Nano rotation stage is widely used as a miniature rotation platform. The high resolution of this device is helpful but it is at the expense of linearity. So the ...
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Physics Procedia 19 (2011) 173–177
ICOPEN2011
Characterization of Piezo rotation stage by multipoint diffraction strain sensor Hui Zhu, Anand Asundi School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore
Abstract Nano rotation stage is widely used as a miniature rotation platform. The high resolution of this device is helpful but it is at the expense of linearity. So the calibration is necessary before usage. In this paper we use the optical diffraction strain sensor to calibrate the nano rotation stage. The system setup and measuring principle of the optical diffraction strain sensor are introduced. In the experiment, a commercial rotation stage (NanoFlex™ 17 ASR 001) is used. The results of measured rotation angles versus driving voltages are shown. An obvious hysteresis phenomenon is measured when applying the driving voltage increasingly and then decreasingly. The measured results can be used for the calibration of this rotation stage.
© 2011 Published by Elsevier B.V. Open access under CC BY-NC-ND license. Selection and/or peer-review under responsibility of the Organising Committee of the ICOPEN 2011 conference Keywords: diffraction strain sensor, piezo rotation stage, characterization
1.
Introduction
Nano rotation stage is widely used as a miniature rotation platform with lasers and optical components such as mirrors and diffraction gratings, in the fields of optical scanning, imprinting and automated alignment. The high resolution of this device is helpful but it is at the expense of linearity. So the calibration is necessary before usage. In this paper we use Multipoint Diffraction Strain Sensor (MDSS), an improved optical diffraction strain sensor to characterize the performance of the piezo rotation stage. First the system setup and measuring principle of the optical diffraction strain sensor are introduced. Then the measurement results of rotation angles versus driving voltages are shown. A hysteresis phenomenon is observed when applying the driving voltage increasingly and then decreasingly. The measured results can be used for the calibration of this rotation stage. 2.
Multipoint Diffraction Strain Sensor
Multipoint Diffraction Strain Sensor (MDSS) is evolved based on ODSS[1-4], as shown in Fig 1. The measuring principle is the same as ODSS but it is able to acquire whole field strain information with high accuracy without the need for numerical differentiation. Two monochromatic collimated laser beams illuminate the grating attached on the specimen surface. And the first order diffracted beams are redirected perpendicularly to the grating
1875-3892 © 2011 Published by Elsevier B.V. Open access under CC BY-NC-ND license. Selection and/or peer-review under responsibility of the Organising Committee of the ICOPEN 2011 conference doi:10.1016/j.phpro.2011.06.144
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surface and sampled by the micro-lens array. The DOE-based lens array is displayed on the liquid crystal spatial light modulator (LC-SLM) to realize the same wavefront sampling functionality as the traditional micro-lens array. One of the advantages is that the key parameters of the DOE lens array can be changed by software, thus the measure range and strain sensitivity are tuneable. The spot images of the diffracted beams through SLM are captured by the CCD camera. Centroids of spots are determined using a MATLAB® program. In-plane strain/rotation and out-of-plane tilt, which are proportional to the spots shifting is then calculated. Fig.1 demonstrates the schematic of MDSS system using SLM for wavefront sampling[5].
Fig 1ˊ Schematic of MDSS based on a moiré interferometer with a LC-SLM.
The relations of spots shifting and strain/rotation and tilt are given below[5, 6] (1) (2) , are the in-plane strain along x-direction and y-direction respectively. , are spot shift in x and y direction respectively, f is focal length of lens array, Į is illuminating angle of laser beam. In practical measurement the out-of-plane tilt may mix up with in-plane strain, since both of them can cause spot shifts. However, by the use of two symmetric beams from both left and right side, the spot shifts along the same direction when specimen tilts, while the spots move in the opposite directions when there is strain applied. So by subtracting the measured results from each beam, the in-plane strain can be calculated without influence by tilt. And by average of the results from each beam, out-of-plane tilt can be separated from strain: (3) (4) For the two beams incident in the plane parallel to the grating principal axis along the horizontal direction (U field), the in-plane rotation of the specimen can be calculated by Eq.(5): (5) Similarly, for the two beams incident in the plane parallel to the grating with the principal direction along the vertical direction(V filed), the in-plane rotation of the specimen can be calculated by Eq.(6): (6) From above equations, it is seen that the strain/rotation and tilt of specimen can be measured by MDSS without aliasing with each other. And the strain sensitivity is inversely proportional to the focal length of lens array. Thus the sensitivity of system can be enhanced by increasing the focal length.
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3.
Measurement and Processing Before measurement, the specimen is prepared with a high frequency (1200lines/mm) crossing grating on its surface and then attached to the rotary surface of the nano rotation stage. A DOE lens array with focal length of 120mm is used on the SLM, the DOE pattern is shown in Fig 2. A DC driving voltage from 0V to 50V in 5V step is applied to the rotation stage. The rotary axis of the stage is perpendicular to the laser beam direction so the rotation of stage is measured as out-of-plane tilt by MDSS.
Fig 2. DOE-based lens array pattern displayed on the SLM. For each step voltage applied, the spot images formed by the left diffracted beam and the right diffracted beam are captured separately. Centroid detection is a crucial part of the measurement. In our experiment, a centroid detection algorithm based on adaptive thresholding and windowing method is used[7]. Windowing is useful to eliminate or suppress noises such as higher order diffractions and background noise. Adaptive thresholding is necessary especially when the intensity of spots fluctuates in each subarea of the spots image. The spots image shown in Fig 3(a) is taken by the CCD camera after diffracted beam going through the DOEbased lens arrays. The lens array is composed by 11 x 8 micro lenses. However the grating sample on the stage is in the size of 1cm so only 9 subareas are sampled. Each sampled spot can be used to calculate the shift and thus the rotation angles. And their standard deviation can be treated as a reference of the measurement sensitivity. Images are captured when each step voltages are applied. Fig 3(b) demonstrates the centroid results with red marks for each spot and the effect of windowing is demonstrated by the yellow boxes. Fig 3(c) shows the spot shift between two successive spot images (the last line is left unmarked intendedly.). The spot shift data are used for the tilt calculation according to the equations (1)-(4).
(a) (b) (c) Fig 3. (a)the spot image captured by CCD; (b)visualized centroid results of single image; (c) visualized centroid results of images in successive rotation angles.
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4.
Results and Discussion The centroid information in the spot images are acquired by the program in Matlab® and spots shifts are calculated by simple subtraction of centroid data from successive spot images with the origin centroid data from the image recorded without voltage applied. Then spot shifts are translated into the rotation angle s of the stage according to the above equations, as shown in Fig 4. The red line indicates the rotation angle of the rotary surface of the stage when driving voltages are applied increasingly, while the blue line indicates the rotation angle when driving voltages are applied decreasingly. The hysteresis phenomenon is observed. Error bars at each point are the standard deviation of measured results from different sampling points, as shown in Fig 3(b), and it is generally used as a reference of the strain sensitivity in static measurements. In our experiment, DOE lens array with different focal length of 80mm, 120mm and 160mm are used for the tilt measurement and the results are in good agreement however there is not obvious change in the standard deviation as in theory. It is possibly due to so few numbers of data (9 points for each image) so that all the standard deviations are comparatively low and no obvious difference among them. This problem can be solved by design much denser lens array so more sample points can be captured then the standard deviation should vary for different focal length, i.e. different measuring sensitivity. Experiment results demonstrate the capability of strain and tilt measurement using MDSS with DOE lens array displayed on a LC-SLM. In theory, the strain sensitivity is tuneable by using DOE-based lens array with different focal lengths. The longer focal length in use, the better strain sensitivity can be achieved. And the strain measure range is also tuneable by alternating lenslet spacing since the measure range is supposed to be confined in half of lenslet spacing to avoid sampling aliasing. Rotation vs Voltage 4 3.5
Voltage rise Voltage fall
Rotation / arc min
3 2.5 2 1.5 1 0.5 0 0
10
20
30
Voltage / V
40
50
60
Fig 4. Plot of rotation angle vs. driving voltage applied. The MDSS system for strain and tilt measurement provides reliable results with tuneable sensitivity and measure range for various circumstance requirements. And the data processing is almost simultaneous due to its simplicity in the principle and equations. However the stability can still be improved, so it is possible to use for dynamic measurement with higher image quality for more accurate centroid detection. Acknowledgement We thank the Optics and Photonics Society of Singapore and the Nanyang Technological University for their support.
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