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Study on fast linear scanning for a new laser scanner
ARTICLE IN PRESS Optics & Laser Technology 42 (2010) 42–46
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Study on fast linear scanning for a new laser scanner Sihua Xiang a,, Sihai Chen a,b, Xin Wu a, Ding Xiao a, Xiawei Zheng a a b
College of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China Wuhan National Laboratory for Optoelectronics, Wuhan 430074, PR China
a r t i c l e in f o
a b s t r a c t
Article history: Received 12 January 2009 Received in revised form 28 March 2009 Accepted 23 April 2009 Available online 29 May 2009
In the field of lidar system design, there is a need for laser scanners that offer fast linear scanning, are small size and have small a rotational inertia moment. Currently, laser scanners do not meet the above needs. A new laser scanner based on two amplified piezoelectric actuators is designed in this paper. The laser scanner has small size, high mechanical resonance frequencies and a small rotational inertia moment. The size of the mirror is 20 mm 15 mm. To achieve fast linear scanning performance, an open-loop controller is designed to compensate the hysteresis behavior and to restrain oscillations that are caused by the mechanical resonances of the scanner’s mechanical structure. By comparing measured scanning waveforms, nonlinearities and scan line images between the uncontrolled and controlled scanner, it was found that the scanning linearity of linear scanning was improved The openloop controlled laser scanner realizes linear scanning at 250 Hz with optical scan angle of 712 mrad. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Laser scanner Fast linear scanning Mechanical resonance
1. Introduction The laser scanner is one of the most important components in a lidar system. Two-dimensional scanning-imaging in two orthogonal axes are employed in many lidar systems. The two orthogonal axes consist of a fast scan axis and a slow scan axis. The imaging speed and imaging resolution of the lidar system are limited by the dynamic behaviour of the laser scanner along the fast scan axis. Galvanometer scanners and rotating mirror scanners (rotating prism scanners) are used in many lidar systems as fast scanners [1,2]. Such systems suffer from disadvantages such as large size, high power consumption, large rotational inertia moment and poor linearity during fast linear scanning (scanning at uniform line velocity with high frequency). The large rotational inertia moment will severely affect the satellite attitude if the lidar is used in a satellite. Linear scanning is used to achieve a uniform scanning field and to provide uniform detection probability. While MEMS scanners have high resonance frequencies and large deflection angles, the small size of their mirrors limits their application in lidar systems [3]. Fast steering mirrors (FSMs) driven by piezoelectric actuators or voice coil actuators can be used in adaptive optics, laser beam steering, tracking, pointing and scanning [4–6]. They offer advantages such as small rotational inertia moment, fast response and small size. FSMs driven by voice coil actuators usually have large deflection angles, whereas
Corresponding author. Tel./fax: +86 27 87792364.
E-mail address: [email protected] (S. Xiang). 0030-3992/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2009.04.019
they have low resonance frequencies and high power consumption. FSMs driven by piezoelectric actuators usually have high resonance frequencies but they offer small deflection angles. Other scanners based on refraction, diffraction, the electro-optic and acousto-optic effects have lower optic transmission efficiency than scanners based on reflection, and thus lidars using these scanners have shorter detection distance than lidars using scanners based on reflection. Closed-loop controllers are used in many FSMs, and they can operate effectively in laser beam pointing, tracking and scanning at low frequency. However, closed-loop controlled FSMs cannot operate in linear scanning at high frequency. The above problem is caused by two major reasons: one is that high frequency linear scanning will excite oscillations that are caused by mechanical resonances of FSMs and the other is that the closed-loop control bandwidth is not high enough to restrain the resonances. An optical tip-tilt actuator based on amplified piezoelectric actuators (APAs) was developed by Claeyssen et al. [7–9]. It has resonance frequency of more than 1 kHz and a mechanical scan angle of 18 mrad. The scan angle is larger than that of traditional piezoelectric-actuated FSMs due to the special structure of the tip-tilt actuator. Accordingly, the optical tip-tilt actuator can be used as a fast scanner in a lidar system with small field of view. It can also be used in lidar systems with large field of view when galvanometer scanners or gimbal mount mirror scanners are used as large view field scanners. In this paper, a fast laser scanner driven by amplified piezoelectric actuators is designed. The structure of the laser scanner is similar to the above optical tip-tilt actuator. The static and dynamic performances of the scanner are measured. An open-loop
ARTICLE IN PRESS S. Xiang et al. / Optics & Laser Technology 42 (2010) 42–46
control method is designed to compensate hysteresis and restrain the oscillations that are caused by the mechanical resonances of the scanner. To demonstrate the effect of the open-loop controller, the actual performances of the uncontrolled scanner and the open-loop controlled scanner are compared.
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and 2553 Hz, respectively (see Fig. 2). The analysis results show that the modes of the scanner are complicated due to its structure. These modes will limit the dynamic performance of the scanner. The third mode is caused by the hinge of the flexure support. The maximal displacement (DMX) of the third mode is largest of all. Consequently, the third mode is the primary effect factor.
2. Scanner design 3. Performance testing of the laser scanner The laser scanner assembly consists of a mirror suspended on a one degree of freedom flexure support that enables the mirror to be tilted along the tilt axis (see Fig. 1a). The size of the mirror and the scanner are 20 mm 15 mm and 60 mm 50 mm 25 mm, respectively. The weight of the scanner is about 70 g. Two APAs are mounted on the back of the flexure support. The concept of APAs relies on the flexural-extensional principle [7–9]. An elastic shell bends under the extension of the piezoelectric actuation. The displacement on contraction is several times larger than that on extension. The displacement amplification ratio depends on the ratio of the length and the height of the elastic shell. Two APAs are arranged in parallel. This arrangement ensures that their actuation axes are close to each other. The displacement amplification of APAs and the parallel arrangements provides a larger tilt angle than traditional piezoelectric-actuated scanners. The mirror is in its equilibrium position when the same voltage is applied to the two APAs. The mirror will deflect when the voltage applied to one APA is increased and that to the other APA is reduced (see Fig. 1b). Finite element analysis is used to analyze the modes of the APA and the laser scanner. The finite element analysis results show that the first mode frequency of the APA is about 2800 Hz, and the first three mode frequencies of the laser scanner are 1950, 2092,
A block diagram of the performance test bench is shown in Fig. 3. The static and dynamic performances of the laser scanner are measured on the test bench. In the dynamic performance testing, the system’s input is the voltage wave generated by the wave generator, and the system’s output is the deflection angle of the scanner. The controller (see Fig. 3) is not used in the static and dynamic performances test, whereas it is used in later section to improve the scanning linearity of the laser scanner. The scanning linearity is not the linearity determined in static performance testing, but rather it is the linearity of scanned path at linear scanning. It reveals the deviation extent of the scanned path to the estimated triangle waveform path. The scanning linearity is different at different scanning frequencies. The relationship between the optical deflection angle and the driving voltage is shown in Fig. 4. The maximal optical deflection angle is 712 mrad. As can be seen in Fig. 4, the hysteresis of the piezoelectric ceramic is significant and it will affect the scanning linearity. Fig. 5 shows the bode plot of the laser scanner system. The bode plot consists of a low pass and several stable resonances. The bode plot reveals that the primary resonance frequencies are the first three resonance frequencies and they are 1872, 1960,
Fig. 1. Design of the laser scanner (a) structure of the scanner assembly and (b) operation principle of the laser scanner.
Fig. 2. The first three modes of the scanner (simulated by ANSYS FEA software).
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2364 Hz, respectively. The first three resonance frequencies correspond to the first three modes which analyzed in above section (see Fig. 2). The response amplitudes of the first three resonances all exceed 15 dB, and the peak response is about 29 dB at 2364 Hz that is caused by the third resonance. Consequently, the first three resonances will reduce scanning linearity of the laser scanner.
4. Controller design
Fig. 3. Block diagram of the performance test bench.
The open-loop control diagram, as shown in Fig. 6, consists of four major components: the laser scanner (which is composed of a mirror, a flexure support, two APAs and a base), voltage amplifier, controller and wave generator. The controller consists of a hysteresis compensator and notch filters. In almost all piezoelectric-actuated systems, the hysteresis of the piezoelectric actuators will affect the movement of the systems. Compensation of the piezoelectric hysteresis has been studied previously [10,11]. Notch filters and low pass filter have been used to reduce mechanical oscillation of FSM [12]. The hysteresis compensator used in this paper is an algorithm that adjusts the generated triangle wave, making sure the hysteresis scan line becomes a straight line. The wave generator and hysteresis compensator are implemented on the same digital signal processor (DSP). The triangle wave is composed of many high-order harmonics. The Fourier series of a triangle wave is given by f ðtÞ ¼
1 np E 4E X sin2 þ cosðnotÞ. 2 2 2 ðnpÞ n¼1
(1)
The high-order harmonics near mechanical resonance frequencies will excite oscillations of the laser scanner. If triangle wave frequency is higher than 50 Hz, the laser scanner starts to oscillate due to its mechanical resonances. As analyzed in the above section, the first three resonance frequencies are the major influences on the oscillation. Three notch filters in series are used to reduce the amplitude of the scanner system at the first three resonance frequencies, resulting in the restraining of the oscillation. Notch filters are implemented in hardware circuits.
5. Experimental results Fig. 4. The relation of optical deflection angle and the driving voltage.
To compare the performance of the open-loop controlled scanner system with the uncontrolled system, scan lines are tested and imaged. The test bench is shown in Fig. 3. The distance of the image surface to the scanner is about 54 cm and the position sensitive detector (PSD) needs to be removed when the scan line is imaged. Fig. 7 shows scanning waveforms (a, b) and nonlinearities (c) of the laser scanner without and with hysteresis compensator at linear scanning of 10 Hz. Fig. 8 shows scanning waveforms (a, b) and nonlinearities (c) of hysteresis compensated laser scanner without and with notch filters at linear scanning of 250 Hz. Scanning nonlinearity of a point in scanning waveform is defined
Fig. 5. Bode plot of the laser scanner.
Fig. 6. Open-loop control diagram.
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Fig. 7. Scanning waveforms (a, b) and nonlinearities (c) of the laser scanner without and with hysteresis compensator at linear scanning of 10 Hz.
Fig. 8. Scanning waveforms (a, b) and nonlinearities (c) of hysteresis compensated laser scanner without and with notch filters at linear scanning of 250 Hz.
Fig. 9. Comparison of the scan line images between the uncontrolled scanner (a) and the controlled scanner (b) at linear scanning of 250 Hz.
in Fig. 8a. The scanning nonlinearity of point A is defined as NonlinearityA ¼
Dy , ymax
(2)
where ymax is 24 mrad. The scanning nonlinearity of the scanning waveform is the maximal nonlinearity of the whole scanning waveform. The scanning linearity is defined as Linearity ¼ 1 Nonlinearity:
(3)
As can be seen in Fig. 7c, the scanning nonlinearities of the uncompensated scanner and the compensated scanner at a linear scanning of 10 Hz are 5.8% and 1.1%, respectively. Fig. 8c shows that the nonlinearities of the hysteresis compensated scanner without and with notch filters at linear scanning of 250 Hz are 6.7% and 2.5%, respectively. The above two figures prove that the scanning linearity is improved by using the open-loop controller. When the linear scan frequency is low, the hysteresis primarily affects the scanning linearity. When linear scanning at high
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and to restrain the oscillations that are caused by the mechanical resonances of the scanner. The comparisons of scanning waveforms, scanning nonlinearities and scan line images between the uncontrolled scanner and the controlled scanner show that the scanning linearity is improved efficiently by using the open-loop controller. Finally, the laser scanner realizes linear scanning at 250 Hz with optical scan angle of 712 mrad. The performances make the laser scanner suitable for use as a fast scanner in lidar systems.
Acknowledgement This work was sponsored by Program for New Century Excellent Talents in University of the Ministry of Education of China. References Fig. 10. Parasitic optical deflection angle of the controlled scanner at linear scanning of 250 Hz.
frequency, the mechanical resonances start to affect the scanning linearity seriously. As can be seen in Fig. 8a, there are about 10 oscillations in a scan cycle, in other words, the oscillation frequency is about 2.5 kHz, close to the third resonance frequency (2364 Hz). Therefore the third resonance is the primary factor of the oscillations. Fig. 9 shows a comparison of the scan line images between the uncontrolled scanner (a) and the controlled scanner (b) at linear scanning of 250 Hz. As can be seen in Fig. 9a, the brightness of scan line is not uniform, and there are about six bright points in the scan line. It also can be seen in Fig. 8b that 10 oscillations appear in a scan cycle. The oscillations result in nonuniform scan velocity, and appear as bright points of the scan line in Fig. 9a. The four bright points in the middle of a half-scan cycle are overlayed with the four bright points in the middle of the next half-scan cycle, therefore, there are six bright points in the scan line. Fig. 9b demonstrates the scan line of open-loop controlled scanner system. It can be seen that the bright points disappear and that the brightness of the scan line is uniform. Consequently, the openloop controller improves the scanning linearity of the scan line. If the scanner is used in a lidar system, parasitic rotation of the scanner will affect the detection accuracy. The parasitic rotation is caused by the machining errors and assembly errors. To verify the parasitic rotation of the controlled scanner, the parasitic scanning waveform was measured on the test bench shown in Fig. 3 at linear scanning of 250 Hz. A 2D PSD was used to measure the principal scanning waveform and parasitic scanning waveform simultaneously. The parasitic scanning waveform is shown in Fig. 10, and the maximal parasitic optical deflection angle is 70.27 mrad (71.1% of the maximal principal optical deflection angle). Therefore, it can be verified that the scanner is indeed a 1D scanner with decoupled structure.
[1] Xiang Jiying, Wu Zhen, Zhang Ping, Huang Dexiu, Wei Gaoshang. The precision improvement of the scanner in optical scanning imaging system. Opt Laser Technol 1998;30:109–12. [2] Golnabi H. Design and operation of a laser scanning system. Opt Laser Technol 2000;32:267–72. [3] Wolter Alexander, Hsu Shu-Ting, Schenk Harald, Lakner Hubert. Applications and requirements for MEMS scanner mirrors. Proc SPIE 2005;5719:64–75. [4] Hafez M, Sidler TC, Salathe RP, Jansen GLM, Computer JC. Design, simulations and experimental investigations of a compact single mirror tip/tilt laser scanner. Mechatronics 2000;10:741–60. [5] He Nanying, Jia Weipu, Gong Mali, Lei Huang. Design and mechanism analysis of a novel type compact single mirror laser scanner. Sensors Actuators A 2006;125:482–5. [6] Sweeney Michael, Rynkowski Gerala, Ketabchi Mehradad, Crowley Robert. Design considerations for fast steering mirrors (FSMs). Proc SPIE 2002;4773:63–73. [7] Claeyssen F, Le Letty R, Barillo F. Mechanisms based on Piezo actuators. SPIE 2001;4332:225–33. [8] Bouchilloux Philippe, Claeyssen F, Le Letty R. Amplified piezoelectric actuators: from aerospace to underwater applications. Proc SPIE 2004;5388:143–54. [9] C1aeyssen F, Lhermet N, Le Letty R, Barillot F, Debarnot M, Six MF, et al. Piezoelectric actuators and motors based on shell structures. Proc SPIE 2000;3991:202–9. [10] Zheng Kai, Yan Shaoze, Wen Shinzhu, Ye Qing. Hysteresis compensation in piezoelectric stack actuators. JTsinghua Univ 2003;43:628–31 [In Chinese]. [11] Becker Jens, Kramer Thomas, Gaul Lothar. Hysteresis and creep compensation for piezoelectric actuators applied to the feedforward control command of flexible structures. Proc ASME 2007;1:1923–32. [12] Li Xinyang, Ling Ning, Chen Donghong, Yu Jilong. Stable control of the fast steering mirror in adaptive optics system. High Power Laser Part beams 1999;11:31–6 [In Chinese].
Sihua Xiang is currently working toward his PhD degree in Optical Engineering at Huazhong University of Science & Technology, China. He received his BS degree in optical engineering from Huazhong University of Science & Technology, China. His current research interests include optics and fine mechanical control.
6. Conclusion A compact laser scanner is designed, which is based on a pair of amplified piezoelectric actuators. The test results show that the laser scanner has high mechanical resonance frequencies. The factors influencing the scanning linearity are analyzed. An openloop controller has been designed to compensate the hysteresis
Sihai Chen is currently working at Huazhong University of Science & Technology, China. She received her PhD degree in optical engineering from Huazhong University of Science & Technology, China. Her current research interests include optics and micro-electromechanical system.
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Study on fast linear scanning for a new laser scanner Sihua Xiang a,, Sihai Chen a,b, Xin Wu a, Ding Xiao a, Xiawei Zheng a a b
College of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China Wuhan National Laboratory for Optoelectronics, Wuhan 430074, PR China
a r t i c l e in f o
a b s t r a c t
Article history: Received 12 January 2009 Received in revised form 28 March 2009 Accepted 23 April 2009 Available online 29 May 2009
In the field of lidar system design, there is a need for laser scanners that offer fast linear scanning, are small size and have small a rotational inertia moment. Currently, laser scanners do not meet the above needs. A new laser scanner based on two amplified piezoelectric actuators is designed in this paper. The laser scanner has small size, high mechanical resonance frequencies and a small rotational inertia moment. The size of the mirror is 20 mm 15 mm. To achieve fast linear scanning performance, an open-loop controller is designed to compensate the hysteresis behavior and to restrain oscillations that are caused by the mechanical resonances of the scanner’s mechanical structure. By comparing measured scanning waveforms, nonlinearities and scan line images between the uncontrolled and controlled scanner, it was found that the scanning linearity of linear scanning was improved The openloop controlled laser scanner realizes linear scanning at 250 Hz with optical scan angle of 712 mrad. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Laser scanner Fast linear scanning Mechanical resonance
1. Introduction The laser scanner is one of the most important components in a lidar system. Two-dimensional scanning-imaging in two orthogonal axes are employed in many lidar systems. The two orthogonal axes consist of a fast scan axis and a slow scan axis. The imaging speed and imaging resolution of the lidar system are limited by the dynamic behaviour of the laser scanner along the fast scan axis. Galvanometer scanners and rotating mirror scanners (rotating prism scanners) are used in many lidar systems as fast scanners [1,2]. Such systems suffer from disadvantages such as large size, high power consumption, large rotational inertia moment and poor linearity during fast linear scanning (scanning at uniform line velocity with high frequency). The large rotational inertia moment will severely affect the satellite attitude if the lidar is used in a satellite. Linear scanning is used to achieve a uniform scanning field and to provide uniform detection probability. While MEMS scanners have high resonance frequencies and large deflection angles, the small size of their mirrors limits their application in lidar systems [3]. Fast steering mirrors (FSMs) driven by piezoelectric actuators or voice coil actuators can be used in adaptive optics, laser beam steering, tracking, pointing and scanning [4–6]. They offer advantages such as small rotational inertia moment, fast response and small size. FSMs driven by voice coil actuators usually have large deflection angles, whereas
Corresponding author. Tel./fax: +86 27 87792364.
E-mail address: [email protected] (S. Xiang). 0030-3992/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2009.04.019
they have low resonance frequencies and high power consumption. FSMs driven by piezoelectric actuators usually have high resonance frequencies but they offer small deflection angles. Other scanners based on refraction, diffraction, the electro-optic and acousto-optic effects have lower optic transmission efficiency than scanners based on reflection, and thus lidars using these scanners have shorter detection distance than lidars using scanners based on reflection. Closed-loop controllers are used in many FSMs, and they can operate effectively in laser beam pointing, tracking and scanning at low frequency. However, closed-loop controlled FSMs cannot operate in linear scanning at high frequency. The above problem is caused by two major reasons: one is that high frequency linear scanning will excite oscillations that are caused by mechanical resonances of FSMs and the other is that the closed-loop control bandwidth is not high enough to restrain the resonances. An optical tip-tilt actuator based on amplified piezoelectric actuators (APAs) was developed by Claeyssen et al. [7–9]. It has resonance frequency of more than 1 kHz and a mechanical scan angle of 18 mrad. The scan angle is larger than that of traditional piezoelectric-actuated FSMs due to the special structure of the tip-tilt actuator. Accordingly, the optical tip-tilt actuator can be used as a fast scanner in a lidar system with small field of view. It can also be used in lidar systems with large field of view when galvanometer scanners or gimbal mount mirror scanners are used as large view field scanners. In this paper, a fast laser scanner driven by amplified piezoelectric actuators is designed. The structure of the laser scanner is similar to the above optical tip-tilt actuator. The static and dynamic performances of the scanner are measured. An open-loop
ARTICLE IN PRESS S. Xiang et al. / Optics & Laser Technology 42 (2010) 42–46
control method is designed to compensate hysteresis and restrain the oscillations that are caused by the mechanical resonances of the scanner. To demonstrate the effect of the open-loop controller, the actual performances of the uncontrolled scanner and the open-loop controlled scanner are compared.
43
and 2553 Hz, respectively (see Fig. 2). The analysis results show that the modes of the scanner are complicated due to its structure. These modes will limit the dynamic performance of the scanner. The third mode is caused by the hinge of the flexure support. The maximal displacement (DMX) of the third mode is largest of all. Consequently, the third mode is the primary effect factor.
2. Scanner design 3. Performance testing of the laser scanner The laser scanner assembly consists of a mirror suspended on a one degree of freedom flexure support that enables the mirror to be tilted along the tilt axis (see Fig. 1a). The size of the mirror and the scanner are 20 mm 15 mm and 60 mm 50 mm 25 mm, respectively. The weight of the scanner is about 70 g. Two APAs are mounted on the back of the flexure support. The concept of APAs relies on the flexural-extensional principle [7–9]. An elastic shell bends under the extension of the piezoelectric actuation. The displacement on contraction is several times larger than that on extension. The displacement amplification ratio depends on the ratio of the length and the height of the elastic shell. Two APAs are arranged in parallel. This arrangement ensures that their actuation axes are close to each other. The displacement amplification of APAs and the parallel arrangements provides a larger tilt angle than traditional piezoelectric-actuated scanners. The mirror is in its equilibrium position when the same voltage is applied to the two APAs. The mirror will deflect when the voltage applied to one APA is increased and that to the other APA is reduced (see Fig. 1b). Finite element analysis is used to analyze the modes of the APA and the laser scanner. The finite element analysis results show that the first mode frequency of the APA is about 2800 Hz, and the first three mode frequencies of the laser scanner are 1950, 2092,
A block diagram of the performance test bench is shown in Fig. 3. The static and dynamic performances of the laser scanner are measured on the test bench. In the dynamic performance testing, the system’s input is the voltage wave generated by the wave generator, and the system’s output is the deflection angle of the scanner. The controller (see Fig. 3) is not used in the static and dynamic performances test, whereas it is used in later section to improve the scanning linearity of the laser scanner. The scanning linearity is not the linearity determined in static performance testing, but rather it is the linearity of scanned path at linear scanning. It reveals the deviation extent of the scanned path to the estimated triangle waveform path. The scanning linearity is different at different scanning frequencies. The relationship between the optical deflection angle and the driving voltage is shown in Fig. 4. The maximal optical deflection angle is 712 mrad. As can be seen in Fig. 4, the hysteresis of the piezoelectric ceramic is significant and it will affect the scanning linearity. Fig. 5 shows the bode plot of the laser scanner system. The bode plot consists of a low pass and several stable resonances. The bode plot reveals that the primary resonance frequencies are the first three resonance frequencies and they are 1872, 1960,
Fig. 1. Design of the laser scanner (a) structure of the scanner assembly and (b) operation principle of the laser scanner.
Fig. 2. The first three modes of the scanner (simulated by ANSYS FEA software).
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2364 Hz, respectively. The first three resonance frequencies correspond to the first three modes which analyzed in above section (see Fig. 2). The response amplitudes of the first three resonances all exceed 15 dB, and the peak response is about 29 dB at 2364 Hz that is caused by the third resonance. Consequently, the first three resonances will reduce scanning linearity of the laser scanner.
4. Controller design
Fig. 3. Block diagram of the performance test bench.
The open-loop control diagram, as shown in Fig. 6, consists of four major components: the laser scanner (which is composed of a mirror, a flexure support, two APAs and a base), voltage amplifier, controller and wave generator. The controller consists of a hysteresis compensator and notch filters. In almost all piezoelectric-actuated systems, the hysteresis of the piezoelectric actuators will affect the movement of the systems. Compensation of the piezoelectric hysteresis has been studied previously [10,11]. Notch filters and low pass filter have been used to reduce mechanical oscillation of FSM [12]. The hysteresis compensator used in this paper is an algorithm that adjusts the generated triangle wave, making sure the hysteresis scan line becomes a straight line. The wave generator and hysteresis compensator are implemented on the same digital signal processor (DSP). The triangle wave is composed of many high-order harmonics. The Fourier series of a triangle wave is given by f ðtÞ ¼
1 np E 4E X sin2 þ cosðnotÞ. 2 2 2 ðnpÞ n¼1
(1)
The high-order harmonics near mechanical resonance frequencies will excite oscillations of the laser scanner. If triangle wave frequency is higher than 50 Hz, the laser scanner starts to oscillate due to its mechanical resonances. As analyzed in the above section, the first three resonance frequencies are the major influences on the oscillation. Three notch filters in series are used to reduce the amplitude of the scanner system at the first three resonance frequencies, resulting in the restraining of the oscillation. Notch filters are implemented in hardware circuits.
5. Experimental results Fig. 4. The relation of optical deflection angle and the driving voltage.
To compare the performance of the open-loop controlled scanner system with the uncontrolled system, scan lines are tested and imaged. The test bench is shown in Fig. 3. The distance of the image surface to the scanner is about 54 cm and the position sensitive detector (PSD) needs to be removed when the scan line is imaged. Fig. 7 shows scanning waveforms (a, b) and nonlinearities (c) of the laser scanner without and with hysteresis compensator at linear scanning of 10 Hz. Fig. 8 shows scanning waveforms (a, b) and nonlinearities (c) of hysteresis compensated laser scanner without and with notch filters at linear scanning of 250 Hz. Scanning nonlinearity of a point in scanning waveform is defined
Fig. 5. Bode plot of the laser scanner.
Fig. 6. Open-loop control diagram.
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Fig. 7. Scanning waveforms (a, b) and nonlinearities (c) of the laser scanner without and with hysteresis compensator at linear scanning of 10 Hz.
Fig. 8. Scanning waveforms (a, b) and nonlinearities (c) of hysteresis compensated laser scanner without and with notch filters at linear scanning of 250 Hz.
Fig. 9. Comparison of the scan line images between the uncontrolled scanner (a) and the controlled scanner (b) at linear scanning of 250 Hz.
in Fig. 8a. The scanning nonlinearity of point A is defined as NonlinearityA ¼
Dy , ymax
(2)
where ymax is 24 mrad. The scanning nonlinearity of the scanning waveform is the maximal nonlinearity of the whole scanning waveform. The scanning linearity is defined as Linearity ¼ 1 Nonlinearity:
(3)
As can be seen in Fig. 7c, the scanning nonlinearities of the uncompensated scanner and the compensated scanner at a linear scanning of 10 Hz are 5.8% and 1.1%, respectively. Fig. 8c shows that the nonlinearities of the hysteresis compensated scanner without and with notch filters at linear scanning of 250 Hz are 6.7% and 2.5%, respectively. The above two figures prove that the scanning linearity is improved by using the open-loop controller. When the linear scan frequency is low, the hysteresis primarily affects the scanning linearity. When linear scanning at high
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and to restrain the oscillations that are caused by the mechanical resonances of the scanner. The comparisons of scanning waveforms, scanning nonlinearities and scan line images between the uncontrolled scanner and the controlled scanner show that the scanning linearity is improved efficiently by using the open-loop controller. Finally, the laser scanner realizes linear scanning at 250 Hz with optical scan angle of 712 mrad. The performances make the laser scanner suitable for use as a fast scanner in lidar systems.
Acknowledgement This work was sponsored by Program for New Century Excellent Talents in University of the Ministry of Education of China. References Fig. 10. Parasitic optical deflection angle of the controlled scanner at linear scanning of 250 Hz.
frequency, the mechanical resonances start to affect the scanning linearity seriously. As can be seen in Fig. 8a, there are about 10 oscillations in a scan cycle, in other words, the oscillation frequency is about 2.5 kHz, close to the third resonance frequency (2364 Hz). Therefore the third resonance is the primary factor of the oscillations. Fig. 9 shows a comparison of the scan line images between the uncontrolled scanner (a) and the controlled scanner (b) at linear scanning of 250 Hz. As can be seen in Fig. 9a, the brightness of scan line is not uniform, and there are about six bright points in the scan line. It also can be seen in Fig. 8b that 10 oscillations appear in a scan cycle. The oscillations result in nonuniform scan velocity, and appear as bright points of the scan line in Fig. 9a. The four bright points in the middle of a half-scan cycle are overlayed with the four bright points in the middle of the next half-scan cycle, therefore, there are six bright points in the scan line. Fig. 9b demonstrates the scan line of open-loop controlled scanner system. It can be seen that the bright points disappear and that the brightness of the scan line is uniform. Consequently, the openloop controller improves the scanning linearity of the scan line. If the scanner is used in a lidar system, parasitic rotation of the scanner will affect the detection accuracy. The parasitic rotation is caused by the machining errors and assembly errors. To verify the parasitic rotation of the controlled scanner, the parasitic scanning waveform was measured on the test bench shown in Fig. 3 at linear scanning of 250 Hz. A 2D PSD was used to measure the principal scanning waveform and parasitic scanning waveform simultaneously. The parasitic scanning waveform is shown in Fig. 10, and the maximal parasitic optical deflection angle is 70.27 mrad (71.1% of the maximal principal optical deflection angle). Therefore, it can be verified that the scanner is indeed a 1D scanner with decoupled structure.
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Sihua Xiang is currently working toward his PhD degree in Optical Engineering at Huazhong University of Science & Technology, China. He received his BS degree in optical engineering from Huazhong University of Science & Technology, China. His current research interests include optics and fine mechanical control.
6. Conclusion A compact laser scanner is designed, which is based on a pair of amplified piezoelectric actuators. The test results show that the laser scanner has high mechanical resonance frequencies. The factors influencing the scanning linearity are analyzed. An openloop controller has been designed to compensate the hysteresis
Sihai Chen is currently working at Huazhong University of Science & Technology, China. She received her PhD degree in optical engineering from Huazhong University of Science & Technology, China. Her current research interests include optics and micro-electromechanical system.