A Compact Three Degrees-of-Freedom Motion Sensor ... - IEEE Xplore

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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 20, NO. 16, AUGUST 15, 2008

A Compact Three Degrees-of-Freedom Motion Sensor Based on the Laser-Self-Mixing Effect Simona Ottonelli, Francesco De Lucia, Michela di Vietro, Maurizio Dabbicco, Gaetano Scamarcio, and Francesco Paolo Mezzapesa

Abstract—The simultaneous measurement of the linear displacement and two rotation angles (yaw and pitch) of a moving object using a laser sensor based on the self-mixing effect is reported. The laser head includes three commercial diode lasers equipped with monitor photodiodes. The target is a plane mirror attached to the moving object. The linear and angular resolutions are 0.7 m and 0:8 2 1003 (2.7 arcsec), respectively. The linearity of the sensor response has been verified over a range of 1 m and 60.4 . Using three retroreflector prisms with a diameter of 10 mm instead of the plane mirror, the angular range of yaw and pitch has been improved by one order of magnitude. Index Terms—Displacement measurements, laser-self-mixing, optical feedback, real-time systems, semiconductor laser, three degrees-of-freedom sensor.

I. INTRODUCTION OHERENT external optical feedback in a semiconductor laser diode can be exploited for metrological applications [1]. The interference between the back-scattered radiation re-entering the cavity and the standing wave inside the cavity, commonly referred to as the “self-mixing” effect, results in the modulation of both the amplitude and the frequency of the laser oscillating field. This modulation carries information on the displacement of a target, acting as an external mirror, with respect to the laser source. The resulting output optical power variation can be monitored as photocurrent fluctuations measured by the photodiode integrated in the laser chip, thus allowing the device to be used both as the source and the detector. Clear benefits of this scheme are the absence of any optical interferometer external to the source, a much simpler optical alignment since there is no external reference arm, and a single quadrature reading required for the detection of the direction of target motion, significantly reducing the complexity of the sensing system and the alignment time. The efficacy of using the self-mixing phenomenon to measure linear [1] and angular [2] displacements has already been demonstrated. In particular, Giuliani et al. [2] demonstrated a method for the measurement of the tilt angle of a remote target

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Manuscript received February 14, 2008; revised April 3, 2008. This work was supported in part by the Regione Puglia, under Progetto Esplorativo PE055 and Progetto Strategico CIP PS093. Research activities developed under a joint research program with Sintesi SCpA, Advanced in Mechatronics. S. Ottonelli, F. De Lucia, M. di Vietro, M. Dabbicco, and G. Scamarcio are with the CNR-INFM Regional Laboratory LIT3, Università degli Studi di Bari, I-70126 Bari, Italy and the Dipartimento Interateneo di Fisica “M. Merlin,” Università degli Studi di Bari, I-70126 Bari, Italy (e-mail: simona.ottonelli@fisica. uniba.it). F. P. Mezzapesa is with Sintesi SCpA, I-70026 Modugno (BA), Italy. Digital Object Identifier 10.1109/LPT.2008.926569

Fig. 1. Schematics of the sensor system.

based on the self-mixing effect in the coherence-collapse (high feedback) regime [3]. This technique shows a good sensitivity but a small angular range (0.06 ), and requires the target sitting at a fixed distance from the laser and the analogic treatment of the measured signal. In this letter, a three degrees-of-freedom laser system based on the self-mixing effect is demonstrated. The sensor simultaneously measures the linear displacement and two rotation angles (yaw and pitch) of a moving object over distances greater than 1 m with an angular range greater than 0.4 , by exploiting robust digital-like signal analysis. The proposed sensor is all-interferometric, and is based on a replication of one single measuring channel, contrary to most existing industrial sensors which relay on hybrid technology for the detection of linear and angular motion. The letter is organized as follows: The measurement technique and the experimental results are reported in Section II. The results and discussion are reported in Section III and the performance and advantages of the proposed system are discussed in Section IV. II. MEASUREMENT PRINCIPLES AND EXPERIMENTAL SETUP The prototype of the sensor is schematically illustrated in Fig. 1. It is composed of a laser head, with three laser diodes mounted side-by-side in an “L”-like configuration, and a single plane square mirror of side 80 mm. The laser sources are distributed-feedback (DFB) laser diodes with nominal wavelength of 1310 nm and current threshold mA. In our experiments, the lasers are driven by a current mA. Each laser is equipped and with a collimating lens (numerical aperture mm) and a monitor photodiode, nominal focal length whose photocurrent is first AC-coupled to a transimpedance V/A), and then fed into a signal amplifier (gain processing board interfaced to a computer. In the present

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OTTONELLI et al.: COMPACT THREE DEGREES-OF-FREEDOM MOTION SENSOR

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and . The small angle approximation considered in these formulas holds throughout the angular range of our measurement. The three degrees-of-freedom are then derived from the following relations:

(2)

Fig. 2. Representative oscilloscope self-mixing waveforms of the three laser sources, obtained at a distance laser-target of 20 cm for a (a) pure translational motion, (b) a translation with a yaw rotation, (c) a translation with a pitch rotation, and (d) a translation with both the yaw and pitch rotations. The number of interference fringes is reported to the right of each waveform for ease of comparison. The vertical axis amplitude is set to 20 mV/div.

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experiment, the target was fixed to a six-axis mechanical stage, mounted onto a 1-m-long linear stage. The minimum distance between the target and the laser head was 15 cm. A commercial six-axis measurement system (API 6D Laser) was used as the reference meter whose nominal resolution is 0.02 m for linear for angular rotations. displacements and The feedback regime, i.e., the relative amount of light coupled back into the laser and giving rise to self-mixing, directly affects the characteristics of the output signal [1]. The interference fringes change from sinusoidal (very weak feedback) to slightly asymmetric (weak feedback) to a sawtooth-like shape (moderate feedback). In the moderate feedback regime, the asymmetry of , the output signal, along with its defined phase periodicity resolution of the target displacement allow for an intrinsic measurement. The easy discrimination of the direction of motion is based on the sign of the fast slopes of the sawtooth-like signal. Fig. 2(a)–(d) shows representative oscilloscope traces of the optical power measured in the moderate feedback regime as a function of time, while the target was moved at a speed of 1 mm/s. The standard analysis in the self-mixing configuration consists of the AC signal derivative, followed by the algebraic sum of the positive negative number of the peaks in the derivative of the output signal. Since each interference fringe corresponds to a target displacement , the linear displacement (see Fig. 1) can be obtained by the following expression: (1) , Each rotation angle of the target around the Y-axis ( , yaw) can be obtained by measuring pitch) and the Z-axis ( the linear displacement of three distinct points in the plane of and , aligned with the the target. With reference to Fig. 1, will measure according Y-axis at a distance , and and , aligned along to will measure the Z-axis and separated by a distance according to , where

The working principle is demonstrated by inspection of the oscilloscope waveforms reported in Fig. 2, where the individual or combined pitch and yaw rotation [Fig. 2(b)–(d)] results in a different number of interference fringes counted by the three detectors with respect to the pure translational motion [Fig. 2(a)]. Given the intrinsic linear resolution of the self-mixing technique, the angular resolution can be derived by (2) while assuming null one of the counters and unitary the other, resulting and . In the in present experiment, the laser wavelength was m and the distances between the laser diodes were mm and mm, so giving an expected linear resolution of 0.7 m and an angular resolution of (2.7 arcsec). The accuracy of the measurement is readily obtained as ( ) for the linear displacements and for the angular rotations, by the error propagation formula. Achieving an accuracy of the same order of magnitude of the resolution for the longest measured linear displacement (1 m) would require the active temperature stabilization of the diode temperature to 0.01 C to guarantee .A the necessary wavelength stabilization of comparable accuracy has been achieved by using a temperature-calibrated DFB laser source and compensating for the wavelength variations induced by changes in the environmental temperature. The correction was performed by continuously monitoring the diode temperature by means of calibrated thermocouples. Concerning the angular measurement, the distance has been evaluated as a fitting parameter upon calibration of the sensor against a reference angular standard, thus reaching . an expected angular accuracy of We checked that only the portions of the laser beam orthogonal to the target surface are reflected back along the same optical path giving rise to the self-mixing effect. Thus, any lack of parallelism between the laser beams does not modify the mutual distance of these portions and guarantees the constancy of the parameter along the X-axis. III. RESULTS AND DISCUSSION For validating the proposed system as a linear displacement sensor, the linear stage was moved along the X-axis in the range 1 m–900 mm at a speed of 10 mm/s. Fig. 3 shows the number as a function of the reference displacement , of counts simultaneously measured by the API system. The linearity over the entire measurement range validates a useful dynamic range of at least six orders of magnitude. The maximum continuous displacement was limited by the length of our linear stage. However, we verified the existence of the sawtooth-like signal over

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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 20, NO. 16, AUGUST 15, 2008

qualitatively verified. It is noteworthy that the output signal is maintained over such a relatively large angle along with linear displacements up to 1.7 m. A further improvement in the angular range can be achieved by using corner cubes in place of plane mirrors. We checked that the front face reflection of a solid corner cube does not modify the self-mixing signal and that the angular range is increased of almost an order of magnitude.

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Fig. 3. Number of counted self-mixing fringes of the laser source L as a function of purely linear displacement (backward or forward with respect to the laser source) measured by the reference meter. The error bars correspond to 1 fringe and are much smaller than the symbol size.

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Fig. 4. Number of counts for both the pair of laser diodes measuring pure (a) yaw and (b) pitch rotations. The horizontal axis reports the rotation angle measured by the reference meter. Full (hollow) marks represent data taken with the target at 20 cm (120 cm). The vertical error bars are within the symbol size.

a continuous range of 1.7 m, with no adjustment required to the optics (the shortest distance from laser head was 0.15 m) and for velocities up to 100 mm/s, limited by the electronic bandwidth. To test the performance of the proposed system as a rotation sensor, the target was kept at a fixed distance (0.2 and 1.2 m from the laser head) and the six-axis platform was rotated by or increasing the yaw or pitch angles in both clockwise directions. The number of counted fringes anti-clockwise is shown in Fig. 4, where the expected linearity is preserved over the entire measurement range. The maximum given rotation for a meaningful comparison was limited by the reference system. On the other hand, a larger range of about 0.8 was

IV. CONCLUSION We have shown that the laser-self-mixing can be used to simultaneously measure in real-time three degrees-of-freedom of a moving object with resolution of 0.7 m for the linear and for the angular displacement. The dynamic ranges are mm for the linear and for the angular motion. The angular range can be improved to more than 2 substituting the plane mirror with three retroreflector prisms. The resolution improves proportionally to the laser wavelength and the distance between the laser sources. To our knowledge, this is the first time that the self-mixing is exploited for the simultaneous measurement of linear and angular degrees-of-freedom. Compared with commercially available multidegrees-of-freedom instruments, the demonstrated sensor would fill the existing gap between the sophisticated and costly systems capable of nanometric resolution, and the off-the-shelf instruments capable of submillimetric resolution. The intermediate micrometric resolution range is today covered by optomechanical encoders, which make use of interpolating functions and are unable to handle target rotations. The proposed sensor, instead, provides direct measurements of displacement by the digital count of the number of interference fringes, with no need of interpolation. This ensures a better accuracy while preserving the compactness of the system at a possibly lower cost, making it suitable for machine-tool calibration and diagnostic. ACKNOWLEDGMENT The authors acknowledge useful discussions with R. Martana, C. Florio, and F. Jovane. REFERENCES [1] G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode selfmixing technique for sensing applications,” J. Opt. Pure Appl. Opt., vol. 4, no. 6, pp. S283–S294, Nov. 1, 2002. [2] G. Giuliani, S. Donati, M. Passerini, and T. Bosch, “Angle measurement by injection detection in a laser diode,” Opt. Eng., vol. 40, no. 1, pp. 95–99, Jan. 2001. [3] D. Lenstra, B. H. Verbeek, and A. J. den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron., vol. QE-21, no. 6, pp. 674–679, Jun. 1985.