Abstract

The dual-frequency laser interferometer is an indispensable instrument to measure length, position, deformation and other parameters with high precision and long measurement distance in the advanced manufacturing industry and scientific research. In general, the light source of interferometer is the dual-frequency He-Ne laser. The disadvantages of He-Ne laser include generally large size, more heat radiation to the environment, and limited service life, which limits its application. In this paper, we study a microchip Nd:YAG dual-frequency laser interferometer with a 17.4 MHz frequency difference, which is formed by the stress-induced birefringence in the microchip itself. The down-conversion mixer is designed to decrease the beat frequency to about 5 MHz in heterodyne signal preprocessing modular to meet the bandwidth of phase meter. The experimental results show that the microchip Nd:YAG dual-frequency laser interferometer has a displacement resolution of 10 nm and a measuring range of 500 mm. Due to the advantages of the microchip dual-frequency laser, such as small size (40×40×35 mm), good portability, less power consumption and almost infinite service life, the microchip Nd:YAG dual-frequency laser interferometer has broad application prospects.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Nowadays, the dual-frequency laser interferometer (or heterodyne interferometer) has been an important instrument for scientific research and industrial application [1,2]. It is widely used in measurements of linear, angular [3], flatness, and straightness [4] with advantages including long range, low uncertainty and high resolution. It is preferred because of its portability, robustness and high accuracy.

In most commercial heterodyne interferometry, the He-Ne laser is used as the light source because of its excellent beam quality, stable wavelength and excellent coherence. The mechanisms of dual-frequency light generation in the He-Ne laser include Zeeman effect [5], acoustic-optic frequency shifter [6], Birefringence-Zeeman effect [7] and so on. However, the He-Ne laser is of some limitations of the structure characteristics of the laser tube, which leads to some deficiencies in size, power consumption and service life [8]. For example, the size of the laser tube, with the addition of the heater strip for frequency stabilization, is greater than Ф30×100 mm. It is almost impossible to reduce the size of the tube for the demand of miniaturization in industry, because the number of oscillation modes is determined by the cavity length. The He-Ne laser can also be deemed as a heat source in the interferometer because of its high energy consumption. The heat radiation will affect the system stability and accuracy. To keep the interferometer optics and the tested objects away from the heat generated by laser, the flexible optical fiber is used to transmit the light from the laser to the interferometer [9,10]. However, the use of the optical fiber will also bring in extra errors inevitably. Another issue of the He-Ne laser is the variation of gas component in the tube due to the infiltration of external gases because the air pressure inside is lower than the atmosphere. This gas leakage shortens the service life of the He-Ne laser. Whether in scientific research or industrial application, the dual-frequency laser with long service life and small size has been expected for a long time.

Many dual-frequency lasers have been investigated and employed in velocimeter. For example, one pair of master-slave semiconductor lasers are combined as the light source [11]. A self-mixing birefringent dual-frequency laser with a He-Ne half-intracavity is also employed so as to simplify the structure of the light source [12]. The minimum part-count scheme can be achieved by one LD at period-one state with external optical feedback [13]. In the applications of these lasers, the microwave beat frequency is utilized to identify the Doppler frequency shift instead of the single frequency light. And the stability of beat frequency is also required. The velocity to be measured is directly proportional to the Doppler frequency shift and inversely proportional to the beat frequency. The different operating principles make these dual-frequency lasers unsuitable for the displacement interferometer. Besides, the lack of the real-time frequency measurement and the traceability of results makes it necessary to study another appropriate dual-frequency laser.

The heterodyne interferometer which utilizes the solid-state microchip laser as the coherent light source is reported in this paper. The light source is a miniature LD end-pumped microchip Nd:YAG laser with the size of diameter 2.8 mm and thickness 1 mm. We mainly focus on the birefringence in microchip laser itself and the orthogonal polarization light with frequency difference. The frequency difference and the beam quality vary with the pump position, which is used in the laser assembling. Based on this feature, a microchip Nd:YAG dual-frequency laser interferometer for displacement measurement (MLDI) is designed and experimented. The results are satisfied for both the linear distance measurement accuracy and the resolution of the MLDI in comparison with the traditional He-Ne dual-frequency laser interferometer.

2. Microchip Nd:YAG dual-frequency laser interferometer

2.1 Dual-frequency laser

The main feature of MLDI is the utilization of the novel microchip Nd:YAG dual-frequency laser (DFML) [14,15]. The structure of DFML is shown schematically in Fig. 1. The <111>-cut, 1% doped and quasi-isotropic Nd:YAG crystal is processed into a Ф2.8×1 mm plate as the gain medium of laser. The diameter matches with the ceramic ferrule. Both faces of the chip are dielectric coated to form a monolithic resonant cavity. When the 808 nm pump light from LD with polarization maintaining fiber is focused with a GRIN lens and incident into the microchip, only one longitudinal mode resonates in the cavity, which is split into two mono-frequency components due to the stress induced birefringence in the Nd:YAG crystal [16]. Thus the laser emits a 4.7 mW, 1064 nm dual-frequency orthogonally polarized radiation. The polarization directions of these two components coincide with the principal stress directions, respectively, and the frequency difference between them is proportional to the difference between the magnitudes of two principle stresses. The GRIN lens and the microchip are fixed with UV glue to enhance the ability of anti-vibration.

 figure: Fig. 1.

Fig. 1. The microchip Nd:YAG dual-frequency laser. (a) The structure diagram, (b) The image.

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In order to minimize the size of the laser, the thermal frequency stabilization method is adopted to achieve the relative stability of the frequency. A negative temperature coefficient thermistor (NTC), a thermoelectric cooler (TEC) and a temperature controller constitute a closed-loop temperature control system, which makes the microchip work at a constant temperature (about 25°C) with the temperature stability of 2×10−4°C. The thermal conductor is also wrapped by a layer of thermal insulation shell to minimize the temperature perturbation caused by the external environment. The long-term frequency stability of 2.1×10−8 (1000 s) is achieved by heterodyning two home-made dual-frequency lasers with the same principle and the similar frequency. The frequency reproducibility of 8.5×10−8 is also obtained with the wavelength meter (HighFiness, WS-7). The size of microchip laser module (excluding LD and the temperature controller) is about 40×40×35 mm, which is much smaller than that of the He-Ne laser tube, and it still has the potential to be further reduced.

The frequency difference and the beam quality are two important parameters of DFML. The frequency difference is determined by the stress at the pump position. The laser beam quality is also affected by the processing error and the local defect in the crystal. In order to demonstrate the distributions of the beat frequency and the quality of the beam energy profile, several bigger microchips (Ф8×1 mm) are investigated, which are of enough area to illustrate the distributions. The distributions in the center of one microchip are shown in Fig. 2. In Fig. 2(a), the frequency difference varies irregularly with the pump position. At some positions (white part in the circular area), the frequency difference signal cannot even be detected. In Fig. 2(b), the beam quality in the center is better than that on the edge. But this phenomenon does not fit all microchips. We infer that the different batches of microchips from the different manufacturers are different. Therefore, it is necessary to select the appropriate microchip and the appropriate pump position when the laser is assembled. Here, the frequency difference of the laser, which we will use in the next step, is about 17.4 MHz. And its beam quality is close to the ideal value 1.

 figure: Fig. 2.

Fig. 2. Distribution maps of the frequency difference (a) and the beam quality (b) in the Ф4 mm central area on a Ф8 mm microchip. The value in (b) means the goodness of Gauss fit, which is measured by the BeamGage Laser Beam Analyzer. The optimum value is 1.

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It should be mentioned that although the frequency difference can be adjusted by applying external force [17], the sensitivity between the frequency difference and the force is too large (about 1 MHz/g [18]) to maintain the long-term stability of the frequency difference in practice. Moreover, the external force application device also increases the structural complexity. Therefore, DFML directly utilizes the birefringence effect caused by the residual stress and the thermal stress in the crystal. These stresses are very stable when the laser is in thermal equilibrium, which makes the associated laser frequency difference maintain stable within a certain degree. The feasibility of this method is demonstrated in the following heterodyne interferometry.

2.2 Configuration of interferometer for displacement measurement

The displacement measurement is the most basic function of the heterodyne interferometer. Other measurements are easily realized by tailoring the displacement interferometer. Therefore, the displacement interferometer with DFML is configured as an example of the application of DFML.

The configuration of MLDI is shown in Fig. 3. The whole system consists of three parts: DFML, the optical layout and the signal processing module. DFML has been introduced in the previous section. The optical layout of MLDI is the same as that of the displacement interferometer with the He-Ne dual-frequency laser except that the operating wavelength of each optics is 1064 nm. The orthogonal polarized dual-frequency laser beam is split into two beams at a beamsplitter. One beam passes through a polarizer to generate the beat signal, which is detected as the reference signal by a photodetector. Its frequency is constant at the known frequency difference Δv of DFML. The other beam travels to a polarizing beamsplitter cube, where one single-frequency component reflects at the splitting surface, while the other component transmits. Both components reflect from the reference and target retroreflectors, respectively, before combining again within the PBS. Another polarizer interferes the combined beam after it is reflected at a right-angle prism. At the end of the optical path, this beam is also detected as the measurement signal by another photodetector. And its frequency is equal to the sum of the frequency difference Δv of DFML and the Doppler shift vd which is proportional to the velocity V of the target retroreflector.

 figure: Fig. 3.

Fig. 3. Configuration of MLDI. BS: beamsplitter; PBS: polarizing beamsplitter cube; RR: reference retroreflector; TR: target retroreflector; RP: right-angle prism; P: polarizer; PD: photodetector.

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The signal processing module is another key part of the interferometer, in which the displacement is precisely calculated with the digital phase meter. The bandwidth of existing digital phase meter is usually less than 10 MHz, which completely meets the requirement of the heterodyne interferometer with He-Ne laser. But it is different in MLDI because the frequency difference of DFML is generally in tens of megahertz, which leads to the frequencies of reference signal and measurement signal exceeding the bandwidth. Although the upper limit of the target velocity (Vmax=(λ/2)Δv) can be improved with the large frequency difference of DFML, it is difficult to realize the high-precision phase comparison under this condition. This problem about the excessive frequency difference in MLDI is innovatively solved by adding a signal preprocessing module before the phase meter, as is shown in Fig. 3.

2.3 Signal preprocessing module

The signal preprocessing module contains two channels with the same structure, which process the reference signal and the measurement signal, respectively. Each channel has four functions: wideband amplification, down-conversion mixing, automatic gain control amplification (AGC) and comparison & transmission. The structure diagram is shown in Fig. 4.

 figure: Fig. 4.

Fig. 4. Structure diagram of signal preprocessing module. AMP, Mixer, LP Filter and Power Splitter are the products of Mini-circuits Corp. Others are the homemade circuit boards.

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Wideband amplification: the weak AC signal from the photodetector is amplified to more than 0 dBm by the coaxial amplifier (Mini-circuits, ZFL-1000H+), so as to avoid the degradation of SNR in the next mixing processing.

Down-conversion mixing: it is composed of frequency mixer, low pass filter, power splitter (Mini-circuits: ZFM-2-S+, SLP-15+, ZFSC-2-5-S+) and homemade oscillator. The RF signal is mixed with the LO signal (from oscillator) and converted to the IF signal. After the IF signal passes through the low pass filter, the signal frequency is decreased to within the bandwidth of the phase meter. Generally, the median frequency of IF is set as the median value (5 MHz) of the phase meter bandwidth so as to maximize the measured speed of the target. It is easily realized by adjusting the frequency of LO according to the frequency difference of DFML. Moreover, two mixers input the same LO signal at the same time in order to minimize the additional phase difference between two channels. These two identical LO signals are divided from the output of the oscillator by the power splitter.

AGC amplification: the gains of amplifier (Analog Device, AD603) are automatically adjusted in order to eliminate the intensity difference between two channels, which will compensate the amplitude fluctuation of beat signal caused by laser relaxation oscillation and eliminate the influence of light intensity fluctuation on phase measurement. The amplitude of output signal matches the threshold of the next comparator.

Comparison & transmission: the signal is converted from the sine wave into the square wave by high-speed comparator (Texas Instrument, TLV3501), and then sent out by differential line driver (Texas Instrument, DS9638). The hysteresis interval of comparator is enlarged for noise immunity, and its upper and lower thresholds are designed to be adjustable, so that the duty cycle of square wave signal can be adjusted to ensure the reliability of transmission.

As is mentioned above, the same designs and the same products are adopted in two channels, which ensure the consistency of phase delay caused by the signal preprocessing module. It is proved by the test results of zero phase difference (ZPD) and non-zero phase difference (NZPD). In ZPD, one signal is sent to two channels at the same time. Because there is no phase difference between the measured signal and the reference signal, the theoretical value of displacement is zero. But in fact, the displacement cannot always be zero because the difference exists. This difference can be evaluated by the calculated displacement. After several hours of testing, the displacement always fluctuates around zero, and the maximum displacement is about 1 nm (the corresponding phase difference is about 0.7°). This means that the signal preprocessing module works stably. In NZPD, two signals with known phase difference are input to the two channels respectively. By comparing the actual displacement value with the theoretical value (corresponding to the known phase difference), we obtain the maximum error of 2.7 nm within a period. The small enough error means the function of this module is realized normally. Thus, the signal preprocessing module can be used in MLDI and has no significant effect on displacement measurement.

3. Results

In order to evaluate the feasibility and the performance of heterodyne interferometry with DFML, the resolution and the linear distance measurement accuracy of MLDI are tested in the indoor environment (non-isothermal, about 25°C), referring to the relevant standard [19].

3.1 Resolution

A piezo linear stage (Physik Instrumente, P-621.1CD) is utilized as a reference in the resolution test of MLDI. Its closed-loop resolution and repeatability are 0.4 nm and ±1 nm respectively, which meet the test requirement. The target retroreflector of MLDI is installed on the stage. The calculated displacements are shown in Fig. 5 when the stage moves at different displacement intervals. In Fig. 5(a), the step motion of stage cannot be distinguished by the displacement curve of MLDI when the stage moves with 5 nm interval. But in Fig. 5(b), the stage movements with 10 nm interval are clearly indicated. Therefore, the resolution of MLDI is determined as 10 nm.

 figure: Fig. 5.

Fig. 5. Resolution testing with 5 nm interval (a) and 10 nm interval (b). Blue line: the displacement of PI stage. Red line: the calculated displacement of MLDI.

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3.2 Length-dependent error

According to the standard [19], the linear distance measurement accuracy of laser interferometer is represented by the length-dependent error (LDE), which means the measurement error of interferometer varies in proportion to the length. This key performance of MLDI can be obtained by the comparison with the reference interferometer (Agilent, 5529A dynamic calibrator). The linear distance measurement accuracy of the dynamic calibrator is ±1.7 nm (in air), and the long term wavelength stability of its He-Ne laser is ±0.02 ppm. The whole test system is shown in Fig. 6, which is composed of three parts: the dynamic calibrator (reference interferometer), MLDI (interferometer under test) and the linear displacement mechanism with precision guide. The mechanism is customized with the maximum travel of 550 mm and the displacement accuracy of millimeter order. Two retroreflectors are installed on the motion platform as the targets of the two interferometers, respectively.

 figure: Fig. 6.

Fig. 6. Schematic diagram of interferometer performance test.

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In the process of testing, 11 target positions are chosen to be equally spaced over the measurement range of 500 mm. The readouts of two interferometers are compared at each target position when the platform moves back and forth 5 times (add up to 10 runs). It is forbidden to re-zero the readouts between runs. The 10 corresponding error curves, which indicate the difference between the readouts at each target position, are shown in Fig. 7.

 figure: Fig. 7.

Fig. 7. The difference between the readouts of two interferometers at each target position. Each color curve corresponds to one run (a). The error bars at each target position (b), which represent the reproducibility of displacement error.

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In Fig. 7(a), these curves are of similar shape and almost overlap. The error bars at each target position are shown in Fig. 7(b), where the maximum standard deviation is about 0.281 µm. According to the data analysis method provided in the standard, the LDE (in air) of MLDI is 5.5 ppm with the expanded uncertainty of ±0.3 ppm in the range of 500 mm. This result represents the performance of MLDI is an order of magnitude lower than the commercial interferometers with He-Ne laser. However, the feasibility of the displacement measurement with microchip Nd:YAG dual-frequency laser interferometer is confirmed. And the microchip laser has the advantages of small volume and long service life, which can meet the special needs of instrument miniaturization and environmental adaptability.

4. Conclusion

In this paper, a microchip Nd:YAG dual-frequency laser interferometer for displacement measurement is studied systematically. Its light source is a microchip laser with the advantages of small size, compact mechanism, low power consumption and long service life. The dual-frequency light is generated by the residual stress of microchip, whose frequency difference is about 17.4 MHz. This frequency exceeds the bandwidth of digital phase meter, so, the signal preprocessing module is designed and inserted before the phase meter to resolve this conflict. Compared with the commercial heterodyne interferometer, the resolution of 10 nm and the LDE (in air) of 5.5 ± 0.3 ppm are obtained. These performances prove that the heterodyne interferometer with the microchip Nd:YAG dual-frequency laser is an attractive alternative to the existing heterodyne interferometer.

Next, we will go deep into the process of the crystal growth and processing process to change the residual stress in the microchip by annealing, so as to achieve the tunable beat frequency. In addition, the optical frequency stability needs to be further improved. And some performance, such as the beat frequency stability and operating temperature, should be tested more comprehensively. All these works aim to develop a higher quality dual-frequency light source for the heterodyne interferometry.

Funding

National Natural Science Foundation of China (61775118).

Disclosures

The authors declare no conflict of interest.

References

1. W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chena, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann-Manuf. Technol. 64(2), 773–796 (2015). [CrossRef]  

2. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993). [CrossRef]  

3. E. Zhang, B. Chen, J. Sun, L. Yan, and S. Zhang, “Laser heterodyne interferometric system with following interference units for large X-Y-θ planar motion measurement,” Opt. Express 25(12), 13684–13690 (2017). [CrossRef]  

4. T. Jin, M. Han, J. Liu, Y. Le, and W. Hou, “A Heterodyne Interferometer for Simultaneous Measurement of Roll and Straightness,” IEEE Access 7, 133257–133264 (2019). [CrossRef]  

5. M. Sargent, W. E. Lamb, and R. L. Fork, “Theory of a Zeeman Laser. I,” Phys. Rev. 164(2), 436–449 (1967). [CrossRef]  

6. H. Fu, J. Tan, P. Hu, and Z. Fan, “Beam combination setup for dual-frequency laser with orthogonal linear polarization,” Chin. Opt. Lett. 13(10), 101201 (2015). [CrossRef]  

7. S. Zhang and W. Holzapfel, Orthogonal Polarization in Lasers: Physical Phenomena and Engineering Applications (Wiley, 2013).

8. M. Eberhard, J. Gerd, H. Tino, and F. Roland, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012). [CrossRef]  

9. A. J. H. Meskers, J. W. Spronck, and R. H. M. Schmidt, “Validation of separated source frequency delivery for a fiber-coupled heterodyne displacement interferometer,” Opt. Lett. 39(15), 4603–4606 (2014). [CrossRef]  

10. B. Knarren, S. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Fiber characterization for application in heterodyne laser interferometry with nanometer uncertainty, part I: polarization state measurements,” Opt. Eng. 44(2), 025002 (2005). [CrossRef]  

11. R. Diaz, S.-C. Chan, and J.-M. Liu, “Lidar detection using a dual-frequency source,” Opt. Lett. 31(24), 3600–3602 (2006). [CrossRef]  

12. J. Chen, H. Zhu, W. Xia, D. Guo, H. Hao, and M. Wang, “Self-mixing birefringent dual-frequency laser Doppler velocimeter,” Opt. Express 25(2), 560–572 (2017). [CrossRef]  

13. Z. Chen, Y. Yu, Y. Ruan, B. Nie, J. Xi, Q. Guo, and J. Tong, “Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser,” Sensors 20(21), 6303 (2020). [CrossRef]  

14. T. Yoshino and Y. Kobayashi, “Temperature characteristics and stabilization of orthogonal polarization two-frequency Nd3+:YAG microchip lasers,” Appl. Opt. 38(15), 3266–3270 (1999). [CrossRef]  

15. T. Yoshino, M. Kawata, B. Qimude, M. Hayashi, and Y. Takahashi, “Fiber-coupling-operated orthogonal-linear-polarization Nd:YAG microchip laser: Photothermal beat-frequency stabilization and interferometric displacement measurement application,” J. Lightwave Technol. 16(3), 453–458 (1998). [CrossRef]  

16. H. Chen, S. Zhang, and Y. Tan, “Effect of pump polarization direction on power characteristics in monolithic microchip Nd:YAG dual-frequency laser,” Appl. Opt. 55(11), 2858–2862 (2016). [CrossRef]  

17. J. Li, Y. Tan, K. Zhu, Y. Lu, and S. Zhang, “Dual-frequency solid-state microchip laser and its frequency difference control,” Opt. Eng. 58(11), 116105 (2019). [CrossRef]  

18. W. Holzapfel and M. Finnemann, “High-resolution force sensing by a diode-pumped Nd:YAG laser,” Opt. Lett. 18(23), 2062–2064 (1993). [CrossRef]  

19. “Performance Evaluation of Displacement-Measuring Laser Interferometers,” ASME B89.1.8-2011.

References

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  • |

  1. W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chena, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann-Manuf. Technol. 64(2), 773–796 (2015).
    [Crossref]
  2. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
    [Crossref]
  3. E. Zhang, B. Chen, J. Sun, L. Yan, and S. Zhang, “Laser heterodyne interferometric system with following interference units for large X-Y-θ planar motion measurement,” Opt. Express 25(12), 13684–13690 (2017).
    [Crossref]
  4. T. Jin, M. Han, J. Liu, Y. Le, and W. Hou, “A Heterodyne Interferometer for Simultaneous Measurement of Roll and Straightness,” IEEE Access 7, 133257–133264 (2019).
    [Crossref]
  5. M. Sargent, W. E. Lamb, and R. L. Fork, “Theory of a Zeeman Laser. I,” Phys. Rev. 164(2), 436–449 (1967).
    [Crossref]
  6. H. Fu, J. Tan, P. Hu, and Z. Fan, “Beam combination setup for dual-frequency laser with orthogonal linear polarization,” Chin. Opt. Lett. 13(10), 101201 (2015).
    [Crossref]
  7. S. Zhang and W. Holzapfel, Orthogonal Polarization in Lasers: Physical Phenomena and Engineering Applications (Wiley, 2013).
  8. M. Eberhard, J. Gerd, H. Tino, and F. Roland, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
    [Crossref]
  9. A. J. H. Meskers, J. W. Spronck, and R. H. M. Schmidt, “Validation of separated source frequency delivery for a fiber-coupled heterodyne displacement interferometer,” Opt. Lett. 39(15), 4603–4606 (2014).
    [Crossref]
  10. B. Knarren, S. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Fiber characterization for application in heterodyne laser interferometry with nanometer uncertainty, part I: polarization state measurements,” Opt. Eng. 44(2), 025002 (2005).
    [Crossref]
  11. R. Diaz, S.-C. Chan, and J.-M. Liu, “Lidar detection using a dual-frequency source,” Opt. Lett. 31(24), 3600–3602 (2006).
    [Crossref]
  12. J. Chen, H. Zhu, W. Xia, D. Guo, H. Hao, and M. Wang, “Self-mixing birefringent dual-frequency laser Doppler velocimeter,” Opt. Express 25(2), 560–572 (2017).
    [Crossref]
  13. Z. Chen, Y. Yu, Y. Ruan, B. Nie, J. Xi, Q. Guo, and J. Tong, “Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser,” Sensors 20(21), 6303 (2020).
    [Crossref]
  14. T. Yoshino and Y. Kobayashi, “Temperature characteristics and stabilization of orthogonal polarization two-frequency Nd3+:YAG microchip lasers,” Appl. Opt. 38(15), 3266–3270 (1999).
    [Crossref]
  15. T. Yoshino, M. Kawata, B. Qimude, M. Hayashi, and Y. Takahashi, “Fiber-coupling-operated orthogonal-linear-polarization Nd:YAG microchip laser: Photothermal beat-frequency stabilization and interferometric displacement measurement application,” J. Lightwave Technol. 16(3), 453–458 (1998).
    [Crossref]
  16. H. Chen, S. Zhang, and Y. Tan, “Effect of pump polarization direction on power characteristics in monolithic microchip Nd:YAG dual-frequency laser,” Appl. Opt. 55(11), 2858–2862 (2016).
    [Crossref]
  17. J. Li, Y. Tan, K. Zhu, Y. Lu, and S. Zhang, “Dual-frequency solid-state microchip laser and its frequency difference control,” Opt. Eng. 58(11), 116105 (2019).
    [Crossref]
  18. W. Holzapfel and M. Finnemann, “High-resolution force sensing by a diode-pumped Nd:YAG laser,” Opt. Lett. 18(23), 2062–2064 (1993).
    [Crossref]
  19. “Performance Evaluation of Displacement-Measuring Laser Interferometers,” ASME B89.1.8-2011.

2020 (1)

Z. Chen, Y. Yu, Y. Ruan, B. Nie, J. Xi, Q. Guo, and J. Tong, “Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser,” Sensors 20(21), 6303 (2020).
[Crossref]

2019 (2)

J. Li, Y. Tan, K. Zhu, Y. Lu, and S. Zhang, “Dual-frequency solid-state microchip laser and its frequency difference control,” Opt. Eng. 58(11), 116105 (2019).
[Crossref]

T. Jin, M. Han, J. Liu, Y. Le, and W. Hou, “A Heterodyne Interferometer for Simultaneous Measurement of Roll and Straightness,” IEEE Access 7, 133257–133264 (2019).
[Crossref]

2017 (2)

2016 (1)

2015 (2)

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chena, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann-Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

H. Fu, J. Tan, P. Hu, and Z. Fan, “Beam combination setup for dual-frequency laser with orthogonal linear polarization,” Chin. Opt. Lett. 13(10), 101201 (2015).
[Crossref]

2014 (1)

2012 (1)

M. Eberhard, J. Gerd, H. Tino, and F. Roland, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

2006 (1)

2005 (1)

B. Knarren, S. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Fiber characterization for application in heterodyne laser interferometry with nanometer uncertainty, part I: polarization state measurements,” Opt. Eng. 44(2), 025002 (2005).
[Crossref]

1999 (1)

1998 (1)

1993 (2)

W. Holzapfel and M. Finnemann, “High-resolution force sensing by a diode-pumped Nd:YAG laser,” Opt. Lett. 18(23), 2062–2064 (1993).
[Crossref]

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
[Crossref]

1967 (1)

M. Sargent, W. E. Lamb, and R. L. Fork, “Theory of a Zeeman Laser. I,” Phys. Rev. 164(2), 436–449 (1967).
[Crossref]

Bobroff, N.

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
[Crossref]

Bosse, H.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chena, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann-Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Chan, S.-C.

Chen, B.

Chen, H.

Chen, J.

Chen, Z.

Z. Chen, Y. Yu, Y. Ruan, B. Nie, J. Xi, Q. Guo, and J. Tong, “Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser,” Sensors 20(21), 6303 (2020).
[Crossref]

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W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chena, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann-Manuf. Technol. 64(2), 773–796 (2015).
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Cosijns, S.

B. Knarren, S. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Fiber characterization for application in heterodyne laser interferometry with nanometer uncertainty, part I: polarization state measurements,” Opt. Eng. 44(2), 025002 (2005).
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Diaz, R.

Eberhard, M.

M. Eberhard, J. Gerd, H. Tino, and F. Roland, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
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W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chena, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann-Manuf. Technol. 64(2), 773–796 (2015).
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W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chena, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann-Manuf. Technol. 64(2), 773–796 (2015).
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M. Eberhard, J. Gerd, H. Tino, and F. Roland, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
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Guo, D.

Guo, Q.

Z. Chen, Y. Yu, Y. Ruan, B. Nie, J. Xi, Q. Guo, and J. Tong, “Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser,” Sensors 20(21), 6303 (2020).
[Crossref]

Haitjema, H.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chena, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann-Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

B. Knarren, S. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Fiber characterization for application in heterodyne laser interferometry with nanometer uncertainty, part I: polarization state measurements,” Opt. Eng. 44(2), 025002 (2005).
[Crossref]

Han, M.

T. Jin, M. Han, J. Liu, Y. Le, and W. Hou, “A Heterodyne Interferometer for Simultaneous Measurement of Roll and Straightness,” IEEE Access 7, 133257–133264 (2019).
[Crossref]

Hao, H.

Hayashi, M.

Holzapfel, W.

W. Holzapfel and M. Finnemann, “High-resolution force sensing by a diode-pumped Nd:YAG laser,” Opt. Lett. 18(23), 2062–2064 (1993).
[Crossref]

S. Zhang and W. Holzapfel, Orthogonal Polarization in Lasers: Physical Phenomena and Engineering Applications (Wiley, 2013).

Hou, W.

T. Jin, M. Han, J. Liu, Y. Le, and W. Hou, “A Heterodyne Interferometer for Simultaneous Measurement of Roll and Straightness,” IEEE Access 7, 133257–133264 (2019).
[Crossref]

Hu, P.

Jin, T.

T. Jin, M. Han, J. Liu, Y. Le, and W. Hou, “A Heterodyne Interferometer for Simultaneous Measurement of Roll and Straightness,” IEEE Access 7, 133257–133264 (2019).
[Crossref]

Kawata, M.

Kim, S. W.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chena, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann-Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Knapp, W.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chena, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann-Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Knarren, B.

B. Knarren, S. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Fiber characterization for application in heterodyne laser interferometry with nanometer uncertainty, part I: polarization state measurements,” Opt. Eng. 44(2), 025002 (2005).
[Crossref]

Kobayashi, Y.

Kunzmann, H.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chena, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann-Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

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M. Sargent, W. E. Lamb, and R. L. Fork, “Theory of a Zeeman Laser. I,” Phys. Rev. 164(2), 436–449 (1967).
[Crossref]

Le, Y.

T. Jin, M. Han, J. Liu, Y. Le, and W. Hou, “A Heterodyne Interferometer for Simultaneous Measurement of Roll and Straightness,” IEEE Access 7, 133257–133264 (2019).
[Crossref]

Li, J.

J. Li, Y. Tan, K. Zhu, Y. Lu, and S. Zhang, “Dual-frequency solid-state microchip laser and its frequency difference control,” Opt. Eng. 58(11), 116105 (2019).
[Crossref]

Liu, J.

T. Jin, M. Han, J. Liu, Y. Le, and W. Hou, “A Heterodyne Interferometer for Simultaneous Measurement of Roll and Straightness,” IEEE Access 7, 133257–133264 (2019).
[Crossref]

Liu, J.-M.

Lu, X. D.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chena, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann-Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Lu, Y.

J. Li, Y. Tan, K. Zhu, Y. Lu, and S. Zhang, “Dual-frequency solid-state microchip laser and its frequency difference control,” Opt. Eng. 58(11), 116105 (2019).
[Crossref]

Meskers, A. J. H.

Nie, B.

Z. Chen, Y. Yu, Y. Ruan, B. Nie, J. Xi, Q. Guo, and J. Tong, “Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser,” Sensors 20(21), 6303 (2020).
[Crossref]

Qimude, B.

Roland, F.

M. Eberhard, J. Gerd, H. Tino, and F. Roland, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

Ruan, Y.

Z. Chen, Y. Yu, Y. Ruan, B. Nie, J. Xi, Q. Guo, and J. Tong, “Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser,” Sensors 20(21), 6303 (2020).
[Crossref]

Sargent, M.

M. Sargent, W. E. Lamb, and R. L. Fork, “Theory of a Zeeman Laser. I,” Phys. Rev. 164(2), 436–449 (1967).
[Crossref]

Schellekens, P. H. J.

B. Knarren, S. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Fiber characterization for application in heterodyne laser interferometry with nanometer uncertainty, part I: polarization state measurements,” Opt. Eng. 44(2), 025002 (2005).
[Crossref]

Schmidt, R. H. M.

Spronck, J. W.

Sun, J.

Takahashi, Y.

Tan, J.

Tan, Y.

J. Li, Y. Tan, K. Zhu, Y. Lu, and S. Zhang, “Dual-frequency solid-state microchip laser and its frequency difference control,” Opt. Eng. 58(11), 116105 (2019).
[Crossref]

H. Chen, S. Zhang, and Y. Tan, “Effect of pump polarization direction on power characteristics in monolithic microchip Nd:YAG dual-frequency laser,” Appl. Opt. 55(11), 2858–2862 (2016).
[Crossref]

Tino, H.

M. Eberhard, J. Gerd, H. Tino, and F. Roland, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

Tong, J.

Z. Chen, Y. Yu, Y. Ruan, B. Nie, J. Xi, Q. Guo, and J. Tong, “Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser,” Sensors 20(21), 6303 (2020).
[Crossref]

Wang, M.

Weckenmann, A.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chena, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann-Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Xi, J.

Z. Chen, Y. Yu, Y. Ruan, B. Nie, J. Xi, Q. Guo, and J. Tong, “Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser,” Sensors 20(21), 6303 (2020).
[Crossref]

Xia, W.

Yan, L.

Yoshino, T.

Yu, Y.

Z. Chen, Y. Yu, Y. Ruan, B. Nie, J. Xi, Q. Guo, and J. Tong, “Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser,” Sensors 20(21), 6303 (2020).
[Crossref]

Zhang, E.

Zhang, S.

Zhu, H.

Zhu, K.

J. Li, Y. Tan, K. Zhu, Y. Lu, and S. Zhang, “Dual-frequency solid-state microchip laser and its frequency difference control,” Opt. Eng. 58(11), 116105 (2019).
[Crossref]

Appl. Opt. (2)

Chin. Opt. Lett. (1)

CIRP Ann-Manuf. Technol. (1)

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chena, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann-Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

IEEE Access (1)

T. Jin, M. Han, J. Liu, Y. Le, and W. Hou, “A Heterodyne Interferometer for Simultaneous Measurement of Roll and Straightness,” IEEE Access 7, 133257–133264 (2019).
[Crossref]

J. Lightwave Technol. (1)

Meas. Sci. Technol. (2)

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
[Crossref]

M. Eberhard, J. Gerd, H. Tino, and F. Roland, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

Opt. Eng. (2)

J. Li, Y. Tan, K. Zhu, Y. Lu, and S. Zhang, “Dual-frequency solid-state microchip laser and its frequency difference control,” Opt. Eng. 58(11), 116105 (2019).
[Crossref]

B. Knarren, S. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Fiber characterization for application in heterodyne laser interferometry with nanometer uncertainty, part I: polarization state measurements,” Opt. Eng. 44(2), 025002 (2005).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. (1)

M. Sargent, W. E. Lamb, and R. L. Fork, “Theory of a Zeeman Laser. I,” Phys. Rev. 164(2), 436–449 (1967).
[Crossref]

Sensors (1)

Z. Chen, Y. Yu, Y. Ruan, B. Nie, J. Xi, Q. Guo, and J. Tong, “Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser,” Sensors 20(21), 6303 (2020).
[Crossref]

Other (2)

“Performance Evaluation of Displacement-Measuring Laser Interferometers,” ASME B89.1.8-2011.

S. Zhang and W. Holzapfel, Orthogonal Polarization in Lasers: Physical Phenomena and Engineering Applications (Wiley, 2013).

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Figures (7)

Fig. 1.
Fig. 1. The microchip Nd:YAG dual-frequency laser. (a) The structure diagram, (b) The image.
Fig. 2.
Fig. 2. Distribution maps of the frequency difference (a) and the beam quality (b) in the Ф4 mm central area on a Ф8 mm microchip. The value in (b) means the goodness of Gauss fit, which is measured by the BeamGage Laser Beam Analyzer. The optimum value is 1.
Fig. 3.
Fig. 3. Configuration of MLDI. BS: beamsplitter; PBS: polarizing beamsplitter cube; RR: reference retroreflector; TR: target retroreflector; RP: right-angle prism; P: polarizer; PD: photodetector.
Fig. 4.
Fig. 4. Structure diagram of signal preprocessing module. AMP, Mixer, LP Filter and Power Splitter are the products of Mini-circuits Corp. Others are the homemade circuit boards.
Fig. 5.
Fig. 5. Resolution testing with 5 nm interval (a) and 10 nm interval (b). Blue line: the displacement of PI stage. Red line: the calculated displacement of MLDI.
Fig. 6.
Fig. 6. Schematic diagram of interferometer performance test.
Fig. 7.
Fig. 7. The difference between the readouts of two interferometers at each target position. Each color curve corresponds to one run (a). The error bars at each target position (b), which represent the reproducibility of displacement error.

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