noise (40 Hz) is

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3 4 5 6

Glucose Concentration C (g/dl)

Rot

atio

nAng

le α

(deg

)

Corr. Coef.= 0.996409Std. Dev = 0.051806 (deg)

Fig. 13. Experimental results with 1 kHz driving signal.

33.1 dB. The power spectrum of the detected signals drivenby 1 kHz frequency is shown in Fig. 15, the highest peak(4 kHz) is the interested signal, and the signal (4 kHz) tonoise (2 kHz) is 23.8 dB. Therefore, the SNR observedwhen using a 1 kHz driving frequency is lower than whena 20 Hz frequency is employed. This can be explained thatthe speed of rotation is essentially limited by the electro-optic response time of the liquid-crystal materials and istypically in millisecond range. In Tables 1–3, three differentfrequencies regarding to six driving amplitudes driven intothe LC ZOC-5044XX were simulated by LCD Master. Aswe can see in tables, high driving frequency would raise thetilt angle and decrease the variation of tilt angle (Dh) at thesame driving voltage. High tilt angle causes small birefrin-gence (Dn), and small variation of tilt angle (Dh) causessmall variation of Dn. For this reason, the driving frequencyis increased; the driving amplitude must also be increasedin order to yield a more rapid variation rate of the LCmolecules. Hence, the variation range of the LC moleculesdecreases, thereby reducing the modulation depth.

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5

-110

-100

-90

-80

-70

-60

-50

-40

-30

Frequency (kHz)

Mag

nitu

de(d

B)

Fig. 15. Power spectrum of 1 kHz driving signal.

Table 1Driving voltage and the variation of tilt angle in LC ZOC-5044XX with20 Hz driving frequency

Driving voltage (V) Tilt angle variation (�) Dh (�)

Driving frequency 20 Hz

2 25.179–29.708 4.533 46.352–57.457 11.114 58.217–74.340 16.126 69.349–87.187 17.848 74.608–89.522 14.9110 77.977–89.911 11.93




2 26.699–27.669 0.973 51.158–52.968 1.814 66.297–68.608 2.316 81.368–83.534 2.178 86.689–88.177 1.4910 88.563–89.520 0.96




2 27.312–27.482 0.173 51.843–52.205 0.364 67.154–67.620 0.476 82.252–82.683 0.438 87.417–87.693 0.2810 89.129–89.278 0.15


The LC polarization modulator is a key component ofthe polarimeter since its behavior determines the overallperformance of the system. If the individual optical ele-ments of the LC modulator shown in Fig. 1 are not per-fectly aligned, the resulting elliptical polarized state of thelight will cause phase errors to be introduced [11]. More-over, the non-perfect sinusoidal retardance variation ofthe LC polarization modulator may introduce errors inthe subsequent demodulation signal processing procedure.In the present study, achieving equilibrium of the drivingfrequency and the modulation depth is a key factor inimproving the resolution of the system.

Also, it is found that if K in Eq. (19) is too big, it meansthat the denominator is very small, so noise in the denom-inator signal is strongly propagated. In other words, bigvalues of K can contribute to increase the error in themeasurements, thus decrease the sensitivity to low glucoseconcentrations. Therefore, a value of K near to one meansthat the signals compared are equilibrated (the system is wellconditioned), so the propagation of errors (noise and oth-ers) to the final ratio is reduced. Looking for a compromisebetween the frequency of modulation and the voltage of

modulation (modulation depth) in order to obtain a valueof K as close as possible to one is also an important proce-dure. However, it is observed that when the driving fre-quency increased, the value of K also increased and thusthe SNR decreased in experiments. The value of K is 2.348when the driving frequency is 20 Hz and K is 134.58 whenthe driving frequency is 1 kHz. It is attributed to the limita-tion of the LCD modulator in deeper modulation depth inhigher frequency.

5. Discussions and conclusions

This study presents a polarimetric glucose sensing sys-tem using a liquid-crystal polarization modulator drivenby a sinusoidal signal. The tilt angle of the LC directorwould vary as a sinusoidal-like function; however the mod-ulating frequency in the sensing system is the double of thedriving signal. A new signal-processing algorithm, there-fore, is designed to extract the polarization rotation angleintroduced by the glucose sample. It shows that the devel-oped system is capable of measuring minimum glucose con-centrations of 0.2 g/dl. A resolution level of rotation anglearound 0.002� is achieved according to Fig. 12. The linear-ity and sensitivity characteristics of the developed systemare comparable to those reported in previous studiesadopting phase sensitive techniques [4]. Consequently, theproposed system using a liquid-crystal based rotator hasconsiderable potential for use in non-invasive glucose mon-itoring applications.

The principal sources of errors or signal noise in thepresent study may be caused by: (1) a misalignment ofthe optical elements within the modulator, (2) the non-perfect sinusoidal variation of the phase retardance in theLC retarder, (3) variations of the rotation angle causedby temperature and perturbations of the glucose solution,and (4) the thermal drift of the LC modulator. In additionto the above reasons, the capability of glucose sensingwould also be influenced by the electro-optic characteristicsof the LC retarder (e.g., slow response time). As shown inthe experimental results, the higher the SNR of the de-tected signal, the more sensitive the glucose concentrationmeasurement. To enhance the SNR of the developed polar-imeter or to improve the measuring sensitivity for the non-invasive glucose detection, adopting a nematic liquid crys-tal with high dielectric anisotropy and low viscosity wouldimprove the modulation capability of the LC modulator.This approach would enable the use of a higher driving fre-quency and would result in a greater modulation depth.

By driving a sinusoidal voltage to the LCVR in the opti-cal rotator, we successfully demonstrate that the LC mod-ulator could be an alternative polarization rotationmodulator in the measurement of glucose concentration.Compared to the electro-optic or Faraday modulators,the LC waveplate has lower operational voltage and lowerpower consumption requirements. As a result, the LCbased modulator has a potential application in sensingdesigns.


Acknowledgment

The current authors gratefully knowledge the financialsupport provided to this study as part of the Ministry ofEducation Program for Promoting Academic Excellenceof Universities under Grant No. A-92-E-FA08-1-4, Tai-wan, ROC.

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A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal