Reflection type heterodyne grating interferometry for in-plane displacement measurement

Reflection type heterodyne grating interferometry for in-plane displacement measurement

Available online at www.sciencedirect.com Optics Communications 281 (2008) 2582–2589 www.elsevier.com/locate/optcom Reflection type heterodyne gratin...

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Available online at www.sciencedirect.com

Optics Communications 281 (2008) 2582–2589 www.elsevier.com/locate/optcom

Reflection type heterodyne grating interferometry for in-plane displacement measurement Cheng-Chih Hsu a,*, Chyan-Chyi Wu a, Ju-Yi Lee b, Hui-Yi Chen b, Han-Fu Weng a b

a Center for Measurement Standards, Industrial Technology Research Institute, 321 Kuang Fu Road, Sec. 2, Hsinchu 300, Taiwan Institute of Opto-Mechatronics Engineering, National Central University, 300 Jhongda Road, Jhongli City, Taoyuan County 320, Taiwan

Received 7 September 2007; received in revised form 26 December 2007; accepted 27 December 2007

Abstract A novel method is presented for one-dimensional (1-D) and two-dimensional (2-D) in-plane displacements measurement that is based on the heterodyne grating interferometry. The novel setup of the optical configuration reduces the airstreams disturbance and maintains the environmental vibration at minimum level, allowing high stability and low measurement error to be achieved. Resulting from the theoretical calculation, our method can be sensitive to the sub-picometer level. With highly controlled isolation system, the low frequency noise can be reduced to minimum level, and only high frequency noises are considered, our method can achieve the resolution about 0.5 nm within 250 lm displacement. In addition, 2-D in-plane displacement measurement can be accomplished with a single interferometer simultaneously. Ó 2008 Published by Elsevier B.V.

1. Introduction Nano-scale positioning devices have become a significant requirement in scientific instruments used for nanotechnology applications. These devices can be applied to nano-handling, nanomanipulation, and nanofabrication. In addition, they are an essential part of the scanning probe microscopy (SPM) and widely used in many research fields. The precision positioning devices consist of three principle parts, which are the rolling component, the driving system and the position sensor. Piezoelectric actuator is the most popular method for driving system and commercial products have been on the market for a few decades. Therefore, the piezoelectric actuator and the position sensor will play the role of the positioning and the feedback control of the rolling element. To achieve the high resolution positioning, the sensing methods of position sensor become more important and have attracted great attention over the last two decades. *

Corresponding author. Tel.: +886 3 574 3727; fax: +886 3 573 5747. E-mail address: [email protected] (C.-C. Hsu).

0030-4018/$ - see front matter Ó 2008 Published by Elsevier B.V. doi:10.1016/j.optcom.2007.12.098

Position-sensing methods reported in the past few years fall into two basic categories: the heterodyne sensing method [1–3] and the homodyne sensing method [4–6]. Wu [1] used a synthesis method which involved synthesizing higher frequency quadrature signals to be mixed with the measurement signals, and adding the resultant two signals to the final signal. This final signal had the heterodyne signal form and carried the testing information. This method demonstrated that precise measurement results of the step-motor for a 25 lm step movement could be achieved. Demarest [2] proposed a double-passed heterodyne interferometer, which can accomplish high resolution and high-speed measurement. Dobosz [4] developed the numerical compensation method to correct the nonlinearity of the laser linear encoder consisting of a laser diode and the reflecting sinusoidal phase grating with 1 lm grating pitch. Jourlin et al. [5] developed the compact displacement sensor consisting of two reflection type gratings with two different grating pitches. This displacement sensor can achieve a compact size with 1  1  3 cm3 but the resolution is larger than 100 nm because of the packaging tolerance. Salbut [6] summarized many articles on grating

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interferometry for the in-plane displacement sensor. He also proposed five different head types of the waveguide grating interferometer and showed that 20 nm accuracy of the in-plane displacement sensing system can achieve with the fringe pattern analysis technique. However, all of the head types used two different gratings and their parallelism might influence the quality of the interferograms. In this paper, we propose a new optical measurement configuration and concentrate on the in-plane displacement measurement. According to the optical configuration and heterodyne interferometry technology, the displacement measurement of high stability, high resolution, and low uncertainty can be achieved. For long-range displacement measurement, the results showed no significant differences between our method and the comparison instrument. For short-range displacement measurement, our method was able to detect the displacement smaller than 10 nm, while the comparison method could not. Hence, our measurement system can monitor the actual movement behavior of the motorized stage, which is down to subnanometer range. According to our measurement results, the smallest identifiable displacement was about 6 pm. To our knowledge, it is the first time to realize the identification of the pico-meter displacement variation with heterodyne interferometry. In this paper, we also demonstrate the results of the two-dimensional (2-D) in-plane displacements and achieve the 2-D measurement with single interferometer. If the optical configuration of this method were miniaturized, it might be suitable for use in the movement monitoring system of the motorized stage. 2. Principles 2.1. One-dimension (1-D) in-plane displacement measurement The schematic diagram of this method is shown in Fig. 1. For convenience, the +z-axis is chosen to be along the direction of propagation and x-axis is along the horizontal direction. A heterodyne light source [7] is incident onto the beam splitter BS and the light beam is divided into two parts: one is the reference beam that is reflected by the BS and the other is the test beam that is passed through the

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BS and directly incident onto the diffraction grating. Therefore, the reference signal detected by the photodetector D1 has the form: 1 ð1Þ I r ¼ ½1 þ cosðxtÞ 2 The test beam is guided into ±1st order diffracted lights and the +1st and 1st order diffracted lights will be collected by a lens L and propagate into two paths: (1) prism P ? polarization beam splitter PBS ? analyzer AN2 (45°) ? detector D2, (2) polarization beam splitter PBS ? analyzer AN3 (45°) ? detector D3. According to the arrangement of the optical configuration, the interference signal detected by the detector D2 interferes with p-polarization of the +1st order diffracted light and s-polarization of the 1st order diffracted light. After Jones calculating, this signal can be written as 1 I D2 ¼ ½r2pðþ1Þ þ r2sð1Þ þ 2rpðþ1Þ rsð1Þ cosðxt þ 2/Þ: 8

ð2Þ

Similarly, the interference signal detected by the detector D3 interferes with s-polarization of the +1st order diffracted light and p-polarization of the 1st order diffracted light; it can be written as 1 I D3 ¼ ½r2pð1Þ þ r2sðþ1Þ þ 2rpð1Þ rsðþ1Þ cosðxt  2/Þ; 8

ð3Þ

where x is the angular frequency difference between the pand s-polarizations of the heterodyne light source, rp(+1), rp(1), rs(+1), and rs(1) are the reflection coefficients of the p- and s-polarizations of the ±1st order diffracted light, respectively. / is the phase shifting which is dependent on the diffraction order m, grating pitch dg and in-plane displacement d. It can be expressed as [2] /¼m

2pd : dg

ð4Þ

All of these three sinusoidal signals, Ir, ID2, and ID3, are sent to the phase meter and the total phase shifting U = 2/(-2/) = 4/ between ID2 and ID3, can be measured immediately. It is obvious that U is four times magnification of the phase shifting /. Hence, the in-plane displacement d can be obtained from Eqs. (1)–(4) and written as d¼

Ud g : 8pm

ð5Þ

If the diffraction order m, the pitch of the diffraction grating dg, and the total phase shifting U are given, the in-plane displacement d can be obtained simultaneously. 2.2. Two-dimensions (2-D) in-plane displacement measurement

Fig. 1. The schematic diagram of the 1-D displacement measurement configuration.

If the diffraction grating is replaced by a 2-D diffraction grating, our method can easily be applied to 2-D in-plane displacement measurement. The schematic diagram is shown in Fig. 2(a) and the actual measurement system in Fig. 2(b). The 2-D diffraction grating is well mounted on

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the x–y stage and located in the x–y plane. Hence, four diffracted beams will propagate on the x–z plane and y–z plane, respectively. Then they will be detected by the detectors Dx1, Dx2, Dy1, and Dy2, which are used to monitor the x- and y-direction in-plane displacement, respectively. The test signals can be written as 1 I Di1 ¼ ½r2piðþ1Þ þ r2sið1Þ þ 2rpiðþ1Þ rsið1Þ cosðxt þ 2/i Þ; 8

ð6aÞ

(i = x and y) 1 I Di2 ¼ ½r2pið1Þ þ r2siðþ1Þ þ 2rpið1Þ rsiðþ1Þ cosðxt  2/i Þ; 8

ð6bÞ

(i = x and y) and /i ¼ m

2pd i ; dg

ð6cÞ

(i = x and y) where rpi(+1), rpi(1), rsi(+1), and rsi(1) are the reflection coefficients of the p- and s- polarizations of the ±1st order diffracted light propagated along x- and y-direction, respectively. /i is the phase shifting coming from the 2-D in-plane displacement di. As previously described, these five sinusoidal signals Ir, IDx1, IDx2, IDy1, and IDy2 are sent to the phase meter and the total phase shifting Ux = 4/x and Uy = 4/y can be measured immediately. According to Eqs. (1) and (6a), (6b), (6c), the relations between the total phase shifts (Ux and Uy) and 2-D in-plane displacements can be expressed as Ux d g ; 8pm Uy d g : dy ¼ 8pm

ð7aÞ

dx ¼

Fig. 2. The 2-D displacement measurement configuration: (a) schematic diagram and (b) actual system. 110

ð7bÞ

If the diffraction order m, the pitch of the diffraction grating dg, Ux, and Uy are given, the 2-D in-plane displacements, dx and dy, can be obtained simultaneously. Our method

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Time (sec) Fig. 3. The results of the 1-D short-range displacement with 10 discontinuous pulse.

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3. Experiments and results A heterodyne light source, consisting of a linearly polarized He–Ne laser at 632.8 nm with frequency stabilized control and an electro-optic modulator EOM (model: 4001, New Focus, Inc.) driven by a function generator with 1 kHz sawtooth signal as shown in Fig. 1 and Fig. 2, was focused on the grating surface with 10 lm in diameter. The fast axis of EOM was located at 45° to the x-axis and the frequency difference between the p- and s-polarizations was 1 kHz. The 1-D and 2-D diffraction gratings were mounted on the precision x–y stage (model: 8095, New Focus, Inc.). The operating principle of this stage was relied on the static and dynamic frictions, which the stage moved as slow action and fast action respectively. The mechanical structure consisted of two jaws grasping an

a

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80-pitch screw; a piezoelectric transducer slides the jaws in opposite directions [7]. The driver (model: LS-773, New Focus, Inc.) of this stage was designed as the openloop circuit without feedback control [7]. The grating pitches were pre-determined by atomic force microscopy (AFM, model: Dimension 3100, Veeco Instrument) and they were 1.6 lm (1-D grating) and 1.1 lm (2-D grating). Both of them are phase grating with the size of 25 mm  25 mm and manufactured by e-beam writer. Their diffraction efficiencies are all about 40% and the contrasts between p-polarization and s-polarization are 95% and 98% respectively. The reference and test signals were received by the detectors and sent into the high speed, multichannel data acquisition card (model: PCI-6143, National Instruments Corporation). Then the phase difference was measured by pc-based software, which was programmed

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Time (sec) Fig. 4. The results of the 1-D short-range displacement at continuous movement: (a) whole and (b) enlarge the initial portion. The speed of the stage is about 3 lm/s.

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a

50

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Our method μ ( m)

by the Labview software (version: 7.0, National Instruments Corporation) with the phase-lock technology. The phase resolution of this program can be adjusted manually from 0.1° to smaller than 0.001°. The experiments were divided into two parts: experiment (I) dealt with the 1-D displacement measurement using 1-D diffraction grating, and experiment (II) treated 2-D displacement measurement using the 2-D diffraction grating. Both were compared with commercial precision laser dimensional measuring systems (model: HP 5528A and HP 5529A, Hewlett-Packard Development Company) which were calibrated by the primer standard system in National Measurement Laboratory (NML) of the Center for Measurement Standards (CMS). The sampling-rate of these experiments was kept the same during the whole measurement process and the value was fixed at 128 measured points per second. In experiment (I), we mounted the 1-D grating on the x– y stage and controlled the stage movement discontinuous or continuous. In Fig. 3, we controlled the stage with 10 separated pulses to form the discontinuous movement. It can be seen that each step variation measured by our method was clearer than commercial precision laser dimensional measuring system (HP 5529A). We also found that the detectable displacement of the HP 5529A must be larger than 10 nm. Hence, the actual movement behavior of the stage could not easily observed by HP 5529A. Then we made the stage movement continuous about 120 nm with the speed 3 lm/s and the results are presented in Fig. 4. The difference of the measurement results were within 10 nm. As can be seen, our measurement results were smoother and more continuous due to the high sensitivity. As the stage started to move, we marked the values of three data points as shown in Fig. 4(b). The differences between each of them were about 17.9 pm and 6 pm respectively. Hence, the sensitivity of our method is so high that it could detect as small as 6 pm displacement variation. These results suggest that our method has pico-meter sensitivity. We also measured the long-trip in-plane displacement and these results are shown in Fig. 5. The speed of the stage was about 6 lm/s and the total displacements were about 50 lm and 250 lm as shown in Fig. 5a and Fig. 5b, and the differences between two measurement methods were less than 30 nm and 1.4 lm, respectively. In experiment (II), we used the 2-D grating to measure the 2-D in-plane displacement directly and compared this simultaneously with two commercial precision laser dimensional measuring system including HP 5529A and HP 5528A. We controlled the movement of the stage at 45° respective to the x-axis and the total displacement was about 180 nm with the speed 3 lm/s. Therefore, the displacements projected onto the x- and y-direction were about 128 nm individually. The measurement results are presented in Fig. 6a and b. In this figure, our results were closely related to the commercial measurement system and the differences were 9.5 nm and 6.7 nm for the xand y-direction, respectively.

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HP 5529A (μ m) Fig. 5. The results of the 1-D long-range displacement at continuous movement: (a) 50 lm and (b) 250 lm. The speed of the stage is about 6 lm/s.

4. Discussion The uncertainty of the grating pitch |Ddg| and phase |DU| will influence the accuracy of the in-plane displacement measurement of our method. The error of the grating pitch [8] could be coming from the tolerance and the non-uniformity of the grating and the uncertainty of the AFM measurement results coming from the interferometer nonlinearity and the measurement repeatability. The uncertainty of the phase [9] will be coming from the angular resolution of the data acquisition card, the secondharmonic error, and the polarization-mixing coming from the measurement system. Hence, the theoretical error of the in-plane displacement |Dd| can be presented as jDdj ¼

dg U jDUj þ jDd g j; 8p 8p

ð8Þ

In Eq. (8), the total phase difference U will vary with the movement of the stage. According to our experimental conditions, the temperature variation smaller than 0.01 °C which might be neglected the effect of the refractive index variation, the |Ddg| and |DU| were better than 0.01 lm and 0.03°, respectively. The grating pitch dg was 1.6 lm and the total phase difference U resulting from the displacement at 400 nm was 360°. Therefore, |Dd| versus the |Ddg|

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X-direction measurement

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Time (sec) Fig. 6. The results of the 2-D short-range displacement at continuous movement: (a) x-direction, (b) y-direction. The speed of the stage is about 3 lm/s.

and U can be shown in Fig. 7 and the theoretical error of the displacement in our method could be better than 4.97 nm as the displacement at 400 nm. According to Eq. (5), the curve of U versus d for different grating pitch can be plotted in Fig. 8. The slopes of curves A, B, and C are about 2.4 (°/nm), 1.44 (°/nm), and 0.9 (°/nm), respectively. Hence, as the phase resolution with 0.001° is considered, the sensitivities are roughly 0.4 pm, 0.7 pm, and 1.1 pm, respectively. It is obvious that the smaller the grating pitch we used, the higher the sensitivity our method achieved. Hence, these theoretical predictions may explain the legitimacy of our measurement results shown in Fig. 4. Furthermore, we simulated the displacement variation versus the phase fluctuation shown in Fig. 9. The phase fluctuation may come from the electrical noise, environment vibration, and the airstream turbulence. The phase fluctuation could be maintained less than 1° under well-controlled conditions, such as the active-isolated table, electric isolation system, and the shelter. In

Fig. 9, the displacement variation will be under 1.2 nm and 10 pm as the phase fluctuation are 1° and 0.01°, respectively. On the other hand, the smaller the grating pitch we used, the lower the fluctuation effect of our method. Therefore, our method may accomplish the pico-meter sensitivity in well-controlled environment by using the commercial grating with micrometer scale of grating pitch. Because of the scattering light intensity is much smaller than diffraction light [10], the scattering effect coming from the grating surface imperfection can be ignored. However, some possible errors that should be considered in our method included the thermal expansion of grating pitch, uniformity of grating pitch, high frequency electronic noise, and the cosine error coming from the misalignment between the grating moving axis, the measured direction of HP system, and the stage movement direction. According to the manufacture’s specification, the uniformity of grating pitch is about 0.1% in our grating sample. Statistically, the corresponding grating pitch variation is about

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Fig. 7. The uncertainty of the in-plane displacement |Dd| versus |Ddg| and U.

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dg = 600 nm

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dg = 1000 nm 6

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±0.1 nm as the travel range is under 250 lm. The ratio of the grating pitch variation to the grating pitch is about 104, and corresponding error is about 0.03 nm. Based on the natural property of the grating material, thermal expansion will cause the grating pitch to enlarge. For the worst case, the grating pitch will expand about 1.1 pm. Therefore, the error due to thermal expansion of the grating pitch is about 0.07 nm as travel range within 250 lm. Based on the derived theory in prior article [11] and the result of the displacement noise also shown in Fig. 10, the low frequency noise can be eliminated by the active-isolated system. Hence, the low frequency noise can be ignored and the high frequency electronics noise is about 0.5 nm [11,12]. Besides, the cosine error coming from the misalignment between the motorized stage, HP apparatus, and the diffracted grating and the angle will easily exceed

0 0

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1°. In our experiments, the best case of misaligned angle between them was about 2° which induced about 30 nm as the travel range was about 50 lm. In Fig. 3, the movement behavior of the stage can be observed easily in our measurement results. Clearly, the stage moved back first and then moved forward pulse by pulse; this situation was also found in the Fig. 4 in which the stage moved continuously. This effect might be caused by reasons such as the expansion and shrinkage of the PZT actuator, driving properties of the motorized stage, and the mechanism structure of the motorized stage. In addition, the fluctuation at the start and the vicinity of the target position caused from total effects on the electronics noise of driven circuit of the motorized stage, thermal effects coming from the friction of the jaws and screw, and

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interferometer. Based on the optical configuration and heterodyne interferometry, this method has some advantages, such as high stability, high resolution, and low uncertainty. From the measurement results, there are no significant differences between our method and the comparison instrument. The smallest displacement variation that can be identified roughly is 6 pm. Moreover, the uncertainty and the sensitivity of our method are better than 5 nm and 1.5 pm, respectively. To compare the theoretical and actual measured results, it was anticipated that the pico-meter resolution might be actualized in our method. These findings lead us to believe that our method can be applied to ultraprecision positioning in controlling the motorized stage movement.

Fig. 10. The displacement noise of our method.

internal noise and optimized carry program of the HP 5529A. Hence, the response curves are shown tiny difference between them in Fig. 3 and Fig. 4. To figure out the dominant reason for this effect, further experiments are ongoing. As can be seen, the quantity of this effect is in nanometer scale or pico-meter scale. That will be a serious problem in ultra-precision positioning. For the long-range displacement measurement, the difference between these two measurement methods might be large especially in the results of Fig. 5b. Because of the coordinate systems of the motorized stage, HP apparatus, and the diffracted grating might be not coincidence. The movement directions of these three elements will be different slightly and enlarged as the movement increases. Hence, proper alignment of them will level down the difference of the measurement results by these two measurement methods. 5. Conclusion In this paper, we demonstrate 1-D and 2-D in-plane displacement measurement results accomplished with single

Acknowledgements This study was supported in part by the Ministry of Economic Affairs, Taiwan, ROC under the Contract Number 6301XS3F10. We also would like to acknowledge the contributions of Mr. Daniel Irwin King and Dr. C. Y. Wang in proofreading this article. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

W.J. Wu, C.K. Lee, C.T. Hsieh, Jpn. J. Appl. Phys. 38 (1999) 1725. F.C. Demarest, Meas. Sci. Technol. 9 (1998) 1024. C.W. Wu, Appl. Opt. 43 (2004) 3812. M. Dobosz, Opt. Eng. 38 (1999) 968. Y. Jourlin, J. Jay, O. Parriaux, Prec. Eng. 26 (2002) 1. L. Salbut, Opt. Eng. 41 (2002) 626. Intelligent Picomotor Control Modules: driver, controllers, I/O modules, joystick, and hand terminal, user’s guide, New Focus. I. Misumi, S. Gonda, T. Kurosawa, K. Takamasu, Meas. Sci. Technol. 14 (2003) 463. M.H. Chu, J.Y. Lee, D.C. Su, Appl. Opt. 38 (1999) 4047. T.A. Germer, C.C. Asmail, Rev. Sci. Instrum. 70 (1999) 3688. J.Y. Lee, H.Y. Chen, C.C. Hsu, C.C. Wu, Sens. Actuators A 137 (2007) 185. X. Liu, W. Clegg, D.F.L. Jenkins, B. Liu, IEEE Trans. Instrum. Meas. 50 (2001) 868.