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Elimination of the measurement error induced by piezoelectric ceramic nonlinearity in phase retardation measurement
Optics & Laser Technology 67 (2015) 155–158
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Elimination of the measurement error induced by piezoelectric ceramic nonlinearity in phase retardation measurement Wenxue Chen n, Yunfeng Wang, Xinhan Hu Department of Opto-electronic Engineering, College of Opto-electronic Science and Engineering, National University of Defense Technology, Hunan 410073, China
art ic l e i nf o
a b s t r a c t
Article history: Received 19 February 2014 Accepted 16 October 2014 Available online 6 November 2014
We introduce a displacement measurement system based on the isotropic optical feedback technique to measure length variations in the feedback cavity. The principle of the system is based on frequency shifting and heterodyne phase-measuring. Using this system, displacements of some feature points in the intensity output of the laser such as polarization switching are measured. Based on the measured results, a linear relation is established between the position of the polarization switching and the anisotropy. This forms the basis of future applications of the polarization control technique in the field of optical measurement. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Laser Feedback Anisotropic
1. Introduction
2. Setup and principle
Polarization is an important property of lasers. Many optical phenomena are determined by the polarization states of the laser involved. Thus, research into the control of laser polarization is an important area that has attracted considerable interest [1–4]. However, in previous research, the timing of polarization switching could not be controlled. Thus, exploiting polarization switching was not possible in the field of optical measurement. Our group has for many years focused on anisotropic optical feedback studying experimental phenomena, theory, and applications. An important area in our research is polarization control within lasers using an anisotropic optical feedback technique. We have used an anisotropic optical feedback technique to control light polarization [5,6]. However, due to the piezoelectric ceramic (PZT) nonlinearity, the error is introduced into the measurement results. We have introduced the system calibration method to eliminate the measurement error [7]. In this paper, we use a displacement measurement system to eliminate error. The length variation of PZT is measured by the displacement measurement system, specifically, an isotropic optical feedback system. Its working principle is based on frequency shifting and heterodyne phase-measuring. Based on the displacement measurement results, a linear relation between polarization switching times and the magnitude of anisotropy is established. This forms the basis of applications of this polarization control technique in the field of optical measurement.
In our experiment, polarization switching is observed through the setup in Fig. 1. This setup consists of two parts: the laser feedback system and the displacement measurement system. The configuration for the displacement measurement system based on this technique is shown in Fig. 1. This isotropic optical feedback technique for displacement measurement is first proposed by Wan et al. [8] and can be used to measure the hysteresis phenomenon of polarization flipping in an optical feedback system [5]. In this displacement measurement system, the light source is a Nd:YAG microchip laser with wavelength of 1064 nm pumped by a laser diode. The output mode of the laser is a single longitudinal mode and the relaxation oscillation frequency is about 200 kHz. The beam B1 passes the convex lens (L), the beam splitter (BS1) and then reaches the acousto-optic frequency modulator (AOM1), which is driven at radio frequency (RF). The 1 order diffracted beam B2 derived from B1 is shifted by AOM1. The shifted frequency Ω1 is about 70.0 MHz. Similarly, the þ 1 order diffracted beam B3 derived from B2 is shifted by AOM2 at frequency Ω2 of þ70.04 MHz. The final frequency shift is Ω¼Ω1 þΩ2 ¼40 kHz. Beam B3 is directed onto the surface of the object and then reflected back to the microchip laser (ML) along the original path, so the total frequency shift is 2Ω¼80 kHz. The feedback light interferes with the oscillating light in ML thus modulating the output power. If the object moves, the phase variation of the intensity output of the laser will reflect the displacement of the object. The output intensity is detected by the photodiode (PD) and amplified by voltage amplification (AMP). The output intensity is referred to as the optical measurement signal (OM). Through frequency mixer (FM) and frequency doubler (FD), the corresponding electrical measurement signal (EM) is transmitted to a filter with the OM. The two channels of
n
Corresponding author. E-mail address: [email protected] (W. Chen).
http://dx.doi.org/10.1016/j.optlastec.2014.10.015 0030-3992/& 2014 Elsevier Ltd. All rights reserved.
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W. Chen et al. / Optics & Laser Technology 67 (2015) 155–158
Fig. 1. Setup for anisotropic and displacement measurement. D1, D2, photodetectors; M1, M2, high reflectors; S, birefringent sample; ME, feedback mirror; PZT, piezoelectric transducer; P, polarizer; DA, digital-to-analog signal conversion; AD, analog-to-digital signal conversion; AMP, voltage amplification.
the filtered signals are sent to the phase card (PHC) to compare the phase and displacement s1 is returned. The displacement contains the movement of the object and the variation of the optical path produced by the optical interference. The beam reflected by Mr is shifted 2Ω¼40 kHz, and the beam is referred to as the optical reference signal (OR). Comparing the phase of OR and the corresponding electrical signal (ER), the interference displacement s2 in the system can be measured. Finally, the displacement s¼ s1 s2 can be accurately obtained. The laser feedback system is composed of four parts: light source, feedback cavity, polarization states detection, and signal processing. The light source is a half-intracavity, linearly polarized, singlemode He–Ne laser using a wavelength of 632.8 nm. The laser resonator, made up of mirrors M1 and M2 with respective reflectivity values of 99.8% and 98.8%, is 150 mm in length. The gas compositions in the resonator are He:Ne¼9:1 and Ne20:Ne22 ¼ 1:1. The feedback cavity is composed of mirrors M2 and ME, interposed by a birefringent material. The mirror ME, with a 10% reflectivity, is used for optical feedback to reflect the beam back along its original path towards the laser resonator. The length of feedback cavity is modulated by a piezoelectric transducer (PZT) which is attached to ME to tune, push, and pull the ME. The displacement of ME is measured by laser feedback interferometry. The polarization state detector is made up of a polarizer P, detector D2, and Oscilloscope 2. This polarizer is used to separate the different polarization states from the laser. If the polarization direction of the laser is parallel to that of the polarizer, the beam can pass through the polarizer and be detected by D2; otherwise, if
the polarization direction is orthogonal to that of the polarizer, the beam cannot reach D2. The output of D2 maintains its minimum. Thus, the variation in output voltage from D2 shows the change in polarization state of the laser. The signal processor consists of detector D1, acquisition card, computer and Oscilloscope 1. Here the detector receives the output intensity of the laser. The computer processes the output of D1 and calculates the physical parameters. When the length of optical feedback cavity is tuned by the PZT, the effective gain of the ordinary and extraordinary rays is modulated, the modulation curve being similar to a cosine function. At a certain length, the effective gain of the ordinary ray is higher than 0 and at another length, the effective gain of the extraordinary ray is higher than 0. However, the effective gain of the ordinary and extraordinary rays cannot be higher than 0 at the same length under our experiment conditions. According to Lamb's theory [9], polarization switching occurs if the effective gain is higher than 0. Therefore, switching occurs when the length of anisotropy optical cavity is tuned by the PZT.
3. Results The experimental results are shown in Fig. 3. The top curve is the intensity output of the laser from detector D1. Some interesting features can be seen. First, intensity dips occur at position B. Second, polarization switching occurs at the position B. The length between positions A and D is half the wave period. The position of polarization switching B is determined by the magnitude of the birefringence of
W. Chen et al. / Optics & Laser Technology 67 (2015) 155–158
157
Fig. 2. Experimental curves of polarization switching. Fig. 4. Phase error between measured data and the linear fit. Table 1 Measured data relating polarization switching to length of optical feedback cavity. Birefringence of sample S Position A (degree) (nm) 16.42 27.89 44.87 69.48 78.95 83.81
L0 þ9 L0 15 L0 53 L0 65 L0 74 L0 163
Position B (nm)
Position C (nm)
Position D (nm)
L0 þ207 L0 þ197 L0 þ23 L0 þ74 L0 þ76 L0 25
L0 þ238 L0 þ251 L0 þ109 L0 þ183 L0 þ202 L0 þ106
L0 þ 351 L0 þ 333 L0 þ 291 L0 þ 218 L0 þ 212 L0 þ 117
L0 denotes the original length of the optical feedback cavity when the voltage across the PZT is zero. A series of wave plates whose phase retardation range between 161 and 901 were measured to investigate the relationship between polarization switching positions and the anisotropy of the optical feedback cavity. The ratio of distance CB to distance DA is used as a measurement. By analyzing the data for this ratio and the anisotropy, we obtain a linear fit expressed as follows: lCB δ ¼ 180 0:05242 lDA
ð1Þ
where δ is the anisotropic of optical feedback cavity, lCB the distance between positions C and B, and likewise lDA the distance between D and A. In Fig. 3, we have plotted the curve of Eq. (1) and measured data into the same coordinate axis, both showing excellent agreement. We analyzed the error between measured data and the linear plot. The maximum error is smaller than 0.51 (see Fig. 4).
4. Conclusion In conclusion, we have introduced our study on polarization control. A displacement measurement system based on the isotropic optical feedback technique was introduced. We used this system to measure the length variation of the cavity. Based on the measured results, a linear relationship between the positions of polarization switch and the anisotropic magnitude of optical feedback cavity was found. This has great significance for the anisotropic optical feedback technique and its future applications in optical measurements. Fig. 3. Measured data and linear fit for the positions of polarization switching and the magnitude of anisotropy of the optical feedback cavity.
Acknowledgment sample S placed in the optical feedback cavity. Position C has intensity that is the same as that of position B. The middle curve in Fig. 2 is the polarization state signal from detector D2. Before starting, we place the polarizer so that the polarization state is orthogonal to the initial polarization state of the laser when the voltage in the PZT is zero. Applying a triangular wave voltage to the PZT, the voltage output of D2 is then similar to a square wave. According to the analysis above, each edge of the square wave marks a switch in polarization. The bottom curve in Fig. 2 represents the voltage applied to the PZT. The maximum voltage of 100 V displaces the PZT 0.5 mm. We studied the relationship between the position of polarization switching and the length of optical feedback cavity (see Table 1).
This work is supported by the Key Program of the National Natural Science Foundation of China (NSFC) (Grant 61036016) and Scientific and Technological Achievements Transformation and Industrialization Project by the Beijing Municipal Education Commission. References [1] Floch AL, Ropars JM, Lenornamed G. Dynamics of laser eigenstates. Phys Rev Lett 1984;52:918–21. [2] Ropars G, Floch AL, Naour RL. Polarization control mechanisms in vectorial bistable lasers for one-frequency systems. Phys Rev A 1992;46:623–40. [3] Stephan G, Hugon D. Light polarization of a quasi-isotropic laser with optical feedback. Phys Rev Lett 1985;55:703–6.
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W. Chen et al. / Optics & Laser Technology 67 (2015) 155–158
[4] Chen YC, Liu JM. Temperature-dependent polarization behavior of semiconductor lasers. Appl Phys Lett 1984;45:731–3. [5] Chen W, Zhang S, Long X. Polarization flipping and hysteresis phenomenon in laser with optical feedback. Opt Express 2013;21:1240–6. [6] Chen W, Zhang S, Long X. Internal stress measurement by laser feedback method. Opt Lett 2012;37:2433–5.
[7] Chen W, Long X, Zhang S, Xiao G. Phase retardation measurement by analyzing flipping points of polarization states in laser with an anisotropy feedback cavity. Opt Laser Technol 2012;44:2427–31. [8] Wan X, Li D, Zhang S. Quasi-common-path laser feedback interferometry based on frequency shifting and multiplexing. Opt Lett 2007;32:367–9. [9] Lamb E. Theory of an optical maser. Phys Rev 1964;134:A1429–50.
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Elimination of the measurement error induced by piezoelectric ceramic nonlinearity in phase retardation measurement Wenxue Chen n, Yunfeng Wang, Xinhan Hu Department of Opto-electronic Engineering, College of Opto-electronic Science and Engineering, National University of Defense Technology, Hunan 410073, China
art ic l e i nf o
a b s t r a c t
Article history: Received 19 February 2014 Accepted 16 October 2014 Available online 6 November 2014
We introduce a displacement measurement system based on the isotropic optical feedback technique to measure length variations in the feedback cavity. The principle of the system is based on frequency shifting and heterodyne phase-measuring. Using this system, displacements of some feature points in the intensity output of the laser such as polarization switching are measured. Based on the measured results, a linear relation is established between the position of the polarization switching and the anisotropy. This forms the basis of future applications of the polarization control technique in the field of optical measurement. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Laser Feedback Anisotropic
1. Introduction
2. Setup and principle
Polarization is an important property of lasers. Many optical phenomena are determined by the polarization states of the laser involved. Thus, research into the control of laser polarization is an important area that has attracted considerable interest [1–4]. However, in previous research, the timing of polarization switching could not be controlled. Thus, exploiting polarization switching was not possible in the field of optical measurement. Our group has for many years focused on anisotropic optical feedback studying experimental phenomena, theory, and applications. An important area in our research is polarization control within lasers using an anisotropic optical feedback technique. We have used an anisotropic optical feedback technique to control light polarization [5,6]. However, due to the piezoelectric ceramic (PZT) nonlinearity, the error is introduced into the measurement results. We have introduced the system calibration method to eliminate the measurement error [7]. In this paper, we use a displacement measurement system to eliminate error. The length variation of PZT is measured by the displacement measurement system, specifically, an isotropic optical feedback system. Its working principle is based on frequency shifting and heterodyne phase-measuring. Based on the displacement measurement results, a linear relation between polarization switching times and the magnitude of anisotropy is established. This forms the basis of applications of this polarization control technique in the field of optical measurement.
In our experiment, polarization switching is observed through the setup in Fig. 1. This setup consists of two parts: the laser feedback system and the displacement measurement system. The configuration for the displacement measurement system based on this technique is shown in Fig. 1. This isotropic optical feedback technique for displacement measurement is first proposed by Wan et al. [8] and can be used to measure the hysteresis phenomenon of polarization flipping in an optical feedback system [5]. In this displacement measurement system, the light source is a Nd:YAG microchip laser with wavelength of 1064 nm pumped by a laser diode. The output mode of the laser is a single longitudinal mode and the relaxation oscillation frequency is about 200 kHz. The beam B1 passes the convex lens (L), the beam splitter (BS1) and then reaches the acousto-optic frequency modulator (AOM1), which is driven at radio frequency (RF). The 1 order diffracted beam B2 derived from B1 is shifted by AOM1. The shifted frequency Ω1 is about 70.0 MHz. Similarly, the þ 1 order diffracted beam B3 derived from B2 is shifted by AOM2 at frequency Ω2 of þ70.04 MHz. The final frequency shift is Ω¼Ω1 þΩ2 ¼40 kHz. Beam B3 is directed onto the surface of the object and then reflected back to the microchip laser (ML) along the original path, so the total frequency shift is 2Ω¼80 kHz. The feedback light interferes with the oscillating light in ML thus modulating the output power. If the object moves, the phase variation of the intensity output of the laser will reflect the displacement of the object. The output intensity is detected by the photodiode (PD) and amplified by voltage amplification (AMP). The output intensity is referred to as the optical measurement signal (OM). Through frequency mixer (FM) and frequency doubler (FD), the corresponding electrical measurement signal (EM) is transmitted to a filter with the OM. The two channels of
n
Corresponding author. E-mail address: [email protected] (W. Chen).
http://dx.doi.org/10.1016/j.optlastec.2014.10.015 0030-3992/& 2014 Elsevier Ltd. All rights reserved.
156
W. Chen et al. / Optics & Laser Technology 67 (2015) 155–158
Fig. 1. Setup for anisotropic and displacement measurement. D1, D2, photodetectors; M1, M2, high reflectors; S, birefringent sample; ME, feedback mirror; PZT, piezoelectric transducer; P, polarizer; DA, digital-to-analog signal conversion; AD, analog-to-digital signal conversion; AMP, voltage amplification.
the filtered signals are sent to the phase card (PHC) to compare the phase and displacement s1 is returned. The displacement contains the movement of the object and the variation of the optical path produced by the optical interference. The beam reflected by Mr is shifted 2Ω¼40 kHz, and the beam is referred to as the optical reference signal (OR). Comparing the phase of OR and the corresponding electrical signal (ER), the interference displacement s2 in the system can be measured. Finally, the displacement s¼ s1 s2 can be accurately obtained. The laser feedback system is composed of four parts: light source, feedback cavity, polarization states detection, and signal processing. The light source is a half-intracavity, linearly polarized, singlemode He–Ne laser using a wavelength of 632.8 nm. The laser resonator, made up of mirrors M1 and M2 with respective reflectivity values of 99.8% and 98.8%, is 150 mm in length. The gas compositions in the resonator are He:Ne¼9:1 and Ne20:Ne22 ¼ 1:1. The feedback cavity is composed of mirrors M2 and ME, interposed by a birefringent material. The mirror ME, with a 10% reflectivity, is used for optical feedback to reflect the beam back along its original path towards the laser resonator. The length of feedback cavity is modulated by a piezoelectric transducer (PZT) which is attached to ME to tune, push, and pull the ME. The displacement of ME is measured by laser feedback interferometry. The polarization state detector is made up of a polarizer P, detector D2, and Oscilloscope 2. This polarizer is used to separate the different polarization states from the laser. If the polarization direction of the laser is parallel to that of the polarizer, the beam can pass through the polarizer and be detected by D2; otherwise, if
the polarization direction is orthogonal to that of the polarizer, the beam cannot reach D2. The output of D2 maintains its minimum. Thus, the variation in output voltage from D2 shows the change in polarization state of the laser. The signal processor consists of detector D1, acquisition card, computer and Oscilloscope 1. Here the detector receives the output intensity of the laser. The computer processes the output of D1 and calculates the physical parameters. When the length of optical feedback cavity is tuned by the PZT, the effective gain of the ordinary and extraordinary rays is modulated, the modulation curve being similar to a cosine function. At a certain length, the effective gain of the ordinary ray is higher than 0 and at another length, the effective gain of the extraordinary ray is higher than 0. However, the effective gain of the ordinary and extraordinary rays cannot be higher than 0 at the same length under our experiment conditions. According to Lamb's theory [9], polarization switching occurs if the effective gain is higher than 0. Therefore, switching occurs when the length of anisotropy optical cavity is tuned by the PZT.
3. Results The experimental results are shown in Fig. 3. The top curve is the intensity output of the laser from detector D1. Some interesting features can be seen. First, intensity dips occur at position B. Second, polarization switching occurs at the position B. The length between positions A and D is half the wave period. The position of polarization switching B is determined by the magnitude of the birefringence of
W. Chen et al. / Optics & Laser Technology 67 (2015) 155–158
157
Fig. 2. Experimental curves of polarization switching. Fig. 4. Phase error between measured data and the linear fit. Table 1 Measured data relating polarization switching to length of optical feedback cavity. Birefringence of sample S Position A (degree) (nm) 16.42 27.89 44.87 69.48 78.95 83.81
L0 þ9 L0 15 L0 53 L0 65 L0 74 L0 163
Position B (nm)
Position C (nm)
Position D (nm)
L0 þ207 L0 þ197 L0 þ23 L0 þ74 L0 þ76 L0 25
L0 þ238 L0 þ251 L0 þ109 L0 þ183 L0 þ202 L0 þ106
L0 þ 351 L0 þ 333 L0 þ 291 L0 þ 218 L0 þ 212 L0 þ 117
L0 denotes the original length of the optical feedback cavity when the voltage across the PZT is zero. A series of wave plates whose phase retardation range between 161 and 901 were measured to investigate the relationship between polarization switching positions and the anisotropy of the optical feedback cavity. The ratio of distance CB to distance DA is used as a measurement. By analyzing the data for this ratio and the anisotropy, we obtain a linear fit expressed as follows: lCB δ ¼ 180 0:05242 lDA
ð1Þ
where δ is the anisotropic of optical feedback cavity, lCB the distance between positions C and B, and likewise lDA the distance between D and A. In Fig. 3, we have plotted the curve of Eq. (1) and measured data into the same coordinate axis, both showing excellent agreement. We analyzed the error between measured data and the linear plot. The maximum error is smaller than 0.51 (see Fig. 4).
4. Conclusion In conclusion, we have introduced our study on polarization control. A displacement measurement system based on the isotropic optical feedback technique was introduced. We used this system to measure the length variation of the cavity. Based on the measured results, a linear relationship between the positions of polarization switch and the anisotropic magnitude of optical feedback cavity was found. This has great significance for the anisotropic optical feedback technique and its future applications in optical measurements. Fig. 3. Measured data and linear fit for the positions of polarization switching and the magnitude of anisotropy of the optical feedback cavity.
Acknowledgment sample S placed in the optical feedback cavity. Position C has intensity that is the same as that of position B. The middle curve in Fig. 2 is the polarization state signal from detector D2. Before starting, we place the polarizer so that the polarization state is orthogonal to the initial polarization state of the laser when the voltage in the PZT is zero. Applying a triangular wave voltage to the PZT, the voltage output of D2 is then similar to a square wave. According to the analysis above, each edge of the square wave marks a switch in polarization. The bottom curve in Fig. 2 represents the voltage applied to the PZT. The maximum voltage of 100 V displaces the PZT 0.5 mm. We studied the relationship between the position of polarization switching and the length of optical feedback cavity (see Table 1).
This work is supported by the Key Program of the National Natural Science Foundation of China (NSFC) (Grant 61036016) and Scientific and Technological Achievements Transformation and Industrialization Project by the Beijing Municipal Education Commission. References [1] Floch AL, Ropars JM, Lenornamed G. Dynamics of laser eigenstates. Phys Rev Lett 1984;52:918–21. [2] Ropars G, Floch AL, Naour RL. Polarization control mechanisms in vectorial bistable lasers for one-frequency systems. Phys Rev A 1992;46:623–40. [3] Stephan G, Hugon D. Light polarization of a quasi-isotropic laser with optical feedback. Phys Rev Lett 1985;55:703–6.
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W. Chen et al. / Optics & Laser Technology 67 (2015) 155–158
[4] Chen YC, Liu JM. Temperature-dependent polarization behavior of semiconductor lasers. Appl Phys Lett 1984;45:731–3. [5] Chen W, Zhang S, Long X. Polarization flipping and hysteresis phenomenon in laser with optical feedback. Opt Express 2013;21:1240–6. [6] Chen W, Zhang S, Long X. Internal stress measurement by laser feedback method. Opt Lett 2012;37:2433–5.
[7] Chen W, Long X, Zhang S, Xiao G. Phase retardation measurement by analyzing flipping points of polarization states in laser with an anisotropy feedback cavity. Opt Laser Technol 2012;44:2427–31. [8] Wan X, Li D, Zhang S. Quasi-common-path laser feedback interferometry based on frequency shifting and multiplexing. Opt Lett 2007;32:367–9. [9] Lamb E. Theory of an optical maser. Phys Rev 1964;134:A1429–50.