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Precision nano-alignment system using machine vision with motion controlled by piezoelectric motor
Available online at www.sciencedirect.com
Mechatronics 18 (2008) 21–34
Precision nano-alignment system using machine vision with motion controlled by piezoelectric motor q W.M. Kuo 1, S.F. Chuang, C.Y. Nian 2, Y.S. Tarng
*
Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan, ROC Received 17 March 2006; accepted 31 July 2007
Abstract In this study, a novel automatic nano-alignment system using machine vision coupled with a piezoelectric motor for motion control was developed. The analytical algorithm of this vision-aided auto-alignment design makes use of inputs of real-time movement captured by CCD to obtain the corresponding output feedback. Through matrix transformation, the algorithm establishes the characteristic matrix of the system. With the feed-in position of the tool, the difference between the fiducial mark and the target position can be obtained by image processing. Alignment commands can then be fed to the two-axis piezoelectric motor to compensate for the positional difference. Both theoretical deductions and experimental trials have proved that the novel automatic vision-aided alignment system is robust and feasible for achieving precision to the nanometer scale. 2007 Elsevier Ltd. All rights reserved. Keywords: Nanometer; Auto-alignment; Piezoelectric motor; Characteristic matrix; Fiducial mark shape
1. Introduction Demand for lighter, thinner, smaller and more compact electronic devices at low manufacturing cost has rendered chips that can only detect energy flow inadequate. Chips are expected to perform integrated optical-electro-mechanical functions. Hence, micro-mechanical machining aims to incorporate various functions in the minute chips, thus enhancing its value and reducing production cost. In view of the minute dimensions of chips, the line width, line distance and hole radius must be minimized in order to meet the expectation of multi-function performance. Hence,
q This paper has not been published elsewhere nor has it been submitted for publication elsewhere. * Corresponding author. E-mail address: [email protected] (Y.S. Tarng). 1 Currently with Department of Mechanical Engineering, St. John’s University, Tamsui, Taipei 251, Taiwan, ROC. 2 Currently with Department of Automatic Engineering, Lan-Yang Institute of Technology, Toucheng, I-Lan 261, Taiwan, ROC.
0957-4158/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2007.07.010
nano-technology will be a preferred choice of technology for semi-conductor manufacturing and manual operations for repeated alignment process are bound to be replaced by automated systems for greater precision and higher efficiency. To manufacturers of electronic devices, productivity has a key role to play in the choice of technology adopted in the production. Nevertheless, quality in terms of high precision is also a prime concern. Besides semi-conductor manufacturing, the electronic industry is the other sector that incorporate machine vision in its production process, in particular the automatic alignment operation. With vision-aided automatic alignment technology, high-quality electronic devices with good precision can be produced efficiently, thus reducing the cost of production and enhancing the competitiveness of the industry. In the literature, there have been abundant studies on automatic alignment operation with image feedback. Considering 2D rigid body transformation with size changes, Lai and Fang [1] have proposed a hybrid image alignment system, known as the Fast Localization with Advanced
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Search Hierarchy (FLASH) algorithm for image comparison to detect deviations in pattern localization. Although the alignment system can achieve both accuracy and efficiency, little has been said on how to apply the difference obtained to the positioning system or how the deviation can be corrected to obtain precise alignment. Lin and Lue [2] have also developed an image system for fast positioning and accuracy inspection of ball grid array (BGA) type printed circuit boards (PCB). For the wafer dicing process, Kim et al. [3] derived a two-step automatic alignment algorithm from inspection data and geometric relations on machine coordinate for detecting deviations from standard positions. According to the calculated compensation values, movements are made to minimize errors in position and orientation, thus achieving precise alignment. An analytic algorithm is employed by Nian and Tarng [4] to calculate the relationship between the rotational center (original position) of the three-axis motion control mechanism and the relative coordinates obtained by two CCD cameras. With the Dx, Dy and Dh determined, the automatic motion control mechanism can make rotational and translational movements along the three axes (X, Y1 and Y2) to achieve fast, efficient and accurate alignment. A general model for automatic alignment in 2D space is developed by Kim et al. [5] under the assumption of precise positioning with visual inspection. The proposed formula had a simple matrix form with motions described by modified rigid body transformation and was applied to a semi-automatic dicing machine. Though experimental results show that the algorithm was valid, the derivation of the matrix form was time-consuming. To achieve alignment with greater efficiency and precision, Nian et al. [6] developed a new algorithm that makes uses of the correlation between the input signals and output feedback. Through matrix transformation, the algorithm establishes the characteristic matrix of the system function between input and output signals. Though rapid and accurate alignment can be achieved with the motion control mechanism, the precision remains at the micrometer scale. To overcome such drawback, this study attempts to couple the motion control mechanism with the piezoelectric motor. Piezoelectric motors have the advantages of high resolution, compact size, light weight, rapid response, high output, low power consumption as well as fast and accurate positioning capability. In particular, piezoelectric ceramic motors exhibit converse piezoelectric effect, making use of friction force for driving the compensation movements. This can avoid the backlash problem due to the use of traditional ball screw device. In view of their many advantageous features, piezoelectric motors have been widely applied to the positioning stage, and when coupled with robust autoalignment algorithm, they can achieve high speed, highprecision positioning, thus enhancing the performance and consistency of repeated auto-alignment at nanometer scale [7]. In actual practice, automated manufacturing process requires repeated positioning of the objects to be aligned.
However, there always exist some small but non-negligible discrepancies between the feed-in positions of the object and the target position. In this study, an automatic nanoalignment system is developed using machine vision inspection. Charge coupled device (CCD) cameras are employed to define the center of the fiducial mark in relation to the original coordinates, thus giving positional reference for motion control to achieve alignment. The auto-alignment algorithm used has its basis on system identification, which provides real-time reference commands. Information on the movement of the fiducial images captured by the CCD cameras serves as important feedback to the system. Through image processing and matrix transformation, the characteristic matrix for the system function between input and output signals can be established. With the matrix established when the object to be aligned falls within the field of view (FOV) of the CCD, positional variation between the fiducial mark and original coordinates can be calculated through matrix transformation. Then according to the difference obtained, the system can issue commands to the two-axis piezoelectric motor to make movements for compensating the above-mentioned difference, thus achieving quick and precise alignment. Extracting high-quality features from the image captured, precise centering of the fiducial marks and accurate calculation of their centers all play significant roles in enhancing alignment accuracy. Therefore, various imageprocessing techniques are applied. For example, binary morphology [8] is employed to extract better and more precise features of the captured image and the best fit circle [9] is utilized to ensure accurate location of the fiducial mark center. The rest of the paper is organized as follows. Section 2 describes the structure and driving principle of the piezoelectric motor. The control algorithm is presented in Section 3. The auto-alignment operations and algorithms involved are detailed in Section 4. Section 5 presents the application of image-processing techniques. Section 6 describes the experiment conducted to test the proposed design. A discussion on the alignments results obtained is included in Section 7. Finally, Section 8 contains the conclusion. 2. Structure and driving principle of piezoelectric motor Piezoelectric materials exhibit two basic phenomena, namely direct and converse piezoelectric effects, permitting them to be used as sensors and motors in a control system [10]. Direct piezoelectric effect refers to the induction of electric charge or voltage in the piezoelectric material when mechanical force or pressure is applied on it. On the other hand, converse piezoelectric effect describes the generation of mechanical force and strain in the piezoelectric material when electrical charge or voltage is imposed on it. In recent years, piezoelectric motors have been widely used in precision positioning applications due to the requirements of high resolution in displacement. Among the many piezoelectric
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Y Stage carriage
X
Ceramic driving plate
Finger tip
A
A
B
B'
A'
B
Tuning inductor
t
Y
A
B
Longitudinal mode
Support spring
Piezoelectric ceramic
t
X
Preload spring Fig. 1. Structure of the piezoelectric ceramic motor.
Bending mode
materials, ceramic is the most popular. Hence, piezoelectric motors are essentially ceramic capacitors that change shape when charged and discharged. They have the advantages of fast mechanical response times without wear or deterioration after repeated operations, no heat generation under constant charge and voltage as well as nanometer precision of component positioning. Fig. 1 displays the structure of the HR4 piezoelectric ceramic motor (produced by Nanomotion Ltd.) employed in this study. As can be seen, it comprises two sets of piezoelectric ceramic, each with four pieces. Four electrodes, denoted as A, A 0 , B and B 0 , are bounded to the front face to form a checkerboard pattern of rectangles, and each electrode substantially covers one-quarter of the surface area. Diagonally located electrodes, A and A 0 , B and B 0 , are electrically connected by wires. On the other hand, the rear face is fully covered with a single electrode, which is grounded via the tuning inductor that can change the resonant frequency. To generate movements in different directions, the electrodes are energized by an AC voltage in the pairs of diagonal electrodes.
e
iag
Y
arr
c age
St
g
n ovi
n
Fig. 2. Changes in shape of piezoelectric materials.
The movement of the motor is constrained by four support strings with large stiffness along the long edges. A relatively hard finger tip is cemented to the center of a short edge of the piezoelectric ceramic. Across at the center of the other short edge is the preload spring designed to supply pressure between the finger tip and the ceramic driving plate, thus generating friction force on the contact surface between the two. The friction force will then transmit the motion of the finger tip to the ceramic driving plate and actuate its motion for alignment purpose. As mentioned above, piezoelectric ceramic motors change shape when charged and discharged. Under the converse piezoelectric effect, the piezoelectric ceramic material will become charged in face of a mechanical force or strain. As a result, the piezoelectric ceramic material assumes a bending mode along the X-axis and a longitudinal mode along the Y-axis, as shown in Fig. 2. When excited by ultrasonic vibration force, the finger tip begins rotating. Driven by mechanical friction effect, piezoelectric
X
tio
ec dir
Ceramic driving plate
Ceramic driving plate
M
Stage base
Mounting base Piezoelectric ceramic motor Traveling wave of finger tip
Fig. 3. Driving principle of the piezoelectric motor.
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W.M. Kuo et al. / Mechatronics 18 (2008) 21–34 Y axis piezoelectric ceramic motor
Sta
Mo
vin
ge
Linear scale
gd
car
ria
ire
cti
ge
on
Y
Mounting base
X
Stage base
Ceramic driving plate
X axis piezoelectric ceramic motor
Base plate
Fig. 4. Configuration of the two-axis piezoelectric motor stage.
motors function like electromagnetic motors. Fig. 3 shows the driving principle of the piezoelectric ceramic motor. The traveling wave of the finger tip is a combination of both the bending and longitudinal modes along the X-axis and Y-axis, respectively. Friction force drives the translational movement of the ceramic driving plate, thus achieving motion control for alignment purpose. The whole setup of the two-axis piezoelectric ceramic motor stage employed in this study is shown in Fig. 4. 3. Control algorithm The linear piezoelectric ceramic motor (LPCM) in this study has merits of high precision, compact size, lightweight, great torque, quick response and absence of electromagnetic interference [11]. However, they also have drawbacks of serious hysteresis behavior and highly nonlinear property, which are difficult to overcome using conventional control strategy [12]. Therefore, a rule-based control algorithm is employed to resolve the nonlinear and random problems of the LPCM in this study and described as follows. 3.1. Characteristic experiments on voltage vs. velocity To investigate the characteristics of driving voltage, 0.3, 0.7 and 1.0 V are selected respectively to actuate the LPCM of the X-axis continuously for 50 times, with step mode, switching the voltage on (Ton = 10 ms) and off (Toff = 20 ms) as shown in Fig. 5. Fig. 6 displays the velocity
responses to the different driving voltages. As can be seen, there exists great variation in the 50 velocity responses to each driving voltage. They seem to be irregular and random and it is difficult to determine the precise velocity and position at any chosen time when voltages of 0.3, 0.7 and 1.0 V are used to actuate the LPCM. The best we can do is to find the probable driving range for each voltage [13]. When the LPCM moves closer to the target position, the driving voltage and relative driving range are both reduced gradually. If the driving range can be less than 0.08 lm, the LPCM can then be enabled to reach precisely the target position. In this study, a statistical method is adopted to obtain the probable driving range of each voltage employed. The most widely used model for the distribution of a random variable is undoubtedly normal distribution or Gaussian distribution. Two numbers are often employed to summarize a normal distribution for a random variable x: the mean (l) defined in Eq. (1) can locate the center of a normal distribution, and the standard deviation (r), which is expressed in Eq. (2), can determine the distributive width. Substituting l and r into Eq. (3) yields the Normal Probability Distribution Functions, which represents the probability of occurrence at x. Eq. (4) denotes the cumulative probability in the interval between x1 and x2. n 1X Xi n i¼1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n 1 X 2 ðXi lÞ r¼ n 1 i¼1
l¼
ðxlÞ2 1 f ðxÞ ¼ pffiffiffiffiffiffi e 2r2 2pr Z x2 f ðxÞ dx pðxÞ ¼
ð1Þ ð2Þ ð3Þ ð4Þ
x1
From standard normal distribution tables, we can find that the cumulative probability values between l 1.96r and l + 1.96r are approximately 95%. The most popular uncertainty estimate is that for the 95% confidence; and hence, the ranges of a sample between l 1.96r and l + 1.96r are usually regarded as the probable ranges of occurrence [14]. In this study, the 200 velocity records of 1.0 V can be converted into a Relative Frequency Distribu-
Fig. 5. Block diagram of characteristic experiment on voltage vs. velocity.
W.M. Kuo et al. / Mechatronics 18 (2008) 21–34
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Fig. 6. Velocity responses to driving voltages of 0.3, 0.7 and 1.0 V.
Fig. 7. 200 velocity statistics of 1.0-V driving voltage.
tion Histogram and normal distribution as shown in Fig. 7. As can be seen, the velocity ranges of 1.0 V fall between
9.98 lm/s (l 1.96r) and 70.2 lm/s (l + 1.96r) at a 95% confidence.
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The above-mentioned statistical method is also employed to define the probable corresponding driving displacements of the X- and Y-axes within a driving time of 30 ms for eight different driving voltages as listed in Table 1. 3.2. Establishment of rule-base This study develops a rule-based controller. The control area of each driving voltage on the two axes is shown in Fig. 8, and E denotes the position error (E = target position–current position). In the initial positioning control, the position error is large; and a higher driving voltage is needed for fast movement of the LPCM. When the LPCM approaches the target step by step, the driving voltage
should be reduced gradually to avoid bigger overshoot. The main control rule is listed as follows: (a) In X-axis: If E < Px1, then Vout = 1.0 V. If Pxi 6 E < Pxi+1, then Vout = Vxi(i = 1 7). IF E P Px8, then Vout = 1.0 V. E = Target position–current position in X-axis, Vout: driving voltage. (b) In Y-axis: If E < Py1, then Vout = 1.0 V. If Pyi 6 E < Pyi+1, then Vout = Vyi (i = 1 7). If E P Py8, then Vout = 1.0 V. E = Target position–current position in Y-axis, Vout: driving voltage.
Table 1 Displacement statistics of X- and Y-axes for 8 driving voltages unit: lm per driving time (30 ms) X-axis Voltage Mean (l) SD (r) M + 1.96r M 1.96r
1.0 V 1.424 0.38 0.679 2.169
0.7 V 0.208 0.094 0.024 0.392
0.4 V 0.157 0.05 0.058 0.256
0.3 V 0.055 0.025 0.006 0.104
0.3 V 0.041 0.02 0.081 0.001
0.4 V 0.134 0.051 0.235 0.034
0.7 V 0.249 0.09 0.425 0.074
1.0 V 1.212 0.48 2.153 0.271
Y-axis Voltage Mean(l) SD(r) M + 1.96r M 1.96r
1.0 V 1.4 0.48 0.459 2.341
0.8 V 0.226 0.105 0.02 0.433
0.5 V 0.13 0.062 0.008 0.251
0.35 V 0.055 0.022 0.012 0.098
0.35 V 0.042 0.016 0.074 0.01
0.5 V 0.113 0.045 0.201 0.025
0.8 V 0.473 0.125 0.718 0.228
1.0 V 1.567 0.419 2.388 0.746
Fig. 8. Control area of X- and Y-axes.
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Table 2 Rule-based table for X- and Y-axes X-axis Px1 0.68 lm Vx1 0.7 V
Px2 0.31 lm Vx2 0.4 V
Px3 0.11 lm Vx3 0.3 V
Px4 0.02 lm Vx4 0V
Px5 0.02 lm Vx5 0.3 V
Px6 0.08 lm Vx6 0.4 V
Px7 0.28 lm Vx7 0.7 V
Px8 0.64 lm Vx8 1.0 V
Y-axis Py1 0.75 lm Vy1 0.8 V
Py2 0.34 lm Vy2 0.5 V
Py3 0.09 lm Vy3 0.35 V
Py4 0.02 lm Vy4 0V
Py5 0.02 lm Vy5 0.35 V
Py6 0.08 lm Vy6 0.5 V
Py7 0.26 lm Vy7 0.8 V
Py8 0.76 lm Vy8 1.0 V
Fig. 9. Block diagram of positioning procedure.
4. Auto-alignment algorithm Using system identification techniques and the correlation between the input and real-time output, the proposed algorithm establishes the characteristic matrix of the system function. The information thus obtained will enable the two-axis piezoelectric motor stage discussed in Section
X axis of CCD
Original position of CCD Target position P1
X
Y
Fig. 9 is the block diagram of positioning procedure. Pt and Pc denote the target position and current position, respectively; and E, which is the position error, ¼ P t P c as mentioned above. The positioning procedure involves first obtaining Pt by linear scale. Subtracting Pc from Pt yields E, which is fed to the Controller. From the rule-based table, a suitable driving voltage is obtained for the Driver to be transformed into high sine-wave voltage of 39.6 kHz so as to drive the LPCM. The procedure is repeated until jEj 6 20 nm. In addition, an uncertain friction force applied on the LPCM may stop its movement even though the driving voltage continues to be fed to the Driver. To prevent such from happening, the Controller automatically provides the proper ‘‘compensating voltage’’ to the smallest driving voltage, including ±0.3 V of the X-axis and ±0.35 V of the Y-axis as shown in Fig. 9.
Y axis of CCD
3.3. Positioning procedure
2 to perform alignment operation. The algorithms involved in the alignment process are as follows. As seen in Fig. 10, P1 is the target position of CCD1. The target position is transferred from the standard template. The images of the object captured by the CCD camera are recorded in the system as target positions to be aligned. The image of P1 does not exist on the object. For ease of system identification, they are marked with crosses as reference for checking the alignment accuracy. On the other hand, P2 shows the location of the fiducial mark center extracted by the CCD, which provide positional references. Therefore, in essence, the alignment operation involves matching location P2 with target position P1. In addition, the target vector for the CCD is [X1
Y axis
The above-mentioned Pxi, Pyi, Vxi and Vyi are listed in Table 2.
P2 Fiducial mark X axis
Original position of mechanism Fig. 10. Definition of the target vector.
W.M. Kuo et al. / Mechatronics 18 (2008) 21–34
T
1
T
Z ¼ ðA AÞ A B
ð6Þ
Note that solutions to Eq. (6) are general solutions which can be applicable even when the vectors A and Z are in different dimensions. Using the correlation between the inputs signals and output feedback, the characteristic matrix issues reference commands for movements along the x and y directions to compensate for the positional difference. The changes in fiducial marks after the translational movements will be recorded and analyzed by the CCD as follows: 2 3 2 3 x1 y 1 X1 6 . 6 . 7 a .. 7 6 . 7 6 7 ð7Þ . 5 b ¼ 4 .. 5 4 . Xm xm y m 2 3 x1 y 1 6 .. 7 are given inputs for constructing a matrix where 4 ... . 5 xm y m a denoted by C and m P 2. is the subvector of the charb X1 acteristic matrix denoted by M, and is the X subvecX2 tor of the target vector B and denoted by D. Hence, Eq. (7) can be rewritten as CM = D and characteristic matrix [a b]T can be obtained from M = (CTC)1CTD. Similarly, characteristic matrix [c d]T can be obtained as follows: 2 3 2 3 x1 y 1 Y1 6 . 6 . 7 c .. 7 6 . 7 6 7 ð8Þ . 5 d ¼ 4 .. 5 4 . Ym xm y m Thus, Eq. (8) can be rewritten as EN = F and characteristic 1 T matrix [c d]T can be obtained from N = (ETE) E F. a b With knowledge of the characteristic matrix Z ¼ , c d T the target vector B = [X Y] obtained from the relative coordinates of the fiducial marks and target position can be substituted into Eq. (5) to get the bias vector
X axis of CCD
Original position of CCD Target position P1
Fiducial mark P2
Y axis of CCD
Y1]T. Because P1 5 P2, there exists positional differences Dx and Dy between them. The characteristic matrix can be obtained by the following equation: a b x X ¼ ð5Þ c d y Y a b where is the characteristic matrix denoted by A, c d x X is the bias vector denoted by Z, and is the target y Y vector denoted by B. Therefore, Eq. (5) can be written as AZ = B. Since the target vector and characteristic matrix can be obtained from relative coordinates of the CCD cameras, the bias vector Z can be obtained by the following equation:
Y axis
28
X axis Original position of mechanism Fig. 11. Schema of algorithm after correction.
Z = (AT A)1 AT B. Finally, Z = [x y]T is transformed into actual commands for the two-axis piezoelectric motor to perform compensation for Dx and Dy. The fiducial mark will then be exactly matched with the target position, thus achieving precise alignment, as shown in Fig. 11. 5. Image-processing techniques The fiducial marks extracted from the digital image captured by the CCD provide reference coordinates for shape matching. Alignment accuracy of these reference coordinates would affect the precision of the whole alignment system. To ensure accurate matching, we employ the library of various image-processing algorithms of Vision Builder 7.0 (from National Instruments Corporation, NI) to define the exact center of the fiducial marks. In this study, the mask serves as the object to be aligned. To facilitate repeated alignment required in the initial manufacturing stage of semi-conductors, in particular the lithography process, and to enhance the accuracy of shape matching, fiducial marks of the mask are marked with symbols, such as circle or cross. The following steps describe the image-processing techniques employed to determine the center of the fiducial mark, indicated by circles on the mask. Step 1: Raw image capture Use the CCD cameras to capture image as the raw image, as shown in Fig. 12a. Step 2: Lookup Table (LUT) processing Perform LUT transformations to improve the contrast and brightness of an image by modifying the dynamic intensity of region with poor contrast. The LUT contains corresponding value between the pixel of the image and its gray-level value. Take an 8-bit image for example. To enhance the image, each gray-level value input is transformed into a new value by a transfer function, which has an intended effect on the brightness and contrast of the image, as shown in Fig. 12b.
W.M. Kuo et al. / Mechatronics 18 (2008) 21–34
29
Fig. 12. Image-processing techniques: (a) raw image, (b) LUT processing, (c) binary image processing, (d) image inverse processing, (e) morphology and (f) best fit circle.
Step 3: Thresholding Segment the raw digital image using binary clustering according to the threshold selected. The purpose of thresholding is to extract the image of the object from the background for further processing. Image points with gray-level values exceeding the threshold will be called object points, which are denoted by 1; while those with gray-level values below the threshold will be called background points, which are denoted by 0. Fig. 12c shows the binary image after thresholding. Step 4: Image inversion Inverse the image. Inversed images appear like the negatives of photos. They are also called negative images, in which the bright areas are turned dim, and vice versa. The sensitivity of human eyes may easily get saturated when viewing bright areas, thus hampering the distinction of fine details. Hence, inversing the image and turning the bright areas into dark ones, as shown in Fig. 12d, can facilitate the recognition of minute differences.
Step 5: Binary morphology Segment the image to find regions that represent the objects or meaningful parts of the objects. Morphological filtering simplifies a segmented image to facilitate the search for objects of interest through smoothing out edges or profiles, filling small holes
Fig. 13. Center location obtained by best fit circle.
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W.M. Kuo et al. / Mechatronics 18 (2008) 21–34
and eliminating small projection, as shown in Fig. 12e. Step 6: Best fit circle Use the spoke two-dimensional edge detection function to locate the center of the fiducial mark and estimate the diameter of the corresponding fiducial circle, as shown in Fig. 12f. Fig. 13 shows how the coordinates of the fiducial mark center can be obtained by best fit circle. Using the following equation, we can locate the initial center and estimate the radius of the fiducial circle: ðx cx Þ2 þ ðy cy Þ2 ¼ R2
ð9Þ
Substituting all the coordinates detected (xi, yi) into Eq. (9) yields
2 P
x2i
6P 4 xi y i P xi
P
xi y i P 2 y P i yi
32
3
3 P x2i ðx2i þ y 2i Þ P 76 7 6 P 2 2 7 y i 54 B 5 ¼ 4 y i ðxi þ y 2i Þ 5 P 2 P D ðxi þ y 2i Þ 1 P
xi
A
2
ð12Þ Solving Eq. (12) yields coefficients of A, B, D. With these obtained and using the best fit circle, weffi can obtain the pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2
2
4D radius of the best circle as R ¼ A þB and the center 2 coordinates of the best circle as ðx0 ; y 0 Þ ¼ ½ A2 ; B2 . With the image-processing techniques detailed above, we can obtain accurate reference coordinates of the fiducial mark center for precise alignment of objects.
6. Experimental design and procedure 6.1. Experimental setup
ðxi cx Þ2 þ ðy i cy Þ2 ¼ r2i ¼ x2i þ y 2i þ Axi þ By i þ C
ð10Þ
The target function can be expressed as follows: S¼
n X
d2 ¼
i¼1
¼
n X
n X
ðr2i R2 Þ
2
i¼1
ðx2i
þ
y 2i
þ Axi þ By i þ DÞ
2
ð11Þ
i¼1
To minimize the deviation, partial differential of target oS functions of A,B,D is taken. Assuming oA ¼ 0, @S ¼ 0 and oB oS ¼ 0, we obtain the following: oD
To enhance the precision of alignment, the whole experimental setup was positioned on a granite stage. As shown in Fig. 14, the experimental setup consists of a machine vision system for image extraction, a CCD camera mounted on an adjustable frame, a two-axis (X and Y) Table 3 Electrical specifications and performance of piezoelectric ceramic motor Maximum voltage Maximum current consumption Maximum power consumption Maximum allowable velocity Dynamic stall force Static holding force Normal preload in stage
Fig. 14. Experiment setup.
270 [Vrms], 39.6 [kHz], sine wave 0.32 [Arms] 15 [W] 250 [mm/s] 15–18 [N] 14 [N] 72 [N]
W.M. Kuo et al. / Mechatronics 18 (2008) 21–34
linear table consisting of two HR4 piezoelectric ceramic motors, two LIE5 linear scales with 20-nm resolution, the independent X-axis table with 150-mm travel, and the Yaxis table with 100-mm travel, the Y-axis table is located above the X-axis table. The piezoelectric motors can be used for motion control and automatic alignment.
The machine vision system for image extraction is made up of a green LED annular light source with a focus of 50 mm, a CCD (XC-ST50, from Sony) of 1/2 in size, having 768 · 494 effective pixels and incorporated with a frame grabber (IMAQ PCI-1409, from NI). The light projected onto the object is captured through the lens by the sensors
Start Yes
Mechanism parameters ? No
Enter new parameters
Go home No
Calibration ? Yes Put mask on carry plate
Adjust CCD position
Calibration Go home
No
Characteristic matrix search ? Yes Characteristic matrix search
Enter target coordinates
Go home
Put new un -aligned mask
No
Auto-alignment ? Yes Auto- alignment
Put new un -aligned mask
Finish ? Yes End program ?
31
No
Yes End Fig. 15. Flowchart of image alignment procedures.
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W.M. Kuo et al. / Mechatronics 18 (2008) 21–34
of the CCD, which is then translated into electrical signals according to its intensity. These electrical signals sent to the frame grabber serve as basic image information. The analogy signals are finally converted into a digital image and transferred to CPU. The CCD camera is mounted on an adjustable shaft fixed to the granite stage equipped with the two-axis piezoelectric motor. The vision system is clamped securely to the shaft while the CCD can be moved steadily along the lateral and vertical directions. Movement along the z-axis can adjust the focus of the image. The main function of the motion control mechanism is to perform the compensation for positional difference as calculated by the analysis software. Through the motion control card (PCI-7344, from NI), the commands are transmitted to the two-axis alignment module. The piezoelectric ceramic motor, which functions like the INCHWORM piezoelectric stepping motor, execute the commands given and transfer the fiducial mark to the target position precisely and complete the alignment operation. Table 3 displays the electrical specifications and performance of the piezoelectric ceramic motor. In this study, the object to be aligned is the mask produced by lithography electroforming micro-molding (LIGA). A hole of 30-lm diameter is drilled on the surface of the mask for positioning. Using the high magnification vision system combined with a 5· extension ring and a 12· magnifying glass, the resolution of its image captured by the CCD is 30 nm/pixel. The software system for image processing is developed on Windows XP using a P-IV 2.4 GHz PC. Its analytic tools include Labview 7 and Vision Builder 7.0. Its main tasks involve processing the image captured, searching and analyzing the corresponding coordinates, calculating the difference in position between the image and the target, and finally, issuing commands to the two-axis piezoelectric motor stage to make adjustments for the alignment operations.
search and (4) automatic alignment. Before starting the operation, users have to decide whether the parameters need to be adjusted. Then the mechanism will return to its initial state and the calibration process begins. As for the alignment process, an object, mask in this study, is placed on the carry plate, then the position of the CCD camera needs to be adjusted manually so that all the fiducial marks will fall in its FOV. After the adjustment, the calibration process is again performed, followed by the search for the characteristic matrix between the input and output signals. The characteristic matrix thus obtained will be saved and the target position is then recorded. Finally, the new object to be matched is placed on the carry plate, and the alignment operations are executed automatically. The alignment operations were performed hundreds of times to test the feasibility of the proposed design.
6.2. Experimental procedure
Case
Fig. 15 displays the flowchart of the experimental procedures involved in the image alignment analysis. The whole alignment process can be divided into four steps: (1) parameter setting, (2) calibration, (3) characteristic matrix
Case I
7. Results and discussion This study has successfully developed a robust automatic vision-aided alignment system. Two sets of experimental results (Cases I and II) are described below for illustration. Fig. 16a shows the fiducial circle extracted from the object image captured by the CCD of Case I. The intersection of the cross indicates the target position. Table 4 shows the characteristic matrix obtained for Cases I and II. According to the image data, the difference in position between the fiducial center and the target position along the X-axis and Y-axis are Dx = 0.200 lm and Dy = 0.211 lm, respectively. Fig. 16b displays the results after the positional difference is compensated for and Table 5 shows the positional error after correction. As can be seen, after compensation, the center of the fiducial circle is closer to the target position and the discrepancies in posiTable 4 Characteristic matrix of Cases I and II
Case II
Result Characteristic matrix 3:50084 0:00076 0:10049 3:60154 3:50077 0:00034 0:10008 3:40009
Fig. 16. Alignment results of Case I: (a) position captured by CCD before alignment and (b) position captured by CCD after alignment.
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33
Table 5 Positional errors after auto-alignment of Cases I and II Error
Case
X Y
Case I
Case II
0.008 lm 0.004 lm
0.006 lm 0.004 lm
tion along the two axes become Dx = 0.008 lm and Dy = 0.004 lm, respectively. Fig. 17a shows the fiducial circle extracted from the object image captured by the CCD of Case II. Again, the intersection of the cross indicates the target position. The characteristic matrix obtained for Case II is also shown in Table 4. According to the image data, the difference in position between the fiducial center and the target position along the X-axis and Y-axis are Dx = 0.305 lm and Dy = 0.202 lm, respectively. Fig. 17b displays the results after the positional difference are compensated for and Table 5 shows the positional error after correction. As can be seen, after compensation, the center of the fiducial circle is closer to the target position and the discrepancies in position along the two axes become Dx = 0.006 lm and Dy = 0.002 lm, respectively. The alignment operations were performed repeatedly over hundreds of times to demonstrate the efficiency and stability of the proposed mechanism. Fig. 18 shows the positions of fiducial center before and after alignment. As can be seen, regardless of the locations of the fiducial center, the alignment process can efficiently move it to the target position. Such precision evidences both the feasibility and reliability of the proposed vision-aided auto-alignment system. 8. Conclusion In this study, a novel automatic nano-alignment system using machine vision coupled with a piezoelectric motor for motion control was developed. The alignment operation makes use of the correlation between the input and output signals. The CCD camera extracted fiducial marks from the images. These image data are employed to establish the characteristic matrix through matrix transformation. With the feed-in position of the tool, the difference in fiducial
Fig. 18. Positional errors of fiducial mark center before and after alignment.
mark as well as positional variation can be obtained by image processing. Alignment commands can then be fed to the two-axis piezoelectric motor to compensate for the difference in position. With the positional variation corrected, exact alignment can be achieved. Precise positioning of the reference coordinates from the extracted fiducial marks has a great impact on the accuracy of the whole alignment system. Therefore, to ensure good alignment results, various image-processing techniques are employed to determine the fiducial circle center. The alignment process in this study incorporates machine vision for extracting image features, a two-axis piezoelectric motor stage for motion control, and software analysis for coordinate determination. This integrated optical-electro-mechanical design has proved to be robust, achieving a precision range within ±20 nm. In addition, the automatic system can perform the alignment task more accurately and efficiently than labor-intensive manual operations. Adopting this design not only can increase the productivity of the manufacturing process, but can also reduce cost, thus enhancing the competitiveness of the industry. Both theoretical deductions and experimental trials have proved that the novel automatic vision-aided alignment system is robust and feasible with potential for industrial applications.
Fig. 17. Alignment results of Case II: (a) position captured by CCD before alignment and (b) position captured by CCD after alignment.
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References [1] Lai SH, Fang M. A hybrid image alignment system for fast and precise pattern localization. Real-Time Imag 2002;8:23–33. [2] Lin CS, Lue LW. An image system for fast positioning and accuracy inspection of ball grid array boards. Microelectron Reliab 2001;41: 119–28. [3] Kim HT, Song CS, Yang HJ. 2-Step algorithm for automatic alignment in wafer dicing process. Microelectron Reliab 2004;44: 1165–79. [4] Nian CY, Tarng YS. An auto-alignment vision system with three-axis motion control mechanism. Int J Advan Manufact Technol 2005;26: 1121–31. [5] Kim HT, Song CS, Yang HJ. Matrix form of automatic alignment algorithm in 2D space. In: Proceedings of the IEEE international conference on mechatronics, ICM’04; 2004. p. 465–9. [6] Nian CY, Chuang SF, Tarng YS. A new algorithm for a three-axis auto-alignment system using vision inspection. J Mater Process Technol 2005;171:319–29.
[7] Henderson D, Ragona S. Nanometer precision robot for active photonics alignment using INCHWORM motors. In: Proceedings of SPIE – the international society for optical engineering, vol 4290; 2001. p. 136–44. [8] Gonzales RC, Woods RE. Digital image processing. 2nd ed. New Jersey: Prentice Hall Publishing Company Inc.; 2002. [9] National Instrument, Vision Builder Version: 7.1.1; 2005. [10] Nanomotion Ltd., HR4 Ultrasonic motor user manual; 2005. [11] Lin W, Ann NK, Ng LE. Concepts for a class of novel piezoelectric self-locking long-stroke actuators. Precision Eng 2002;26(2): 141–54. [12] Liu YT, Fung RF, Wang CC. Precision position control using combined piezo-VCM actuators. Precision Eng 2005;29:411–22. [13] Douglas CM, George CR. Applied statistics and probability for engineers. New York: John Wiley & Sons; 2002. [14] Thomas GB, Roy DM, John HL. Mechanical measurements. 5th ed. Addison-Wesley; 1995.
Mechatronics 18 (2008) 21–34
Precision nano-alignment system using machine vision with motion controlled by piezoelectric motor q W.M. Kuo 1, S.F. Chuang, C.Y. Nian 2, Y.S. Tarng
*
Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan, ROC Received 17 March 2006; accepted 31 July 2007
Abstract In this study, a novel automatic nano-alignment system using machine vision coupled with a piezoelectric motor for motion control was developed. The analytical algorithm of this vision-aided auto-alignment design makes use of inputs of real-time movement captured by CCD to obtain the corresponding output feedback. Through matrix transformation, the algorithm establishes the characteristic matrix of the system. With the feed-in position of the tool, the difference between the fiducial mark and the target position can be obtained by image processing. Alignment commands can then be fed to the two-axis piezoelectric motor to compensate for the positional difference. Both theoretical deductions and experimental trials have proved that the novel automatic vision-aided alignment system is robust and feasible for achieving precision to the nanometer scale. 2007 Elsevier Ltd. All rights reserved. Keywords: Nanometer; Auto-alignment; Piezoelectric motor; Characteristic matrix; Fiducial mark shape
1. Introduction Demand for lighter, thinner, smaller and more compact electronic devices at low manufacturing cost has rendered chips that can only detect energy flow inadequate. Chips are expected to perform integrated optical-electro-mechanical functions. Hence, micro-mechanical machining aims to incorporate various functions in the minute chips, thus enhancing its value and reducing production cost. In view of the minute dimensions of chips, the line width, line distance and hole radius must be minimized in order to meet the expectation of multi-function performance. Hence,
q This paper has not been published elsewhere nor has it been submitted for publication elsewhere. * Corresponding author. E-mail address: [email protected] (Y.S. Tarng). 1 Currently with Department of Mechanical Engineering, St. John’s University, Tamsui, Taipei 251, Taiwan, ROC. 2 Currently with Department of Automatic Engineering, Lan-Yang Institute of Technology, Toucheng, I-Lan 261, Taiwan, ROC.
0957-4158/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2007.07.010
nano-technology will be a preferred choice of technology for semi-conductor manufacturing and manual operations for repeated alignment process are bound to be replaced by automated systems for greater precision and higher efficiency. To manufacturers of electronic devices, productivity has a key role to play in the choice of technology adopted in the production. Nevertheless, quality in terms of high precision is also a prime concern. Besides semi-conductor manufacturing, the electronic industry is the other sector that incorporate machine vision in its production process, in particular the automatic alignment operation. With vision-aided automatic alignment technology, high-quality electronic devices with good precision can be produced efficiently, thus reducing the cost of production and enhancing the competitiveness of the industry. In the literature, there have been abundant studies on automatic alignment operation with image feedback. Considering 2D rigid body transformation with size changes, Lai and Fang [1] have proposed a hybrid image alignment system, known as the Fast Localization with Advanced
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W.M. Kuo et al. / Mechatronics 18 (2008) 21–34
Search Hierarchy (FLASH) algorithm for image comparison to detect deviations in pattern localization. Although the alignment system can achieve both accuracy and efficiency, little has been said on how to apply the difference obtained to the positioning system or how the deviation can be corrected to obtain precise alignment. Lin and Lue [2] have also developed an image system for fast positioning and accuracy inspection of ball grid array (BGA) type printed circuit boards (PCB). For the wafer dicing process, Kim et al. [3] derived a two-step automatic alignment algorithm from inspection data and geometric relations on machine coordinate for detecting deviations from standard positions. According to the calculated compensation values, movements are made to minimize errors in position and orientation, thus achieving precise alignment. An analytic algorithm is employed by Nian and Tarng [4] to calculate the relationship between the rotational center (original position) of the three-axis motion control mechanism and the relative coordinates obtained by two CCD cameras. With the Dx, Dy and Dh determined, the automatic motion control mechanism can make rotational and translational movements along the three axes (X, Y1 and Y2) to achieve fast, efficient and accurate alignment. A general model for automatic alignment in 2D space is developed by Kim et al. [5] under the assumption of precise positioning with visual inspection. The proposed formula had a simple matrix form with motions described by modified rigid body transformation and was applied to a semi-automatic dicing machine. Though experimental results show that the algorithm was valid, the derivation of the matrix form was time-consuming. To achieve alignment with greater efficiency and precision, Nian et al. [6] developed a new algorithm that makes uses of the correlation between the input signals and output feedback. Through matrix transformation, the algorithm establishes the characteristic matrix of the system function between input and output signals. Though rapid and accurate alignment can be achieved with the motion control mechanism, the precision remains at the micrometer scale. To overcome such drawback, this study attempts to couple the motion control mechanism with the piezoelectric motor. Piezoelectric motors have the advantages of high resolution, compact size, light weight, rapid response, high output, low power consumption as well as fast and accurate positioning capability. In particular, piezoelectric ceramic motors exhibit converse piezoelectric effect, making use of friction force for driving the compensation movements. This can avoid the backlash problem due to the use of traditional ball screw device. In view of their many advantageous features, piezoelectric motors have been widely applied to the positioning stage, and when coupled with robust autoalignment algorithm, they can achieve high speed, highprecision positioning, thus enhancing the performance and consistency of repeated auto-alignment at nanometer scale [7]. In actual practice, automated manufacturing process requires repeated positioning of the objects to be aligned.
However, there always exist some small but non-negligible discrepancies between the feed-in positions of the object and the target position. In this study, an automatic nanoalignment system is developed using machine vision inspection. Charge coupled device (CCD) cameras are employed to define the center of the fiducial mark in relation to the original coordinates, thus giving positional reference for motion control to achieve alignment. The auto-alignment algorithm used has its basis on system identification, which provides real-time reference commands. Information on the movement of the fiducial images captured by the CCD cameras serves as important feedback to the system. Through image processing and matrix transformation, the characteristic matrix for the system function between input and output signals can be established. With the matrix established when the object to be aligned falls within the field of view (FOV) of the CCD, positional variation between the fiducial mark and original coordinates can be calculated through matrix transformation. Then according to the difference obtained, the system can issue commands to the two-axis piezoelectric motor to make movements for compensating the above-mentioned difference, thus achieving quick and precise alignment. Extracting high-quality features from the image captured, precise centering of the fiducial marks and accurate calculation of their centers all play significant roles in enhancing alignment accuracy. Therefore, various imageprocessing techniques are applied. For example, binary morphology [8] is employed to extract better and more precise features of the captured image and the best fit circle [9] is utilized to ensure accurate location of the fiducial mark center. The rest of the paper is organized as follows. Section 2 describes the structure and driving principle of the piezoelectric motor. The control algorithm is presented in Section 3. The auto-alignment operations and algorithms involved are detailed in Section 4. Section 5 presents the application of image-processing techniques. Section 6 describes the experiment conducted to test the proposed design. A discussion on the alignments results obtained is included in Section 7. Finally, Section 8 contains the conclusion. 2. Structure and driving principle of piezoelectric motor Piezoelectric materials exhibit two basic phenomena, namely direct and converse piezoelectric effects, permitting them to be used as sensors and motors in a control system [10]. Direct piezoelectric effect refers to the induction of electric charge or voltage in the piezoelectric material when mechanical force or pressure is applied on it. On the other hand, converse piezoelectric effect describes the generation of mechanical force and strain in the piezoelectric material when electrical charge or voltage is imposed on it. In recent years, piezoelectric motors have been widely used in precision positioning applications due to the requirements of high resolution in displacement. Among the many piezoelectric
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23
Y Stage carriage
X
Ceramic driving plate
Finger tip
A
A
B
B'
A'
B
Tuning inductor
t
Y
A
B
Longitudinal mode
Support spring
Piezoelectric ceramic
t
X
Preload spring Fig. 1. Structure of the piezoelectric ceramic motor.
Bending mode
materials, ceramic is the most popular. Hence, piezoelectric motors are essentially ceramic capacitors that change shape when charged and discharged. They have the advantages of fast mechanical response times without wear or deterioration after repeated operations, no heat generation under constant charge and voltage as well as nanometer precision of component positioning. Fig. 1 displays the structure of the HR4 piezoelectric ceramic motor (produced by Nanomotion Ltd.) employed in this study. As can be seen, it comprises two sets of piezoelectric ceramic, each with four pieces. Four electrodes, denoted as A, A 0 , B and B 0 , are bounded to the front face to form a checkerboard pattern of rectangles, and each electrode substantially covers one-quarter of the surface area. Diagonally located electrodes, A and A 0 , B and B 0 , are electrically connected by wires. On the other hand, the rear face is fully covered with a single electrode, which is grounded via the tuning inductor that can change the resonant frequency. To generate movements in different directions, the electrodes are energized by an AC voltage in the pairs of diagonal electrodes.
e
iag
Y
arr
c age
St
g
n ovi
n
Fig. 2. Changes in shape of piezoelectric materials.
The movement of the motor is constrained by four support strings with large stiffness along the long edges. A relatively hard finger tip is cemented to the center of a short edge of the piezoelectric ceramic. Across at the center of the other short edge is the preload spring designed to supply pressure between the finger tip and the ceramic driving plate, thus generating friction force on the contact surface between the two. The friction force will then transmit the motion of the finger tip to the ceramic driving plate and actuate its motion for alignment purpose. As mentioned above, piezoelectric ceramic motors change shape when charged and discharged. Under the converse piezoelectric effect, the piezoelectric ceramic material will become charged in face of a mechanical force or strain. As a result, the piezoelectric ceramic material assumes a bending mode along the X-axis and a longitudinal mode along the Y-axis, as shown in Fig. 2. When excited by ultrasonic vibration force, the finger tip begins rotating. Driven by mechanical friction effect, piezoelectric
X
tio
ec dir
Ceramic driving plate
Ceramic driving plate
M
Stage base
Mounting base Piezoelectric ceramic motor Traveling wave of finger tip
Fig. 3. Driving principle of the piezoelectric motor.
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W.M. Kuo et al. / Mechatronics 18 (2008) 21–34 Y axis piezoelectric ceramic motor
Sta
Mo
vin
ge
Linear scale
gd
car
ria
ire
cti
ge
on
Y
Mounting base
X
Stage base
Ceramic driving plate
X axis piezoelectric ceramic motor
Base plate
Fig. 4. Configuration of the two-axis piezoelectric motor stage.
motors function like electromagnetic motors. Fig. 3 shows the driving principle of the piezoelectric ceramic motor. The traveling wave of the finger tip is a combination of both the bending and longitudinal modes along the X-axis and Y-axis, respectively. Friction force drives the translational movement of the ceramic driving plate, thus achieving motion control for alignment purpose. The whole setup of the two-axis piezoelectric ceramic motor stage employed in this study is shown in Fig. 4. 3. Control algorithm The linear piezoelectric ceramic motor (LPCM) in this study has merits of high precision, compact size, lightweight, great torque, quick response and absence of electromagnetic interference [11]. However, they also have drawbacks of serious hysteresis behavior and highly nonlinear property, which are difficult to overcome using conventional control strategy [12]. Therefore, a rule-based control algorithm is employed to resolve the nonlinear and random problems of the LPCM in this study and described as follows. 3.1. Characteristic experiments on voltage vs. velocity To investigate the characteristics of driving voltage, 0.3, 0.7 and 1.0 V are selected respectively to actuate the LPCM of the X-axis continuously for 50 times, with step mode, switching the voltage on (Ton = 10 ms) and off (Toff = 20 ms) as shown in Fig. 5. Fig. 6 displays the velocity
responses to the different driving voltages. As can be seen, there exists great variation in the 50 velocity responses to each driving voltage. They seem to be irregular and random and it is difficult to determine the precise velocity and position at any chosen time when voltages of 0.3, 0.7 and 1.0 V are used to actuate the LPCM. The best we can do is to find the probable driving range for each voltage [13]. When the LPCM moves closer to the target position, the driving voltage and relative driving range are both reduced gradually. If the driving range can be less than 0.08 lm, the LPCM can then be enabled to reach precisely the target position. In this study, a statistical method is adopted to obtain the probable driving range of each voltage employed. The most widely used model for the distribution of a random variable is undoubtedly normal distribution or Gaussian distribution. Two numbers are often employed to summarize a normal distribution for a random variable x: the mean (l) defined in Eq. (1) can locate the center of a normal distribution, and the standard deviation (r), which is expressed in Eq. (2), can determine the distributive width. Substituting l and r into Eq. (3) yields the Normal Probability Distribution Functions, which represents the probability of occurrence at x. Eq. (4) denotes the cumulative probability in the interval between x1 and x2. n 1X Xi n i¼1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n 1 X 2 ðXi lÞ r¼ n 1 i¼1
l¼
ðxlÞ2 1 f ðxÞ ¼ pffiffiffiffiffiffi e 2r2 2pr Z x2 f ðxÞ dx pðxÞ ¼
ð1Þ ð2Þ ð3Þ ð4Þ
x1
From standard normal distribution tables, we can find that the cumulative probability values between l 1.96r and l + 1.96r are approximately 95%. The most popular uncertainty estimate is that for the 95% confidence; and hence, the ranges of a sample between l 1.96r and l + 1.96r are usually regarded as the probable ranges of occurrence [14]. In this study, the 200 velocity records of 1.0 V can be converted into a Relative Frequency Distribu-
Fig. 5. Block diagram of characteristic experiment on voltage vs. velocity.
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25
Fig. 6. Velocity responses to driving voltages of 0.3, 0.7 and 1.0 V.
Fig. 7. 200 velocity statistics of 1.0-V driving voltage.
tion Histogram and normal distribution as shown in Fig. 7. As can be seen, the velocity ranges of 1.0 V fall between
9.98 lm/s (l 1.96r) and 70.2 lm/s (l + 1.96r) at a 95% confidence.
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The above-mentioned statistical method is also employed to define the probable corresponding driving displacements of the X- and Y-axes within a driving time of 30 ms for eight different driving voltages as listed in Table 1. 3.2. Establishment of rule-base This study develops a rule-based controller. The control area of each driving voltage on the two axes is shown in Fig. 8, and E denotes the position error (E = target position–current position). In the initial positioning control, the position error is large; and a higher driving voltage is needed for fast movement of the LPCM. When the LPCM approaches the target step by step, the driving voltage
should be reduced gradually to avoid bigger overshoot. The main control rule is listed as follows: (a) In X-axis: If E < Px1, then Vout = 1.0 V. If Pxi 6 E < Pxi+1, then Vout = Vxi(i = 1 7). IF E P Px8, then Vout = 1.0 V. E = Target position–current position in X-axis, Vout: driving voltage. (b) In Y-axis: If E < Py1, then Vout = 1.0 V. If Pyi 6 E < Pyi+1, then Vout = Vyi (i = 1 7). If E P Py8, then Vout = 1.0 V. E = Target position–current position in Y-axis, Vout: driving voltage.
Table 1 Displacement statistics of X- and Y-axes for 8 driving voltages unit: lm per driving time (30 ms) X-axis Voltage Mean (l) SD (r) M + 1.96r M 1.96r
1.0 V 1.424 0.38 0.679 2.169
0.7 V 0.208 0.094 0.024 0.392
0.4 V 0.157 0.05 0.058 0.256
0.3 V 0.055 0.025 0.006 0.104
0.3 V 0.041 0.02 0.081 0.001
0.4 V 0.134 0.051 0.235 0.034
0.7 V 0.249 0.09 0.425 0.074
1.0 V 1.212 0.48 2.153 0.271
Y-axis Voltage Mean(l) SD(r) M + 1.96r M 1.96r
1.0 V 1.4 0.48 0.459 2.341
0.8 V 0.226 0.105 0.02 0.433
0.5 V 0.13 0.062 0.008 0.251
0.35 V 0.055 0.022 0.012 0.098
0.35 V 0.042 0.016 0.074 0.01
0.5 V 0.113 0.045 0.201 0.025
0.8 V 0.473 0.125 0.718 0.228
1.0 V 1.567 0.419 2.388 0.746
Fig. 8. Control area of X- and Y-axes.
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27
Table 2 Rule-based table for X- and Y-axes X-axis Px1 0.68 lm Vx1 0.7 V
Px2 0.31 lm Vx2 0.4 V
Px3 0.11 lm Vx3 0.3 V
Px4 0.02 lm Vx4 0V
Px5 0.02 lm Vx5 0.3 V
Px6 0.08 lm Vx6 0.4 V
Px7 0.28 lm Vx7 0.7 V
Px8 0.64 lm Vx8 1.0 V
Y-axis Py1 0.75 lm Vy1 0.8 V
Py2 0.34 lm Vy2 0.5 V
Py3 0.09 lm Vy3 0.35 V
Py4 0.02 lm Vy4 0V
Py5 0.02 lm Vy5 0.35 V
Py6 0.08 lm Vy6 0.5 V
Py7 0.26 lm Vy7 0.8 V
Py8 0.76 lm Vy8 1.0 V
Fig. 9. Block diagram of positioning procedure.
4. Auto-alignment algorithm Using system identification techniques and the correlation between the input and real-time output, the proposed algorithm establishes the characteristic matrix of the system function. The information thus obtained will enable the two-axis piezoelectric motor stage discussed in Section
X axis of CCD
Original position of CCD Target position P1
X
Y
Fig. 9 is the block diagram of positioning procedure. Pt and Pc denote the target position and current position, respectively; and E, which is the position error, ¼ P t P c as mentioned above. The positioning procedure involves first obtaining Pt by linear scale. Subtracting Pc from Pt yields E, which is fed to the Controller. From the rule-based table, a suitable driving voltage is obtained for the Driver to be transformed into high sine-wave voltage of 39.6 kHz so as to drive the LPCM. The procedure is repeated until jEj 6 20 nm. In addition, an uncertain friction force applied on the LPCM may stop its movement even though the driving voltage continues to be fed to the Driver. To prevent such from happening, the Controller automatically provides the proper ‘‘compensating voltage’’ to the smallest driving voltage, including ±0.3 V of the X-axis and ±0.35 V of the Y-axis as shown in Fig. 9.
Y axis of CCD
3.3. Positioning procedure
2 to perform alignment operation. The algorithms involved in the alignment process are as follows. As seen in Fig. 10, P1 is the target position of CCD1. The target position is transferred from the standard template. The images of the object captured by the CCD camera are recorded in the system as target positions to be aligned. The image of P1 does not exist on the object. For ease of system identification, they are marked with crosses as reference for checking the alignment accuracy. On the other hand, P2 shows the location of the fiducial mark center extracted by the CCD, which provide positional references. Therefore, in essence, the alignment operation involves matching location P2 with target position P1. In addition, the target vector for the CCD is [X1
Y axis
The above-mentioned Pxi, Pyi, Vxi and Vyi are listed in Table 2.
P2 Fiducial mark X axis
Original position of mechanism Fig. 10. Definition of the target vector.
W.M. Kuo et al. / Mechatronics 18 (2008) 21–34
T
1
T
Z ¼ ðA AÞ A B
ð6Þ
Note that solutions to Eq. (6) are general solutions which can be applicable even when the vectors A and Z are in different dimensions. Using the correlation between the inputs signals and output feedback, the characteristic matrix issues reference commands for movements along the x and y directions to compensate for the positional difference. The changes in fiducial marks after the translational movements will be recorded and analyzed by the CCD as follows: 2 3 2 3 x1 y 1 X1 6 . 6 . 7 a .. 7 6 . 7 6 7 ð7Þ . 5 b ¼ 4 .. 5 4 . Xm xm y m 2 3 x1 y 1 6 .. 7 are given inputs for constructing a matrix where 4 ... . 5 xm y m a denoted by C and m P 2. is the subvector of the charb X1 acteristic matrix denoted by M, and is the X subvecX2 tor of the target vector B and denoted by D. Hence, Eq. (7) can be rewritten as CM = D and characteristic matrix [a b]T can be obtained from M = (CTC)1CTD. Similarly, characteristic matrix [c d]T can be obtained as follows: 2 3 2 3 x1 y 1 Y1 6 . 6 . 7 c .. 7 6 . 7 6 7 ð8Þ . 5 d ¼ 4 .. 5 4 . Ym xm y m Thus, Eq. (8) can be rewritten as EN = F and characteristic 1 T matrix [c d]T can be obtained from N = (ETE) E F. a b With knowledge of the characteristic matrix Z ¼ , c d T the target vector B = [X Y] obtained from the relative coordinates of the fiducial marks and target position can be substituted into Eq. (5) to get the bias vector
X axis of CCD
Original position of CCD Target position P1
Fiducial mark P2
Y axis of CCD
Y1]T. Because P1 5 P2, there exists positional differences Dx and Dy between them. The characteristic matrix can be obtained by the following equation: a b x X ¼ ð5Þ c d y Y a b where is the characteristic matrix denoted by A, c d x X is the bias vector denoted by Z, and is the target y Y vector denoted by B. Therefore, Eq. (5) can be written as AZ = B. Since the target vector and characteristic matrix can be obtained from relative coordinates of the CCD cameras, the bias vector Z can be obtained by the following equation:
Y axis
28
X axis Original position of mechanism Fig. 11. Schema of algorithm after correction.
Z = (AT A)1 AT B. Finally, Z = [x y]T is transformed into actual commands for the two-axis piezoelectric motor to perform compensation for Dx and Dy. The fiducial mark will then be exactly matched with the target position, thus achieving precise alignment, as shown in Fig. 11. 5. Image-processing techniques The fiducial marks extracted from the digital image captured by the CCD provide reference coordinates for shape matching. Alignment accuracy of these reference coordinates would affect the precision of the whole alignment system. To ensure accurate matching, we employ the library of various image-processing algorithms of Vision Builder 7.0 (from National Instruments Corporation, NI) to define the exact center of the fiducial marks. In this study, the mask serves as the object to be aligned. To facilitate repeated alignment required in the initial manufacturing stage of semi-conductors, in particular the lithography process, and to enhance the accuracy of shape matching, fiducial marks of the mask are marked with symbols, such as circle or cross. The following steps describe the image-processing techniques employed to determine the center of the fiducial mark, indicated by circles on the mask. Step 1: Raw image capture Use the CCD cameras to capture image as the raw image, as shown in Fig. 12a. Step 2: Lookup Table (LUT) processing Perform LUT transformations to improve the contrast and brightness of an image by modifying the dynamic intensity of region with poor contrast. The LUT contains corresponding value between the pixel of the image and its gray-level value. Take an 8-bit image for example. To enhance the image, each gray-level value input is transformed into a new value by a transfer function, which has an intended effect on the brightness and contrast of the image, as shown in Fig. 12b.
W.M. Kuo et al. / Mechatronics 18 (2008) 21–34
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Fig. 12. Image-processing techniques: (a) raw image, (b) LUT processing, (c) binary image processing, (d) image inverse processing, (e) morphology and (f) best fit circle.
Step 3: Thresholding Segment the raw digital image using binary clustering according to the threshold selected. The purpose of thresholding is to extract the image of the object from the background for further processing. Image points with gray-level values exceeding the threshold will be called object points, which are denoted by 1; while those with gray-level values below the threshold will be called background points, which are denoted by 0. Fig. 12c shows the binary image after thresholding. Step 4: Image inversion Inverse the image. Inversed images appear like the negatives of photos. They are also called negative images, in which the bright areas are turned dim, and vice versa. The sensitivity of human eyes may easily get saturated when viewing bright areas, thus hampering the distinction of fine details. Hence, inversing the image and turning the bright areas into dark ones, as shown in Fig. 12d, can facilitate the recognition of minute differences.
Step 5: Binary morphology Segment the image to find regions that represent the objects or meaningful parts of the objects. Morphological filtering simplifies a segmented image to facilitate the search for objects of interest through smoothing out edges or profiles, filling small holes
Fig. 13. Center location obtained by best fit circle.
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and eliminating small projection, as shown in Fig. 12e. Step 6: Best fit circle Use the spoke two-dimensional edge detection function to locate the center of the fiducial mark and estimate the diameter of the corresponding fiducial circle, as shown in Fig. 12f. Fig. 13 shows how the coordinates of the fiducial mark center can be obtained by best fit circle. Using the following equation, we can locate the initial center and estimate the radius of the fiducial circle: ðx cx Þ2 þ ðy cy Þ2 ¼ R2
ð9Þ
Substituting all the coordinates detected (xi, yi) into Eq. (9) yields
2 P
x2i
6P 4 xi y i P xi
P
xi y i P 2 y P i yi
32
3
3 P x2i ðx2i þ y 2i Þ P 76 7 6 P 2 2 7 y i 54 B 5 ¼ 4 y i ðxi þ y 2i Þ 5 P 2 P D ðxi þ y 2i Þ 1 P
xi
A
2
ð12Þ Solving Eq. (12) yields coefficients of A, B, D. With these obtained and using the best fit circle, weffi can obtain the pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2
2
4D radius of the best circle as R ¼ A þB and the center 2 coordinates of the best circle as ðx0 ; y 0 Þ ¼ ½ A2 ; B2 . With the image-processing techniques detailed above, we can obtain accurate reference coordinates of the fiducial mark center for precise alignment of objects.
6. Experimental design and procedure 6.1. Experimental setup
ðxi cx Þ2 þ ðy i cy Þ2 ¼ r2i ¼ x2i þ y 2i þ Axi þ By i þ C
ð10Þ
The target function can be expressed as follows: S¼
n X
d2 ¼
i¼1
¼
n X
n X
ðr2i R2 Þ
2
i¼1
ðx2i
þ
y 2i
þ Axi þ By i þ DÞ
2
ð11Þ
i¼1
To minimize the deviation, partial differential of target oS functions of A,B,D is taken. Assuming oA ¼ 0, @S ¼ 0 and oB oS ¼ 0, we obtain the following: oD
To enhance the precision of alignment, the whole experimental setup was positioned on a granite stage. As shown in Fig. 14, the experimental setup consists of a machine vision system for image extraction, a CCD camera mounted on an adjustable frame, a two-axis (X and Y) Table 3 Electrical specifications and performance of piezoelectric ceramic motor Maximum voltage Maximum current consumption Maximum power consumption Maximum allowable velocity Dynamic stall force Static holding force Normal preload in stage
Fig. 14. Experiment setup.
270 [Vrms], 39.6 [kHz], sine wave 0.32 [Arms] 15 [W] 250 [mm/s] 15–18 [N] 14 [N] 72 [N]
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linear table consisting of two HR4 piezoelectric ceramic motors, two LIE5 linear scales with 20-nm resolution, the independent X-axis table with 150-mm travel, and the Yaxis table with 100-mm travel, the Y-axis table is located above the X-axis table. The piezoelectric motors can be used for motion control and automatic alignment.
The machine vision system for image extraction is made up of a green LED annular light source with a focus of 50 mm, a CCD (XC-ST50, from Sony) of 1/2 in size, having 768 · 494 effective pixels and incorporated with a frame grabber (IMAQ PCI-1409, from NI). The light projected onto the object is captured through the lens by the sensors
Start Yes
Mechanism parameters ? No
Enter new parameters
Go home No
Calibration ? Yes Put mask on carry plate
Adjust CCD position
Calibration Go home
No
Characteristic matrix search ? Yes Characteristic matrix search
Enter target coordinates
Go home
Put new un -aligned mask
No
Auto-alignment ? Yes Auto- alignment
Put new un -aligned mask
Finish ? Yes End program ?
31
No
Yes End Fig. 15. Flowchart of image alignment procedures.
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of the CCD, which is then translated into electrical signals according to its intensity. These electrical signals sent to the frame grabber serve as basic image information. The analogy signals are finally converted into a digital image and transferred to CPU. The CCD camera is mounted on an adjustable shaft fixed to the granite stage equipped with the two-axis piezoelectric motor. The vision system is clamped securely to the shaft while the CCD can be moved steadily along the lateral and vertical directions. Movement along the z-axis can adjust the focus of the image. The main function of the motion control mechanism is to perform the compensation for positional difference as calculated by the analysis software. Through the motion control card (PCI-7344, from NI), the commands are transmitted to the two-axis alignment module. The piezoelectric ceramic motor, which functions like the INCHWORM piezoelectric stepping motor, execute the commands given and transfer the fiducial mark to the target position precisely and complete the alignment operation. Table 3 displays the electrical specifications and performance of the piezoelectric ceramic motor. In this study, the object to be aligned is the mask produced by lithography electroforming micro-molding (LIGA). A hole of 30-lm diameter is drilled on the surface of the mask for positioning. Using the high magnification vision system combined with a 5· extension ring and a 12· magnifying glass, the resolution of its image captured by the CCD is 30 nm/pixel. The software system for image processing is developed on Windows XP using a P-IV 2.4 GHz PC. Its analytic tools include Labview 7 and Vision Builder 7.0. Its main tasks involve processing the image captured, searching and analyzing the corresponding coordinates, calculating the difference in position between the image and the target, and finally, issuing commands to the two-axis piezoelectric motor stage to make adjustments for the alignment operations.
search and (4) automatic alignment. Before starting the operation, users have to decide whether the parameters need to be adjusted. Then the mechanism will return to its initial state and the calibration process begins. As for the alignment process, an object, mask in this study, is placed on the carry plate, then the position of the CCD camera needs to be adjusted manually so that all the fiducial marks will fall in its FOV. After the adjustment, the calibration process is again performed, followed by the search for the characteristic matrix between the input and output signals. The characteristic matrix thus obtained will be saved and the target position is then recorded. Finally, the new object to be matched is placed on the carry plate, and the alignment operations are executed automatically. The alignment operations were performed hundreds of times to test the feasibility of the proposed design.
6.2. Experimental procedure
Case
Fig. 15 displays the flowchart of the experimental procedures involved in the image alignment analysis. The whole alignment process can be divided into four steps: (1) parameter setting, (2) calibration, (3) characteristic matrix
Case I
7. Results and discussion This study has successfully developed a robust automatic vision-aided alignment system. Two sets of experimental results (Cases I and II) are described below for illustration. Fig. 16a shows the fiducial circle extracted from the object image captured by the CCD of Case I. The intersection of the cross indicates the target position. Table 4 shows the characteristic matrix obtained for Cases I and II. According to the image data, the difference in position between the fiducial center and the target position along the X-axis and Y-axis are Dx = 0.200 lm and Dy = 0.211 lm, respectively. Fig. 16b displays the results after the positional difference is compensated for and Table 5 shows the positional error after correction. As can be seen, after compensation, the center of the fiducial circle is closer to the target position and the discrepancies in posiTable 4 Characteristic matrix of Cases I and II
Case II
Result Characteristic matrix 3:50084 0:00076 0:10049 3:60154 3:50077 0:00034 0:10008 3:40009
Fig. 16. Alignment results of Case I: (a) position captured by CCD before alignment and (b) position captured by CCD after alignment.
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Table 5 Positional errors after auto-alignment of Cases I and II Error
Case
X Y
Case I
Case II
0.008 lm 0.004 lm
0.006 lm 0.004 lm
tion along the two axes become Dx = 0.008 lm and Dy = 0.004 lm, respectively. Fig. 17a shows the fiducial circle extracted from the object image captured by the CCD of Case II. Again, the intersection of the cross indicates the target position. The characteristic matrix obtained for Case II is also shown in Table 4. According to the image data, the difference in position between the fiducial center and the target position along the X-axis and Y-axis are Dx = 0.305 lm and Dy = 0.202 lm, respectively. Fig. 17b displays the results after the positional difference are compensated for and Table 5 shows the positional error after correction. As can be seen, after compensation, the center of the fiducial circle is closer to the target position and the discrepancies in position along the two axes become Dx = 0.006 lm and Dy = 0.002 lm, respectively. The alignment operations were performed repeatedly over hundreds of times to demonstrate the efficiency and stability of the proposed mechanism. Fig. 18 shows the positions of fiducial center before and after alignment. As can be seen, regardless of the locations of the fiducial center, the alignment process can efficiently move it to the target position. Such precision evidences both the feasibility and reliability of the proposed vision-aided auto-alignment system. 8. Conclusion In this study, a novel automatic nano-alignment system using machine vision coupled with a piezoelectric motor for motion control was developed. The alignment operation makes use of the correlation between the input and output signals. The CCD camera extracted fiducial marks from the images. These image data are employed to establish the characteristic matrix through matrix transformation. With the feed-in position of the tool, the difference in fiducial
Fig. 18. Positional errors of fiducial mark center before and after alignment.
mark as well as positional variation can be obtained by image processing. Alignment commands can then be fed to the two-axis piezoelectric motor to compensate for the difference in position. With the positional variation corrected, exact alignment can be achieved. Precise positioning of the reference coordinates from the extracted fiducial marks has a great impact on the accuracy of the whole alignment system. Therefore, to ensure good alignment results, various image-processing techniques are employed to determine the fiducial circle center. The alignment process in this study incorporates machine vision for extracting image features, a two-axis piezoelectric motor stage for motion control, and software analysis for coordinate determination. This integrated optical-electro-mechanical design has proved to be robust, achieving a precision range within ±20 nm. In addition, the automatic system can perform the alignment task more accurately and efficiently than labor-intensive manual operations. Adopting this design not only can increase the productivity of the manufacturing process, but can also reduce cost, thus enhancing the competitiveness of the industry. Both theoretical deductions and experimental trials have proved that the novel automatic vision-aided alignment system is robust and feasible with potential for industrial applications.
Fig. 17. Alignment results of Case II: (a) position captured by CCD before alignment and (b) position captured by CCD after alignment.
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