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Procedia Engineering

ProcediaProcedia Engineering 00 (2011) Engineering 29 000–000 (2012) 2737 – 2743 www.elsevier.com/locate/procedia

2012 International Workshop on Information and Electronics Engineering (IWIEE)

Image Based PZT Control Calibration for 3D Measurement Bing Luoa*, Jinsheng Liub b

a Wuyi University, 22 Dongcheng Village of Jiangmen, Guangdong 529020, China Aleader Vision Technology Co., Building F in Xinhua Industry Park of Dongguan, Guangdong 523128, China

Abstract Creep drift of piezoelectric actuators in solder paste 3D inspection was difficult to be accurate calibrated. Connected with actuated projecting grating, this paper proposed a new calibration method that a quarter-cycle sinusoidal grating was used for projection to substitute normal cycle grating and two phase-shift sinusoidal gray images were matched to calculate displacements. As calibration conditions including image capturing time delay were the same as in 3D measuring working, the creep drift and non-linear of PZT were all considered. Experimental results show that the PZT was delicate calibrated and 3D reconstructed accuracy was effectively improved.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Harbin University of Science and Technology Open access under CC BY-NC-ND license. Keywords: creep; piezoelectric actuator; calibration; machine vision; 3D measurement; surface mounted technology

1. Introduction In electronics manufacturing industry, surface mounted technology (SMT) has been widely used for PCB assembly. PCB SMT assembly line was shown in fig. 1. However, more than 80% electronic products faults were caused by solder paste deposit defects [1]. So solder paste inspection (SPI) after its deposition in SMT assembly line is important to improve products quality. SPI needs 3D measurement to inspect deposit solder paste volume. 3D SPI based on phase measuring profilometry (PMP) has completely surpassed traditional laser triangulation method in accuracy as well as in speed [2]. Four π/2 phase-shift sinusoidal grating projected images are needed for PMP based 3D SPI. Projected sinusoidal grating cycle here is about 200 μm, so phase-shift distance is about 50 μm. Piezoelectric

* Corresponding author. Tel.: +0-86-750-3299360; fax: +0-86-750-3358395. E-mail address: [email protected].

1877-7058 © 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. doi:10.1016/j.proeng.2012.01.382

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transducer (PZT) is fit for phase-shift grating moving actuator as its accurate voltage control and quick reflection characters [3][4].

Fig. 1. PCB SMT assembly line

However, nonlinear relation between PZT displacement and control voltage as well as creep drift characters of PZT influence its actuating accuracy [5]. Traditional method to solve this problem was calibrating PZT by micro displacement measurement instrument [6]. Many new approaches have been proposed to calibrate PZT nonlinear control voltage and creep drift after researchers working [7][8]. But these approaches were expensive and slow, and calibrated accuracy was not satisfied for 3D SPI application. This paper proposes a new PZT control calibration method based on image matching. The method is specially convenient and accurate for 3D SPI as projected sinusoidal grating and images acquisition are already available and accurate in 3D SPI system. The rest of this paper is organized as follows. In section 2, the system structure of 3D SPI based on PMP and its principle are described. In section 3, the characters of PZT actuator for SPI projecting grating phase-shift are analyzed. And in section 4, new calibration approach of PZT control is designed and described. In section 5, experimental results are presented. Finally in section 6, conclusions are drawn and several issues for future works are indicated. 2. System Structure of 3D SPI based on PMP PMP based 3D SPI system mainly consists of two parts: sinusoidal grating projection unit and image acquisition unit [4]. Fig. 2 illustrates the system structure.

Fig. 2. System structure of 3D SPI (a) designed structure; (b) actual 3D SPI system

In grating projection unit, a LED light source projects through a sinusoidal grating glass and a

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telecentric lens to image sinusoidal gray gratings on PCB deposited solder paste. The sinusoidal glass mounted on PZT and actuated moving by it. Fig. 3 illustrates the grating glass moving control.

Fig. 3. Sinusoidal grating glass moving control diagram

In image acquisition unit, a CCD or CMOS camera captures four images through a polarizer and a lens along with projection grating phase-shift four times [9]. And the modulated phase connected with its height of pixel (x, y ) is calculated by formula (1). ⎡ I 4 ( x, y ) − I 2 ( x, y ) ⎤ ⎥ ⎣ I 3 ( x, y ) − I 1 ( x, y ) ⎦

φ (x, y ) = arctan ⎢

(1)

Here I i (x, y ) is gray data of the pixel (x, y ) in the image captured after phase-shift i as formulae (2). ⎧ I1 (x, y ) = I b (x, y ) + I r (x, y ) ⋅ cos[φ (x, y )] ⎪ I (x, y ) = I (x, y ) + I (x, y ) ⋅ cos[φ (x, y ) + π / 2] ⎪ 2 b r ⎨ ( ) ( ) , = , + I x y I x y I b r (x, y ) ⋅ cos[φ ( x, y ) + π ] ⎪ 3 ⎪⎩ I 4 (x, y ) = I b (x, y ) + I r (x, y ) ⋅ cos[φ (x, y ) + 3π / 2]

(2)

Here, I b (x, y ) is the background gray independent with projection grating phase and I r (x, y ) is the projecting sinusoidal grating amplitude. The sinusoidal grating glass we used was manufactured by Applied Image Inc. in America and its sinusoidal cycle is 200 μm. The phase-shift of π / 2 every time needs quarter cycle displacement that is 50 μm length that is fit for being actuated by PZT. From formulae above we can see that 3D measurement accuracy is closely connected with phase-shift accuracy of projected sinusoidal grating, which is actuated by PZT [2]. 3. PZT Micro Moving Control for Sinusoidal Grating Piezoelectric transducer (PZT) actuator is based on piezoelectric effect that pressure on piezoelectric materials results voltage on the materials, and conversely direct current voltage applied on the materials leads to its displacement. This character makes PZT a quick and accurate micro displacement actuator, which is used for sinusoidal grating glass phase shifting in SPI system [10]. However the relation between control voltages applied on PZT with its displacements is nonlinear, and displacements under the same voltage but in different way with ascent voltage and descent voltage are different. The ascent curve and descent curve of this relation of PZT are shown on fig. 4 (a). Even though, PZT has good repeatable performance with this nonlinear relation. So accurate control voltage calibration at phase-shift displacement position is important for SPI 3D measurement [7][8]. Traditional calibration method is measuring control voltage for the positioning displacements which are 50 μm, 100 μm, 150 μm and 200 μm by micro displacement measurement instrument [11]. Unfortunately, another important character of PZT that is creep drift influences the accuracy of PZT

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calibration by this way [12].

Fig. 4. (a) Relation curves between voltage and displacement of PZT; (b) PZT creep drift curve at 50 μm ascent position

Creep drift of PZT is a smaller and slower change following an initial PZT motion produced by a step change in the applied voltage. Creep drift will even last over 15 minutes. Fig. 4 (b) shows a PZT creep drift curve after it moves to 50 μm under ascent voltage. Creep drift of a PZT is connected with time and applied voltage as formula (3) [12]. ⎛ t c(t ) = d t0 ⋅ ⎜⎜1 + γ ⋅ log t0 ⎝

⎞ ⎟⎟ ⎠

(3)

Here c(t ) is the creep drift position at time t, and d t0 is the motion length at t 0 time after ending of rise time of the voltage, where t 0 is usually set at 0.1 second. And γ is creep coefficient depending on the piezoelectric materials, structure and environmental conditions. As creep drift is changing with different control voltage even within the same time delay between PZT control for grating phase shift and image capturing, traditional PZT control voltage calibration cannot be accurate for micro displacement measurement instrument measuring time delay is different from actual image capturing. 4. PZT Calibration based on grating images In PZT actuator applied for SPI projecting sinusoidal grating phase-shift, captured images can reflect accuracy of phase shifting actuated by PZT. Fig. 5 (a) shows two captured white paper images projected by 200 μm cycle sinusoidal grating light with π / 2 phase-shift. Fig. 5 (b) illustrates gray of two rows pixels on the middle of the images. Because of inhomogeneous illumination and diversity reflection on the surface of the paper, gray data of a row of pixels in fig. 5 (b) is not ideal sinusoid. The two approximate sine cures with π / 2 phase-shift that is 50 μm displacement here are difficult to judge whether the phase is accurate. But substituted by a quarter cycle sinusoidal grating the projecting images with also 50 μm displacement will appear a simple mode. For a quarter cycle grating that sinusoid cycle is 50 μm, 50 μm displacement is equal to π / 2 phase-shift that phase-shift images should be coincided as shown in fig. 6 (b). In SPI 3D measurement application, the calibrated PZT positions are times of 50 μm, so we can design the PZT actuator for SPI

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Bing LuoLuo, andJinsheng JinshengLiu/ Liu /Procedia ProcediaEngineering Engineering00 29(2011) (2012)000–000 2737 – 2743 Bing

calibration method based on images matching with a quarter of normal working cycle sinusoidal grating projection.

Fig. 5. (a) Sinusoidal grating with

π /2

phase shift; (b) Gray data of pixels in the middle horizontal row on two images

With the new designing, the PZT actuator control calibration can be converted to an optimization problem as formula (4). ⎡ min ⎢d (U C ) = UC ⎢ ⎣

⎤

∑∑ (I1 (x, y ) − I 2 (x, y ))2 ⎥ x

y

(4)

⎥⎦

U C is the PZT actuator control voltage for sinusoidal grating phase-shift, I1 (x, y ) and I 2 (x, y ) are

gray of pixel (x, y ) on two images captured before and after a phase-shift. The purpose of PZT control calibration is to set right control voltage to position at 50 μm, 100 μm, 150 μm and 200 μm that all relative displacements are 50 μm. As a quarter of normal working cycle sinusoidal grating that is 50 μm is applied to substitute a 200 μm normal working cycle grating. 50 μm displacement which is π / 2 phase-shift for normal cycle grating means 2π phase-shift for the quarter normal working cycle grating. Two images captured before and after a 50 μm relative displacement would be completely matching. So, to minimize formula (4) by adjusting control voltage can get accurate control voltage data. 5. Experiments

As a comparison, traditional calibration method with a micro displacement measurement instrument and the proposed new approach were all taken for experiments. Calibrated control voltages are list on table 1. Table 1. Comparison of calibrated control voltages Calibration method \ Displacements

50 μm (V)

100 μm (V)

150 μm (V)

200 μm (V)

Traditional measurement method

28.14

53.07

80.08

111.77

Image based approach

28.21

54.25

81.81

113.51

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From table 1, we can see that there is a considerable difference for calibrated control voltages between two methods. Captured images under different calibrated control voltages are shown on fig. 6.

Fig. 6. (a) Gray data with

2π

phase shift traditional calibration; (b) Calibrated with a quarter cycle sinusoidal grating

From fig. 6, we can see that images captured before and after phase-shift match better for control voltages calibrated by proposed new approach. 5 times experiments of gray difference of the two images calculated by formula (4) are shown on table 2. Table 2. Comparison of phase-shift images matching difference (106 gray) under control voltages calibrated by different methods Calibration method \ Experiment

1

2

3

4

5

Average

Traditional measurement method

2.7455

2.4957

1.9384

2.7840

1.5621

2.3051

Image based approach

0.7734

0.8932

0.9723

0.9674

0.7522

0.8717

Table 2 also shows that images captured under proposed approach calibrated control voltages match better. That means control voltages calibrated by proposed approach is more accurate.

Fig. 7. (a) Part of solder paste images under a grating projecting; (b) 3D reconstructed result of solder paste in (a)

Bing LuoLuo, andJinsheng JinshengLiu/ Liu /Procedia ProcediaEngineering Engineering00 29(2011) (2012)000–000 2737 – 2743 Bing

With a normal cycle sinusoidal grating projection, a solder paste on PCB was 3D measured by the SPI system. One image of a part solder paste is shown on fig. 7 (a) and reconstructed result is shown on (b). 6. Conclusions

There are two important characters for PZT actuator in SPI 3D measurement: nonlinear relation between control voltage and displacement, creep drift. PZT control voltage calibration is necessary and difficult. Connected with SPI application, a quarter of normal working cycle sinusoidal grating is designed to project on white background to calibrate PZT based on image matching. Experimental results show that the proposed approach can calibrate PZT accurately and can be implemented easily. Acknowledgements

This paper was supported by National Education Dept & Guangdong province Enterprise & University Cooperation Project (2010B090400026), Science & Technology Planning Project of Jiangmen City Government (Jiang Cai Gong[2010]210). References [1] Z.Y. Du. Surface Mounted Technology for PCB Assembly. Beijing: Electronics Industry Press, 2009. [2] B. Luo, L.Y. Zhang. SMT solder paste deposit inspection based on 3D PMP and 2D image features fusion. Proc. of IEEE Int. Conf. on Wavelet Analysis and Pattern Recognition, 2010, p. 190–194. [3] Z.W. Li, Research on 3D measurement system designing and technology based on grating projecting. Doctor thesis of Huazhong University of Science and Technology, p. 10–64, June 2009. [4] B. Luo, G.Z. Kou. Image acquisition designing for SMT solder paste deposition 3D inspection. Proc. of Int. Conf. on Multimedia & Signal Processing, 2011, p. 256–260. [5] W. Fan, X.F. Yu. Study on PZT actuator creep characteristics. Chinese Journa1 of Scientific Instrumen. 2006, vol.27(11): p. 1383–1386. [6] Y.Y. Wang, X.Z. Zhao. Inverse control algorithm to compensate the hysteresis and creep effect of piezoceramic, Optics and Precision Engineering. 2006, vol. 14(6): p. 1032–1040. [7] A.N. Rybyanets, A.A. Rybyanets. Ceramic piezocomposites: Modeling, technology, and characterization. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control. 2011, vol. 58(9): p. 1757–1773. [8] L. Pardo, A. García, F.M. De Espinosa, K. Brebøl. Shear resonance mode decoupling to determine the characteristic matrix of piezoceramics for 3-D modeling. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control. 2011, vol. 58(3): p. 646–657. [9] C. Steger, M. Ulrish, C. Wiedemann. Machine Vision Algorithms and Applications. Weinheim: Wiley-VCH, 2007. [10] B. M. Badr, W.G. Ali. Identification and control for a single-axis PZT nanopositioner stage. Proc. of 4th Int. Conf. on Modeling, Simulation and Applied Optimization. 2011: p. 1–6. [11] R. Legarda-Saenz, T. Bothe, W.P. Juptner. Accurate procedure for the calibration of a structured light system. Optical Engineering. 2004, vol. 43(4): p. 464–471. [12] C.R. Bowen. Modeling and characterization of piezoelectrically actuated bistable composites. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control. 2011, vol. 58: p. 1737–1750.

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