Laser heterodyne interferometric system with ... - OSA Publishing

Vol. 25, No. 12 | 12 Jun 2017 | OPTICS EXPRESS 13684

Laser heterodyne interferometric system with following interference units for large X-Y-θ planar motion measurement ENZHENG ZHANG, BENYONG CHEN,* JIANJUN SUN, LIPING YAN, AND SHIHUA ZHANG Nanometer Measurement Laboratory, Zhejiang Sci-Tech University, Hangzhou 310018, China * [email protected]

Abstract: A novel laser heterodyne interferometric system with following interference units is proposed for large X-Y-θ planar motion measurement. In this system, two interference units moved by two separate linear stages along x-axis and y-axis are used to follow the large movement of the measured stage so that the simultaneous measurement of three degrees of freedom X-Y-θ parameters of large planar motion is realized. The optical configuration of the proposed system is designed by using the orthogonal linearly polarized beam return method, the measurement principle is described and the mathematic model for simultaneously measuring X-Y-θ planar motion is derived. To verify the feasibility of the proposed system, the experimental setup was constructed and a series of experiments were performed. © 2017 Optical Society of America OCIS codes: (120.0120) Instrumentation, measurement, and metrology; (120.3180) Interferometry; (120.4570) Optical design of instruments; (120.4820) Optical systems.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

C. W. Lee and S. W. Kim, “An ultraprecision stage for alignment of wafers in advanced microlithography,” Precis. Eng. 21(2), 113–122 (1997). W. Jywe, T. H. Hsu, and C. H. Liu, “Non–bar, an optical calibration system for five-axis CNC machine tools,” Int. J. Mach. Tools Manuf. 59, 16–23 (2012). Y. M. Liu, M. Q. Yuan, J. R. Cao, J. W. Cui, and J. B. Tan, “Use of two planar gratings to measure 3-DOF displacements of planar moving stage,” In Proceedings of IEEE Trans. Instrum. Meas. (IEEE, 2015), pp.163– 169. T. J. Quinn, “Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards,” Metrologia 40(2), 103–133 (2003). H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16(11), 2155–2166 (2005). J. Lazar, O. Cip, M. Cizek, J. Hrabina, M. Sery, and P. Klapetek, “Laser interferometric measuring system for positioning in nanometrology,” WSEAS Trans. Cir. and Sys. 9(10), 660–669 (2010). Y. Lou, L. Yan, B. Chen, and S. Zhang, “Laser homodyne straightness interferometer with simultaneous measurement of six degrees of freedom motion errors for precision linear stage metrology,” Opt. Express 25(6), 6805–6821 (2017). J. H. Zhang and C. H. Menq, “A linear/angular interferometer capable of measuring large angular motion,” Meas. Sci. Technol. 10(12), 1247–1253 (1999). C. H. Menq, J. H. Zhang, and J. Shi, “Design and development of an interferometer with improved angular tolerance and its application to x-y theta measurement,” Rev. Sci. Instrum. 71(12), 4633–4638 (2000). S. Ottonelli, F. D. Lucia, M. Dabbicco, and G. Scamarcio, “All interferometric 6 Degree of freedom sensor based on the laser-self-mixing,” Proc. SPIE 73891L, 1–10 (2009). B. Chen, E. Zhang, L. Yan, C. Li, W. Tang, and Q. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009). B. Chen, B. Xu, L. Yan, E. Zhang, and Y. Liu, “Laser straightness interferometer system with rotational error compensation and simultaneous measurement of six degrees of freedom error parameters,” Opt. Express 23(7), 9052–9073 (2015). S. J. Zhao, H. Y. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 084112 (2015). B. Chen, E. Zhang, L. Yan, and Y. Liu, “An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer,” Rev. Sci. Instrum. 85(10), 105103 (2014). Q. B. Feng, Optical Measurement Techniques and Applications (Tsinghua University Press, 2008), Chap. 2.

#292564 Journal © 2017

https://doi.org/10.1364/OE.25.013684 Received 11 Apr 2017; revised 24 May 2017; accepted 31 May 2017; published 7 Jun 2017


16. E. Zhang, B. Chen, L. Yan, T. Yang, Q. Hao, W. Dong, and C. Li, “Laser heterodyne interferometric signal processing method based on rising edge locking with high frequency clock signal,” Opt. Express 21(4), 4638– 4652 (2013).

1. Introduction Precision stages play an important role in the field of precision machining and semiconductor photolithography for providing motion with high accuracy [1–3]. A common configuration in these precision applications is a planar stage which provides two degrees of freedom (DOFs) translational and one DOF rotational displacements about the mutually orthogonal axes, that is, X-Y-θ planar motion. The technical specifications of the machining and manufacturing equipment are directly subject to the positioning accuracy of these stages. Thus, the X-Y-θ stages are required to be measured and calibrated in order to guarantee their accuracy in these precision equipment. Laser interferometry is widely used to realize precision displacement measurement for its advantages of direct traceability to the standard of length and large measurement range with high accuracy [4–7]. However, the traditional laser interferometer is usually used to measure single DOF parameter separately to achieve multiple DOFs measurement, which is a time consuming measurement process. And many researchers are dedicated to realizing the multiple DOFs measurement based on laser interferometry. For example, Zhang J. H. et al. proposed a linear/angular interferometer capable of measuring large angular motion by using the combination of a corner-cube retroreflector and a plane mirror [8]. Menq C. H. et al. proposed an interferometer with improved angular tolerance for the application of x-y theta measurement [9]. Ottonelli S. et al. developed an all-interferometric sensor based on laserself-mixing for the simultaneous detection of multi-degrees-of-freedom displacement of a remote target by using three reciprocally tilted plane mirrors [10]. Chen B. Y. et al. proposed a laser heterodyne interferometer for measuring straightness and its position by improving the traditional straightness interferometer [11,12]. Zhao S. J. et al. proposed a heterodyne interferometer for simultaneously measuring displacement and angle by using only one reference retroreflector and an assembled measurement mirror composed of two corner cubes [13]. In addition to these researches above, the commercial interferometers are used to realize multiple DOFs measurement, such as Agilent 5517C multi-axis measurement system and Zygo 7705 multi-axis measurement system. In these systems, L-shaped arranged plane mirrors are used to measure precision x-y stage with large travel range along x-axis and yaxis, while the measurement range of rotation angle around the mutually orthogonal axis is very small. To summarize the laser interferometric multiple DOFs measurement methods above, the simultaneous measurement of three DOFs X-Y-θ parameters of large planar motion has seldom been given in the past decades. The reason is that interference will not formed when a large angular rotation of the measured stage occurs in a planar motion measurement system using L-shaped mirror composed of plane mirrors or when a large lateral movement of the measured stage perpendicular to the measurement beam occurs using corner cubes as measurement mirror [14]. Hence, the large X-Y-θ planar motion measurement based on interferometry is the key issue to be addressed in precision measurements and calibrations. In this paper, a laser heterodyne interferometric system with following interference units is proposed for large X-Y-θ planar motion measurement. Compared with the traditional interferometric system for planar motion measurement with small angle, the proposed system with following interference units can ensure the planar motion measurement with large angle. The optical configuration of the proposed system is designed in the section 2. The measurement principle is described and the mathematic model for simultaneously measuring X-Y-θ planar motion is derived in the section 3. Lastly, the experimental setup was constructed and a series of experiments were performed to demonstrate its feasibility.


2. Configuration Figure 1 shows the schematic of the proposed laser heterodyne interferometric system with following interference units for measuring X-Y-θ planar motion. The proposed system mainly consists of a stabilized dual-frequency He-Ne laser, x-axis measurement module (Part I), yaxis measurement module (Part II) and the measurement mirror (MR) composed of four corner cubes. Each axis measurement module includes a following interference unit (FIU) and a linear stage (LS). The stabilized dual-frequency laser emits an orthogonal linearly polarized beam with two frequencies and the beam is divided into two beams by a beam splitter (BS1), the reflected beam gets into FIU1 and the transmitted beam enters FIU2. There are two heterodyne interference units (HIUs) in each FIU. In FIU1, the incident beam is divided by BS2 into two parts: the reflected beam gets into HIU1 and after being reflected by the corresponding corner cube in MR, the first interference signal (Sig1) is generated in HIU1; the transmitted beam is reflected by a reflector (R1) and gets into HIU2, and the second interference signal (Sig2) is generated in HIU2. Similarly in FIU2, the third and fourth measurement signals (Sig3 and Sig4) are generated in HIU3 and HIU4, respectively. Each HIU shown in the blue dashed box employs the orthogonal return method for linearly polarized beam based on the Faraday Effect to produce heterodyne interference measurement signal, and the rotational angle error of Faraday rotator does not affect interferometric measurement result [14]. The reference signal (Ref) for each measurement signal is provided by the stabilized laser.

Fig. 1. Schematic of the laser heterodyne interferometric system with following interference units for measuring X-Y-θ planar motion. FR: faraday rotator, M: mirror, PBS: polarizing beam splitter, QP: quarter-wave plate, P: polarizer, PD: photodetector, CC: corner cube.

In the X-Y-θ planar motion measuring process, when the measured stage has a large movement along x-axis, the stage’s x-axis displacement and rotation angle of θ can be obtained by signal acquisition and processing of Ref, Sig1 and Sig2, at the same time, FIU2 will be moved by LS2 to follow the movement of the measured stage according to the measured displacement change along x-axis in order to guarantee that the measurement beam does not exceed the effective aperture of the measuring corner cube; and the y-axis displacement can be obtained simultaneously by processing Ref, Sig3 and Sig4 signals. Similarly, FIU1 will be moved by LS1 to follow the movement of the measured stage according to the measured displacement change along y-axis when the measured stage has a large movement along y-axis. Therefore, the arrangement of the proposed system can achieve the measurement of not only large displacement but also large angle in planar motion.


3. Principle As the displacement measurement along x-axis or y-axis is same, the x-axis movement is taken as an instance to introduce the X-Y-θ measurement principle. As shown in Fig. 2, the rotation center O is chosen at the middle of the measured stage. A displacement Lx along xaxis and a rotation angle θ around z-axis occur when the measured stage moves from P0 to P1. The displacement Lx obviously exceeds the effective aperture of CCs of HIU3 and HIU4. In order to guarantee that the measurement beams can be captured by the corresponding CCs, HIU3 and HIU4 are driven by LS2 to follow MR.

Fig. 2. Schematic for simultaneously measuring X-Y-θ parameters.

The displacement Lx along x-axis can be obtained by processing the Sig1, Sig2 and Ref signals. Lx can be derived by   n sin θ l11 +l12 +8nH sin θ tan  arc sin   n′  Lx = 8n

   − 4Δl (θ ) 

− s (1 − cos θ )

(1)

where s is the distance between the rotation center and the incident surface of MR. l11 and l12 are the optical path differences determined by HIU1 and HIU2, respectively. n is the refractive index of air and n′ denotes the refractive index of CC’s material. H is the height of CC. The increment of the optical path length Δl(θ) inside CC is proportional to the incident angle and can be given by [15] Δl (θ ) =

2n′H

− 2n′H 2  n sin θ  1−    n′  Similarly, the y-axis displacement Ly can be given by   n sin θ l21 +l22 +8nHsinθ tan arcsin   n′  Ly = 8n

   − 4Δl (θ ) 

(2)

− s (1 − cos θ )

(3)

where l21 and l22 are the optical path differences determined by HIU3 and HIU4, respectively. The rotation angle θ can be calculated by  l12 − l11   l22 − l21   = arc sin    4nL0   4nL0 

θ = arc sin 

(4)


where L0 is the distance between the two CCs at the same side of MR. According to Eqs. (1), (3) and (4), three DOFs X-Y-θ parameters of large planar motion can be achieved. From the Eq. (4), the rotation angle θ can be obtained firstly by the difference of l12 - l11 or l22 - l21 which can eliminate the influence of the angle in each optical path difference of HIU. And then by substituting the measured angle θ into the Eqs. (1) and (3), the displacements Lx and Ly can be obtained. Therefore, the crosstalk between the angle and the displacement can be decoupled in the proposed system. In addition, for the motion errors of the following LS, the positioning error of LS along the following axis, the vertical straightness error along z-axis of LS and the pitch error of LS have no effect on the planar motion measurement because these errors do not influence the optical path length of each measuring optical path, the influence of the roll error of LS can be negligible when a precision linear stage is chosen as LS [14], and the influence of the yaw and horizontal straightness errors of LS should be considered and handled. Since the position of the yaw and straightness errors can be determined beforehand, the influence of the yaw and straightness errors can be removed by means of measurement data processing. For the motion direction of each following LS, it is required that the motion axial direction of the following LS should be parallel to that of the measured stage. This can be aligned by evaluating the displacement change between the following LS and the measured stage until the displacement change does not exceed the horizontal straightness of LS. 4. Experiments In order to verify the feasibility of the proposed system, an experimental setup was constructed as shown in Fig. 3. In this setup, the laser is a dual-frequency stabilized He-Ne laser (5517B, Keysight) which emits a pair of beams with the frequency difference of 1.9-2.4 MHz and the wavelength λ of 632.991372 nm. Four high-speed PIN photodetectors (PT1303C, Beijing Pretios) are used to detect the measurement signals with the maximum detection frequency of 10 MHz. The signal acquisition and processing board based on FPGA was developed with dual-mode phase measuring method [16]. A precision linear stage (M531.DD, Physik Instrumente) with the resolution of 0.1 μm and the travel range of 300 mm is used for displacement measurement experiment. A rotation stage (M-038.DG1, Physik Instrumente) with the design resolution of 3.5 × 10−5 is used for angle measurement experiment. Another linear stage (XML350, Newport) with the positioning accuracy of 0.5 μm and the travel range of 350 mm is used as following linear stage to move FIU2. Besides, a commercial interferometer (XL-80, Renishaw) is used to test the measured stage for comparison.

Fig. 3. Experimental setup for X-Y-θ planar motion measurement


4.1 Simultan neous measurrement experriment for X-Y Y-θ planar mo otion This experim ment was carrieed out to veriffy the feasibillity of simultaaneous measurrement of three DOFs X-Y-θ X parameteers of planar motion. m In this eexperiment, FIIU2 was mountted on the linear stage XML350, X MR together with the retroreflecctor of Renishaaw interferomeeter were moved by thee measured stag ge M-531.DD with w the displaacement increm ment of 1 mm, FIU2 was driven by thee linear stage XML350 X to fo ollow the meassured stage’s m movement along x-axis with the samee increment. Th he proposed sy ystem determinned the three D DOFs X-Y-θ paarameters every time. At A the same tim me, the Renishaaw interferomeeter measured the displacemeent of the measured stag ge. The experim mental results are a shown in F Fig. 4. Figure 4((a) shows thee displacement results alonng x-axis, whhich indicates that the maximum diisplacement deviation d betw ween the prooposed system m and the R Renishaw interferometerr is 326.76 nm m with the staandard deviatioon of 113.27 nm and the m maximum displacement deviation betw ween the proposed system aand the measurred stage is 8556.45 nm dard deviation n of 0.36 μm. Figure F 4(b) shhows the displaacement resultt along ywith the stand axis, which in ndicates that th he straightness of the measureed stage and thhe following linnear stage is 6.5 μm. Fiigure 4(c) sho ows the angle results aroundd z-axis obtainned by FIU1 aand FIU2, which indicattes that the maximum angle deviation d betw ween FIU1 and FIU2 is 1.01E--04° with the standard deviation of 4.01E-5°. The experimentaal results dem monstrate that FIU can effectively traack the large movement of the measuredd stage and thee proposed syystem can realize the sim multaneous measurement of X-Y-θ X planar m motion of the m measured stage.

Fig. 4. 4 Experimental results r of X-Y-θ simultaneous meeasurement experriment. (a) x-axiss displaacement measurem ment. To make thee plots visible, thee red dot line is sshifted by 10 mm m from the t actual values. (b) y-axis displacement measuremeent. (c) angle meassurement. The redd dot lin ne is shifted by 0.0 001° from the actu ual values.


4.2 Large angle measurement experiment Although the rotation angle of the measured stage can be measured in the X-Y-θ simultaneous measurement experiment above, it does not verify the capability of large angle measurement of the proposed system. In this experiment, the rotation stage M-038.DG1, which was mounted on the measured stage M-531.DD, was moved to a position, then it rotated with the step of 0.1° in the range of ± 10°. The proposed system and the Renishaw interferometer measured the rotation angle simultaneously. The experimental results are shown in Fig. 5.

Fig. 5. Experimental results of angle measurement comparison in range of ± 10°. (a) positive rotation angle measurement and (b) negative rotation angle measurement. The red dot line is shifted by 1° from the actual values.

Figure 5(a) indicates that the maximum angle deviation between the proposed system and the Renishaw interferometer is 2.62E-05° with the standard deviation of 9.84E-06° in the positive direction angle comparison. Figure 5(b) indicates that the maximum angle deviation is 2.58E-05° with the standard deviation of 1.11E-05° in the negative direction angle comparison. The experimental results show that the proposed system has good coincidence with the Renishaw interferometer, and it can be used to realize the measurement of large rotation angle in the planar motion. 5. Conclusions In this paper, the laser heterodyne interferometric system capable of measuring large X-Y-θ planar motion is proposed. The configuration and measurement principle of the proposed system are described in detail. The advantage of the proposed system is that the use of the following interference units moved by the linear stages can realize the tracking of the large movement of the measured stage and avoid that the measurement beam exceeds the effective aperture of the measuring corner cube, which guarantees the large X-Y-θ planar motion measurement. An experimental setup was constructed to verify the feasibility of the proposed system. The simultaneous measurement experiment of X-Y-θ planar motion verifies that the proposed system can effectively track the large movement of the measured stage by using the following interference units and can achieve the simultaneous measurement of X-Y-θ planar motion. The large angle measurement experiment shows the large angle measurement capability of the proposed system in planar motion measurement. All these indicate that the proposed system could be applied in the measurements and calibrations for precision stages. Funding National Natural Science Foundation of China (NSFC) (51605445, 51375461 and 51527807); Program for Changjiang Scholars and Innovative Research Team in University (IRT13097); China Postdoctoral Science Foundation (2016M601969). Acknowledgments Authors acknowledge the Science Foundation of Zhejiang Sci-Tech University.