Parallel multiplex laser feedback interferometry Song Zhang, Yidong Tan, and Shulian Zhang Citation: Review of Scientific Instruments 84, 123101 (2013); doi: 10.1063/1.4829637 View online: http://dx.doi.org/10.1063/1.4829637 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/84/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in New surface forces apparatus using two-beam interferometry Rev. Sci. Instrum. 79, 043701 (2008); 10.1063/1.2903404 A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques Rev. Sci. Instrum. 78, 095105 (2007); 10.1063/1.2786272 Effect of recycled light in two-beam interferometry Rev. Sci. Instrum. 76, 053106 (2005); 10.1063/1.1899483 Improvement of the beam quality of a broad-area diode laser using double feedback from two external mirrors Appl. Phys. Lett. 85, 1107 (2004); 10.1063/1.1783017 Microstitching interferometry for x-ray reflective optics Rev. Sci. Instrum. 74, 2894 (2003); 10.1063/1.1569405
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REVIEW OF SCIENTIFIC INSTRUMENTS 84, 123101 (2013)
Parallel multiplex laser feedback interferometry Song Zhang, Yidong Tan, and Shulian Zhanga) State Key Laboratory of Precision Measurements, Department of Precision Instruments, Tsinghua University, Beijing 100084, China
(Received 22 July 2013; accepted 26 October 2013; published online 4 December 2013) We present a parallel multiplex laser feedback interferometer based on spatial multiplexing which avoids the signal crosstalk in the former feedback interferometer. The interferometer outputs two close parallel laser beams, whose frequencies are shifted by two acousto-optic modulators by 2 simultaneously. A static reference mirror is inserted into one of the optical paths as the reference optical path. The other beam impinges on the target as the measurement optical path. Phase variations of the two feedback laser beams are simultaneously measured through heterodyne demodulation with two different detectors. Their subtraction accurately reflects the target displacement. Under typical room conditions, experimental results show a resolution of 1.6 nm and accuracy of 7.8 nm within the range of 100 μm. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4829637] I. INTRODUCTION
Laser feedback, also known as laser self-mixing, is a physical phenomenon in which a portion of the laser output is reflected or scattered back into the laser cavity to cause the oscillation of the laser power. The feedback in class-B lasers, especially LD pumped microchip laser, has attracted considerable attention, mainly because class-B lasers are much more sensitive to feedback light. So exciting applications such as laser optical feedback imaging, laser Doppler velocimetry,1, 2 vibrometry,2–5 tomography,6–8 etc., have appeared. By introducing heterodyne phase-measuring methods into LFI (laser feedback interferometer), the displacement resolution of LFI has reached several nanometers.9 However, at this resolution level, since the whole external cavity belongs to dead path, the air refractive index fluctuations, the component deformation caused by temperature changes and other unstable factors seriously affect the stability of the system. Therefore, the traditional LFI is very demanding for measurement environment, which is not fit for practical use. In order to eliminate the negative effects of dead path, Wan et al. have developed a quasicommon-path laser feedback interferometer (QLFI) based on the principle of frequency shifting and frequency multiplexing and demonstrated high performances.10 However, because the feedback beams are too close to each other, it is easy for this scheme to bring signal cross talk, especially when the target is close to the reference mirror. That is, besides the reference signal, the reference mirror can also generate the measurement 2 signal. And besides the measurement 2 signal, the target can also generate the reference signal. The signal crosstalk can bring large measurement error. Figure 1 shows the measurement results of a triangle vibration, whose amplitude is about 600 nm. The measurement result of reference feedback light Lr reflects the variation of the environment, which is not expected to have periodicity. However, we can see clearly that there is a sinusoidal-like displacement vibration in Lr . Its amplitude is about 20 nm, which cannot be ignored in the measurement. So Wan’s QLFI needs accurate a) [email protected]
0034-6748/2013/84(12)/123101/4/$30.00
adjustment and usually the target must be some distance away from QLFI. In this paper, we introduce a parallel multiplex LFI based on spatial multiplexing which avoids the crosstalk. II. SYSTEM CONFIGURATION
The system configuration is shown in Figure 2. A fiber splitter divides the pump power into two. The two fiber heads both have GRIN lens and are parallel to each other. Their distance is 2.8 mm. The two pump 808 nm laser beams are focused in the middle of the Nd:YAG microchip, whose diameter is 5 mm. The Nd:YAG outputs two parallel laser beams since they are generated by the same flat-flat cavity. The two beams are both fundamental transverse modes and single longitudinal modes. Their relaxation oscillation frequency ωR is about 200 kHz. Two acousto-optic modulators (AOMs) are used in series to shift the frequencies of the feedback lights. AOM1 is driven by an rf signal generator (RF1) at 70.0 MHz, and AOM2 by RF2 at (70.0 MHz + ), with an adjustable value. The apertures of the two AOMs are large enough
FIG. 1. The crosstalk in QLFI based on frequency multiplexing. For clear show, the curve of Lm is shifted up 100 nm to separate from Lf . Lr : Measurement result of reference light; Lm : Measurement result of measurement light; and Lf : Final measurement result is the subtraction of Lm and Lr .
84, 123101-1
© 2013 AIP Publishing LLC
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123101-2
Zhang, Tan, and Zhang
Rev. Sci. Instrum. 84, 123101 (2013)
FIG. 2. Configuration of the parallel multiplex LFI. LD: laser diode; FS: fiber splitter; BS: beam splitter; AOM1, AOM2: acousto-optic modulators; M: reference mirror; T: target under test; PD1, PD2: photodiode; RF1, RF2: drive of AOM; FM: frequency mixer; FD: frequency multiplier; SF: three-channel signal filter and amplifier; PM: phase meter; and PC: personal computer.
compared to the distance of the two laser beams so that the two beams can pass through together. When the two laser beams, labeled B1 and B2, impinge on AOM1 at the Bragg incidence angle, the −1-order diffracted beams are generated. The distance between the two AOMs is kept short enough to ensure that both B1 and B2 pass the aperture of AOM2. After AOM2, the +1-order diffracted beams of B1 and B2 are generated. Now the total frequency shift is . All beams other than B1 and B2 are blocked. A reference mirror Mr, a glass plate with about 4% reflectivity, is placed in the optical path of B1 near the target T. B1 is reflected by Mr and collimated back into the corresponding laser cavity along the same path as B1, forming the reference feedback light with a final frequency shift of 2 due to its round trip through the AOMs. Part of the target reflected or diffused light of B2 is collimated back into the corresponding laser cavity along the same path as B2, forming the measuring feedback light with a final frequency shift of 2, too. The two feedback lights induce two 2-frequency laser intensity modulations,2 respectively, Ii = G(2)Ki cos(2t + Pi + ϕi ) i = 1, 2.
(1)
The modulated signals S1 and S2 are detected by two photo diodes respectively and then are extracted by filters with center frequency 2. In our experiment, is set at 40 kHz, which is not too close to ωR , so G(2) offers moderate amplification to the feedback lights, avoiding the nonlinear effect and chaos. Figure 3 shows the intensity modulations after the filter and amplifier in the time domain of B1 and B2 and their power spectra, which have the same signal peak 80 kHz. Both the signal to noise ratio is higher than 40 dB, which is adequate for the phase meter. The phase variations of the two beams are detected by a two-pair phase meter (PT1313B) at the same time through heterodyne phase measurement. A stable 2-frequency sinusoidal signal SR is generated with RF1 and RF2 as a standard reference signal. By sending the signal SR and S1 into the first pair of channels of phase meter, the phase variation of B1 named P1 is precisely measured. Similarly, the phase variation of B2 named P2 is measured by sending the signal SR and S2 into the other pair of channels of the phase meter. The phase variation of B2 P2 reflects the displacement of the target plus optical path drift caused by environmental disturbance while the phase variation of B1 P1 reflects the optical path drift caused by environmental disturbance, respectively. Since B1 and B2 are so close to each other, the environmental disturbance is nearly the same for them. So their subtraction (P = P2 −P1 ) eliminates the environmental disturbance and accurately reflects the target displacement, similar to the outcome in common-path interferometers. Because there are two laser beams B1 and B2 working simultaneously and the laser beams are parallel, we call this scheme the parallel multiplex feedback interferometry (PLFI). The target displacement L is related to the feedback light phase variation P by L = (c/2nω)P ,
(2)
where n is the refractive index of the air, and c is the light velocity in a vacuum. This scheme can eliminate the crosstalk from the principle. On one hand, only when the laser beam goes back exactly the same path where they comes to the target can their frequencies be shifted by 2 and demodulated by the heterodyne phase measurement. On the other hand, as we know, a minor difference between the cavity lengths can cause a large laser frequency difference. Although the two beams
FIG. 3. Reference and measurement signals in time and frequency domain.
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123101-3
Zhang, Tan, and Zhang
FIG. 4. Displacement measuring stability test results. For clear show, the measurement result Lm is shifted up 30 nm to separate from Lr .
are generated from the same microchip, their frequencies have a big difference since the cavity length is not exactly the same, so they cannot interfere with each other. Another advantage of this scheme is that the reference mirror can be flexibly placed. In the situation of a long work distance but short measuring range, we can place the reference mirror near the target to compensate the error caused by the long dead path. III. EXPERIMENTAL RESULTS
First, we test the displacement measuring stability of the parallel multiplex LFI. The external cavity length is about 250 mm. Mr is placed 10 mm before the target, a milled metal piece. The target remains stationary. Lm and Lr are measured simultaneously for 3 min. The results, shown in Figure 4, clearly indicate that the dead path induced a fake displacement variation of about 60 nm in Lm . But the displacement variation of Lf is limited in ± 8 nm, indicating that an accuracy of ± 8 nm can be achieved within 3 min in
Rev. Sci. Instrum. 84, 123101 (2013)
FIG. 6. PLFI’s compensation effect. (a) Measurement results of Lm ; (b) measurement results of Lr ; and (c) subtraction of Lm and Lr , namely, Lf .
a common lab without temperature control, which is enough for most measurements. Next we measured the vibration of a piezoelectric transducer (PZT) to test the short period accuracy of the system. We directly focus B2 onto the PZT end face, which is driven by a 0.5 Hz triangle wave signal. Measured Lm , Lr , and Lf are shown in Figure 5(a). It is difficult to judge the PZT vibration waveform from Lm . In contrast, Lf accurately reflects the amplitude to be 30 nm. We extract the linear part of the Lf data and determine the maximum nonlinear error to be 1.6 nm, indicating that its short-period resolution is better than 2 nm. What is more, the irregular jitters in Lm are also eliminated by the compensation of Lr . Figure 5(b) displays the nonlinear errors of Lm and Lf , indicating that the linearity of Lf is much better than that of Lm . Figure 6 shows another example of the PLFI’s compensation effect. The 30 nm-amplitude triangle vibration is disturbed by a damped vibration with an initial amplitude of
FIG. 5. (a) Measurement results of PZT vibration. (b)The nonlinear error distribution maps of Lm and Lf .
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123101-4
Zhang, Tan, and Zhang
Rev. Sci. Instrum. 84, 123101 (2013)
crosstalk between reference and measurement signal is eliminated. The method successfully keeps LFI unaffected by its long dead path. The system’s short-period displacement resolution proves to be better than 2 nm, and its accuracy within 100 μm range is 7.8 nm. All of these measurements are carried out under common room conditions and the surfaces of the targets are all rough and diffusive, indicating its environmental robustness and noncontact feature. This parallel multiplex LFI approach presents good potential application prospects in precise displacement measurement, especially in the non-contact measurement of the non-cooperative targets. By impinging the two laser beams on the same target and measuring the displacement difference, we can easily obtain the angle change or tilt of the guide. ACKNOWLEDGMENTS FIG. 7. Contrast results of the proposed PLFI and PI nanopositioning system.
100 nm. So the movement information of the target is immerged in the strong disturbance and we cannot distinguish the movement form of Lm at all. However, after compensation, the disturbance is successfully filtered out and Lf can precisely reflect the real movement of the PZT. The PLFI performance is verified by calibration with the PI nanopositioning system, which has a resolution of 0.4 nm and repeatability of 2 nm. The measured target, a milled aluminium block, is fixed onto the PI stage and the laser beam is directly focused onto the target. The PI stage is driven by closed-loop controller (E753) from 0 to 100 μm. The contrast results of the LFI and PI nanopositioning system are determined by synchronously measuring the displacement with a step of 10 μm (Figure 7). The proposed PLFI exhibits good stability with the maximum nonlinear error of 7.8 nm, and linearity is about 7.8 × 10−5 . IV. CONCLUSION
In conclusion, a parallel multiplex laser feedback interferometer based on spatial multiplexing is realized and the
This work is supported National Natural Science Foundation of China (Grant No. 61036016). The authors thank Ms. Xiao Ting for her contribution to the experiment. 1 R.
Kawai, Y. Asakawa, and K. Otsuka, “Ultrahigh-sensitivity self-mixing laser Doppler velocimetry with laser-diode-pumped microchip LiNdP4O12 lasers,” IEEE Photon. Technol. Lett. 11, 706–708 (1999). 2 T. Suzuki, T. Okada, O. Sasaki, and T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36, 2496–2502 (1997). 3 E. Lacot, R. Day, and F. Stoeckel, “Laser optical feedback tomography,” Opt. Lett. 24, 744–746 (1999). 4 E. Lacot, R. Day, J. Pinel, and F. Stoeckel, “Laser relaxation-oscillation frequency imaging,” Opt. Lett. 26, 1483–1485 (2001). 5 E. Lacot, O. Hugon, and F. Stoeckel, “Laser optical feedback imaging,” J. Phys. IV 119, 215–216 (2004). 6 S. Okamoto, H. Takeda, and F. Kannari, “Ultrahighly sensitive laserdoppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995). 7 K. Otsuka, K. Abe, J. Y. Ko, and T. S. Lim, “Real-time nanometer-vibration measurement with a self-mixing microchip solid-state laser,” Opt. Lett. 27, 1339–1341 (2002). 8 P. A. Roos, M. Stephens, and C. E. Wieman, “Laser vibrometer based on optical-feedback-induced frequency modulation of a single-mode laser diode,” Appl. Opt. 35, 6754–6761 (1996). 9 E. Lacot and O. Hugon, “Phase-sensitive laser detection by frequencyshifted optical feedback,” Phys. Rev. A 70, 053824 (2004). 10 X. Wan, D. Li, and S. Zhang, “Quasi-common-path laser feedback interferometry based on frequency shifting and multiplexing,” Opt. Lett. 32, 367–369 (2007).
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 137.189.170.231 On: Fri, 19 Dec 2014 05:42:22
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 137.189.170.231 On: Fri, 19 Dec 2014 05:42:22
REVIEW OF SCIENTIFIC INSTRUMENTS 84, 123101 (2013)
Parallel multiplex laser feedback interferometry Song Zhang, Yidong Tan, and Shulian Zhanga) State Key Laboratory of Precision Measurements, Department of Precision Instruments, Tsinghua University, Beijing 100084, China
(Received 22 July 2013; accepted 26 October 2013; published online 4 December 2013) We present a parallel multiplex laser feedback interferometer based on spatial multiplexing which avoids the signal crosstalk in the former feedback interferometer. The interferometer outputs two close parallel laser beams, whose frequencies are shifted by two acousto-optic modulators by 2 simultaneously. A static reference mirror is inserted into one of the optical paths as the reference optical path. The other beam impinges on the target as the measurement optical path. Phase variations of the two feedback laser beams are simultaneously measured through heterodyne demodulation with two different detectors. Their subtraction accurately reflects the target displacement. Under typical room conditions, experimental results show a resolution of 1.6 nm and accuracy of 7.8 nm within the range of 100 μm. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4829637] I. INTRODUCTION
Laser feedback, also known as laser self-mixing, is a physical phenomenon in which a portion of the laser output is reflected or scattered back into the laser cavity to cause the oscillation of the laser power. The feedback in class-B lasers, especially LD pumped microchip laser, has attracted considerable attention, mainly because class-B lasers are much more sensitive to feedback light. So exciting applications such as laser optical feedback imaging, laser Doppler velocimetry,1, 2 vibrometry,2–5 tomography,6–8 etc., have appeared. By introducing heterodyne phase-measuring methods into LFI (laser feedback interferometer), the displacement resolution of LFI has reached several nanometers.9 However, at this resolution level, since the whole external cavity belongs to dead path, the air refractive index fluctuations, the component deformation caused by temperature changes and other unstable factors seriously affect the stability of the system. Therefore, the traditional LFI is very demanding for measurement environment, which is not fit for practical use. In order to eliminate the negative effects of dead path, Wan et al. have developed a quasicommon-path laser feedback interferometer (QLFI) based on the principle of frequency shifting and frequency multiplexing and demonstrated high performances.10 However, because the feedback beams are too close to each other, it is easy for this scheme to bring signal cross talk, especially when the target is close to the reference mirror. That is, besides the reference signal, the reference mirror can also generate the measurement 2 signal. And besides the measurement 2 signal, the target can also generate the reference signal. The signal crosstalk can bring large measurement error. Figure 1 shows the measurement results of a triangle vibration, whose amplitude is about 600 nm. The measurement result of reference feedback light Lr reflects the variation of the environment, which is not expected to have periodicity. However, we can see clearly that there is a sinusoidal-like displacement vibration in Lr . Its amplitude is about 20 nm, which cannot be ignored in the measurement. So Wan’s QLFI needs accurate a) [email protected]
0034-6748/2013/84(12)/123101/4/$30.00
adjustment and usually the target must be some distance away from QLFI. In this paper, we introduce a parallel multiplex LFI based on spatial multiplexing which avoids the crosstalk. II. SYSTEM CONFIGURATION
The system configuration is shown in Figure 2. A fiber splitter divides the pump power into two. The two fiber heads both have GRIN lens and are parallel to each other. Their distance is 2.8 mm. The two pump 808 nm laser beams are focused in the middle of the Nd:YAG microchip, whose diameter is 5 mm. The Nd:YAG outputs two parallel laser beams since they are generated by the same flat-flat cavity. The two beams are both fundamental transverse modes and single longitudinal modes. Their relaxation oscillation frequency ωR is about 200 kHz. Two acousto-optic modulators (AOMs) are used in series to shift the frequencies of the feedback lights. AOM1 is driven by an rf signal generator (RF1) at 70.0 MHz, and AOM2 by RF2 at (70.0 MHz + ), with an adjustable value. The apertures of the two AOMs are large enough
FIG. 1. The crosstalk in QLFI based on frequency multiplexing. For clear show, the curve of Lm is shifted up 100 nm to separate from Lf . Lr : Measurement result of reference light; Lm : Measurement result of measurement light; and Lf : Final measurement result is the subtraction of Lm and Lr .
84, 123101-1
© 2013 AIP Publishing LLC
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123101-2
Zhang, Tan, and Zhang
Rev. Sci. Instrum. 84, 123101 (2013)
FIG. 2. Configuration of the parallel multiplex LFI. LD: laser diode; FS: fiber splitter; BS: beam splitter; AOM1, AOM2: acousto-optic modulators; M: reference mirror; T: target under test; PD1, PD2: photodiode; RF1, RF2: drive of AOM; FM: frequency mixer; FD: frequency multiplier; SF: three-channel signal filter and amplifier; PM: phase meter; and PC: personal computer.
compared to the distance of the two laser beams so that the two beams can pass through together. When the two laser beams, labeled B1 and B2, impinge on AOM1 at the Bragg incidence angle, the −1-order diffracted beams are generated. The distance between the two AOMs is kept short enough to ensure that both B1 and B2 pass the aperture of AOM2. After AOM2, the +1-order diffracted beams of B1 and B2 are generated. Now the total frequency shift is . All beams other than B1 and B2 are blocked. A reference mirror Mr, a glass plate with about 4% reflectivity, is placed in the optical path of B1 near the target T. B1 is reflected by Mr and collimated back into the corresponding laser cavity along the same path as B1, forming the reference feedback light with a final frequency shift of 2 due to its round trip through the AOMs. Part of the target reflected or diffused light of B2 is collimated back into the corresponding laser cavity along the same path as B2, forming the measuring feedback light with a final frequency shift of 2, too. The two feedback lights induce two 2-frequency laser intensity modulations,2 respectively, Ii = G(2)Ki cos(2t + Pi + ϕi ) i = 1, 2.
(1)
The modulated signals S1 and S2 are detected by two photo diodes respectively and then are extracted by filters with center frequency 2. In our experiment, is set at 40 kHz, which is not too close to ωR , so G(2) offers moderate amplification to the feedback lights, avoiding the nonlinear effect and chaos. Figure 3 shows the intensity modulations after the filter and amplifier in the time domain of B1 and B2 and their power spectra, which have the same signal peak 80 kHz. Both the signal to noise ratio is higher than 40 dB, which is adequate for the phase meter. The phase variations of the two beams are detected by a two-pair phase meter (PT1313B) at the same time through heterodyne phase measurement. A stable 2-frequency sinusoidal signal SR is generated with RF1 and RF2 as a standard reference signal. By sending the signal SR and S1 into the first pair of channels of phase meter, the phase variation of B1 named P1 is precisely measured. Similarly, the phase variation of B2 named P2 is measured by sending the signal SR and S2 into the other pair of channels of the phase meter. The phase variation of B2 P2 reflects the displacement of the target plus optical path drift caused by environmental disturbance while the phase variation of B1 P1 reflects the optical path drift caused by environmental disturbance, respectively. Since B1 and B2 are so close to each other, the environmental disturbance is nearly the same for them. So their subtraction (P = P2 −P1 ) eliminates the environmental disturbance and accurately reflects the target displacement, similar to the outcome in common-path interferometers. Because there are two laser beams B1 and B2 working simultaneously and the laser beams are parallel, we call this scheme the parallel multiplex feedback interferometry (PLFI). The target displacement L is related to the feedback light phase variation P by L = (c/2nω)P ,
(2)
where n is the refractive index of the air, and c is the light velocity in a vacuum. This scheme can eliminate the crosstalk from the principle. On one hand, only when the laser beam goes back exactly the same path where they comes to the target can their frequencies be shifted by 2 and demodulated by the heterodyne phase measurement. On the other hand, as we know, a minor difference between the cavity lengths can cause a large laser frequency difference. Although the two beams
FIG. 3. Reference and measurement signals in time and frequency domain.
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123101-3
Zhang, Tan, and Zhang
FIG. 4. Displacement measuring stability test results. For clear show, the measurement result Lm is shifted up 30 nm to separate from Lr .
are generated from the same microchip, their frequencies have a big difference since the cavity length is not exactly the same, so they cannot interfere with each other. Another advantage of this scheme is that the reference mirror can be flexibly placed. In the situation of a long work distance but short measuring range, we can place the reference mirror near the target to compensate the error caused by the long dead path. III. EXPERIMENTAL RESULTS
First, we test the displacement measuring stability of the parallel multiplex LFI. The external cavity length is about 250 mm. Mr is placed 10 mm before the target, a milled metal piece. The target remains stationary. Lm and Lr are measured simultaneously for 3 min. The results, shown in Figure 4, clearly indicate that the dead path induced a fake displacement variation of about 60 nm in Lm . But the displacement variation of Lf is limited in ± 8 nm, indicating that an accuracy of ± 8 nm can be achieved within 3 min in
Rev. Sci. Instrum. 84, 123101 (2013)
FIG. 6. PLFI’s compensation effect. (a) Measurement results of Lm ; (b) measurement results of Lr ; and (c) subtraction of Lm and Lr , namely, Lf .
a common lab without temperature control, which is enough for most measurements. Next we measured the vibration of a piezoelectric transducer (PZT) to test the short period accuracy of the system. We directly focus B2 onto the PZT end face, which is driven by a 0.5 Hz triangle wave signal. Measured Lm , Lr , and Lf are shown in Figure 5(a). It is difficult to judge the PZT vibration waveform from Lm . In contrast, Lf accurately reflects the amplitude to be 30 nm. We extract the linear part of the Lf data and determine the maximum nonlinear error to be 1.6 nm, indicating that its short-period resolution is better than 2 nm. What is more, the irregular jitters in Lm are also eliminated by the compensation of Lr . Figure 5(b) displays the nonlinear errors of Lm and Lf , indicating that the linearity of Lf is much better than that of Lm . Figure 6 shows another example of the PLFI’s compensation effect. The 30 nm-amplitude triangle vibration is disturbed by a damped vibration with an initial amplitude of
FIG. 5. (a) Measurement results of PZT vibration. (b)The nonlinear error distribution maps of Lm and Lf .
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123101-4
Zhang, Tan, and Zhang
Rev. Sci. Instrum. 84, 123101 (2013)
crosstalk between reference and measurement signal is eliminated. The method successfully keeps LFI unaffected by its long dead path. The system’s short-period displacement resolution proves to be better than 2 nm, and its accuracy within 100 μm range is 7.8 nm. All of these measurements are carried out under common room conditions and the surfaces of the targets are all rough and diffusive, indicating its environmental robustness and noncontact feature. This parallel multiplex LFI approach presents good potential application prospects in precise displacement measurement, especially in the non-contact measurement of the non-cooperative targets. By impinging the two laser beams on the same target and measuring the displacement difference, we can easily obtain the angle change or tilt of the guide. ACKNOWLEDGMENTS FIG. 7. Contrast results of the proposed PLFI and PI nanopositioning system.
100 nm. So the movement information of the target is immerged in the strong disturbance and we cannot distinguish the movement form of Lm at all. However, after compensation, the disturbance is successfully filtered out and Lf can precisely reflect the real movement of the PZT. The PLFI performance is verified by calibration with the PI nanopositioning system, which has a resolution of 0.4 nm and repeatability of 2 nm. The measured target, a milled aluminium block, is fixed onto the PI stage and the laser beam is directly focused onto the target. The PI stage is driven by closed-loop controller (E753) from 0 to 100 μm. The contrast results of the LFI and PI nanopositioning system are determined by synchronously measuring the displacement with a step of 10 μm (Figure 7). The proposed PLFI exhibits good stability with the maximum nonlinear error of 7.8 nm, and linearity is about 7.8 × 10−5 . IV. CONCLUSION
In conclusion, a parallel multiplex laser feedback interferometer based on spatial multiplexing is realized and the
This work is supported National Natural Science Foundation of China (Grant No. 61036016). The authors thank Ms. Xiao Ting for her contribution to the experiment. 1 R.
Kawai, Y. Asakawa, and K. Otsuka, “Ultrahigh-sensitivity self-mixing laser Doppler velocimetry with laser-diode-pumped microchip LiNdP4O12 lasers,” IEEE Photon. Technol. Lett. 11, 706–708 (1999). 2 T. Suzuki, T. Okada, O. Sasaki, and T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36, 2496–2502 (1997). 3 E. Lacot, R. Day, and F. Stoeckel, “Laser optical feedback tomography,” Opt. Lett. 24, 744–746 (1999). 4 E. Lacot, R. Day, J. Pinel, and F. Stoeckel, “Laser relaxation-oscillation frequency imaging,” Opt. Lett. 26, 1483–1485 (2001). 5 E. Lacot, O. Hugon, and F. Stoeckel, “Laser optical feedback imaging,” J. Phys. IV 119, 215–216 (2004). 6 S. Okamoto, H. Takeda, and F. Kannari, “Ultrahighly sensitive laserdoppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995). 7 K. Otsuka, K. Abe, J. Y. Ko, and T. S. Lim, “Real-time nanometer-vibration measurement with a self-mixing microchip solid-state laser,” Opt. Lett. 27, 1339–1341 (2002). 8 P. A. Roos, M. Stephens, and C. E. Wieman, “Laser vibrometer based on optical-feedback-induced frequency modulation of a single-mode laser diode,” Appl. Opt. 35, 6754–6761 (1996). 9 E. Lacot and O. Hugon, “Phase-sensitive laser detection by frequencyshifted optical feedback,” Phys. Rev. A 70, 053824 (2004). 10 X. Wan, D. Li, and S. Zhang, “Quasi-common-path laser feedback interferometry based on frequency shifting and multiplexing,” Opt. Lett. 32, 367–369 (2007).
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