Enhancing central fringe identification using two optical beams with different power and wavelengths in white light interferometric sensing

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SEltSgRS

ACTUATORS A

ELSEVIER

Sensors and Actuators A 71 (1998) 179-182

PHYSICAL

Enhancing central fringe identification using two optical beams with different power and wavelengths in white light interferometric sensing Qi Wang, K.T.V. Grattan *, A.W. Palmer Department of Electrical, Electronic and Information Engineering, City University,School of Engineer, Northampton Square, London, ECIV OHB, UK

Received2 March 1998;receivedin revisedform 19 May 1998

Abstract Results of a study to enhance the relative amplitude of the central fringe in the output of a white light interferometric system with two optical beams has been described, where the approach is based on the electronic multiplication of the output signals corresponding to the two optical beams. The outputs were generated by separating the sensilig beam with a wavelength selective filter and detected using two separate photodetectors. The results obtained show that the relative amplitude of the central fringe of the multiplied output is independent of the power ratio of the two beams. Comparisons between this approach and the more conventional use of the dual wavelength technique are also included. @ 1998 Elsevier Science S.A. All rights reserved. Keywords: Interfemmetry;Fringeidentification;Infra-redlaser systems

1. Introduction White light interferometric (WLI) systems for optical fibre sensing have been attracting much attention in recent years [ 1,2]. One of the distinguishing features of such systems is that the output interferometric pattern obtained shows a distinctive central fringe, the position of which is intimately linked to the measurand. By determining the position of the central fringe, high precision measurement over alarge range can potentially be achieved. However, in a system with a single wavelength illuminating source, the central fringe may not readily be identified, simply by investigating its amplitude, if a sufficiently high level of noise is present. A dual wavelength technique has been proposed to ease the problem of the identification of the central fringe [3,4], where in this technique, a fringe beating pattern is generated. Thus, the relative amplitude of the central fringe is considerably enhanced and therefore it can be much more easily identified. However, this type of dual wavelength technique requires that the powers of the optical beams at different wavelengths are approximately equal to each other, such that the maximum relative amplitude of the central fringe can be achieved. This may restrain practical applications of the technique, especially where laser diode (LD) or light emitting diode (LED) * Corresponding author. Tel.: +44-171-477-8120; Fax: +44-171-477-

sources, selected to operate at the appropriate frequencies, with optimum wavelength separations, have different relative power outputs. An alternative approach is to multiply the output signals associated with the optical beams [5]. In doing so, it has been found that the relative amplitude of the central fringe can also be enhanced by this process, and that this resultant multiplied output may be shown to be greater than that of the conventional two wavelength system described by earlier workers [3,4]. However, the characteristics of the system when the powers of the two beams are not equal has not been fully investigated at this stage, where the principle of the scheme is illustrated. In this work, the relationship between the relative amplitude of the central fringe and the power ratio of the two beams has been analyzed. Comparisons between the approach and that of the conventional dual wavelength technique are included, together with results from an experimental investigation of this effect.

2. Theoretical background A schematic diagram of the system discussed is shown in Fig. 1. The arrangement is a simple dual laser diode based system (670 nm and 780 nm) with a modulation (peak-to-

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Q. Wanget aL/ SensorsandActuatorsA 71(1998)779-t82

180

M SX(67Onm)

F-1

BS

Lens

Lens

0 [71 0 0 i'-t.

1

I

0

fibre

Modulation

BS

Lens

F PD2

S1(780nm)

Lens PD 1

Multiplied output

~

1

X

Fig, 1. Experimentalarrangementof the systemwithtwo detectors.S1:780nm wavelengthlaserdiode;$2:670 nmwavelengthlaserdiode;BS: beamsplitter; M: mirror;F: wavelengthselectivefilter;PD1,PD2:photodiodes;× : multiplicationcircuit.

peak) applied to the mirror of several micrometers. The two wavelengths used in the system are sufficiently different for ease of separation at the filter, F. The experimental system is designed to be low-cost, using 'off-the-shelf' components and standard fibre, laser diodes and photodetectors from the manufacturer's catalogues. The two output beams of the system generated by means of a wavelength-selective filter were detected by using two photodetectors. Following that, the outputs from these two detectors are multiplied by using an analogue electronic circuit. In order to consider the underpinning theory and to simplify the situation, the system under investigation can be described as one with two detectors and its output as the multiplied output. By contrast, the systems described by Chert et al. [3] and Rao et at. [4] are defined as those using one detector and its output as the summed output. For the arrangement shown in Fig. 1, the optical power of the output beams, I1 (lxL) and II(&L), which may be detected by the photodiodes (PDs) illustrated can be expressed as [3] Ii(AL)=~L

[

[ l+exp

[2AL'~°i

{2"n'AL'I

--t'-~-~ } J ~ ° ' t - - X - - J J

(')

and

I2(AL)=[-~[l+exp[-(2&Ltllcos(2"~'&Ltl

jj

(2)

where A1 and "~2 are the average wavelengths of the beams, respectively; zXLis the optical path difference (OPD)introduced by the interferometer; Lo is the coherence length of the sources used (for simplicity assumed the same)and Iot and Io2 represent the peak-peak values o f the central fringes before the multiplication is carried out. From Eqs. (1) and (2), the normalized summed output can be written as

{2~r&L~l r

Xc°st

r

[2AL~ll

[2~r6L~l)

JJ + [l+exp[- t--LT) jcost-l-T-2 )J/

(3) where R = (Ion) / (Io2), and the normalized multiplied output can be expressed as

I,o(rI,)=¼11+exp[-(L]llcos(-t] L

×[l+exp[

L ~ °/J

~

'/J

[2AL'll [2 AL,1 -~-~ } jcos~--~--B }j

(4)

From Eq. (4), it can be seen that the multiplied output is independent of the power ratio of the two beams, Iot/Io2.

3. E x p e r i m e n t a l m e t h o d

When the maximum visibility method is used, which identifies the central fringe by comparing the amplitudes of the fringes, the identification depends on the amplitude difference between the central fringe and the second largest fringe and the value of the associated noise in the fringe pattern. If the maximum r.m.s, value of the noise allowed for the identification is defined as the half the amplitude difference, and the signal to noise ratio (SNR) may be defined as that peakpeak value of the central fringe divided by the r.m.s, value of noise, there exists a minimum SNR at which the central fringe can be identified by using the maximum visibility method. This minimum SNR can be termed as SNRmin. Then, the SNRm~n of the summed output given by Eq. (3), given as SNRmins, can be expressed as (in dB)

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Q. Wang et aL / Sensors and Actuators A 71 (1998) 179-182

1 where A/~, is the amplitude difference between the central fringe and the second largest fringe in the normalized summed output shown in Eq. (3). The SNR required to identify the multiplied output shown in Eq. (4), S N R ~ ,~, can be expressed as (in dB)

[~I,n~

S N P, minm(dB) = - 2 Olog~--~'--)

(6)

where Aim is the amplitude difference between the central fringe and the second largest fringe in the normalized multiplied output shown in Eq. (4).

4. Results obtained The values of the SNRmin given by Eqs. (5) and (6) as a function of the power ratio of the beams have been calculated, and the results are shown in Fig. 2. The values of the parameters, At, A2, L~, were chosen to be 0.67 Ixm, 0.78 Ixm and 25 Ixm, respectively in the calculation, being typical of practical devices. A simulation of this situation shows that the first side fnnge was the second largest fringe when the coherence lengths of the illuminating sources (with wavelengths of 0.67 txm and 0.78 ~m) are shorter than 27 ~m. In this case, the value of SNRm~n is determined by the difference between the central fringe and the first side fringe. It can be seen from the diagram that SNRm~, of the multiplied output, is lower than that of the summed output and is independent of the power ratio of the beams. The figure further shows that the SNRmin of the summed output (shown as upper curve) depends on the power ratio of the beams and reaches its minimum value (about 31 dB) when the powers of the two beams were about same. Although the system with one detector has a relatively simple optical arrangement, the requirement is that the pow44

ers of the two beams are about the same to optimize the system, i.e., the relative amplitude of the summed output reaches its maximum value when the powers of the two beams are about equal to each other. In addition, when the first side fringe is the second largest fringe, the SNRmm of the summed output is 6 dB higher than that of the multiplied output, even if the powers of the beams are about the same. This can be seen from Fig. 2. In contrast, the system with two detectors offers the advantage that its SNRm~n is independent of the ratio Ioi/Io2 and is lower than that of the summed output. The characteristics of an experimental arrangement of the system with two detectors, which is shown in Fig. 1, has been investigated, where optical beams from the two multimode laser diodes (LPM3 670 (Power Technology) and LT023MDO (Sharp)), with central wavelengths of 670 nm and 780 nm, respectively, was injected into a multimode fibre (with a core diameter of 200 Ixm and a length of about 4 m) via an objective lens. The collimated beam was modulated by a Michelson interferometer following which the sensing beam was separated by a wavelength-selective filter (part No. 16 BH 16, supplied by Comer Instruments) according to their wavelengths. The separated beams were detected with two photodiodes. The outputs of the two detectors were then multiplied by using proprietary analogue circuits (type MPY634, supplied by Burr-Brown International). A digital oscilloscope was used to record output fringe pattern of the system, in which the coherence lengths of the sources were estimated to be about 20 ixm. Fig. 3 shows experimentally obtained fringe patterns, where (a) represents the output fringe patterns obtained before the multiplication and (b) represents the pattern obtained after the multiplication. It can be seen from the diagram that, before the multiplication, the amplitude differences between the central fringe and the adjacent fringe were very small, and the difference has been considerably increased by the use of the multiplication. A SNRm~n of 27 dB has been obtained from the multiplied output, which is similar to the value (of25 dB) that is given by Fig. 2. The difference between the experimental and the theoretical results may partially be explained by considering that the

'l

42 4O

38 ~- 36 n*" Z

34

(a)

32 3O

©

28

(b)

26 24

I

-2

I

I

-1 0 1 Logarithm of the power ratio of the beams (1og(Iol/1o2))

Fig, 2, SNRrn~nagainst the logarithm of the power ratio of the two beams, log ((/ol)/(/02)). The lower line represents the result of the multiplied output and the upper curve represents the result of the summed output.

ii, -20

-10

0

10

20

Optical path difference(p.m)

Fig. 3. Experiment result showing (a) output fringe patterns of the system before the multiplication and (b) the fringe pattern of the multiplied output.

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Q. Wang et at. / Sensors and Actuators A 71 (t998) 179-t82

contrast of the experimentally obtained fringe patterns is lower, resulting in a smaller amplitude difference between the central fringe and second largest fringe in the experimental output. It should also be noticed that the theoretical results shown in Fig. 2 were obtained assuming no noise is present in the systems and no cross-coupling occurs between the two separated beams. In practice, some WLI systems can provide an output with a very high SNR and the cross-coupling can be reduced by choosing an appropriate wavelength selective filter and aligning it carefully. The cross-coupling in the experiment has been estimated to be lower than 10% due to the filter used. This could be reduced by use of a custom-built filter, designed for a 45 ° orientation, to < 1%, although such filters are comparatively expensive. The above result was achieved with an 'off-the-shelf' component and demonstrated the principle of the method, albeit with a higher cross-coupling level than would be optimum. 5. Conclusion A source-synthesizing technique for a WLI system based on the multiplication of two optical beams with different power levels and wavelengths has been investigated. The approach offers the potential advantage that the relative amplitude of the central fringe of the multiplied output is enhanced considerably and the output is independent of the power ratio of the two optical beams used.

References [ 1] H.C. Lefevre, White Light Interferometry in Optical Fibre Sensors, in Proceedings of the 7th International Optical Fibre Sensors Conference, Sydney, Australia, 1990, pp. 345-352. [2] A. Koch, R. Ulrich, Fibre-optic displacement sensor with 0.02 txm resolution by white light intefferometry, Sensors and Actuators A 2527 (1991) 201-207. [3] S. Chert, K.T.V. Grattan, B.T. Meggitt, A.W. Palmer, Instantaneous fringe-order identification using dual broadband sources with widely spaced wavelength, Electron. Lett. 29 (4) (1993) 334-335. [4] Y.J. Rao, Y.N. Ning, D.A. Jackson, Synthesized source for whitelight sensing systems, Opt. Lett. 18 (6) (1993) 462---464. [5] Y.J. Rao, D.A. Jackson, Improved synthesized source for white fight interferometry, Electron. Lett. 30 (t7) (1994) 1440-1441.

Biographies Kenneth Thomas Victor Grattan was born in County Armagh, Northern Ireland, on 9 December, 1953. He received his B.Sc. degree in physics and PhD degree from Queen's University,

Belfast, Northern Ireland, in 1974 and 1978, respectively, and D.Sc. degree from City University, London, in 1992. His Ph.D. research involved the development of ultraviolet gas discharge lasers and their application to the study of the photophysics of vapour-phase organic scintillators. From 1978 to 1983, he was a research assistant at Imperial College, University of London, UK, working in the field of ultraviolet and vacuum ultraviolet lasers and their application to measurement on excited states of atoms and molecules. In 1983, he was appointed a 'New Blood' lecturer in measurement and instrumentation at City University, London; in 1987, he became a senior lecturer; and in 1988, a reader. In 1990, he was appointed professor of measurement and instrumentation and head of the Department of Electrical, Electronic and Information Engineering at the same institution, where his research interests are currently in the field of optical sensing with industrial, environmental, and bioengineering applications. He has authored and co-authored over 300 journal and conference papers in the field of optical measurement and sensing. Professor Grattan is a fellow and chairman of the Applied Optics Division of the Institute of Physics, a fellow of the Institution of Electrical Engineers, and a fellow of the Institute of Measurement and Control. Andrew William Palmer was born in New Zealand on March 15, 1938. He received his B.Eng. degree in electrical engineering from Canterbury University, New Zealand, and M.Phil. and Ph.D. degrees from the City University, London, UK. He has lectured at the City University in the Department of Electrical, Electronic and Information Engineering, where he is currently doing research in the field of fibre-optic sensing for a range of measurement purposes. He has recently been appointed professor of electrical engineering at City University and is the author of some 200 journal and conference papers in the field. Wang Qi was born in China on October 5, 1958. He was awarded the B.S. degree in applied physics by Huazhong University of Science and Technology, Wuhan, China, in 1982 and M.S. degree in optical engineering from the same university in 1988. He has been employed since 1988 as a lecturer in the Department of Physics in Huazhong University, teaching courses in advanced physics and transducer techniques. Since 1994, he has been a visiting scholar and a research student at City University, London, where he has now completed a Ph.D. in the field of optical-fibre interferometry, representing his main research interest.