interferometric signals in fiber optic methane sensors with wavelength modulation of the dfb laser...

lnterferometric noise in fibre optic methane sensor with wavelength modulation of the

DFB laser source.

G Stewart, A Mencaglia, W Philp and W Jinr

Department of Electronic and Electrical Engineering

University of Strathclyde

Glasgow Gl lXW

Tel: +44 (0)141 552 4400 ext. 2887

Fax: +44(0) 141 553 1955

e-mail : g. stewart@eee. strath.ac.uk

Abstract

We examine the perfornance limitations of a fibre optic methane sensor using micro-

optic GRIN lens cells in either transmission or reflective mode. We derive the worst

case values of sensitivity due to interference effects caused by reflections within the

cell as a function of the cell parameters. We also show both theoretically and

experimentally how the interference noise may be minimised by suitable choice of the

amplitude of the frequency modulation. Although, theoretically, reflective cells could

match the performance of transmission cells, in practice, transmission cells are

superior in terms of interferometric noise levels.

I Department of Electrical EngineeringThe Hong Kong Polytechnic UniversityHung Hom, Kowloon, Hong Kong.

INTRODUCTION

Recently a number of distributed feedback (DFB) lasers have been developed in the

1.2-2.0pm region specifically for trace gas monitoring [1,2]. A number of important

gases, including methane, carbon dioxide, carbon monoxide, hydrogen sulphide,

ammonia, etc., possess overtone or combination absorption lines in the near-IR and

although these lines are weak, high sensitivity detection can be obtained with the DFB

laser systems. Detection of HzS l2l, CO2l2l, Cru [3] and simultaneous detection of

CH+ and CzH2 l4l have been experimentally demonstrated. The key features of the

DFB lasers are (i) their very narrow linewidth, typically < 50MHz and hence much

less than the linewidth of a single rotational gas absorption line and (ii) the ability to

modulate the wavelenglh of the laser output through the injection current. High

sensitivity detection is obtained by wavelength or frequency modulation spectroscopy

and by monitoring first, second or higher order harmonics of the modulation

frequency in the detected output signal [1,5-9].

Currently we are developing a fibre optic multi-point sensor system for methane

detection, using several micro-optic cells with GRIN lenses, as illustrated in Figure 1.

Because of the very long coherence length of the DFB laser, multi-reflections

occurring within the cells and from fibre joints/connectors give rise to interference

signals which produce harmonics in the output indistinguishable from the gas signal.

This is a serious problem which must be dealt with for successful operation of the

sensor [10]. The effect may be reduced by the use of high quality anti-reflection

coatings and angled connectors, but the interference may still be the limiting factor in

the system performance. Additionally the cost of a multi-point system is greatly

increased if high quality GRIN lenses are specified for satisfactory operation. The

same problem has been reported by a number of other authors in optical gas sensors

employing bulk or multi-pass cells [11-15]. In these cases, special steps have been

devised to reduce the etalon fringes such as (i) the introduction of a second low-

frequency jitter [11] and low pass frltering [12], (ii) frequency modulation combined

with wavelength modulation using a triangular waveform [13,14] and more recently

(iii) the development of digital signal processing algorithms 116,17l. Similar methods

may be applied to the fibre optic system.

ln earlier work [18,19] we reported some theoretical calculations for the limitations

imposed by interferometric noise in fibre optic gas sensors using differential

absorption spectroscopy, that is, where the output is an intensity ratio at two distinct

wavelengths, one at the centre of the absorption line, the other displaced to a point

where the absorption is negligible. Here we report both ow theoretical and

experimental investigation into the interference noise specifically for the fibre optic

methane sensor using wavelength modulation of the DFB laser source. We determine

the limitations imposed on the sensitivity and demonstrate how the interference

signals depend on the operating parameters.

II SIGNAL OUTPUT FROM THE MICRO-OPTIC CELL

For the fibre optic system we assume that the dominant source of interferometric noise

will be from the micro-optic cell which may be used in either transmission or

reflectance mode, Figure 2(a) and (b). The cell length, i, is typically 5 - 25cm and is

very much less than the coherence length of the DFB laser source. The surfaces of the

GRIN lenses have reflection coefficients rt and 12 and we assume that, with anti-

reflection coatings, tt , 12 <<1 and transmission coefficient, t -1. For the reflective

cell we assume a back-reflection of tr at the inner surface of the GRIN lens and a

reflection coefficient ,,eiL- at the reflector. Additionally, the collimation/focusing

action of the GRIN lenses will not be perfect, so we should allow for a cell

(amplitude) attenuation factor ry Qt < l). The attenuation will depend on cell length

and has a typical experimental value of - 2dB power loss (ry2 - 0.6) for a transmission

cell of length 5cm with the GRIN lenses mounted in a v-groove.

Under the above conditions (low finesse Fabry-Perot cavity) we need only consider

first order reflections and the field output for the transmission cell may be written as

(see Figure 2):

Er = l,{Eo exp(-a "Cl)cos(at)+

rTlr,rrEoexp(-3a,Cl)cos[a\t- ")]] (l

4

and for the reflective cell as:

E * x r7r,Eo exp(-2a "C/)

cos[ar(r - ,) * 0,]

- rtE o cos(a;/) + rrrT'rj E o exp(-4a "Cli

cos[a{r - 2c) + 2Q -f

Note that for the reflective cell, ? coresponds to the round trip (amplitude)

attenuation factor. From equation (2) we can combine the effects of ry and r-to form

an effective cell reflectivity factor, 4, = rlt,. We denote rl? as an (intensity)

efficiency factor for light passing through a transmission cell arrd rtl the effrciency

factor for the return of light from a reflectance cell.

In th. ^bor. equations, a, is the (amplitude) attenuation coefficient for methane in the

cell, C is the methane concentration and z is the round-trip delay time of the cell,

r =2llc.

The output intensity is the time averag e < E2 > and with the assumptions that rr, rz

<< 1 and aoCl <<.1, we obtain:

* - | - o C tl+ 2ql r,rrcos(arz)

(2

and:

(3

(4h " lr - z a c 4-'; t, - n?) co4r, - O,)-2r,2 cos2(ot, - 0,)

where a: 2ao is the methane absorption coefficient and Io = Ei lZ.

In equations (3) and (4), the first term represents the methane signal while the

remaining term(s) represents the interferometric noise. We consider each term in tum

in the following two sections.

m METHANE SIGNAL

The absorption spectrum of methane in the near infrared contains a number of

individual rotational lines centred around 1660nm and labelled as P, Q and R lines.

(These correspond to the second harmonic of the fundamental methane absorption

spectrum at 3.3pm). For trace gas monitoring at atmospheric pressure, the individual

lines can be described as a Lorcntzian function (pressure-broadened line) [20] so we

may write the methane absorption coefficient as a function of wavelength or

wavenumbat, v : lf )", as:

where a. is the absorption at the line centre, vo is the wavenumber at the line centre

and 7,is the half-linewidth.

(s

6

with wavelength modulation of the DFB raser source (through moduration of theinjection current) we can write the raser output wavenum ber, vr as:

v t = (vo + Av) + dvsin(at ;)

where av is the offset of the raser output from the absorptionamplitude of the modulation and a^the modulation frequency.

Combining equations (5) anO (6) we obtain:

a(v)=ffiwhere A = A vfy and F, = 6r/y .

In order to obtain the harmonic content of theFourier series:

methane signal we expand a into the

where o0, at, o2, .....-..onare the Fourier coefficients and depen d, on / and. F, .

(6

Iine centre, dy is the

(7

(8

o - dn{r,.ir, sinlrr^, * e,)}

The magnitude of the n-th

equation(3) and (4):

harmonic of the methane signal is therefore from

(e

for the transmission and reflective cells, respectively.

The coefficients a, may easily be calculated by numerical integration and Figure 3

shows at, a2 and a3 as a function of A for F* : 1.5. To gain an idea into the

magnitude of the signals involved, consider the case where the DFB laser output is

locked to the absorption line centre (A : 0) and the second harmonic component is

used to monitor the methane concentration. From Figure 3 we see that a2: 0.32.

(Actually, the maximum value of az:0.35 is obtained when F. is increased to 2.2).

The absorption coefficient at the line centre, a*has been reported as - O.4cm-latm-l

for the Q6 line at 1665.5nm [3] and - 0.14cm-ratm-r for the R4 line at 165lnm [1].

Our measurements on the Q6 line yielded a value of - 0.25cm-latm-1. Hence if we

take a typical value of a* = 0.2cm-latm-l we obtain a second harmonic in terms of the

methane concentration in ppm.metre as:

for the transmission cell.

!,-l =6.4xppm'me*elni t,l, to6

(10

IV INTERFEROMETRIC SIGNAL

We now consider the terms in equations (3) and (4) which describe the interference

effects. Writing equation (6) for the laser output in terms of angular frequency ar

gives:

ar=@+Sossin(at,t)

where o :2rc(vo + Lv) and 5a = 2rc5v

Hence the interference term for the transmission cell from equation (3) is:

(11

h = 2172,rrrrcos {ar +lSarlsin(ar,r)} (r2

For the reflective cell, from equation (4) there are two terms contributing to the

interference effects. If the cell efficiency factor approaches IOO% (rt? -+ 1), the

second term -+ 0 and the remaining term gives interference similar to a transmission

cell (exceptthat r is replaced by 2r). Specifically, comparison of the magnitude of

the two terms shows that this is true if ,tl >>(l-r,rt,) = (1-4). nor example if the

GRIN lens has a surface reflectance of -30dB, (rr' = l0'), then the efficiency factor

of the cell, rTlneeds to be >> 97o/o. This is unlikely to be true in practice for a GRIN

lens cell; for example, with a round trip loss in the cell of 4dB and mirror reflectance

of 80%, r7l has value of only - 0.3. Hence the main contribution to interference will

be from the second term in equation (4), namely:

* - -|tt- n1)crs{.t +[6an]sin(a.r,r) - O,\ (13

We can expand equation (12) or (13) into its harmonic components using:

cos{or+fda;r]sin(at ^t)\ = Jo(5an)cos(or) -iO,sin(na *t + Q) 04n=l

where An =2J,(6an)sin(ot - 0) and 0n = 0 for n: t, 3, 5, ....., 0n = nl2 for n =

2, 4, 6,....(converts from sine to cosine).

Hence the magnitude of the rz-th harmonic of the interference is

l*1,=2qtr,r,A.

for the transmission cell and similarly for the reflective cell.

Note that ll,l=lJ,l^^*. Consider the second harmonic component from the

interference. The maximum value of Jz is - 0.5 so we have ltr l ry? trla qlr,r, for the

transmission cell and lr, I ,tlt rl= \r, I q,\(, - ,',) ror the reflective cell.

(1s

10

V SENSITIVITY LIMIT FROM INTERFERENCE

We can determine the limitations imposed on the sensitivity from interference effects

by comparing the methane signal, equation (9) and the interference signal, equation

(15). By equating the methane and the interference signals we obtain a noise

equivalent methane concentration (the minimum detectable methane concentration)

for detection at the n-th harmonic as:

2r7lr,rrA,

d -an(16

(t7

[c/]-," =

for the transmission cell and

[c/].,, =,,(t- r7i),1,

?'l ,d ran

for the reflective cell. Q.{ote the absence of the factor of 2 in equation ( 1 7) compared

with equation(16) because of the double pass in a reflective cell).

We can estimate the worst case values of [C/].in for second harmonic detection using

the typical values quoted earlier. If the surface reflectance is -30dB 1r2 :lO-3 ) then

[C/]*i" < l00ppm.metre for a transmission cell with ,i - 0.6, and < 30O0ppm.metre

for a reflective cell with r7l - 0.3. The reflectance cell is clearly much poorer in

performance. The value obtained here for the transmission cell is similar to that

derived in our earlier analysis of a system using differential absorption spectroscopy

[18, 19] where a value of 200ppm.metre was obtained for a transmission cell with

l1

4? = l. Our experiments on a fibre optic methane system employing micro-optic

transmission cells with standard GRN lenses (- -30dB reflectivity) and second

harmonic detection have indicated a resolution around 20Oppm.metre [10]. The above

results imply that to achieve a resolution of lppm.metre in a transmission cell, high

quality GRIN lenses are required with surface reflections < -50dB. This makes for

much greater expense, especially in a multipoint system and other means of dealing

with the interference noise is required.

VI REDUCTION OF INTERI'ERENCE EFFECTS

Examination of equation (14) shows that the magnitude of the interference signals

depends on the Bessel function .I,. Hence it should be possible in principle to

eliminate the interference effects for a particular harmonic by choosing an appropriate

value of the frequency modulation amplitude dar so that J,(6an) = g.

In practice the interference from a single cell cannot be totally eliminated because the

frequency modulation of the DFB laser also produces a degree of amplitude

modulation. We can take this into account as follows.

With simultaneous frequency and amplitude modulation equation (12) becomes:

1,,= 2 r7l r,rrfl + m sin(a S))cos {or + [dar] sin (ar,t)\

ry? ro

t2

(18

where rz is the amplitude modulation index, m = k6o where ,t is a constant.

(Experimentally for our DFB laser, fr - -1 .6x 10-t MH, -';

Expansion of equation (18) into its harmonics gives:

where:

I-. { @ I

;t=2r7lr,rr\Aocos(or + V)-\,l,sin(na,t * O)l (19

A, = @.r(dan) - J,-r@aflf'z sin(or + v/, - O,) eo

(21

2J,(6at)*{J,,,(6an) - J,_t@an) rl (22

vo=tan-'\1ryffi] o,

and Q,= 0 for h: 1,3,5, ....., d, = ol2 for n:2,4,6,.....'..as before.

A similar result may be obtained for the reflective cell.

13

From equation (20) it can be seen that the amplitude of the n-th harmonic may be

minimised, but not necessarily reduced to zero, by suitable choice of 6at

The above analysis has dealt with interference arising from a single cavity only. In

practice, reflections from other surfaces and fibre connections in the system will give

rise to multiple cavities as illustrated in Figure 4. This may be taken into account by

adding additional reflection terms on to equation (1) and under the assumption of

small reflectivities, t1, ri 11 1 equation (18) takes the form:

+ :2ll + *srn(, -l)>n?, r r, "or{., ,

+filar ,fsin(a ,t1\4'lo ' ,.,

which also may be expanded into harmonic components.

Vil EXPERIMENTAL OBSERVATION OF INTERFERENCE

Interference signals at first and second harmonic frequencies were experimentally

measured as a function of the frequency modulation amplitude \ot for both

transmission and reflective cells (with no methane present) in order to compare with

equation (20). For different data sets we expect the cell length to fluctuate over a few

wavelengths giving random fluctuations in r. The fluctuations in or will cause the

sine term in equation (20) to drift over a few cycles but the effect on 6atr will be

(24

t4

insignificant. Hence for each cell, four sets of measurements were taken for the full

range of 5o and the standard deviation computed. Results are shown in Figures 5-9.

Each figure shows the first and second harmonic signals experimentally measured

compared with a theoretical fit (in bold) from equation (20) for Figures 5-7 and using

equation (24) for Figures 8 and 9. (The vertical scale is arbitrary, adjusted to give best

fit between experimental and theoretical curves.)

Experimentally, the frequency modulation amplitude was varied by the application of

a sinusoidal voltage (through a 10dB attenuator) to the current driver of the laser

diode and so the horizontal scale of Figures 5-9 is given in units of millivolts (rms).

This may be related to the FM amplitude 6a as follows:

*=lT)*=lT)ff)(il* (2s

where [4] tr the current tuning rate of the DFB laser and\ r,/

i-V charucteristic.

e is the slope of its

We estimated these parameters experimentally by scanning through the Q6 line of

methane (a 3V ramp produced - 56mA current change, scanning through - 0.14nm1.

rhe values obtained *, (q) - 0.002snm/mA and (#) - lemA/v. Bearing in

mind that the voltage shown in the graphs is in millivolts (rms), applied through a

1OdB attenuator, the conversion factor is:

t5

# =[o.s ' ro'] to.oozsl ee x J) x0.32x 10-3) = 0.0r 5 GHz I mv,,,

This conversion factor was used in plotting the theoretical curves. Clearly there is

excellent agreement both in the general shape of the curves as Bessel functions and in

the positions of the minima.

As noted earlier the amplitude modulation index, m = k6a. The value of t is

obtained using the fact that the experimental slope of the power/current curve of the

DFB is 4- o.oornwmA ar an output power of 1.5mw *d f+l - 0.0025nm/rnA,5i \ r,/

giving k- -L6x10-s MHz-r.

Examination of Figures 6 and 7 for the reflective cell show that while the general

shape is well predicted by the theoretical cruves based on equation (20) for a single

cavity, there is a secondary high frequency ripple in the experimental curves. This

suggests the presence of a much longer second cavity also contributing to the

interference signal. On this basis, Figure 8 and 9 show the same experimental curves

as Figures 6 and 7, respectively, but here the theoretical curve is based on two cavities

using equation (24), as illustrated in Figure 4, the second cavity having a additional

(physical) length of 5metres (optical length 5x1.456m). This model appears to

provide a good description of the experimental data and suggests there is a secondary

reflection from a fibre connector within our experimental fibre system (FC/PC

connectors were used which introduce a back reflection of - -40dB). It is to be noted

(26

16

that while the results

evidence of a slight

reflective cells.

for the transmission cell, Figures 5 and 6, also show some

ripple, the effect is clearly much more pronounced in the

VM CONCLUSION

In this paper we have examined the limitations imposed on the sensitivity of a fibre

optic methane sensor due to interference effects. We have shown both theoretically

and experimentally how the interference signals can be reduced by choice of the

amplitude of the frequency modulation. Our experimental results indicate that

reflective-t1pe cells give poorer performance and tend to enhance interference effects

from connectors and joints within the fibre system and this is consistent with the

theoretical results. Theoretically, a reflective cell with a very high reflectance

efficiency ( ry]) could provide similar performance to a transmission cell but this

would be difficult to achieve in practice with GRIN lens systems. In a future paper we

will show how the results presented here can be used along with digital signal

processing methods to obtain accurate measurements of methane concentrations in the

f,rbre optic system.

t7

ACKNOWLEDGMENT

This work was supported by the EPSRC/DTI LINK Photonics Programme in the UK

(OMEGA Project). The authors thank Chris Tandy of Gas Measurements Instruments

(GMD and the other industrial partners, British Gas and OptoSci for helpful co-

operation.

18

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[2]. V Weldon, J O'Gorman and P Phelan, "Gas Sensing with ],:1.57pm Distributed

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[3]. K Uehara and H Tai, "Remote Detection of Methane with a 1.66pm Diode

Laser," Appl. Opt., vol. 31, pp. 809-1 4, 1992.

[4]. H Tai, K Yamamoto, M Uchida, S Osawa and K Uehara, "Long Distance

Simultaneous Detection of Methane and Acetylene by Using Diode Lasers Coupled

with Optical Fibres," IEEE Photon. Technol. Lett., vol. 4, pp. 804-7, 1992.

[5] D E Cooper, R U Martinelli, "Near-Infrared Diode Lasers Monitor Molecular

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[6]. J Reid and D Labrie, "Second-harmonic detection with tuneable diode lasers -

comparison of experiment and theory," Appl. Phys. B, vol. 26,pp.203-10, 1981.

19

l7l. J A Silver, "Frequency-modulation spectroscopy for trace species detection:

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[8]. J M Supplee, E A Whittaker and W Lenth, "Theoretical description of frequency

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[9].V G Avetisov and P Kauranen, "Two-tone frequency modulation spectroscopy for

quantitative measurements of gaseous species," Appl. Opt., vol. 35, pp. 4705-4723,

t996.

[0]. W R Philp, W Jin, A Mencaglia, G Stewart and B Culshaw, "Interferometric noise

in frequency modulated optical gas sensors," ACOFT '96, 2lst Australian Conference

on Optical Fibre Technolog,t, Conrad Jupiters, Gold Coast, Queensland, December 1-4,

1996.

U 1]. D T Cassidy and J Reid, "Harmonic detection with tuneable diode lasers - two-

tone modulation," Appl. Phys. .8, vol. 29,pp.279-285,1982.

ll2l. C B Carlisle, D E Cooper and H Preier, "Quantum noise limited FM

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20

U3]. H C Sun and E A Whittaker, 'Novel etalon fringe rejection technique for laser

absorption spectroscopy," Appl. Opt., vol. 3 1, pp. 4998-5002, 1992.

[14]. H C Sun, E A Whittaker, Y W Bae, C KNg, V Patel, W H Tam, S McGuire, B

Singh and B Gallois, "Combined wavelength and ftequency modulation spectroscopy:

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t993.

[15] D S Bomse, A C Stanton and J A Silver, "Frequency modulation and wavelength

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diode laser," Appl. Opt., vol. 31, pp.718-7311992.

[16] H Riris, C B Carlisle, L W Carr, D E Cooper, R U Martinelli and R J Menna,

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[17] H Riris, C B Carlisle, R E Warren and D E Cooper, "Signal-to-noise ratio

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2t

[19]. W Jin, G Stewart, W Philp and B Culshaw, "Limitation of absorption based fibre

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22

FIGURE CAPTIONS

l. Fibre optic multi-point methane sensor system employing micro-optic cells.

2. Micro-optic cells using GRIN lenses showing reflected beams that contribute

to interference effects in the system output

(a) transmission cell (b) reflective cell.

3. Fourier coeffrcients for first, second and third harmonics of the laser

wavelength modulation frequency as a function of fractional offset from line

centre. (Lorentzian lineshape and normalised modulation amplitude, F*: 1.5)

Reflective cell with secondary reflection from a fibre corurector.

Experimental and theoretical results for the first and second harmonic

components of interference noise as a function of the amplitude of the

frequency modulation.

5-9

23

(

l.-modulation

micro-optic cells

detector reference cell

single mode

fibre

methane concentration

at each micro-optic cell

ELECTRONICSlaser controllock-in amplifierscomputer interface

(q)

(e)

lndur

0uEr.l]0ru

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Chartl

OFFSET FROM LINE CENTRE AS MULTIPLE OF HALF-LINEWIDTH

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2nd harmonic: 12.5cm reflective cellSingle cavity model

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interferometric signals in fiber optic methane sensors with wavelength modulation of the dfb laser...

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