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Laser encoder system for X-Y positioning stage
Mechatronics 63 (2019) 102274
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Laser encoder system for X-Y positioning stage ✩ Chung-Ping Chang a,∗, Yi-Chieh Shih b, Syuan-Cheng Chang a, Yung-Cheng Wang c a
Department of Mechanical and Energy Engineering, National Chiayi University, Chiayi 600, Taiwan Department of Mechanical Engineering, National Central University, Taoyuan 320, Taiwan c Department of Mechanical Engineering, National Yunlin University of Science and Technology, Yunlin 640, Taiwan b
a r t i c l e
i n f o
Keywords: Geometrical error Laser encoder system Pentaprism beam splitter Precision positioning Positioning stage Interferometer
a b s t r a c t In this investigation, a novel opto-mechatronics design of linear Laser encoder system which can eliminate geometrical errors of X-Y positioning stage was proposed. The eliminated geometrical errors, which are squareness error, straightness error and Abbe error, can be reduced by this Laser encoder system. Those errors are induced by the mechanical components and assemblies. In this design, a pentaprism beam splitter was employed to divide the laser beam into two encoder axes which are perpendicular to each other. For this arrangement, a real zero point of the positioning stage was set inside the pentaprism beam splitter. Therefore, those specific geometrical errors can be minimized by the proposed system. In this research, the design of the opto-mechatronics structure and its theoretical simulations will be studied. The experimental results which were obtained in the ordinary environment revealed that the resolution of the proposed positioning stage is about 15.8 nm. In addition, the maximum standard deviation of static positioning error is about 50 nm. The Laser encoder system presented in this study is recommended to be used in the precision machinery and semiconductor industries for the precision positioning purpose.
1. Introduction Precision machinery and semiconductor industries are one of the most important industries in worldwide. The positioning system with multidimensional axes and high accuracy is the key to the next generation of those industries. For example, mask aligner, mass transfer of 𝜇LED, imprint of quantum dots and Laser cutting technology [1–4]. Those technologies are based on the high accuracy positioning stage of sub-micrometer to nanometre scale. For this reason, the positioning technology is one of the most important tasks of the current precision machinery and semiconductor industries. The Laser interferometric technologies have the advantages of large measuring range, noncontact measurement and resolution of nanometer scale. Laser also can trace to the definition of length [5]. Because of those features, Laser interferometers play an important role in the modern length measurement and positioning technology [6]. However, the precision measuring and positioning technology are not only just focusing on the linear motion, but also the straightness and the squareness of the moving axes. Therefore, the multidimensional positioning technology became a key to the next generation of precision positioning technology [7–9]. Currently, the positioning technologies are restricted by the mechanical and optical structure. The opto-mechatronics design of the position✩ ∗
ing system provided by G. Jaeger et al., in 2013 [10–12] had been established. This design is focused on the alignment for six optical axes of the laser interferometers to minimize the Abbe error. The dual-axis nanopositioning stages for analyzing the crosscoupling effect had been proposed by ChaBum Lee et al., in 2017 [13]. In this structure, two optical knife-edge sensor (OKES) based on the interferogram are utilized to determine the displacement of the stage in X and Y axes. In this structure, the voice coil motor is aligned with the movement axis of the stage, and the two sensors are placed perpendicularly with each other to minimize the geometric error. A 2D nanopositioning stage is developed by L.C.Díaz-Pérez et al., in 2017 [14]. In this research, the laser interferometers are employed in the stage as the encoder systems for obtaining the high resolution. By the integrating of the linear motors, Laser interferometers, and control system, the XYRz positioning stage with nanometer resolution and the working distance of 50×50 mm2 can be realized. The translational displacement algorithm of the grating interferometer had been constructed by Weinan Ye et al., in 2018 [15]. The algorithm is based on Taylor series expansion and polynomial regression. In the experimental structure, two ZYGO ZMI compact 3-axis high stability plane mirror interferometer are employed to verify the feasibility of the algorithm. By this way, the calculation of the translational displacement
This paper was recommended for publication by Associate Editor “Dr. Lianqing Liu”. Corresponding author. E-mail address: [email protected] (C.-P. Chang).
https://doi.org/10.1016/j.mechatronics.2019.102274 Received 30 March 2019; Received in revised form 31 July 2019; Accepted 11 September 2019 0957-4158/© 2019 Elsevier Ltd. All rights reserved.
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Mechatronics 63 (2019) 102274
Table 1 The comparison of positioning encoder systems.
Proposed encoder system of Laser interferometer Previous encoder system of Laser interferometer Conventional encoder system of optical grating interferometer
Installing method
Characteristics
Installing with internal zero point method Installing with external zero point method Installing without zero point
Encoder systems are installed by Zero point with a pentaprism, and no further alignment procedure is needed. Encoder systems are installed by Zero point method with the manual procedure, so the additional auxiliaries for alignment are needed. Encoder systems are installed in different leveling, so the geometrical errors are significant. For this reason, the further alignment and compensation method are needed.
can be improved, and the geometric error can be eliminated in the wafer stage. From the summary of the above mentioned, the elimination of the geometric error and the simplification of the instrument installation are the important tasks for the high accuracy positioning system. The comparisons between proposed Laser encoder system and existing structure in the relevant references are presented in the Table 1. In light of this, the costs of the high accuracy positioning stages are usually expensive. Therefore, in this research, a compact optomechatronics design for specific geometrical errors reduction was realized. By this way, the accuracy of the positioning error, straightness error, and squareness error of the positioning stage can be guaranteed to a certain tiny range by the proposed Laser encoder system. 2. Principle and theory In this study, the geometrical error reducing method was presented which is different from the method mentioned by the reference [10–12]. Two of quaternary phase shift keying (QPSK) Fabry-Perot interferometers (FPIs) are employed as the linear encoder system. The optical design of this encoder system is according to the zero point setting method which is proposed by this research. For the QPSK FPI, its interferometric structure and theoretical simulations will be described as following. The principle of geometrical error reducing is also demonstrated eventually.
Fig. 2. Squareness error of two axes.
2.1. Geometrical error in X-Y positioning stage There are several geometrical errors will reduce the positioning accuracy of X-Y positioning stage (Fig. 1). In this research, the squareness, straightness and Abbe error will be discussed [16,17]. All of these errors can be reduced by the proposed method which is shown as follows. 2.1.1. Squareness error If there is no squareness error between the two axes, it means that these two axes are completely perpendicular to each other. In the practical situation, not only the angle between two measuring axes but also the angle between two moving axes are not a perfect right angle, which
Fig. 3. Straightness error of axis.
shown in Fig. 2. Those errors will cause the positioning error, which is called cosine error. Therefore, if the positioning accuracy of submicrometer or nanometre scales needs to be guaranteed, the squareness error must be measured and compensated [11]. 2.1.2. Straightness error The straightness error is the lateral difference between moving path and its theoretical axis. In an ideal stage, the moving path is a straight line, so the straightness error must be zero. But in the practical situation, the moving path will be affected by the accuracy of mechanical components and its assembly conditions, which is shown in Fig. 3. When the stage is moving along the X-axis, the straightness error can cause a tiny displacement on Y-axis. If we went to reduce this error, the stage needs a fine assembly and calibration [16]. That will be an extra cost for the manufacturer.
Fig. 1. X-Y positioning stage.
2.1.3. Abbe error Abbe error is a geometrical error which describes the magnification of term of angular error (𝜃) over distance (L) [17]. The sketch and equation of Abbe error is shown in Fig. 4 and Eq. (1) when 𝜃 is approaching to zero. The terms 𝜃 and L are the main parameters of this error. If one of these terms is set to zero, the Abbe error will be minimized.
C.-P. Chang, Y.-C. Shih and S.-C. Chang et al.
Mechatronics 63 (2019) 102274
Fig. 6. Proposed QPSK FPIs.
n is the order number of the transmitted Laser beams.
Fig. 4. Sketch of Abbe error.
A1 = A0 TT′
1∕2 0
(2)
A2 = A0 TT′
3∕2 1
(3)
A3 = A0 TT′
5∕2 2
(4)
R R R
√ An =
Fig. 5. Abbe error reducing method proposed by G. Jaeger et al. [8–10].
To achieve this goal, some previous research by G. Jaeger et al. gives us a method [10–12], which is shown in Fig. 5. This method controls the angular error (𝜃) within a small value, and sets the two measuring beams passing through a zero point to make the distance (L) close to zero. Therefore, the Abbe error in this research can be approximated to zero. This method needs a fine alignment of the measuring beams of the Laser interferometer. Otherwise, the Abbe error will not be eliminated. Abbe error = L × tan(𝜃) ≈ L × sin(𝜃) ≈ L𝜃
(1)
2.2. QPSK Fabry-Perot interferometer FPI is a kind of interferometer with the common path optical structure where the displacement measured is precisely defined by the distance in the optical cavity. For this reason, FPI has the feature to reduce the measuring error which is induced by environmental disturbances [18,19]. In this research, the modified FPIs were employed as the Laser encoder system. The structure of the proposed QPSK FPIs is illustrated in Fig. 6. The He-Ne Laser source is separated into two optical axes which are X and Y axes by the pentaprism beam splitter. Each separated Laser beam pass through the optical cavity of FPI, and the quaternary phase shift is formed by the one-eighth waveplate which is arranged in the optical cavity. By this configuration, the interferometric signals can be obtained by two photodiodes as the feedback signals. The equations of the proposed QPSK FPI are derived in detail as followings. The amplitude of the transmitted beam can be presented in Eqs. (2) to (5), where A0 is the amplitude of the incident Laser, R and T are the reflectance and transmittance of the plane mirror, T’ is the resultant transmittance of the optical components in the cavity [20], and
2 (2n−1)∕2 𝑛−1 A TT′ R 2 0
(5)
The relevant electric field of the s-type and p-type can be illustrated in Eqs. (6) to (13). In this optical design, 𝛿 is the phase difference of the optical cavity which is 2𝜋d/𝜆, where d is the distance of the optical cavity of FPI. For the electric field of s-type transmitted Laser beams, √ 1 2 Es1 = A TT′ 2 R0 cos (ωt + kx + 1δ) (6) 2 0 √ 3 2 Es2 = A TT′ 2 R1 cos (ωt + kx + 3δ) (7) 2 0 √ Es3 =
5 2 A TT′ 2 R2 cos (ωt + kx + 5δ) 2 0
(8)
√ Esn =
2n−1 2 A TT′ 2 Rn−1 cos (ωt − kr + (2n − 1) ⋅ δ) 2 0
For the electric field of p-type transmitted Laser beams, √ ( ) 1 2 π Ep1 = A TT′ 2 R0 cos ωt + kx + 1δ + 2 0 4 √ ( ) 3 2 3π Ep2 = A0 TT′ 2 R1 cos ωt + kx + 3δ + 2 4
(9)
(10)
(11)
√ Ep3 =
( ) 5 2 5π A0 TT′ 2 R2 cos ωt + kx + 5δ + 2 4
(12)
√ Epn =
( ( )) 2n−1 2 π A TT′ 2 Rn−1 cos ωt + kx + (2n − 1) δ + 2 0 4
(13)
In order to obtain the intensity distribution of the FPI, the summation of the electric field for s-type and p-type are determined by Eqs. (14) and (15). For the summation of the electric field (s-type), √ 2 T′ 1∕2 × ei⋅δ Es = A Tei(ωt +kx) × (14) 2 0 1 − T ̀ × R × ei⋅2δ For the summation of the electric field (p-type), ) ( √ i⋅ δ+ π4 2 T′ 1∕2 × e i(ωt +kx) Ep = A Te ) ( 2 0 i⋅ 2δ+ π2 1 − T ̀× R × e
(15)
C.-P. Chang, Y.-C. Shih and S.-C. Chang et al.
Mechatronics 63 (2019) 102274
Fig. 7. Simulation results of signal distribution. Fig. 9. Compensation of straightness error.
Fig. 8. Proposed internal zero point setting method.
The intensity distribution of s-type and p-type can be denoted by Eqs. (16) and (17). For the intensity of s-type transmitted Laser beams, Is = Es × E∗s =
1 2 A 2 0 ′2
× T2 × T′
1 + R2 × T − 2 × T′ × R × cos (2δ)
(16)
For the intensity of p-type transmitted Laser beams, Ip = Ep × E∗p =
1 A 2 2 0
× T2 × T′
( ) 1 + R2 × T′ 2 − 2 × T′ × R × cos 2δ + π2
point, the deviation distance (L) which is mentioned in Eq. (1) is closed to zero. For this reason, Abbe error can be eliminated. After splitting of the Laser source, the two split Laser beams are almost being perpendicular to each other, because of the feature of the pentaprism beam splitter. Therefore, whether the two axes of the positioning stage are perpendicular to each other or not, the control and feedback system will always lead the stage moving along the axes defined by the Laser encoder system. By this way, the squareness error can be minimized. For the straightness error, the control system of two axes will always be compensated by each other, which is shown in Fig. 9. The straightness error of X-axis is a term of the positioning error of Y-axis. When the Xaxis is moving, the straightness error will be measured and compensated by the measuring and control systems of Y-axis. Therefore, by the internal zero point setting method, the squareness error, straightness error and Abbe error can be minimized. In the proposed method, the key of geometrical error reducing is based on the tolerance of the pentaprism. The tolerance of the high quality commercial pentaprism is about ± 1 arcsec. According to this condition, the geometrical error of the stage is about 0.5 𝜇m /100 mm. Furthermore, some existing researches mentioned about the advanced manufacturing or aligning method for the pentaprism [21–23]. According to these results, the geometrical error of the proposed method can be reduced into a tiny range of 0.5 nm /100 mm. This accuracy meets the positioning requirements of precision machinery and semiconductor industries.
(17)
The resultant transmittance of the whole optical cavity and the reflectance of the plane mirror are substituted into the equation Eqs. (16) and (17). The simulated intensity distributions are illustrated in Fig. 7. From the simulated results, it reveals that the reflectance of the plane mirrors and the resultant transmittance of the optical components in the cavity will influence the intensity and the fineness of the signal. Therefore, in order to reduce the interpolation error of the signal processing, the above-mentioned parameters must be set in an appropriate value. In this research, the reflectance of 20% to 25% will be recommended for this QPSK FPI optical cavity. 2.3. Novel zero point setting method In the present research [10–12], the zero point of the positioning stage is set by external laser beams which are shown in Fig. 5. In this article, a zero point is set by two internal laser beams which are split from one Laser source (shown in Fig. 8). By this opto-mechatronics design, if the control system is robust, the squareness error, straightness error, and Abbe error will be minimized. Because the Laser beam is split at the zero
3. Design of proposed positioning system Figs. 10 and 11 are the proposed positioning system which is using the internal zero point setting method. The interferometric system is based on QPSK FPI. The interferometric signals are received by four Photodiodes (PDs). The signal amplification processing is shown in Fig. 12. After the signal amplification processing, the signals will be delivered to the interpolator which can transform the analog signals into digital signals, and enhance the signal resolution, which is shown in Fig. 13. Then the transformed digital signals are received by the motion control device as the feedback signals. In this system, the two Laser encoders use the same Laser source which is split by the proposed zero point setting method, so the wavelength compensation of these measuring systems can be integrated easily. This is also an additional advantage of the proposed system. The interferometric Laser encoders are utilized as the feedback control signal for the X-Y positioning stage. Therefore, by this optomechatronics design, the above mentioned geometrical errors can be eliminated. In this design, the moving direction of the X and Y axes are not necessary to be perpendicular to each other, so the cost of mechanical components and assemblies can be reduced.
C.-P. Chang, Y.-C. Shih and S.-C. Chang et al.
Mechatronics 63 (2019) 102274
Fig. 10. Opto-mechantronics design of the X-Y positioning stage.
Fig. 12. Interferometric signals processing.
Fig. 11. Positioning system with the proposed method.
4. Experimental results In order to verify the ability of the proposed Laser encoder system, a positioning experiment was implemented. Fig. 14 is the experimental interference signal of QPSK FPI. The reflectances of plane mirrors are about 20%. In this reflectances setting, the finesse of the interferometric signal is quite low, so the signal pattern is similar to a sinusoid in the time domain, and circular form in the X-Y domain. By this way, the interpolation error can be reduced to a tiny amount which is negligible in this experiment.
Fig. 13. Interference signal interpolation.
The Y-axis of the positioning stage was controlled to hold on the zero position, and X-axis was moving from 0 to 3 mm with the positioning interval of 0.3 mm. In this experiment, the Laser encoder signals were counted and stored by the motion controller. The data of 1,000 points was acquired by the controller at each position, after the stage has been
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Mechatronics 63 (2019) 102274
Table 2 1st experiment result. Position (mm)
Positioning error of X-axis
Standard deviation of X-axis
Positioning error of Y-axis
Standard deviation of Y-axis
0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3
−0.0520 −0.1000 0.0310 0.0710 0.0290 −0.0640 0.0280 −0.0070 0.0170 −0.0020
2.2154 1.6281 1.8065 2.6550 0.5749 2.1110 1.3413 1.4646 2.6706 0.0632
−0.1020 0.3680 0.9720 1.6620 2.0020 1.8510 0.6970 −0.9060 −0.9640 −1.0000
1.2487 1.2939 1.0278 1.7908 0.0447 0.6865 0.4994 0.2920 0.1917 0.0000
Unit: count. Table 3 2nd experiment result. Position (mm)
Positioning error of X-axis
Standard deviation of X-axis
Positioning error of Y-axis
Standard deviation of Y-axis
0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3
−0.0140 0.0080 0.0000 −0.0980 −0.0020 −0.0960 −0.0030 −0.0360 −0.0030 −0.0280
3.0164 0.3662 2.8478 1.6362 1.7085 2.6072 0.0707 2.8655 1.9023 1.4524
−0.9950 −1.0000 0.1550 2.1200 3.2930 2.7720 2.9990 1.5800 1.0280 −0.9910
0.0706 0.0000 1.1732 0.4877 0.4576 0.4798 0.0316 1.6408 1.2445 0.1045
Unit: count. Table 4 3rd experiment result. Position (mm)
Positioning error of X-axis
Standard deviation of X-axis
Positioning error of Y-axis
Standard deviation of Y-axis
0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3
−0.0620 −0.0540 0.0380 0.0050 0.0610 −0.1180 0.0650 −0.0040 −0.0440 0.0960
2.1295 2.6967 1.3290 2.7071 1.7141 1.7387 2.9078 0.1414 2.8245 1.5534
−0.1060 0.1280 2.3460 −0.9240 2.7120 −0.9220 −1.0000 −1.0000 0.2020 2.1750
1.2034 1.3241 1.0906 0.3665 0.4746 0.2828 0.0000 0.0000 1.4674 0.5502
Unit: count.
Fig. 14. Experimental signal of QPSK FPI. (a) Time domain, (b) X-Y domain.
Fig. 15. Positioning error of X-axis.
set. The experiment results are shown in Fig. 15 and Tables 2–4. The results show that the positioning error of the moving axis (X-axis) is within one count (15.8 nm), and the maximum standard deviation is about 3 counts (47.4 nm). By the following axis (Y-axis), the positioning error is about 3.3 counts (52.1 nm), and the maximum standard deviation is about 1.8 counts (28.4 nm).
5. Conclusion and future work This article presents a positioning system which can be free from those specific errors which are above mentioned by the zero point setting
C.-P. Chang, Y.-C. Shih and S.-C. Chang et al.
method. To compare with the previous method, the proposed zero point setting method can get the zero point without complicated adjustment. Because the beams are split from one Laser source, the zero point which is set by the proposed method is much more precise than other methods. This is a significant benefit to the high accuracy positioning system. The available positioning range of proposed X-Y stage is within 20 mm square which is limited by the size of measuring mirror. According to the result of positioning experiment, the resolutions of both axes are about 15.8 nm, and the maximum standard deviation of static positioning error is about 50 nm in the ordinary environment. These results show that the proposed Laser encoder system has a high potential for the precision positioning purpose of precision machinery and semiconductor industries. As future work, more related experiments must be done for figuring out the ability and limitation of the proposed encoder system, after the integration of the advanced opto-mechatronics structure. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The paper is supported by the Ministry of Science and Technology, Taiwan, under Grant no. MOST 106–2218-E-415–003. References [1] Ming-Hsien Wu, Yen-Hsiang Fang, “Picking-up and placing process for electronic devices and electronic module”, US patent, US 20160268491 A1, Industrial Technology Research Institute, Sep. 15, 2016. [2] Mizuno T, Tomoda K, Oohata T. “Method of transferring device”, US patent, US 20100258543 A1, Sony Corporation, Oct. 14, 2010. [3] Golda D, Higginson JA, Bibl A, Parks PA, Bathurst SP, “Mass transfer tool manipulator assembly”, US patent, US 9308649 B2, LuxVue Techonology Corporation, US 9308649 B2, June 12, 2016. [4] Yu-Chu Li, Yu-Hung Lai, Tzu-Yang Lin, “Method for transferring light-emitting elements onto a package substrate”, US patent, US 9583450 B2, PlayNitride Inc., Feb. 28, 2017. [5] BIPM, “17th General Conference on Weights and Measures (1983), Resolution 1”, Retrieved 19 September 2012. [6] Bobroff Norman. Recent advances in displacement measuring interferometry. Measure Sci Tech May 1993;4(9):907–26. [7] Donmez MA, Blomquist DS, Hocken RJ, Liu CR, Barash MM. A general methodology for machine tool accuracy enhancement by error compensation. Precision Eng October 1986;8(4):187–96. [8] Chen JS, Kou TW, Chiou SH. Geometric error calibration of multi-axis machines using an auto-alignment laser interferometer. Precision Eng October 1999;23(4):243–52. [9] Qin Jie, Gao Zhan, Wang Xu, Yang Shanwei. Three-dimensional continuous displacement measurement with temporal speckle pattern interferometry. Sensors November 2016;16(12). [10] Jaeger G. Three-dimensional nanopositioning and nanomeasuring machine with a resolution of 0.1 nm. Optoelectron Instrument Data Process 2010;46(4):318–23. [11] Jaeger G. Limitations of precision length measurements based on interferometers. J Measure 2010;43(5):652–8 June 2010. [12] H Q, Wu K, Wang C, Li R, Fan KC, Fei Y. Development of an Abbe error free micro coordinate measuring machine. Appl Sci 2016;6(4):97. [13] Lee C, Jeon S, Stepanick CK, Zolfaghari A, Tarbutton JA. Investigation of optical knife edge sensor for low-cost, large-range and dual-axis nanopositioning stages. Measurement 2017;103:157–64. [14] Díaz-Pérez LC, Torralba M, Albajez JA, Yagüe-Fabra JA. Implementation of the control strategy for a 2D nanopositioning long range stage. Procedia Manufactur 2017;13:458–65. [15] Ye W, Zhang M, Zhu Y, Wang L, Hu J, Li X, Hu C. Translational displacement computational algorithm of the grating interferometer without geometric error for the wafer stage in a photolithography scanner. Opt Express 2018;26(26):34734–52.
Mechatronics 63 (2019) 102274 [16] International Organization for Standardization, “Test code for machine tools – Part 1: geometric accuracy of machines operating under no-load or quasi-static conditions”, ISO 230-1, 2012. [17] Zhang GX. A study on the Abbe principle and Abbe error. CIRP Ann 1989;38(1):525–8. [18] Lawall JR. Fabry-Perot metrology for displacements up to 50 mm. J Optic Soc Am A 2005;22(12). [19] Kong Jing, Zhou Ai, Yuan Libo. Temperature insensitive one-dimensional bending vector sensor based on eccentric-core fiber and air cavity Fabry-Perot interferometer. J Optic March 2017;19(4). [20] Shyu LH, Chang CP, Wang YC. Influence of intensity loss in the cavity of a folded Fabry-Perot interferometer on interferometric signals. Rev Sci Instrument May 2011;82(6):063103. [21] Geckeler RD. Optimal use of pentaprisms in highly accurate deflectometric scanning. Measure Sci Tech 2007;18(1). [22] Barber SK, Yashchuk VV, Geckeler RD, Gubarev MV, Buchheim J, Siewert F, Zeschke T. Optimal alignment of mirror-based pentaprisms for scanning deflectometric devices. Optic Eng July 2011;50(7). [23] Yellowhair J, Burge JH. Analysis of a scanning pentaprism system for measurements of large flat mirrors. Appl Opt December 2007;46(35):8466–74. Chung-Ping Chang received the B.S. degree in Mechanical and Mechatronic Engineering from National Taiwan Ocean University, Keelung, Taiwan, and the M.S. degree in Mechanical Engineering from National Yunlin University of Science and Technology, Yunlin, Taiwan, in 2007 and 2009 respectively. His Ph.D. degree received form Department of Mechanical Engineering from National Central University, Taoyuan, Taiwan, in 2013. From 2013 to 2016, he was a Postdoctoral Fellow with the mechanical engineering in National Yunlin University and Technology University. He is currently an Assistant Professor with the Department of Mechanical and Energy Engineering, National Chiayi University, Chiayi, Taiwan. His research interests include optical measurement technology, Laser interferometer design, machine tool calibration technology, in particular, micro/nano positioning technology. Yi-Chieh Shih received the B.S. and M.S. degree in Mechanical and Mechatronic Engineering and Mechanical Engineering from National Ilan University, Ilan, Taiwan, and National Yunlin University and Technology University, Yunlin, Taiwan, in 2014 and 2016 respectively. He is currently a Ph.D. candidate in the Department of Mechanical Engineering, National Central University, Taoyuan, Taiwan. He has been a lecturer in National Yunlin University of Science and Technology. His research interests are in the field of the precision mechanical and the semiconductor industry including optical metrology, precise positioning, and machine tool calibration technology.
Syuan-Cheng Chang completed two-year’s Japanese studies course in National Taichung University of Science and Technology, Taichung, Taiwan, in 2014. He was an industrial wiring work trainee with Vocational Training Bureau, Taichung, Taiwan, in 2016. He is currently a M.S. student from the Department of Mechanical and Energy Engineering, National Chiayai University, Chiayi, Taiwan. His research interests include automation control system, optical measurement technology, and Laser interferometer design.
Yung-Cheng Wang received his Dr Ing. from the Institute of Process Measurement and Sensor Technology at the Ilmenau University of Technology (TU Ilmenau) in 2003. He is now a professor in the Department of Mechanical Engineering at the National Yunlin University of Science and Technology (Yuntech). His research interests include optical metrology and its applications in precision mechanical engineering, the development of Fabry-Perot interferometers, inspection technologies for machine tools and on-line automated measurements. He has published over 50 research papers and holds 30 patents.
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Laser encoder system for X-Y positioning stage ✩ Chung-Ping Chang a,∗, Yi-Chieh Shih b, Syuan-Cheng Chang a, Yung-Cheng Wang c a
Department of Mechanical and Energy Engineering, National Chiayi University, Chiayi 600, Taiwan Department of Mechanical Engineering, National Central University, Taoyuan 320, Taiwan c Department of Mechanical Engineering, National Yunlin University of Science and Technology, Yunlin 640, Taiwan b
a r t i c l e
i n f o
Keywords: Geometrical error Laser encoder system Pentaprism beam splitter Precision positioning Positioning stage Interferometer
a b s t r a c t In this investigation, a novel opto-mechatronics design of linear Laser encoder system which can eliminate geometrical errors of X-Y positioning stage was proposed. The eliminated geometrical errors, which are squareness error, straightness error and Abbe error, can be reduced by this Laser encoder system. Those errors are induced by the mechanical components and assemblies. In this design, a pentaprism beam splitter was employed to divide the laser beam into two encoder axes which are perpendicular to each other. For this arrangement, a real zero point of the positioning stage was set inside the pentaprism beam splitter. Therefore, those specific geometrical errors can be minimized by the proposed system. In this research, the design of the opto-mechatronics structure and its theoretical simulations will be studied. The experimental results which were obtained in the ordinary environment revealed that the resolution of the proposed positioning stage is about 15.8 nm. In addition, the maximum standard deviation of static positioning error is about 50 nm. The Laser encoder system presented in this study is recommended to be used in the precision machinery and semiconductor industries for the precision positioning purpose.
1. Introduction Precision machinery and semiconductor industries are one of the most important industries in worldwide. The positioning system with multidimensional axes and high accuracy is the key to the next generation of those industries. For example, mask aligner, mass transfer of 𝜇LED, imprint of quantum dots and Laser cutting technology [1–4]. Those technologies are based on the high accuracy positioning stage of sub-micrometer to nanometre scale. For this reason, the positioning technology is one of the most important tasks of the current precision machinery and semiconductor industries. The Laser interferometric technologies have the advantages of large measuring range, noncontact measurement and resolution of nanometer scale. Laser also can trace to the definition of length [5]. Because of those features, Laser interferometers play an important role in the modern length measurement and positioning technology [6]. However, the precision measuring and positioning technology are not only just focusing on the linear motion, but also the straightness and the squareness of the moving axes. Therefore, the multidimensional positioning technology became a key to the next generation of precision positioning technology [7–9]. Currently, the positioning technologies are restricted by the mechanical and optical structure. The opto-mechatronics design of the position✩ ∗
ing system provided by G. Jaeger et al., in 2013 [10–12] had been established. This design is focused on the alignment for six optical axes of the laser interferometers to minimize the Abbe error. The dual-axis nanopositioning stages for analyzing the crosscoupling effect had been proposed by ChaBum Lee et al., in 2017 [13]. In this structure, two optical knife-edge sensor (OKES) based on the interferogram are utilized to determine the displacement of the stage in X and Y axes. In this structure, the voice coil motor is aligned with the movement axis of the stage, and the two sensors are placed perpendicularly with each other to minimize the geometric error. A 2D nanopositioning stage is developed by L.C.Díaz-Pérez et al., in 2017 [14]. In this research, the laser interferometers are employed in the stage as the encoder systems for obtaining the high resolution. By the integrating of the linear motors, Laser interferometers, and control system, the XYRz positioning stage with nanometer resolution and the working distance of 50×50 mm2 can be realized. The translational displacement algorithm of the grating interferometer had been constructed by Weinan Ye et al., in 2018 [15]. The algorithm is based on Taylor series expansion and polynomial regression. In the experimental structure, two ZYGO ZMI compact 3-axis high stability plane mirror interferometer are employed to verify the feasibility of the algorithm. By this way, the calculation of the translational displacement
This paper was recommended for publication by Associate Editor “Dr. Lianqing Liu”. Corresponding author. E-mail address: [email protected] (C.-P. Chang).
https://doi.org/10.1016/j.mechatronics.2019.102274 Received 30 March 2019; Received in revised form 31 July 2019; Accepted 11 September 2019 0957-4158/© 2019 Elsevier Ltd. All rights reserved.
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Mechatronics 63 (2019) 102274
Table 1 The comparison of positioning encoder systems.
Proposed encoder system of Laser interferometer Previous encoder system of Laser interferometer Conventional encoder system of optical grating interferometer
Installing method
Characteristics
Installing with internal zero point method Installing with external zero point method Installing without zero point
Encoder systems are installed by Zero point with a pentaprism, and no further alignment procedure is needed. Encoder systems are installed by Zero point method with the manual procedure, so the additional auxiliaries for alignment are needed. Encoder systems are installed in different leveling, so the geometrical errors are significant. For this reason, the further alignment and compensation method are needed.
can be improved, and the geometric error can be eliminated in the wafer stage. From the summary of the above mentioned, the elimination of the geometric error and the simplification of the instrument installation are the important tasks for the high accuracy positioning system. The comparisons between proposed Laser encoder system and existing structure in the relevant references are presented in the Table 1. In light of this, the costs of the high accuracy positioning stages are usually expensive. Therefore, in this research, a compact optomechatronics design for specific geometrical errors reduction was realized. By this way, the accuracy of the positioning error, straightness error, and squareness error of the positioning stage can be guaranteed to a certain tiny range by the proposed Laser encoder system. 2. Principle and theory In this study, the geometrical error reducing method was presented which is different from the method mentioned by the reference [10–12]. Two of quaternary phase shift keying (QPSK) Fabry-Perot interferometers (FPIs) are employed as the linear encoder system. The optical design of this encoder system is according to the zero point setting method which is proposed by this research. For the QPSK FPI, its interferometric structure and theoretical simulations will be described as following. The principle of geometrical error reducing is also demonstrated eventually.
Fig. 2. Squareness error of two axes.
2.1. Geometrical error in X-Y positioning stage There are several geometrical errors will reduce the positioning accuracy of X-Y positioning stage (Fig. 1). In this research, the squareness, straightness and Abbe error will be discussed [16,17]. All of these errors can be reduced by the proposed method which is shown as follows. 2.1.1. Squareness error If there is no squareness error between the two axes, it means that these two axes are completely perpendicular to each other. In the practical situation, not only the angle between two measuring axes but also the angle between two moving axes are not a perfect right angle, which
Fig. 3. Straightness error of axis.
shown in Fig. 2. Those errors will cause the positioning error, which is called cosine error. Therefore, if the positioning accuracy of submicrometer or nanometre scales needs to be guaranteed, the squareness error must be measured and compensated [11]. 2.1.2. Straightness error The straightness error is the lateral difference between moving path and its theoretical axis. In an ideal stage, the moving path is a straight line, so the straightness error must be zero. But in the practical situation, the moving path will be affected by the accuracy of mechanical components and its assembly conditions, which is shown in Fig. 3. When the stage is moving along the X-axis, the straightness error can cause a tiny displacement on Y-axis. If we went to reduce this error, the stage needs a fine assembly and calibration [16]. That will be an extra cost for the manufacturer.
Fig. 1. X-Y positioning stage.
2.1.3. Abbe error Abbe error is a geometrical error which describes the magnification of term of angular error (𝜃) over distance (L) [17]. The sketch and equation of Abbe error is shown in Fig. 4 and Eq. (1) when 𝜃 is approaching to zero. The terms 𝜃 and L are the main parameters of this error. If one of these terms is set to zero, the Abbe error will be minimized.
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Mechatronics 63 (2019) 102274
Fig. 6. Proposed QPSK FPIs.
n is the order number of the transmitted Laser beams.
Fig. 4. Sketch of Abbe error.
A1 = A0 TT′
1∕2 0
(2)
A2 = A0 TT′
3∕2 1
(3)
A3 = A0 TT′
5∕2 2
(4)
R R R
√ An =
Fig. 5. Abbe error reducing method proposed by G. Jaeger et al. [8–10].
To achieve this goal, some previous research by G. Jaeger et al. gives us a method [10–12], which is shown in Fig. 5. This method controls the angular error (𝜃) within a small value, and sets the two measuring beams passing through a zero point to make the distance (L) close to zero. Therefore, the Abbe error in this research can be approximated to zero. This method needs a fine alignment of the measuring beams of the Laser interferometer. Otherwise, the Abbe error will not be eliminated. Abbe error = L × tan(𝜃) ≈ L × sin(𝜃) ≈ L𝜃
(1)
2.2. QPSK Fabry-Perot interferometer FPI is a kind of interferometer with the common path optical structure where the displacement measured is precisely defined by the distance in the optical cavity. For this reason, FPI has the feature to reduce the measuring error which is induced by environmental disturbances [18,19]. In this research, the modified FPIs were employed as the Laser encoder system. The structure of the proposed QPSK FPIs is illustrated in Fig. 6. The He-Ne Laser source is separated into two optical axes which are X and Y axes by the pentaprism beam splitter. Each separated Laser beam pass through the optical cavity of FPI, and the quaternary phase shift is formed by the one-eighth waveplate which is arranged in the optical cavity. By this configuration, the interferometric signals can be obtained by two photodiodes as the feedback signals. The equations of the proposed QPSK FPI are derived in detail as followings. The amplitude of the transmitted beam can be presented in Eqs. (2) to (5), where A0 is the amplitude of the incident Laser, R and T are the reflectance and transmittance of the plane mirror, T’ is the resultant transmittance of the optical components in the cavity [20], and
2 (2n−1)∕2 𝑛−1 A TT′ R 2 0
(5)
The relevant electric field of the s-type and p-type can be illustrated in Eqs. (6) to (13). In this optical design, 𝛿 is the phase difference of the optical cavity which is 2𝜋d/𝜆, where d is the distance of the optical cavity of FPI. For the electric field of s-type transmitted Laser beams, √ 1 2 Es1 = A TT′ 2 R0 cos (ωt + kx + 1δ) (6) 2 0 √ 3 2 Es2 = A TT′ 2 R1 cos (ωt + kx + 3δ) (7) 2 0 √ Es3 =
5 2 A TT′ 2 R2 cos (ωt + kx + 5δ) 2 0
(8)
√ Esn =
2n−1 2 A TT′ 2 Rn−1 cos (ωt − kr + (2n − 1) ⋅ δ) 2 0
For the electric field of p-type transmitted Laser beams, √ ( ) 1 2 π Ep1 = A TT′ 2 R0 cos ωt + kx + 1δ + 2 0 4 √ ( ) 3 2 3π Ep2 = A0 TT′ 2 R1 cos ωt + kx + 3δ + 2 4
(9)
(10)
(11)
√ Ep3 =
( ) 5 2 5π A0 TT′ 2 R2 cos ωt + kx + 5δ + 2 4
(12)
√ Epn =
( ( )) 2n−1 2 π A TT′ 2 Rn−1 cos ωt + kx + (2n − 1) δ + 2 0 4
(13)
In order to obtain the intensity distribution of the FPI, the summation of the electric field for s-type and p-type are determined by Eqs. (14) and (15). For the summation of the electric field (s-type), √ 2 T′ 1∕2 × ei⋅δ Es = A Tei(ωt +kx) × (14) 2 0 1 − T ̀ × R × ei⋅2δ For the summation of the electric field (p-type), ) ( √ i⋅ δ+ π4 2 T′ 1∕2 × e i(ωt +kx) Ep = A Te ) ( 2 0 i⋅ 2δ+ π2 1 − T ̀× R × e
(15)
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Mechatronics 63 (2019) 102274
Fig. 7. Simulation results of signal distribution. Fig. 9. Compensation of straightness error.
Fig. 8. Proposed internal zero point setting method.
The intensity distribution of s-type and p-type can be denoted by Eqs. (16) and (17). For the intensity of s-type transmitted Laser beams, Is = Es × E∗s =
1 2 A 2 0 ′2
× T2 × T′
1 + R2 × T − 2 × T′ × R × cos (2δ)
(16)
For the intensity of p-type transmitted Laser beams, Ip = Ep × E∗p =
1 A 2 2 0
× T2 × T′
( ) 1 + R2 × T′ 2 − 2 × T′ × R × cos 2δ + π2
point, the deviation distance (L) which is mentioned in Eq. (1) is closed to zero. For this reason, Abbe error can be eliminated. After splitting of the Laser source, the two split Laser beams are almost being perpendicular to each other, because of the feature of the pentaprism beam splitter. Therefore, whether the two axes of the positioning stage are perpendicular to each other or not, the control and feedback system will always lead the stage moving along the axes defined by the Laser encoder system. By this way, the squareness error can be minimized. For the straightness error, the control system of two axes will always be compensated by each other, which is shown in Fig. 9. The straightness error of X-axis is a term of the positioning error of Y-axis. When the Xaxis is moving, the straightness error will be measured and compensated by the measuring and control systems of Y-axis. Therefore, by the internal zero point setting method, the squareness error, straightness error and Abbe error can be minimized. In the proposed method, the key of geometrical error reducing is based on the tolerance of the pentaprism. The tolerance of the high quality commercial pentaprism is about ± 1 arcsec. According to this condition, the geometrical error of the stage is about 0.5 𝜇m /100 mm. Furthermore, some existing researches mentioned about the advanced manufacturing or aligning method for the pentaprism [21–23]. According to these results, the geometrical error of the proposed method can be reduced into a tiny range of 0.5 nm /100 mm. This accuracy meets the positioning requirements of precision machinery and semiconductor industries.
(17)
The resultant transmittance of the whole optical cavity and the reflectance of the plane mirror are substituted into the equation Eqs. (16) and (17). The simulated intensity distributions are illustrated in Fig. 7. From the simulated results, it reveals that the reflectance of the plane mirrors and the resultant transmittance of the optical components in the cavity will influence the intensity and the fineness of the signal. Therefore, in order to reduce the interpolation error of the signal processing, the above-mentioned parameters must be set in an appropriate value. In this research, the reflectance of 20% to 25% will be recommended for this QPSK FPI optical cavity. 2.3. Novel zero point setting method In the present research [10–12], the zero point of the positioning stage is set by external laser beams which are shown in Fig. 5. In this article, a zero point is set by two internal laser beams which are split from one Laser source (shown in Fig. 8). By this opto-mechatronics design, if the control system is robust, the squareness error, straightness error, and Abbe error will be minimized. Because the Laser beam is split at the zero
3. Design of proposed positioning system Figs. 10 and 11 are the proposed positioning system which is using the internal zero point setting method. The interferometric system is based on QPSK FPI. The interferometric signals are received by four Photodiodes (PDs). The signal amplification processing is shown in Fig. 12. After the signal amplification processing, the signals will be delivered to the interpolator which can transform the analog signals into digital signals, and enhance the signal resolution, which is shown in Fig. 13. Then the transformed digital signals are received by the motion control device as the feedback signals. In this system, the two Laser encoders use the same Laser source which is split by the proposed zero point setting method, so the wavelength compensation of these measuring systems can be integrated easily. This is also an additional advantage of the proposed system. The interferometric Laser encoders are utilized as the feedback control signal for the X-Y positioning stage. Therefore, by this optomechatronics design, the above mentioned geometrical errors can be eliminated. In this design, the moving direction of the X and Y axes are not necessary to be perpendicular to each other, so the cost of mechanical components and assemblies can be reduced.
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Mechatronics 63 (2019) 102274
Fig. 10. Opto-mechantronics design of the X-Y positioning stage.
Fig. 12. Interferometric signals processing.
Fig. 11. Positioning system with the proposed method.
4. Experimental results In order to verify the ability of the proposed Laser encoder system, a positioning experiment was implemented. Fig. 14 is the experimental interference signal of QPSK FPI. The reflectances of plane mirrors are about 20%. In this reflectances setting, the finesse of the interferometric signal is quite low, so the signal pattern is similar to a sinusoid in the time domain, and circular form in the X-Y domain. By this way, the interpolation error can be reduced to a tiny amount which is negligible in this experiment.
Fig. 13. Interference signal interpolation.
The Y-axis of the positioning stage was controlled to hold on the zero position, and X-axis was moving from 0 to 3 mm with the positioning interval of 0.3 mm. In this experiment, the Laser encoder signals were counted and stored by the motion controller. The data of 1,000 points was acquired by the controller at each position, after the stage has been
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Mechatronics 63 (2019) 102274
Table 2 1st experiment result. Position (mm)
Positioning error of X-axis
Standard deviation of X-axis
Positioning error of Y-axis
Standard deviation of Y-axis
0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3
−0.0520 −0.1000 0.0310 0.0710 0.0290 −0.0640 0.0280 −0.0070 0.0170 −0.0020
2.2154 1.6281 1.8065 2.6550 0.5749 2.1110 1.3413 1.4646 2.6706 0.0632
−0.1020 0.3680 0.9720 1.6620 2.0020 1.8510 0.6970 −0.9060 −0.9640 −1.0000
1.2487 1.2939 1.0278 1.7908 0.0447 0.6865 0.4994 0.2920 0.1917 0.0000
Unit: count. Table 3 2nd experiment result. Position (mm)
Positioning error of X-axis
Standard deviation of X-axis
Positioning error of Y-axis
Standard deviation of Y-axis
0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3
−0.0140 0.0080 0.0000 −0.0980 −0.0020 −0.0960 −0.0030 −0.0360 −0.0030 −0.0280
3.0164 0.3662 2.8478 1.6362 1.7085 2.6072 0.0707 2.8655 1.9023 1.4524
−0.9950 −1.0000 0.1550 2.1200 3.2930 2.7720 2.9990 1.5800 1.0280 −0.9910
0.0706 0.0000 1.1732 0.4877 0.4576 0.4798 0.0316 1.6408 1.2445 0.1045
Unit: count. Table 4 3rd experiment result. Position (mm)
Positioning error of X-axis
Standard deviation of X-axis
Positioning error of Y-axis
Standard deviation of Y-axis
0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3
−0.0620 −0.0540 0.0380 0.0050 0.0610 −0.1180 0.0650 −0.0040 −0.0440 0.0960
2.1295 2.6967 1.3290 2.7071 1.7141 1.7387 2.9078 0.1414 2.8245 1.5534
−0.1060 0.1280 2.3460 −0.9240 2.7120 −0.9220 −1.0000 −1.0000 0.2020 2.1750
1.2034 1.3241 1.0906 0.3665 0.4746 0.2828 0.0000 0.0000 1.4674 0.5502
Unit: count.
Fig. 14. Experimental signal of QPSK FPI. (a) Time domain, (b) X-Y domain.
Fig. 15. Positioning error of X-axis.
set. The experiment results are shown in Fig. 15 and Tables 2–4. The results show that the positioning error of the moving axis (X-axis) is within one count (15.8 nm), and the maximum standard deviation is about 3 counts (47.4 nm). By the following axis (Y-axis), the positioning error is about 3.3 counts (52.1 nm), and the maximum standard deviation is about 1.8 counts (28.4 nm).
5. Conclusion and future work This article presents a positioning system which can be free from those specific errors which are above mentioned by the zero point setting
C.-P. Chang, Y.-C. Shih and S.-C. Chang et al.
method. To compare with the previous method, the proposed zero point setting method can get the zero point without complicated adjustment. Because the beams are split from one Laser source, the zero point which is set by the proposed method is much more precise than other methods. This is a significant benefit to the high accuracy positioning system. The available positioning range of proposed X-Y stage is within 20 mm square which is limited by the size of measuring mirror. According to the result of positioning experiment, the resolutions of both axes are about 15.8 nm, and the maximum standard deviation of static positioning error is about 50 nm in the ordinary environment. These results show that the proposed Laser encoder system has a high potential for the precision positioning purpose of precision machinery and semiconductor industries. As future work, more related experiments must be done for figuring out the ability and limitation of the proposed encoder system, after the integration of the advanced opto-mechatronics structure. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The paper is supported by the Ministry of Science and Technology, Taiwan, under Grant no. MOST 106–2218-E-415–003. References [1] Ming-Hsien Wu, Yen-Hsiang Fang, “Picking-up and placing process for electronic devices and electronic module”, US patent, US 20160268491 A1, Industrial Technology Research Institute, Sep. 15, 2016. [2] Mizuno T, Tomoda K, Oohata T. “Method of transferring device”, US patent, US 20100258543 A1, Sony Corporation, Oct. 14, 2010. [3] Golda D, Higginson JA, Bibl A, Parks PA, Bathurst SP, “Mass transfer tool manipulator assembly”, US patent, US 9308649 B2, LuxVue Techonology Corporation, US 9308649 B2, June 12, 2016. [4] Yu-Chu Li, Yu-Hung Lai, Tzu-Yang Lin, “Method for transferring light-emitting elements onto a package substrate”, US patent, US 9583450 B2, PlayNitride Inc., Feb. 28, 2017. [5] BIPM, “17th General Conference on Weights and Measures (1983), Resolution 1”, Retrieved 19 September 2012. [6] Bobroff Norman. Recent advances in displacement measuring interferometry. Measure Sci Tech May 1993;4(9):907–26. [7] Donmez MA, Blomquist DS, Hocken RJ, Liu CR, Barash MM. A general methodology for machine tool accuracy enhancement by error compensation. Precision Eng October 1986;8(4):187–96. [8] Chen JS, Kou TW, Chiou SH. Geometric error calibration of multi-axis machines using an auto-alignment laser interferometer. Precision Eng October 1999;23(4):243–52. [9] Qin Jie, Gao Zhan, Wang Xu, Yang Shanwei. Three-dimensional continuous displacement measurement with temporal speckle pattern interferometry. Sensors November 2016;16(12). [10] Jaeger G. Three-dimensional nanopositioning and nanomeasuring machine with a resolution of 0.1 nm. Optoelectron Instrument Data Process 2010;46(4):318–23. [11] Jaeger G. Limitations of precision length measurements based on interferometers. J Measure 2010;43(5):652–8 June 2010. [12] H Q, Wu K, Wang C, Li R, Fan KC, Fei Y. Development of an Abbe error free micro coordinate measuring machine. Appl Sci 2016;6(4):97. [13] Lee C, Jeon S, Stepanick CK, Zolfaghari A, Tarbutton JA. Investigation of optical knife edge sensor for low-cost, large-range and dual-axis nanopositioning stages. Measurement 2017;103:157–64. [14] Díaz-Pérez LC, Torralba M, Albajez JA, Yagüe-Fabra JA. Implementation of the control strategy for a 2D nanopositioning long range stage. Procedia Manufactur 2017;13:458–65. [15] Ye W, Zhang M, Zhu Y, Wang L, Hu J, Li X, Hu C. Translational displacement computational algorithm of the grating interferometer without geometric error for the wafer stage in a photolithography scanner. Opt Express 2018;26(26):34734–52.
Mechatronics 63 (2019) 102274 [16] International Organization for Standardization, “Test code for machine tools – Part 1: geometric accuracy of machines operating under no-load or quasi-static conditions”, ISO 230-1, 2012. [17] Zhang GX. A study on the Abbe principle and Abbe error. CIRP Ann 1989;38(1):525–8. [18] Lawall JR. Fabry-Perot metrology for displacements up to 50 mm. J Optic Soc Am A 2005;22(12). [19] Kong Jing, Zhou Ai, Yuan Libo. Temperature insensitive one-dimensional bending vector sensor based on eccentric-core fiber and air cavity Fabry-Perot interferometer. J Optic March 2017;19(4). [20] Shyu LH, Chang CP, Wang YC. Influence of intensity loss in the cavity of a folded Fabry-Perot interferometer on interferometric signals. Rev Sci Instrument May 2011;82(6):063103. [21] Geckeler RD. Optimal use of pentaprisms in highly accurate deflectometric scanning. Measure Sci Tech 2007;18(1). [22] Barber SK, Yashchuk VV, Geckeler RD, Gubarev MV, Buchheim J, Siewert F, Zeschke T. Optimal alignment of mirror-based pentaprisms for scanning deflectometric devices. Optic Eng July 2011;50(7). [23] Yellowhair J, Burge JH. Analysis of a scanning pentaprism system for measurements of large flat mirrors. Appl Opt December 2007;46(35):8466–74. Chung-Ping Chang received the B.S. degree in Mechanical and Mechatronic Engineering from National Taiwan Ocean University, Keelung, Taiwan, and the M.S. degree in Mechanical Engineering from National Yunlin University of Science and Technology, Yunlin, Taiwan, in 2007 and 2009 respectively. His Ph.D. degree received form Department of Mechanical Engineering from National Central University, Taoyuan, Taiwan, in 2013. From 2013 to 2016, he was a Postdoctoral Fellow with the mechanical engineering in National Yunlin University and Technology University. He is currently an Assistant Professor with the Department of Mechanical and Energy Engineering, National Chiayi University, Chiayi, Taiwan. His research interests include optical measurement technology, Laser interferometer design, machine tool calibration technology, in particular, micro/nano positioning technology. Yi-Chieh Shih received the B.S. and M.S. degree in Mechanical and Mechatronic Engineering and Mechanical Engineering from National Ilan University, Ilan, Taiwan, and National Yunlin University and Technology University, Yunlin, Taiwan, in 2014 and 2016 respectively. He is currently a Ph.D. candidate in the Department of Mechanical Engineering, National Central University, Taoyuan, Taiwan. He has been a lecturer in National Yunlin University of Science and Technology. His research interests are in the field of the precision mechanical and the semiconductor industry including optical metrology, precise positioning, and machine tool calibration technology.
Syuan-Cheng Chang completed two-year’s Japanese studies course in National Taichung University of Science and Technology, Taichung, Taiwan, in 2014. He was an industrial wiring work trainee with Vocational Training Bureau, Taichung, Taiwan, in 2016. He is currently a M.S. student from the Department of Mechanical and Energy Engineering, National Chiayai University, Chiayi, Taiwan. His research interests include automation control system, optical measurement technology, and Laser interferometer design.
Yung-Cheng Wang received his Dr Ing. from the Institute of Process Measurement and Sensor Technology at the Ilmenau University of Technology (TU Ilmenau) in 2003. He is now a professor in the Department of Mechanical Engineering at the National Yunlin University of Science and Technology (Yuntech). His research interests include optical metrology and its applications in precision mechanical engineering, the development of Fabry-Perot interferometers, inspection technologies for machine tools and on-line automated measurements. He has published over 50 research papers and holds 30 patents.