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An overview and a contribution to the optical measurement of linear displacement


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IEEE SENSORS JOURNAL, VOL. 1, NO. 4, DECEMBER 2001

An Overview and a Contribution to the Optical Measurement of Linear Displacement
Pedro M. B. Silva Gir?o, Sen

ior Member, IEEE, Octavian A. Postolache, Member, IEEE, José A. Brand?o Faria, Senior Member, IEEE, and José M. C. Dias Pereira

Abstract—The present work is a contribution to the field of linear displacement measurements by optical means. For that purpose, a brief overview of some existing solutions is presented and two systems for axial linear displacement measurement based on light intensity detection are introduced. The systems have redundancy and were designed with the purpose of achieving identification and automatic correction of errors arising from inadvertent angular variations between the sensor and the light beam positions. Index Terms—Interferometry, laser measurements, light intensity modulation, optical distance measurement, optical position measurement, optical transducers, sensors.

I. INTRODUCTION: AN OVERVIEW OF OPTICAL LINEAR DISPLACEMENT MEASURING SYSTEMS HE measurement of linear displacement is a very important topic encompassing a large number of solutions. Due to its ruggedness and often contactless characteristics, optical systems are one of the most adopted, particularly when fast changes in displacement need to be measured. Moreover, due to the physical principles that support the operation of some of those systems (e.g., optical interferometry), they allow the measurement of linear displacements with resolutions and accuracies below the nanometer. A brief overview of the measurement of linear displacement by optical or electro-optical means is presented in the following sections. A. Interferometric Methods Optical interferometry is mostly used in a large number of situations requiring high resolution and accuracy in the measurement of small or very small linear displacements. Among others, this technique is used for linear displacement measurements in machine tools, for calibrating scales, in material science (e.g., determination of anisotropy of thermal coefficients and elastic-modulus of single crystals), in dimensional metroloManuscript received September 27, 2000; revised October 17, 2001. The associate editor coordinating the review of this paper and approving it for publication was Dr. Arnaldo D’Amico. P. M. B. S. Gir?o is with the Instituto de Telecomunica??es, 1049-001 Lisboa, Portugal (e-mail: psgirao@alfa.ist.utl.pt). O. A. Postolache is with the Technical University of Iasi, 6600 Iasi, Romania (e-mail: opostola@alfa.ist.utl.pt). J. A. B. Faria is with the Centro de Electrotecnia Teórica e Medidas Eléctricas, Instituto Superior Técnico, 1049-001 Lisboa, Portugal (e-mail: brandao.faria@ieee.org). J. M. C. D. Pereira is with the Escola Superior de Tecnologia, Instituto Politécnico de Setúbal, Estefanilha, 2910 Setúbal, Portugal (e-mail:joseper@est.ips.pt). Publisher Item Identifier S 1530-437X(01)11077-8.

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Fig. 1. Michelson interferometer.

gies (e.g., to obtain Avogadro’s constant), and for strain evaluation. The principle of optical interferometry is well known [1], [2]. Fig. 1 shows the configuration of perhaps the simplest, but also more used, dual beam interferometer (Michelson interferometer). Other types of two beam interferometers, such as Mach-Zender and Sagnac’s, have been less used for linear displacement measurements. The two light beams at A have a phase difference that depends on their optical path lengths. The interference of those beams produces fringes that alternate from bright to dark when the phase difference goes from 0 to . Since the path length of beam 1 is constant, the fringes inform on the change of beam 2 path length, the same is to say, on the displacement of the moving element [the horizontally movable mirror in Fig. 1(a), or the vertically movable dielectric body, in Fig. 1(b)]. The counting of bright and dark fringes yields the value of the displacement, since the transition from dark to bright, or vice-versa, corresponds to a path length shift of , where is the wavelength of the light used. The simplicity of the principle supporting optical interferometry does not mean that the implementation of linear displacement measuring systems is straightforward. In fact, the practical utilization of interferometric means relies critically on the monocromaticity and coherence degree of the light

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source being used. This explains why interferometric methods began to be more implemented when LASER sources became available. Moreover, when low resolution and high accuracy of the displacement measurements are required, demands on the quality of the light source are higher. If one takes into in the wavelength of consideration that a stability of a LASER diode (an interesting source due to its compactness, low-cost and ease of modulation) implies that its temperature must be kept stable to 0.01 C, it is easy to understand the importance of the temperature control of the light sources when displacement measurements with resolutions of 1 nm and accuracies of 1 m are required. For even higher accuracies, attentionmustbepaidtotheintensitydistributionofthelightbeam so as to minimize diffraction effects [3]. Another requirement of optical interferometry is the mechanical stability of all the components of the measuring system. Finally, the efficient and practicable use of optical Michelson interferometers is possible only when some user independent system for fringe counting is implemented. The simplest system consists of an electronic circuit that produces a pulse for each bright fringe, which leads to a displacement measuring system with a resolution of the order of (0.6238 m for a He-Ne LASER source). The improvement in resolution was investigated by ( nm for a different authors [4]–[6] and values of He-Ne LASER source) were reported by Hagiwara et al. [7]. Optical interferometry for linear displacement measurements has developed basically according to two domains of application: industry and research. For the first, the main requirements are robustness (sometimes interferometers must operate in difficult environmental conditions, e.g., high temperatures), portability, ease of use, wide range of applications, low cost and accuracy, and resolution not better than 1 m; for the latter, high resolution and accuracy are usually the more desired features. Most of the abundant research conducted in the field of optical interferometry for the last 30 years has addressed directly or indirectly at least one the above mentioned goals. The basic Michelson interferometer, usually using a LASER source, has been modified in several ways: (a) so that the reflected light beam does not return back to the light source (e.g., [7]); (b) in order to use one light source but two beams with two different frequencies and polarizations [8], or two light sources producing beams of different wavelengths [9], so that the information about displacement can be obtained from the phase of an electrical signal (heterodyne LASER interferometer) or from the Doppler frequency shift of one of the beams (ac or Doppler interferometer) [10], [11]. The heterodyne LASER interferometer introduces some fringe distortions whose effect is discussed and a solution is presented by Tanaka et al. [12]; (c) complemented with components so that the displacement is obtained by subtracting a reference phase from the interferometer phase [13], [14]. This so-called double-pass Michelson interferometer aims at picometer precision, which means that noise (quantum noise of the light source, mechanical noise due to mechanical vibrations, or deformations of the interferometer optical components and thermal noise due to fluctuations of temperature) must be reduced as much as possible [14]. Also, making use of light interferometry are many other systems such as those proposed by Zagar, based on Young’s double-slit experiment [15] and Do-

nati et al., based on the output power variation of a LASER when a small fraction of its emitted power is reflected back by a reflective body and re-injected inside the LASER cavity (LASER feedback interferometer) [16]. Free-space interferometry based on air propagation of optical beams is affected by alterations in the air environmental conditions. When the air pressure, temperature, or humidity change, the air refractive index will also change and with it the speed of light and the light wavelength. Even if in some applications the error introduced in the wavelength by 0.4 ppm per mm Hg change in air pressure and 1.1 ppm per degree Celsius may be neglected, some commercial interferometers include transducers that allow on-line correction of such errors (e.g., HewlettPackard 5510). An even more advanced solution consists in the inclusion of a wavelength measuring system (wavelength tracker) [17]. For many industrial applications, either because of environmental limitations or because some characteristics are required (e.g., flexibility of the measuring system), guided interferometry using polarization-maintaining optical fibers [18], [19] may prove to be a better solution than free-space interferometry. The interferometer described by Minoni et al. [19] has the advantage of having no electronic components in the sensing head (moving part of the interferometer) and, using a nonstabilized 5mW He-Ne LASER, it achieved a reported resolution of about ), an overall accuracy of 1 m over a measuring 80 nm ( range of 20 mm. The performance of fiber optical based interferometers depends, however, on several factors and quantities, some of which are analyzed by Minoni et al. [20], which means that some of the advantages resulting from the use of optical fibers may be cancelled by the introduction of other disturbing factors (e.g., fiber stress). Nowadays, it is possible to find commercial optical interferometers able to measure linear axial (in the direction of the light propagation) displacements of up to several tens of meters with a resolution and accuracy around 1 nm (e.g., Hewlett-Packard 10 716A). B. Methods Based on the Measurement of Light Intensity A large number of systems to measure displacement by optical means are based on a light source and a light sensor (detector). In the simplest implementations, the displacement produces a change of the optical power reaching the detector. In Fig. 2, several possible configurations that use this idea are presented, (a), (b), and (c) for axial, and (d), (e), and (f) for transversal displacements. The light sources are usually visible or infrared light emitting diodes (LEDs) and LASERs for longer ranges. Modulation of the source is advisable when the noise due to background light is high, since it allows better separation between signal and noise in the detector. For the widely used configuration (c), the relationship between the optical power in the detector and the displacement is of the type shown in Fig. 3. The good linearity and high slope of the ascending flank of the curve recommends the utilization of such configurations for small displacements. Configuration (a) has the disadvantage of requiring the change of position of either the light source or of the detector. Configuration (c), in

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Fig. 2.

Linear displacement measurement by light intensity.

particular, has been widely implemented using optical fibers bundles [21]; one or several fibers transmit the light emitted by a source to illuminate the reflective moving surface and one or several fibers receive the reflected light and guide it to a photodetector. The fibers must be of the total internal reflection type to avoid crosstalk between transmitting and receiving fibers, the sensitivity depending on the arrangement of both types of fibers in the bundle. Common to the generality of other optical measuring systems, the performance of this one depends on the environmental light (noise) and on the relative position of the optical fiber bundle and reflective surface;

however it also depends on the changes of the reflectivity of the surface. This last problem is mitigated by using a mirror or through automatic compensation [22]. In what concerns the last three configurations for transversal displacement shown in Fig. 2, it is worth mentioning that their measuring ranges are upper-bounded by the dimension of the detector in the direction of displacement. The relationship between the light reaching the detector and the displacement is essentially linear even if it depends on the shape of the object that interrupts the beam, on the detector cross section and also on the spatial distribution of the light intensity emitted by the source.

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Fig. 3. Light intensity linear displacement system: normalized optical power as a function of normalized distance. d in the sensor is maximum.

= 1 is the distance for which the power

Some commercially-available optical displacement measuring systems utilize one of the configurations just presented. LG5 and LG10 from Banner Engineering Corporation [23], use visible LASER sources whose light is detected by a sensor upon being diffused by the target object. Their ranges are 45 to 60 mm and 75 to 125 mm, respectively, with resolutions of 3 m at 50 mm and 10 m at 100 mm, respectively. Their sensibility to the color of the target is as small as 100 m. NanoVIBE from Ultrafast Sensors and Applications Company [24] makes use of a similar measuring principle but the reported resolution of 10 nm in a range of 1 mm is independent of the target surface shape (flat or curved) and reflectivity (metallic or specular).

C. Methods Based on Position Detection Linear displacement of a moving object is the overall change of position it suffers during a certain amount of time. Several are the solutions nowadays used to access displacement values through the use of sensors that are sensible to the position on their detection area a light beam impinges on. The solutions can be classified according to the type of light position detector they use and have nowadays a characteristic that is almost common: the use of a LASER light source. Here are some of them. Optical Potentiometer [25]: An optical potentiometer is a photoluminescent material, usually cylinder shaped, having a length depending on the displacement to be measured and terminated by two photodiode detectors. A focused light source exciting the material orthogonally to the cylinder axis causes luminescence to propagate toward the ends of the cylinder, the intensity of light detected by the photodiodes informing on the position of the source relatively to the cylinder. Laguesse implemented the potentiometer using fluorescent optical fibers [26] and reported resolutions of 0.2 mm, 0.6 mm and 1.5 mm for fibers having lengths of 372 mm, 1143 mm and 3098 mm, respectively. Lang et al. [25] reported a resolution of 1 mm for a total distance of 3 m. Optical potentiometer based displacement measuring systems are low cost and quite durable, providing an interesting solution for medium resolution, medium and large range transversal displacements. Axial displacement can also be measured provided that the light beam and the optical potentiometer axis make an angle smaller than 90 by some

5–10 , so as to convert an axial displacement into a transversal one. Position-Sensitive Detector: The term position-sensitive-detector (PSD) has been coined in the literature to designate devices that are based on the lateral photoeffect in an illuminated pn junction. This effect, first described by Schottky [27] and later elaborated by Wallmark [28], materializes under the form of a photocurrent that is collected by electrodes mounted on the surface of the junction according to a law that depends on the distance between the electrodes and the point of the junction surface illuminated by the centroid of the light beam. The intensive research work done on PSDs includes studies on the performance of different implementations [29]–[31] and on the influence that background illumination and noise sources have on the performance of such devices as position detectors [32], [33]. The activity around the use of PSDs in position measurement is also very impressive [34]–[39]. Two main types of solutions have been considered: amplitude detection of the light beam from the difference of the dc photocurrents generated by a steady-state light excitation and detection of phase difference between the ac photocurrents generated by a sinusoidal light excitation. Both methods have advantages and disadvantages [33], [35] with phase detection particularly suitable for the simultaneous measurement of multiple light sources positions and displacements using a single PSD [35]. Both transversal and axial linear displacements can be measured using a one-dimensional PSD. In the first case, the detector must be installed such that its surface stays orthogonal to the light beam while in the second the detector and light beam should make an angle smaller than 90 by some 5–10 in order that the axial displacement is converted into a transversal one. PSDs of high linearity, good resolution (better than 1 m) and fast response are presently available from a few different vendors. Discrete Position Detectors: PSDs are continuous light position detectors. Using arrays of photosensors, like in [40], it is also possible to detect position and thus displacement, by optical means. The resolution depends basically on the size of the individual sensing elements of the array, the separation of their centers and the intensity distribution of the light source. Since perfectly focused light beams are impossible to obtain, more than one photosensor is usually illuminated, leading to a

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TABLE I PERFORMANCE OF SOME OPTICAL DISPLACEMENT MEASURING TRANSDUCERS

problem of position detection. Gonnason et al. proposed in [40] a possible solution that is upgraded in [41] and [42]. Once again adequate orientation of the light beam and of the sensor array allows the measurement of both axial and transversal displacements. Charged coupled devices (CCDs) are also used as discrete light detectors for displacement measurement. Feiel and Wilksch [43] introduced a measuring system, mainly aimed at the detection and measurement of strain in objects, that uses a 512 512 CCD array, having a reported sensitivity of 50 nm. Like in this case, the displacement measurement usually requires additional processing of the CCDs output information (images), something that can be particularly heavy and only possible using signal processors [44]. D. Other Methods Interference in a Semi-Insulating Semiconductor: Photoelectromotive Force: Jin et al. [45] have recently proposed a displacement measuring system that is based on the photoelectromotive force effect [46] in a CdTe:V semiconductor. This technique is quite simple and rugged and the implementation reported in [45] leads to linear measuring ranges of about 2 mm periodically distributed with resolutions better than 1 m. Shack-Hartmann Sensors: Ares et al. presented in [47] a position and displacement sensor system based on the determination of the coordinates of a self-luminous object through the measurement of the wave fronts emitted by the object and detected by a Shack-Hartman wave-front sensor. The solution is limited to

displacements of objects located some tens of centimeters from the sensor and the reported system, assembled using off-the-shelf components, allows axial position uncertainties lower than 1 m when the object is 30 cm away from the sensor. Optical Incremental Encoders: Linear displacement optical encoders are basically made of a light source and a light detector mounted in the same structure either as in Fig. 2(a) or (e) and a ruler. The ruler fixed to the moving object slides between source and detector in the first case and in front of both source and detector in the second. Along its longitudinal dimension, the ruler has a track of alternate constant size transparent and opaque zones in the first configuration and alternate constant size reflecting and nonreflecting zones in the second configuration. The displacement of the ruler leads to exposure of the detector to light with a periodicity that depends on the distance between two consecutive transparent or reflecting zones. This distance is thus the resolution of the sensor. The inclusion of a second track parallel to the first with zones slightly spatially shifted and a second detector transversally aligned with the other detector allows the determination of displacement direction. When the displacement takes place in a very short time interval, reading of the detectors output may be difficult and techniques like interfering patterns may be required. Ready-to-use optical linear encoders are available from several vendors (e.g., Solartron [48], for instance, markets systems providing 0.05 m resolution and ranges of 12 and 25 mm and GPI [49]). Table I summarizes the characteristics of the different types of displacement solutions referred to in the previous paragraphs.

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The values included in the table must be considered as indicative and not absolute. Some of them concern advanced research work reported in papers included in the references, and others are extracted from specifications of devices and systems available on the market. II. DETECTION AND AUTOMATIC CORRECTION OF TILT ANGLE IN LINEAR DISPLACEMENT OPTICAL MEASURING SYSTEMS The relative position of the light source and detector is important in the generality of the solutions used for linear displacement measurement by optical means. This is particularly true for the methods based on the measurement of the intensity of light by a light detector mentioned in Section I-A. In those methods, a change of the angle between the light beam and detector surface (tilt angle) introduces an error that is significant even when the angular variation is small [50]. It is, thus, desirable to provide the measuring systems that use such methods with simple means of auto correction of the tilt angle or, at least, of means of detection of that angle for servicing purposes. The problem has been already addressed namely by Faria et al. [50] in the context of a system that uses a bifurcated optical fiber bundle [51] according to the configuration presented in Fig. 2(c) and Sagrario and Mead [52] have provided a solution for that particular case. In the following paragraphs, we further contribute to the subject of tilting error correction by introducing two systems with the topology of Fig. 2(a), one using an array of light sensors as a position transducer and another individual light sensors. A. Axial Linear Displacement Transducer With Tilting Detection Using an Array of Light Sensors and Two Light Sources Let us consider the optical transducer of Fig. 4 that uses a 1 linear array of light sensors (AS) and two light sources, LD1 and LD2, that make an angle with the displacement axis (xx). Considering perfectly collimated light beams, the active the zones of the sensors reduce to their centers; denoting by initial reference position of the array AS that corresponds to the

Fig. 4. Schematic configuration of an optical transducer using two light sources.

illumination of sensors #1 and and denoting by one of the middle positions in the measuring range, the relationship between , , and excited sensors order can be written as (1) where is the distance between the center of two consecutive is the total distance between the censensors, values represent the order of ters of sensors 1 and , the , . For the considered the excited sensor, and . In this case, the displaceoptical sensor, ment is expressed by (2) By analyzing the equation above, one can see that in the absence of sensor tilting perturbation, the system is a redundant one, and it is a system with a reservation reliability scheme [53], [54].

(3)

(4)

(5)

(6)

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Fig. 5 shows the geometry of the system when the array is tilted by an angle . After some algebraic manipulation, the following relations can be obtained: (see (3)–(6) at the bottom of previous page). Once the sensors that are illuminated by each beam are known, it becomes possible to determine the tilting angle using (5) and the displacement value using (6). It can be argued that the present solution solves one problem (tilt angle) by introducing two new ones (the angles of the two LASER sources). However, we assume that the two LASERs are mounted in a fixed structure and that the array of sensors is solidary with the moving object. In such case, both angles of the light sources can be made equal and time invariant. Experimental work was carried out to verify the validity of the solution now introduced. The array of sensors used was the TSL 218 and the light sources where two LASER diodes. The LASER beams used were not collimated and so simultaneous excitation of the TSL218 leads to an output signal from which it is difficult to extract the excited sensor (pixel) order information. Each LASER beam excites more than one pixel and superposition and merging of the excited pixel regions may occur. Experimentally, it was determined that, for the considered LASER sources, the number of excited pixels for one beam is up to 20 pixels, which represents more than 4% of the sensor active pixels. Using special LASER diodes or an adequate optical convergent system, the number of the excited pixels can be reduced to less than 1% of the sensor active pixels. In this case, the increase of measurement system resolution implies the increase of system costs. On the other hand, system robustness and reliability are strongly diminished when a lens system is added to each light source. In order to overcome the above-mentioned problems and to better discriminate the pixel that is in the center of the excited region, the following procedure was used. a) Excitation of the sensor by LD1 and evaluation of the pixel order in the center of the excited region (median pixel evaluation). b) Repetition of (a) for LD2. c) Evaluation of tilt angle using (5) and the displacement using (6). The results obtained were qualitatively correct, but quantitatively unsatisfactory, even with the procedure just described which uses the LASERs in a switched mode. The authors are working on the improvement of the setup in order to increase the performance of the transducer that they will report in a near future. B. Axial Linear Displacement Transducer With Tilting Correction Using Two Matched Light Detectors Fig. 6(a) represents an axial displacement transducer that uses a light source LD and a detector according to the basic configuration of Fig. 2(a). The light source is a LASER diode of the same type used in the transducer of Fig. 4 with a Gaussian illuminance. The detector S1 is a TLS250 whose output is a voltage proportional to light intensity. As mentioned before and can be seen in Fig. 6(b) experimentally obtained, the output of the sensor depends heavily on the angle between the light beam and the sensor. Fig. 6(c) makes it evident that a tilt angle as small

Fig. 5. Schematic configuration of the optical transducer for a tilting angle of .

as 5 introduces an apparent displacement error of 8.2 mm when the distance between source and detector is 10 mm. Let us, then, consider the inclusion of a second matched light detector, S2, to implement a transducer as shown in Fig. 7(a). Detectors S1 and S2 are equidistant from the axis of the light beam. The normalized measured output voltage of the detectors in this new configuration is as shown in Fig. 7(b). Due to the fact that the light beam is Gaussian and that the two detectors are matched and placed orthogonally to the light beam at equal distances from the beam axis, the two characteristics have, for a given tilt angle, symmetric variations around the value for (no tilting). This suggests a straightforward algorithm to automatically correct tilt induced errors: evaluation of the arithmetic average of the normalized output voltages of the detectors. Such a procedure leads in the present case and for the interval of the considered tilt angle, to a reduction of the error to 1% in the worst case. Even if the light beam is not Gaussian and the two detectors are not matched, a calibration procedure to obtain the characteristic curves of Fig. 7(b) should lead to this or even better level of accuracy. In that case, the arithmetic average must be a weighted one. III. CONCLUSION A brief overview of optical based solutions for linear displacement measurement has been presented. The error introduced in the measurements by undesirable and unpredictable geometrical alterations of the components of the transducers were emphasized by considering the perturbations due to tilting of the light sensor in light intensity based configurations for axial displacement measurement. Two situations were considered: one involving an array of sensors used as a position detector and another involving a single sensor. In the first case, it was shown that the use of two light sources conveniently oriented leads to a set of equations that allow the evaluation of the array tilting and of the corrected displacement. The validity of the solution proposed depends very much on the shape of the light beam, on the dimension of the sensors of the array, and on

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(a)

(b)

(c)

Fig. 6. (a) Axial displacement transducer:  35 ; (b) dependence of detector output normalized voltage with tilt angle for d = 10 mm; (c) dependence of detector output normalized voltage with distance and apparent displacement due a tilt angle of 5 when the distance between source and detector is 10 mm.

=

(a)

(b)

Fig. 7. (a) Axial displacement transducer with two matched detectors; (b) dependence of detectors output normalized voltages with tilt angle for d = 10 mm.

the spacing between them and so should be investigated on a case by case basis. For the second situation analyzed, it was experimentally evidenced that the inclusion of a second detector leads to the possibility not only of detecting the tilt angle, but also to the implementation of an easy algorithm for its automatic correction. With these two examples, it was shown that the use of redundancy in optical measuring systems (two light sources in one case and two light detectors in the other) can be a solution to overcome errors in linear displacement measurement due to geometric alterations of system components. REFERENCES
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Pedro M. B. Silva Gir?o (M’00, SM’90) was born in Lisbon, Portugal, on February 27, 1952. He received the Ph.D. degree in electrical engineering from the Instituto Superior Técnico of the Technical University of Lisbon (IST/UTL) in 1988. In 1975, he joined the Department of Electrical Engineering at IST/UTL, first as an Assistant Professor and, since 1988, as a Professor. His main research interests concern instrumentation, measurement techniques, and physical and mathematical problems involved in modeling magnetic materials. Metrology, quality, and electromagnetic compatibility are also areas of regular activity mainly as auditor for the Portuguese Institute for Quality (IPQ).

Octavian A. Postolache (M’99) was born in Piatra Neamt, Romania, on July 29, 1967. He received the electrical engineering diploma from the Faculty of Electrical Engineering, Technical University of Iasi, Iasi, Romania, in 1992. In 1992, he joined the Faculty of Electrical Engineering Iasi, Department of Electrical Measurements, as an Assistant Professor, where he is currently Professor In the last two years, he has been developing a research activity at the Instituto Superior Tecnico of Lisbon, Portugal. His main research interests concern intelligent sensor, laser systems, and neural processing in automated measurement systems.

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José A. Brand?o Faria (SM’01) was born in Portugal, in 1952. He received the degree in electrical engineering in 1986 and the Ph.D. degree, as well as the title of Aggregate Professor, in 1992, both from the Instituto Superior Técnico of the Technical University of Lisbon, Portugal. He has been teaching since 1975 at the Department of Electrical Engineering of the Instituto Superior Técnico, where he is a Full Professor. From 1994 to 2000, he served as President of the Centro de Electrotecnia Teórica e Medidas Eléctricas—a University Center for research and development in Lisbon. His areas of interest include wave propagation phenomena in multiconductor transmission-line structures, optical fibers, and electrooptical phenomena. Professor Faria has published extensively; he authored two books and contributed over sixty papers to conferences and journals. Prof. Faria is a member of the Optical Society of America.

José M. C. Dias Pereira received the degree in electrical engineering from the Instituto Superior Técnico (IST) of the Technical University of Lisbon (UTL), Lisbon, Portugal, in 1982. In 1995, he received the M.Sc. degree, and in 1999 the Ph.D. degree, in electrical engineering and computer science, respectively, both from IST. He worked for eight years for Portugal Telecom, Setubal, in digital switching and transmission systems. In 1992, he returned to teaching as Assistant Professor in Escola Superior de Tecnologia of Instituto Politécnico de Setúbal, Setúbal, Portugal, where he is, at present, a Coordinator Professor. His main research interests are in the instrumentation and measurements areas.


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