ARTICLE IN PRESS

OpticsOptikOptikOptik 117 (2006) 95–100

0030-4026/$ - se

doi:10.1016/j.ijl

�Correspondfax: +86010 51

E-mail addr

www.elsevier.de/ijleo

A smart optical liquid level sensor based on Hg cladding optical waveguide

Pei Li�, Ning Tigang, H Wang Lei, Yang Bin, Li Yantao, Jian Shuisheng

Institute of Lightwave Technology, Beijing Jiaotong University, Beijing, China

Received 27 October 2004; accepted 25 September 2005

Abstract

A smart optical liquid level sensor based on the theory of connected vessels is introduced. The Hg cladding opticalwaveguide (HCOW) is taken as its probe, and the change of liquid level is presented by the change of the HCOWlength. Both the theoretical analysis and experiments show that when the waveguide diameter and the light wavelengthare certain, the optical power loss decreased linearly with the increase of the HCOW length. By detecting the powerloss of HCOW, optimizing the structure of probe and selecting the appropriate apparatus for detection, the real timedetection of liquid level with high precision can be got. The experimental results show that the measurement accuracyis 5.2mm within 10m liquid level, and its theoretical precision can be up to 0.02%.r 2005 Elsevier GmbH. All rights reserved.

Keywords: Fiber optics components; Fiber optics sensors; Remote sensing

1. Introduction

In many practical applications, optical fiber sensorsmay offer significant metrological improvement byreason of their electrical passivity, high bandwidth,safety in corrosive or explosive environments, andimmunity to EMI, high sensitivity, miniature dimen-sions, possibility of remote operation and directcompatibility with increasingly present fiber-optic datatransmission networks. Liquid level sensors usingoptical fibers hold particular promise as replacementsfor many existing sensing technologies, especially inharsh environments [1–3].

In this paper, a smart optical liquid level sensor withHg cladding optical waveguide (HCOW) as its probe isintroduced. It works based on the theory of connected

e front matter r 2005 Elsevier GmbH. All rights reserved.

eo.2005.09.009

ing author. Tel.: +86010 51688016;

683625.

ess: lipei@center.njtu.edu.cn (P. Li).

vessels, which changed the liquid level according to thechange of the HCOW length, so that this sensor probecan prevent the measurement error from the inter-change of acousto-optic effect, magneto-optic effect orthermo-optic effect that occur in the other kind ofsensors. Both the theoretical analysis and experimentsshow that when the waveguide diameter and the lightwavelength are fixed, the optical power loss decreasedlinearly with the increase of the HCOW length. Bydetecting the power loss of HCOW, optimizing thestructure of probe and selecting the appropriateapparatus for detection, the real time detection of liquidlevel with high precision can be got. This optical fiberliquid level sensor has the advantages of good linearity,high precision, simple structure, stabilized characteris-tics, real time detection and so on. It is powermodulated, and the power detection is easy, simpleand cheap. In addition, this liquid level sensor has bigdynamic range, and can be used in security. It will havewide usage in the fields of science, industry, national

ARTICLE IN PRESSP. Li et al. / Optik 117 (2006) 95–10096

defense, especially in the liquid level detection of oildepot.

According to the technology requirement of thesensor, the optoelectronic detection terminal is designedin detail, its function is adjusted, and a lot of softwareprograms are edited. At last, the real time detection ofliquid level with high precision can be got. Theexperimental results show that the measurement accu-racy is 5.2mm within 10m liquid level, and itstheoretical precision can be up to 0.02%. This detectionterminal can also be widely used in the real time andaccurate detection of the weak optical power in theoptical fiber transmission system.

The paper is organized as follows. In Section 2, thecharacteristics of HCOW are analyzed in classic electro-magnetic theory, its attenuation coefficient is derivedand the numerical results are given. In Section 3, thework theory of the liquid level sensor is investigated. InSection 4, the overall design of the detection terminal isgiven. In Section 5, the experimental results arepresented and the measurement results are comparedwith those of the theoretical analysis results. Lastly, theresults are summarized in Section 6.

2. Characteristics of HCOW

2.1. Theoretical analysis

Under normal temperature, metal Hg is in liquidstate, there is no space between the Hg cladding and thenaked fiber core. In fact, the HCOW is a kind of coaxialwaveguide with diameter of 2a, glass material withuniform refractive index as its core, and Hg as itscladding. The advantage of HCOW is that its claddinglength can be changed, and its power loss is related withthe cladding length, the size of the diameter, the lightwavelength and so on. The loss characteristics ofHCOW can be analyzed by the classic electromagnetictheory.

As the conductance s of the metal conductor is verybig, the metal surface can be considered as an idealconductor, then the calculation will be simplified, andthe result error introduced is small.

First, assume E ¼ Emejðwt�bzÞ, from the Maxwell

equations, the Hr, Hf, Hz and Er, Ef, Ez of TM andTE mode in the coaxial waveguide can be got.

Second, the surface current Js at r ¼ a can be derivedfrom

Js ¼ ~n� ~H ¼ ~nz~Hf �~nfHz. (1)

Third, the resistance Rs of the wall can be calculated asfollows:

From the characteristics of metal cladding mediumwaveguide, its conductance can be expressed as

s ¼Ne2

mðB0 þ joÞ, (2)

where B0 is the damping constant per quantity, it isabout 1014 s�1, m is the electron quantity, e is theelectron current and N is the number of electric chargesper volume.

We define the attenuation coefficient asa, and thephase coefficient as b, then the propagation constant canbe described by

r2 ¼ ðaþ jbÞ2 ¼ �meo2 þ jmos. (3)

The nature resistance of conductor is

RR ¼ Rs þ jX s ¼ joma� jbaþ jb

. (4)

From Eq. (2)–(4) the resistance Rs of the wall can begot.

Fourth, the power loss PlTM;PlTE of TM and TEmode can be calculated from

Pl ¼1

2apRsJs, (5)

where the surface current Js and the resistance Rs of thewall are obtained from the above calculation.

Fifth, the transmitted power PTM;PTE of TM and TEmode can be calculated as

P ¼1

2O

Z 2p

0

Z a

0

ð Erj j2 þ Ef

�� ��2Þrdrdf, (6)

where O is the wave impedance of TM and TE mode,respectively.

At last, the attenuation coefficient a (dB/mm) can begot

a ¼10

Zlg

Pi

Pie�2AZ¼ 20lge

XLiAi, (7)

where Z is the length of HCOW,Li and Ai are theweighted factor and attenuation constant for the ithmode, respectively. And

ATM ¼PlTM

2PTM, (8)

ATE ¼PlTE

2PTE. (9)

2.2. Numerical results

The schematic diagram of the HCOW is depicted inFig. 1.

When the diameter of the HCOW is fixed(2a ¼ 150; 125 mm), the relationship between the at-tenuation coefficient and light wavelength is shown in

ARTICLE IN PRESS

Fig. 1. Schematic diagram of the HCOW.

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0.075

0.08

0.085

0.09

0.095

0.1

0.105

0.11

0.115

0.12

atte

nu

atio

n (

dB

/mm

)

wavelength (�m)

2a=125 �m

2a=150 �m

Fig. 2. The attenuation coefficient of HCOW versus different

light wavelengths.

100 150 200 250 300 3500.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

atte

nu

atio

n (

dB

/mm

)

λ=1.55 �m

λ=1.31 �m

diameter of the fiber core (�m)

Fig. 3. The attenuation coefficient of HCOW versus different

waveguide diameters.

P. Li et al. / Optik 117 (2006) 95–100 97

Fig. 2. When light wavelength is fixed (l ¼ 1:31;1:55 mm), the relationship between the attenuationcoefficient and the diameter of the HCOW is shown inFig. 3.

We can see that when the diameter of the HCOW isfixed, the longer the light wavelength, the smaller theattenuation coefficient. But when the light wavelength iscertain, the smaller the diameter of HCOW, the biggerits attenuation coefficient. The loss characteristic ofHCOW can also be analyzed by the ray optics theory:when the light is injected into the waveguide, it istransmitted along the length through the reflection atthe core-cladding surface. Every time, part of the opticalpower will be absorbed by the cladding. When thewaveguide length is certain, the thinner the waveguide,the more the light will be reflected, and the bigger thepower loss.

Because that when the waveguide diameter and thelight wavelength are fixed, the optical power lossdecreased linearly with the increase of the HCOWlength, we designed a liquid level sensor based on theHCOW.

3. Work theory of the liquid level sensor

The HCOW has very good loss characteristics, and itscladding length is changeable, so the change of theoutside parameters can be presented by the change ofthe HCOW length, then the power loss will be increased,correspondingly. By measuring the optical power, wecan get the outside parameters.

The schematic diagram of the liquid level sensorsystem is shown in Fig. 4. The pressure of measuredliquid is put on the piston of the wide duct of theconnected vessels. At the thin duct, a naked optical fiberis put into the connected vessels with liquid Hg aroundit. When the liquid level is increased or decreased, theHg cladding length of the naked fiber will be increasedor decreased too, then the power loss of the HCOW willbe changed, and we can get the liquid level from thechange of the optical power.

The sensor probe size can be made very small becauseHg has a much higher density than those of most of theliquids, which is nearly 13.5 g/ml under normal tem-perature. But at the same time Hg also has a dis-advantage of being easily vaporized, its steam isnoxious, and the characteristics of Hg are easilyinfluenced by its chemical effect with air. Because ofthe above disadvantages, strict technology is requiredfor the design of the liquid level sensor basedon HCOW. After many experiments, the difficulttechnology problems have been solved. A piston whichcan move precisely is designed in the wide duct of theconnected vessels, its motion is decided by the fluidpressure put on it and it can also separate the liquidfrom Hg. The thin duct of the connected vessels issealed, then the volatilization of Hg is avoided and thevolume of the air on the top of the thin duct can bedesigned to make the probe small.

Original state: The temperature is T0, the air volumeon the top of the thin duct is V 0, the liquid level isH ¼ 0;P1 ¼ P0, and P0 is the air pressure. The Hg levelat this time is defined as the zero level. Then

V 0P0 ¼ K0T0 (10)

and

K0 ¼2pl. (11)

Measurement state: The temperature is T0 þ t, the Hglevel in the thin duct is f ðxÞ, so the air volume on the top

ARTICLE IN PRESS

Mod

ulat

ed o

ptic

al s

igna

l Naked fiber

Air

Liquid level H

P0

Hg

f(x)

Wide duct

P1

Thin duct

Sensor probe

CM SCM

I/

U

logarithmic

amplifier

Optoelectronic

detector

Commutation

& filtering

Detection terminal

A/D

SCM: single chip micyoco;; CM: Comparer

Fig. 4. Schematic diagram of the liquid level sensor system.

P. Li et al. / Optik 117 (2006) 95–10098

of the thin duct is

V ¼ V 0 � f ðxÞs, (12)

where s is the area of the cross section.The liquid level is H, and the density of the liquid is

Dl, so we can get

P1 ¼ P0 þHDl. (13)

Further,

½V0 � f ðxÞs�½P0 þHD� f ðxÞDg� ¼ K0ðT0 þ tÞ, (14)

where Dg is the density of Hg.From Eqs. (10) and (12):

½V0Dl � f ðxÞsDl�H ¼ K0tþ V 0f ðxÞDg

þ P0f ðxÞs� f ðxÞ2Dgs. ð15Þ

So we can get

H ¼K0tþ V0f ðxÞDg þ P0f ðxÞs� f ðxÞ2Dgs

V 0Dl � f ðxÞsDl

¼ H½f ðxÞ; t�. ð16Þ

If we get the HCOW length, then from Eq. (16), theliquid level under different temperatures can all beobtained.

4. Detection terminals

The detection terminal structure is shown in Fig. 4 inthe dashed frame. The signal is modulated and thecompare circuit is introduced in order to eliminate thesystem error. The minimum optical power that can bemeasured by the detection terminal is �70 dBm, itsresolution is 0.02 dB, and the measurement results canbe repeated very well.

At first, the 10 kHz square wave produced by thesingle chip micyoco (SCM) is transmitted to the injected

circuit through its high speed data channel HSO, andthe light source is modulated. Considering both theperformance and cost, SLD is chosen to be the lightsource; it has the advantage of small volume, lightweight, simple structure, high efficiency and long life.The SLD is also compatible with the optical fiber verywell.

The 10 kHz modulated signal is divided into twoparts, one part is transmitted through the single modefiber and the sensor probe, and then detected by theoptoelectronic detector. The other part is injected intothe compare circuit for compensating and correcting theinstability of the light source. In this system, FC typeoptoelectronic detector is used, because its inner circuitcoupled very well, and the measurement precision ishigh.

In order to simplify the signal processing, we choosethe trans-impedance pre-amplify I/U convertor; it hasvery good transition characteristics, wide dynamicrange, low noise, and the circuit is very simple.

The voltage then is filtered by a 10 kHz band passfilter after it is amplified. The Gauss spurious light willbe eliminated. By comparing, we choose the improvedlogarithm pre-amplifier, which can avoid the complexityof grade and measuring amplifier. Then, the signalchanged from alternating current to direct current by adiode demodulation circuit, and a p type filter circuit isused to filter the ripple.

At last, the data are processed by a SCM, and theresults are displayed at real time.

5. Experiments

Experiments of the liquid level sensor system havebeen done. The experiment parameters are as follows,2a ¼ 125, 150 mm, respectively. l ¼ 1:31mm, the liquid

ARTICLE IN PRESS

0 10 20 30 40 50 60 70-10

0

10

20

30

40

50

60

70

loss

(d

B)

Length of metal cladding fiber (cm)

Theory 2a=125 �mExperiment 2a=125 �m

Theory 2a=150 �mExperiment 2a=150 �m

Fig. 5. Power loss versus HCOW length.

0 200 400 600 800 1000-60

-50

-40

-30

-20

-10

0

Rec

eive

d p

ow

er (

dB

m)

Liquid level H (cm)

Fig. 6. Received optical power versus liquid level H.

0 200 400 600 800 10000

100

200

300

400

500

600

700

800

900

1000

Mea

sure

d li

qu

id le

vel (

cm)

Actual liquid level H (cm)

2a=125 �m

Fig. 7. Relationship between measured and actual liquid

levels.

0 200 400 600 800 1000-10

-8

-6

-4

-2

0

2

4

6

8

10

Del

t H

(m

m)

Actual liquid level H (cm)

2a=125 �m

Fig. 8. Measurement error of measured and actual liquid

levels.

P. Li et al. / Optik 117 (2006) 95–100 99

to be measured is water and its density is Dl ¼ 1�103 kg=m3, the density of Hg is Dg ¼ 13:558�103 kg=m3.

The power loss versus HCOW length is tested at first,the results are shown in Fig. 5, and the measured resultsare compared with those of the theoretical analysis. Wecan see that the experimental results agree very well withthe theoretical analyzed results. Then, the liquid level H

is changed, and the received optical power with differentH is tested, the results are shown in Fig. 6. We can seethat the higher the H, the smaller the received opticalpower, because the Hg level is increased, which meansthe power loss caused by HCOW is increased.

The measured liquid level is shown in Fig. 7, and it iscompared with the actual liquid level. The measurementerror is shown in Fig. 8.

The experimental results show that the maximumerror is 5.2mm within 10m liquid level, the reasons forthe error include the precision of tested apparatus, thepurity of Hg, and so on. Its theoretical relative accuracyis up to 0.02%.

6. Conclusions

Both the theoretical analysis and experimental resultsprove that the particular loss characteristics of HCOWwill make it to be widely used in the optical fiber sensorsystem.

The optical power measurement is perfect, simple,cheap and has a high precision. By far, the optical powermeasurement can range from �70 dBm to 20 dBm, oreven more. The measurement resolution can be up to0.01 dB. In our detection terminal, if we choose the bestquality LD as the light source, high resolution PIN asthe optoelectronic detector, high accuracy electroniccircuit and more digit A/D for signal processing andtransition. The measurement results can attain thetheoretical accuracy.

This liquid level sensor based on HCOW hasadvantages of small probe, light weight, good transitioncharacteristics and small error. It can work in corrosiveor explosive environments, especially in some dangerousenvironment such as the liquid level measurement of oildepot. The same technique could be extended to othersensors introducing the change of the Hg claddinglength by the parameters which should be measured.

Acknowledgments

This work is jointly supported by the National ‘‘863’’Project (2001AA312230), the National Natural Science

ARTICLE IN PRESSP. Li et al. / Optik 117 (2006) 95–100100

Foundation of China (60337010), the Fok Ying TungEducation Foundation (91062) and the Pandeng Foun-dation of Beijing Jiaotong University.

References

[1] C.P. Nemarich, Time domain reflectometry liquid level

sensors, Instrum. Meas. Mag. IEEE 4 (2001) 40–44.

[2] S.W. James, S. Khaliq, R.P. Tatam, A long period grating

liquid level sensor. Optical Fiber Sensors Conference

Technical Digest, OFS 1 (2002) 127–130.

[3] I.K. Ilev, R. W. Waynant, All-fiber-optic evanescent liquid

level and leak sensor, In: Lasers and Electro-Optics, CLEO

’99, 1999, pp. 157–158.