1160 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 46, NO. 5 , OCTOBER 1997

a1 Enco tial Domain Multip

tical Fiber Sensor Yiqun Hu and Shiping Chen, Senior Member, IEEE

Abstruct- This paper studies a novel two-dimensional (2-D) encoding scheme to increase the multiplexing capacity of the newly developed digital spatial domain multiplexing technique used for integration of large-scale interferometric fiber-sensor arrays. The feasibility of the scheme is assessed via computer simulation and a preliminary experiment which involved strain measurement at multipositions on a cantilever beam.

Index Terms-Digital image processing, fast Fourier transform (FFT), multiplexing sensor, optical fibers.

I. INTRODUCTION IBER-OPTIC sensors can make an ideal “nerve sys- tem” for engineering structures because optical fibers are

compact and lightweight, resistant to corrosion and fatigue, immune to electrical interference, safe in fire- or explosion- hazard environments and compatible with composites which are becoming widely used as body or reinforcement materials for engineering structures. In particular, the interferometric fiber sensors are being widely researched because of their distinct advantages of high resolution and wide dynamic range. However, difficulty in interrogation of interferometric output has led to a complicated system architecture. A single conventional interferometric fiber sensor consists of many discrete optical devices including an optical source, two-fiber couplers, at least one electromechanical modulation device, and electronics for signal processing and feedback control. These devices are weak points in the sensing system because, in contrast to the good characteristics of optical-fiber itself, op- tical fiber devices are comparatively expensive, lossy, heavy, rigid, and bulky.

In many sensing applications, an integrated system with many sensors is required. A suitable multiplexing technique must be employed in order to reduce the overall system cost and improve ruggedness. A number of multiplexing techniques have been developed SO far. They can be classified into time [l], wavelength [2] , frequency [3] , and coherence [4] domain multiplexing techniques. However, the complexity of the network architecture is increased because an increased number of optical fiber devices has to be used to integrate the

Manuscript received December 22, 1995. This work was supported by the

Y. Hu is with the School of Electronic, Electrical, and Information Engi-

S. Chen is with the Department of Mechanical Engineering, University of

Publisher Item Identifier S 0018-9456(97)09122-5.

Overseas Research Scholarship.

neering, South Bank University, London SE1 OAA, U.K.

Maryland, College Park, MD 20742 USA.

system. These shortcomings limit the potential of optical fiber sensors to be fully realized in a wide range of applications, especially in the subject area of smart structures and materials. Furthermore, the multiplexing capacities of these techniques are far from satisfactory.

Recently, the authors have reported a number of encoding schemes to multiplex optical fiber interferometric type sensor arrays [5]-[7] in digital spatial domain. They all make use of a digital signal processing technique to significantly reduce the number of optical fiber devices in the network and greatly simplify the system architecture. There are no mechanical moving parts throughout the fiber network, and no special devices are required to hold the system at quardrature. This leads to a lower system construction and maintenance cost, and a potentially better utilization of the unique characteristics of optical fibers for sensing applications. Study has shown that if monoreference scheme [6] is used, a minimum of 4(M - 1) charge coupled device (CCD) pixels are required to interrogate M fiber channels. At the other extreme, if a full mutual reference scheme [7] is used, the required minimum pixel number becomes 2M(M - 1). Linear CCD arrays used in previously reported systems may not be able to provide enough pixels to interrogate large-scale sensor arrays. We will report a system to enhance the multiplexing capacity of the digital, spatial multiplexing technique by employing a two- dimensional (2-D) encoding scheme.

11. SYSTEM DESCRIPTION

The interferometric optical sensing system using the digi- tal spatial multiplexing technique is shown schematically in Fig. 1. The light from a laser is coupled into a single-mode 1 x M star coupler via a lead fiber. Sensing fibers, connected to the coupler, carry the light past the sensing field, then are linked, one to one, to a cabled fiber bundle and led to the processing unit. At the end of the fiber bundle, the end-faces of the fibers are arranged in a 2-D array parallel to an area CCD array with a reference fiber end-face being placed some distance away from the sensing fiber end-face group, as shown in Fig. 2(a). The far-field interferogram, which is formed by the interference of the light waves from all fibers, is digitized by a frame grabber and sent to a computer for processing. When the number of optical fibers M = 2, the system reduces to the optical fiber Young’s topology investigated before [8]. Here, where M >> 2, the interferogram on the CCD is the

0018-9456/97$10.00 0 1997 IEEE

HU AND CHEN 2-D ENCODING SCHEME FOR OPTICAL FIBER SENSOR ARRAYS 1161

Fig. 1. The experimental on a cantilever beam.

CCD monitor

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1 0 0 0 0 0 1 I

I sensing reference I ‘ . - - - - - - - - - - - - - - - - J

setups of using a 2-D digital spatial domain multiplexed optical fiber sensor array to monitor strains

superposition of all the Young’s fringes formed by every combination of every two fibers in the bundle, and thus is much more complicated.

The variation of physical measurands in the sensing area introduces phase changes in the sensing fibers and results in a fluctuation of the intensity distribution on the interferogram. Therefore, the phase information in each sensing fiber can be viewed as encoded, or multiplexed, “spatially” in the interferogram and can be retrieved by the computer using an appropriated digital processing algorithm.

111. 2-D ENCODING

The positioning arrangement of the end-faces in the bundle plays a crucial role in the described technique. A particular way of positioning is termed a special encoding scheme because it determines the way in which phase signals are encoded into the far-field interferogram.

In previously reported systems, fibers in the bundle were positioned in a linear array, and a one-dimensional (1-D) CCD array was used to sample the far-field speckles. In this paper, we demonstrate that fibers can be positioned into a 2-D array and accordingly, an area CCD would be used to record 2-D interferograms.

According to Fourier optics theory, the light-amplitude field on the CCD, F ( u , v), is the Fourier transform of the field on the fiber end-face plane f(z,y) when the distance between the fiber end-face plane and the CCD is much larger than the maximum separation between fiber end-faces. The signal recorded by the CCD is the intensity, P(u, v)P*(u, v) or the power spectrum of f ( IC, y) .

The task to recover the complete optical information of an object, including phase and amplitude, from its power spectrum has been referred as the “phase retrieval” problem [9]. Phase retrieval has been an important subject area of research with well-established applications including X-ray

at multiple positions

crystallography, Fourier-transform spectroscopy, astronomy, electron microscopy, holography, etc. Many phase-retrieval algorithms have been developed. The most widely used algo- rithm is the iterative Fourier transform algorithm (a descendant of the Gerchberg-Saxton type) because it has better conver- gence characteristics and is not oversensitive to noise. In the algorithm, the object can be expressed as a function

and its Fourier transform as

where ~ ( z , y) and 9(u , u) are the phase distribution of f ( z , y) and F ( u , v ) ; z , y , and u,w the object and Fourier domain coordinates, respectively. The procedure is to transform back and forth between the Fourier domain, where the Fourier module data are applied, and the object domain, where the a priori object support constraints are applied, to converge to the object itself after a number of iterations.

This algorithm, as well as other algorithms developed, have been successfully demonstrated in recovering an “incoherent” object, i.e., f ( ~ , y ) is real, which is adequate in most of the applications reported. The optical fiber end-face array, however, is a coherent light field and can be presented as a “complex” function. Previous studies [IO] showed that all existing algorithms experienced difficulty in recovering a general complex object function. In a recent work [5] , the authors have demonstrated that the conventional iterative phase retrieval algorithm can be successfully employed to retrieve phase information in the fiber bundle when the end- faces are arranged in a 1-D array. However, the procedure is very time consuming especially when a large number of sensors are addressed. In this paper, we demonstrate that a 2-D coherent object can be retrieved with a single noniterative fast Fourier transform (FFT) algorithm, if positions of the end

1162 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 46, NO. 5, OCTOBER 1997

Sensing fibre end face array I

fi

I ,,$, Reference fibre c/ I ' e x

-wi2 wi2

out on the signal recorded by the CCD, Le., F ( u , v )F*(u , w), the calculated output I'f(x, y) is a function in digital spatial domain and can be expressed as

where @ stands for correlation operation and * for complex conjugate. By bringing (3) into (4), we get

In the digital spatial domain shown in Fig. 2(b), fs(z,y) 63 f s (z , y) should have values in the area [-w < z < w, -H < y < HI. But if the total digital, spatial domain range in the z direction is W < 2w, the output of fs(x,y) 8 f s ( z , g ) outside this range will be folded over or aliased into this range [ 111. Fortunately, in the applications here, we do not utilize f s (z, y) 63fs (z, y). Therefore, by positioning the fiber end-face in such a way so that yo > H , yo < H+W/2 , and 1x1 < W/2, the light field of the object domain f s ( z ,y ) , which includes all the phase signals, can be separated from all other terms in (5) and retrieved from the digital spatial domain, i.e.,

T * * * * * + " * ** e I * * u u I. e s * I $$bA";I%"Q I t (I

* * l ) b t l * E l * * U * I * #

(b)

Fig. 2. Illustration of monoreference 2-D encoding scheme (a) position arrangement in object domin and (b) nonzero data points in digital spatial domain.

faces of the fibers are carefully designed. As a result, the multiplexing capacity can be greatly enhanced.

In this scheme, the plane where all fibers terminate is referenced as object domain with z,y as coordinates. The plane of the CCD array is referred as Fourier domain with u, v as coordinates. In a 2-D monoreference encoding scheme shown in Fig. 2(a), all sensing fibers in the bundle are arranged into a w x H grid with a signal reference fiber being positioned some distance away.

Because of the small core size of the single-mode fiber, light from each fiber can be treated as a point source. Referring to Fig. 2(a), the origin of the object plane (x,y) , where all the fibers terminate is located at the position of the reference fiber for which the light field can be expressed by a real Dirac function, S(z,y). The total light field there can then be expressed as

(3)

where fs(lc, y) is a 2-D complex function representing the light field from the sensing fiber group, that is the one to be detected. Then, if a digital inverse Fourier transform (IVF) is carried

f(., Y) = f s ( x , Y) + S(5, Y)

Being a complex function, the retrieved f s (x ,y ) in (6) can be presented separately as a magnitude spectrum and a phase spectrum. The magnitude spectrum represents the visibility of the Young's fringe sets formed by every individual sensing fiber and the reference. This visibility depends on their relative coherence and polarization status. The digital spatial domain coordinates corresponding to the position of each sensing fiber depend on the relative location of that particular sensing fiber and the reference, which are known a priori and are the key to address the sensors. The readings in the phase spectrum at the coordinates mentioned are the relative phase between light in the particular sensing fiber and that in the reference.

In the system, since the Fourier plane is digitized by a CCD using a 2-D N x N pixel array with a pixel size of p x p , an inverse FFT produces a corresponding N x N grid on the digital spatial domain. According to discrete Fourier transform and Fourier optics theory, this grid has an equivalent physical size of g x g with g expressed as

XL g = -

NP (7)

where X is the wavelength and L is the distance between the CCD and the end-face plane. The maximum capacity of this encoding technique is reached when the separation of two adjacent sensing fibers in the object domain equals the grid pitch of the digital spatial domain, g, and yo = H. From (2b), the theoretical maximum multiplexing capacity of this encoding scheme is N2/4 .

HU AND CHEN 2-D ENCODING SCHEME FOR OPTICAL FIBER SENSOR ARRAYS

Fig. 3. camera.

Photograph of the far-field interferogram recorded by the CCD

Iv. EXPERIMENTAL DEMONSTRATION AND RESULTS

Preliminary experiments were carried out to test the 2-D digital spatial multiplexing concept and its feasibility. As shown in Fig. 1, a laser diode with a wavelength of 830 nm and output power of 3 mW was used as the source. A single-mode 1 x 8 tree coupler was connected in the system with seven of the eight output fibers used as sensing ones. Along six of the seven sensing fibers, short sections of about 20 mm in length were bound to a cantilever beam at different positions, with the other one being free of strain to monitor the stability of the environment. The distance from the CCD array to the fiber end-face plane was 215 mm. A 128 x 128 area of pixels were read out in each frame and the inverse FFT was performed by a computer. Fig. 3 shows a frame of the far field interferogram recorded by the area CCD camera. Fig. 4 is part of its inverse FFT magnitude spectrum representing I fa (IC, y) I.

A concentrated force is applied at the free end of the beam to deflect it from its balance position. The measured outputs are shown in Fig. 5. Clearly, the phase changes, and thus the strains of the sensors, were successfully addressed and traced.

V. DISCUSSION

The technique presented has the potential capacity of multi- plexing several hundred sensors fundamentally because when there are more fibers in the object domain. The speckles in the Fourier domain become finer, and hence require more pixels in the CCD array to sample them, but the pattern visibility, i.e., the signal-to-noise ratio, still remains the same. However, although the theoretical maximum capacity of a sensing system employing the presented technique is N2/4, in practice, the capacity is limited by several factors. In an ideal situation, the retrieved light field of each fiber should be a perfect 6- function located exactly at a grid point in the digital spatial domain. But the imperfection of the optical arrangement, such as the positioning errors of the fiber end-faces, the intensity noise, etc., results in spreading of the light field which occupies a small area of m x m pixels as shown in Fig. 4. Then, the capacity of multiplexing is N2/4m2. Obviously, the spreading

6

5

4

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Fig. 4. Part of the magnitude spectrum of the inverse Fourier transform of the fringe patitem in Fig. 3; the peaks are the correlation intensity of the light fields from thie sensing fibers and the reference.

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240 h

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Phase and strain output of the fiber sensor array when the beam was

Intensity noise level ' * T 1

0 8

0 6

0 4

0 2

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Digitisation error only

I A

0 100 200 300 400 500

Number of sensors

Fig. 6. multiplexed in the system with a 64 x 64 pixel CCD.

Computer simulated phase trace errors versus the numbers of fibers

is one of the most significant factors affecting the multiplexing capacity. In an experiment, for example, if m = 3, according

1164 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 46, NO. 5, OCTOBER 1997

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Fig. 7. ment in Object domain.

Illustration of dual reference 2-D encoding scheme. Position arrange-

to Fig. 4, then about 450 sensors can be multiplexed using a 128 x 128 CCD array, which is still a huge multiplexing capacity.

The described spread of the retrieved fiber light field in the digital spatial domain creates crosstalk among sensing fibers and tproduces errors in the signal. A computer simulation has been carried out to assess the effects of such crosstalk resulting from intensity noise. In the simulation, a 64 x 64 area CCD was employed and different levels of random noise were added to the noise-free interferogram. The level of noise is defined as the ratio of average noise intensity over that of noise-free interference fringe. The statistical phase measurement errors versus the numbers of multiplexed fibers at different intensity noise levels is calculated and shown in Fig. 6. It is clear from the figure that the phase error is proportional to the number of fibers multiplexed in the system, and while the digitization error, which represents the error introduced when the fringe intensity, is digitized to an %bit grey scale, it has little effect on the phase measurement accuracy.

Furthermore, our experiments have shown that the proposed system is not prone to the problem of polarization-induced fading (PIF). In applications where total immunity of PIF is required, a dual-reference encoding scheme shown in Fig. 7 can be adapted. The multiplexing capacity in this scheme becomes M2/8m2 which is still very large compared with currently available techniques.

VI. CONCLUSION The multiplexing capacity is greatly improved in a digital

spatial domain multiplexing technique by employing a 2-D en- coding scheme. The system architecture is simple, robust, and inexpensive. Therefore, it is applicable in a lot of engineering measurement applications, in particular, in the subject area of smart structures and materials. The prsliminary experimental results have demonstrated its feasibility.

REFERENCES

[l] J P Dakm, C A Wade, and M L Henning, “Novel optical fiber hydrophone array using a single laser source and detector,” Electron Let t , vol 20, pp 53-54, Jan 1984

[2] R Duratians, G Anglaret, C J Hugues, and G W Fehrebach, “Spe cific design of optical fiber sensor systems for wavelength division multiplexed networks,” Sprznger Proc Physics, Optical Fiber Sensors Berlin, Germany Springer-Verlag, 19S9, vol 44, pp 504-512

[3] I Sakai, G Parry, and R C Youngquistl, “Multiplexing fiber-optic sensors by frequency modulated source and gated output,” J Lightwave Technol, vol LT-5, pp 932-940, July 1987

[4] K L Brooks, R H Wentworth, C R Youngquist, M Tur, B Y Kim, and H J Show, “Coherent multiplexing of fiber optic interferometric sensors,” J Lightwave Technol, vol LT-3 pp 1062-1070, Oct 1985

[5] Y Hu, G Yang, and S Chen, “Spatial multiplexing technique for interrogation of interferometric optical fiber sensor arrays,” Pure Appl O p t , vol 4, pp 523-527, Sept 1995

[6] Y Hu and S Chen, “An electronic scanning spatial multiplexing technique for interferometric optical fiber sensor arrays,” IEEE Phoron Technol Let t , vol 7 , pp 673-675, June 1995

[7] __, “Spatial frequency multiplexing of optical fiber sensor mays,” Opt Let t , vol 20, pp 1207-1209, May 1995

[8] S Chen, A J Rogers, and B T Maggot, “Electronically scanned optical-fiber Young’s white-light interferometer,” Opt Lett , vol 16, pp _. 761-763, May 1991.

191 J. R. Fienup, “Phase retrieval algorithm: A comparison,” Auul. Out., .~ ^ ^ - vol. 21, pp: 2758-2769, Aug. 1982.

[lo] ~, “Reconstruction of a complex-valued object from the modules of its Fourier transform using a support constraint,” J. Opt. SOC. Amer. A, Opt. Image Sei., vol. 4, pp. 118-123, Jan. 1987.

[ll] Numerical Recipes in C-The Art of Scientijk Computing, 2nd ed., H. P. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Eds. Cambridge, U.K.: Cambridge Univ. Press, 1994, pp. 500-504.

Yiqun Hu received the M.Eng. degree in optical engineering from the Institute of Optics and Electronics, Chinese Academy of Sciences, Sichuan, China, in 1984, the B.Eng. degree in optical engineering from the Changchun Institute of Optics and Fine Mechanics, Jilin, China, and the Ph.D. degree in electronic engineering from South Bank University, London, U.K.

He was a Lecturer and Associate Professor at Changsha Railway University, Hunan, China. He was also a Visiting Scholar with the University of Glasgow, Glasgow, Scotland. He is currently a research fellow at South Bank University. His major research interests are optical instrumentation and metrology. He has been carrying on research on optical fiber sensing, optical planner waveguide biosensors, digital image processing, digital signal processing, 3-D optical profiling, holography, speckle metrology, and experimental mechanics. He has authored more than 35 academic papers.

Shiping Chen (SM’96) received the B.Eng. degree in mechanical engineering, the M.Sc. degree in optical engineering, and the Ph.D. in electronic engineer- ing from King’s College, London, U.K.

His p r i m w research interest is in the area of measurement and instrumen- tation. He has carried out extensive research in optical fiber interferometry, quasidistributed optical fiber sensors, digital acoustic and image processsing, and 3-D measurement techniques, and has authored more than 50 journal and conference papers in these areas. He is currently an Assistant Professor in the Department of Mechanical Engineering and a Faculty Member in the Smart Materials and Structures Research Center, University of Maryland, College Park.

Dr. Chen was the recipient of the 1996 Metrology Award, which is the most prestigious award in the field of measurement and instrumentation given in the U.K.