Design and Control of Phase-Detection Mode Atomic Force Microscopy for Cells Precision Contour Reconstruction under Different Environments

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1 2013 American Control Conference (ACC) Washington, DC, USA, June 17-19, 2013 Design and Control of Phase-Detection Mode Atomic Force Microscopy for Cells Precision Contour Reconstruction under Different Environments Jim-Wei Wu, Jyun-Jhih Chen, Kuan-Chia Huang, Chih-Lieh Chen, Yi-Ting Lin, Mei-Yung Chen, and Li-Chen Fu, Fellow, IEEE Abstract Atomic force microscope (AFM) is equipped with height recognition with nano and sub-nano meter scale, and it can accurately build three-dimensional (3D) imaging of samples with micro-structure. In this paper, we propose a homemade phase-detection mode atomic force microscopy (PM-AFM). In measuring system, here we use a compact CD/DVD pick-up-head to measure the cantilever deflection. In scanning system, we use piezoelectric stages as the planar scanner. For the sake of accurately obtaining the contour of tender cells, first we design an MIMO adaptive double integral sliding mode controller (ADISMC) in xy-plane to increase the positioning accuracy and provide precision cell size. Second, in z-axis we design an adaptive complementary sliding-mode controller (ACSMC) to improve the scanning accuracy and to overcome the inconvenience for user with traditional proportional-integration controller. Besides, we use phase feedback signal, which features with higher sensitivity and faster response. Finally, the extensive experimental results are used to validate the performance of the proposed controller, quantify the scanning image quality of standard grating and reconstruct cells topography. Index Terms Atomic force microscopy, phase-detection mode, CD/DVD PUH, adaptive complementary sliding mode control, adaptive double integral sliding mode control I. INTRODUCTION TOMIC force microscopy (AFM) was invented in A1986 [1]. The capability of AFM particularly noteworthy is that it can provide high resolution 3D topographic images of sample surface. Based on such capability, AFM becomes a powerful instrument of cell biology. Conventionally, we use optical microscope (OM) to observe cell condition. However, the image resolution of OM is restricted to micron meter scale due to the diffraction limitation, and the sample s height features can only be judged by the shades of color from the OM image due to lacking real height information. These disadvantages would cause wrong judgment to some important application such as early diagnosis and observation of tumor cell, which requires high credibility. Therefore, AFM is adopted to provide cell information such as surface area, size and height This work was supported by the National Science Council, R.O.C. under Grant NSC E MY3. J. W. Wu, J. J. Chen, K. C. Huang, C. L. Chen, Y. T. Lin, and L. C. Fu are with the Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan ( lichen@ntu.edu.tw). to enhance the credibility. AFM can be classified into two categories, first one is static mode and second one is dynamic mode [2]. Compared with static AFM, dynamic AFM can provide more information about the tip-sample interactions, e.g., frequency, phase, and it can also reduce damage on sample from tip-sample force. In this mode, there are three kinds of detection methods, which are referred to as amplitude detection, phase detection and frequency detection (AM-, PM- and FM-AFM). We take the summary of these three methods from the literatures [2, 3], and we find PM-AFM can have higher image resolution, speed and lower cost. These advantages have encouraged us to utilizing phase detection method in our homemade AFM system. In 2000, Morita [4] introduced the phase-detection technique to obtain a vertical and a lateral resolutions of 1 and 100 image resolution of Si (111). In 2004, Nishi in Japan adopted the concept of phase detection method of AFM, and applied on scanning mica and graphite in octamethylcyclotetrasiloxane (OMCTS) [5]. In 2006, Fukuma [3] showed that PM-AFM can reach atomic-scale capability, and theoretically proved PM-AFM is more sutible for high speed scanning than other modes. Due to the powerful advantages of phase-detection technique, there are various applications on the basis of PM-AFM. In 2008, Van used PM-AFM to scan monocrystalline [6] and polymer surface was investigated by Li in 2010 [7]. In 2011, Lee rebuilt highly oriented pyrolytic graphite (HOPG) topography [8]. From the paper survey we can find that PM-AFM has been gradually used to investigate sample surface in recent years, but it still has not been applied on cell scanning. In this paper, we propose a homemade PM-AFM system, which design is detailed in Section II. The analytical models and dynamic formulations of scanners, which are derived as basis for subsequent controller design, are presented in Section III. Furthermore, to overcome the external noises, and model uncertainties of piezoelectric actuated stages, two advanced controllers, named MIMO adaptive double integral sliding mode controller (ADISMC) in xy-plane and adaptive complementary sliding mode controller (ACSMC) in z-axis are developed in Section IV. The detailed experimental results are presented in Section V, validating the scanning ability of our homemade PM-AFM system. Finally, the summarization of this paper would be arranged as conclusion in Section VI /$ AACC 5488

2 II. SYSTEM DESIGN Fig. 1. Schematic drawing of the AFM system. The overall AFM system scheme is shown in Fig. 1. The system is mainly divided into two parts: the measuring system and the scanning system. The main function of the measuring system is detecting the tip-sample interaction from probe behavior (deflection, amplitude, phase, frequency, etc.). Additionally, in order to keep tip-sample distance fixed, we need to control the z-axis scanning stage. Besides we have a xy-plane scanner with strain gauge sensor to move the sample. These two stages form the scanning system. The whole PM-AFM system will be detailed in the following sections. A. AFM Measuring System From Fig. 1, the measuring system consists of two parts, 1) probe excitation, and 2) cantilever dynamic detection: 1) Probe excitation The probe used in AFM consists of a cantilever and a tip. The selection of probe is decided by the sample type and operation mode of AFM. In this work, the probe we choose is NANOSENSORS PointProbe NCHR, which is suitable for tapping mode AFM. From the sweep-sin identification test, the resonant frequency of the probe is about 294 khz. Here, we would use function generator based on direct digital synthesized (DDS) technology to provide stable sinusoidal energy (so called CE mode) to a bimorph attached to probe, and thus providing stable scanning environments. When the energy arouses the bimorph, which is composed of piezoelectric material, the probe is oscillated simultaneously. In practical implementation, the probe will be located on a magnetic circle mount, and the bimorph is attached to the mount. 2) Cantilever dynamic detection In this PM-AFM system, we will make use of the CD/DVD pickup system to measure the cantilever deflection for the compact system design. The setup of the probe position should be located on the focus of pickup head. B. AFM Scanning System Two commercial piezoelectric positioners, Piezosystem Jena PXY 38 SG T , which has the motion range of 38 m in x,y axes with strain gauge to measure the actual motion, and PZ 38 T , which has the motion range of 38 m in z-axis, are located at the central part and the topmost part of the scanning system. III. MODELING AND FORMULATION A. Dynamics Formulation of xy-plane scanner The dynamics of the scanners with parallelogram structure can be well described by partial differential equations. However, practically the working frequency of piezoelectric scanner is usually below their first resonances [9]. Hence we use a spring mass-damper model to describe the system. Furthermore, the hysteresis phenomenon of piezoelectric actuator results in highly-nonlinear motion in a relation with input voltage, so it is necessary to consider the hysteresis effect as a nonlinear function in the dynamics. First, we build xy-plane scanner s model. We define and as the displacements along x and y axes, respectively, and according to Newton s Law, the system dynamics can be expressed in the following form: (1) where is the mass composed of the moving stage. The notations and are the coefficients of elasticity, and are the damping constants; and are the linear piezoelectric force, and, represent forces due to nonlinear hysteresis effect. Substituting the practical piezoelectric forces analyzed, we can then rewrite dynamic equations of the two SISO systems as: (2) To simplify the representation of equations of motion, we define a state vector as and reformulate the dynamical equations as: (3) where is the inertia term, is the stiffness term, is the damping term, is force-voltage coefficient, is the hysteresis coefficient, and is the control effort, which are respectively defined as: (4) with the coupling effect considered as the off-diagonal terms. B. Dynamics Formulation of z-scanner The design concept and structure of z-axis scanning stage is almost the same as the xy-plane one, but the hysteresis effect could be ignored for the reason that the motion of the stage is usually very small in the scanning process. 5489

3 (5) where is the mass composed of the moving stage and the transmission lever along z-axis only. The notation is the coefficients of stiffness; is the damping constants, and is the force-voltage coefficient. IV. CONTROLLER DESIGN A. Tip-Sample Distance Control 1) Control Approach In order to precision reconstruct the true cell contour, we have to prevent serious damage on the cell in scanning process. We proposed an adaptive complementary sliding mode controller (ACSMC) [10] with phase feedback signal to implement tip-sample distance control. First of all, we take the model uncertainty, external disturbance into consideration to design a robust controller. Hence, Eq. (5) can be rewrite as, (6) The constant disturbance stands for model uncertainty, and varying disturbance stands for external disturbance from air and ground in scanning. Suppose the varying uncertainty term is assumed to be bounded, i.e.,, where is a constant. The control goal is to change the displacement of z-axis scanner to track the variation of sample topography, so we can keep tip-sample distance fixed. The error can be defined as. According to Eq. (6), we can obtain the error dynamics. Besides, in order to simply the notations, we define as, as and as, then the error dynamics can be shown below: (7) 2) Adaptive Complementary Sliding Mode Controller Assuming the sliding surface and the complementary one, are defined with the following form, (8) (9) where is a positive constant to be designed and. The relationship between and can be defined as the following equation (10) From Eqs. (8) and (9), it is obvious that both and consist of the error term, its first order time derivative, and its integral. The purpose of the whole control is to force the state of the system to reach the sliding surface, and thus drives and to zero. In turn, and are also driven to zero. From the above, the adaptive complementary sliding mode controller intuitively is capable of online estimating system parameters and tuning suitable control gain to satisfy the control object. By adopting the proportional rate reaching law [11], the control law is designed as : (11) where,,, and are the estimated value of,, and, respectively; is the high gain constant used to bound the time varying uncertainty, such that 3) Stability Analysis Define a Lyapunov candidate function, which is a positive definite function: (12) where are positive constants;,, and are the estimation errors, defined as,,,. By differentiating the Lyapunov function candidate, we obtain: (13) The first two terms of Eq. (13) can be reformulated by Eq. (9) as: (14) Here, the term can be reformulated by Eq. (7), (8) and (11) as: (15) Then, Eq. (13) can be rewritten as follows: (16) Adopting the adaptive law with -modification [12], the bound in the presence of modeling error term can be defined in the following: (17) where,, are all positive constants. Substituting Eq. (17) into (16), and take boundary layer into consideration. Then, the upper bound on can be assessed as: (18) where is chosen, then we apply Lyapunov stability theorem for when (19) which means that, and therefore,,,,,,. From Eq. (18), we know the would converge to a residual set, and consists of and. Hence, and are bounded. Besides, the 5490

4 error dynamics can be obtained by the sliding surface enter a stable filter, so it will ensure that starting from initial state the error trajectories will reach the boundary layer in finite time. Finally, we can conclude that will also converge to a residual set whose size is in the order of. Hence, the tracking topography performance can be improved by appropriate parameter choice. B. Precision Positioning Control 1) Control Approach In order to precisely obtain the size of sample, precision positioning ability is indispensable. We design the adaptive double integral sliding mode controller (ADISMC) with multi-input multi-output (MIMO) form. Compared with conventional sliding mode controller, double integral sliding mode controller generally can provide strong robustness and regulation property. First, we take the hysteresis effect, model uncertainty, external noise and disturbance into consideration in the dynamics of xy-plane scanning stage. (20) where constant uncertainty is denoted as the model uncertainty, varying uncertainty and are denoted as the external noise and hysteresis effect, respectively. Assume the varying uncertainty of the external noise and the hysteresis effect is bounded. i.e.. Let the desired position vector be defined as, and the error state vector. According to Eq. (20), we can obtain the error dynamics. Besides, in order to simply the notations, we define as, as, as, then the error dynamics can be shown below: (21) 2) Adaptive Double Integral Sliding Mode Controller Assuming the double integral sliding surface, with the following form. (22) where, are designed positive diagonal matrices, and. The sliding surface consists of the error term, its time derivative, its integral term and double integral term. Our purpose is to carry sliding surface to zero, which also drive and to zero simultaneously. Then, we use the adaptive sliding mode to online estimate system parameters and tune the suitable controller gains to satisfy the control object. Based on the sliding surface dynamics and proportional rate reaching law, the control law is designed as: (23) where,,, and are the estimated value of,, and, respectively; is positive definite.,, is the high gain used to bound variable uncertainty and, satisfying. 3) Stability Analysis Define a Lyapunov function candidate, which is positive definite: (24) where, are positive diagonal matrices, is the trace of a matrix;,,, and are the estimation errors, defined as,,,. Next, by differentiating the Lyapunov function candidate, we obtain: (25) Here, can be calculated by Eqs (21), (22) and then reformulated by substituting into Eq. (23): (26) so that Eq. (25) becomes (27) By choosing the adaptive law with -modification, the bound in the presence of modeling error term can be determined in the following: (28) where, are all positive diagonal matrices. By substituting Eq. (28) into Eq. (27), and take boundary layer into consideration. Then, the upper bound on can be assessed as: (29) where,, is chosen. Then we apply Lyapunov stability theorem for when (30) 5491

5 which means that, and therefore,,,,,. From Eq. (24), we know thewould converge to a residual set, and consists of. Hence, is bounded. Besides, the error dynamics can be obtained by the sliding surface enter a stable filter, so it will ensure that starting from initial state the error trajectories will reach the boundary layer in finite time. Finally, we can conclude that will converge to a residual set whose size is in the order of. Hence, the precision positioning performance can be improved by appropriate parameter choice. V. EXPERIMENTAL RESULTS A. Experimental Setup axis means the tip-sample distance related to z-axis input voltage, and the vertical axis represents the cantilever phase. 2) Standard Grating In this section, we scan the standard grating in the dimension of 8 8, and the post-process image is formed by pixels. Here, we use phase detection mode (PM) and adopt ACSMC in z-axis feedback control to accomplish grating scanning in the dimension of 8 8 as shown in Fig. 4 (a). Besides, we also use amplitude detection mode (AM) with PI controller for 8 8 standard grating scanning, as shown in Fig. 4 (b). Because of the sample is contaminated, there are some blots on the sample observed in the scanned image. Fig. 2. Practical setup of the proposed AFM system. The overall AFM system, including the measuring part and the scanning part, is shown in Fig. 2. Since the system is tend to be disturbed, an optical table is used as the vibration isolator. The sample used in the following experiment is a standard grating (Calibration grating set TGZ1 is intended for XZ-axis calibration of scanning probe microscopes. The vertical depth is 107.5nm, and the horizontal pitch is 3, NT-MDT Inc.). In the experiments, MATLAB xpc targets is utilized for real time control. (a) (b) Fig. 4. 3D image of grating 8 8 (a) PM+ACSMC (b) AM+PI Next, we compare the image quality. Generally, we use the index of roughness, flatness, straightness, settling time to quantify the image quality. The quantification methods is referenced from [13] [15]. The roughness of PM is 2 nm and AM is about 3.2 nm; the flatness of PM is 13 nm and AM is 15.2 nm; the straightness of PM is 0.92% (73.6nm) and AM is 1.89% (151.2nm) and the settling time of PM is 0.37 sec and AM is about sec. From the evaluation results, the roughness and flatness of PM+ACSMC is better than the AM+PI ones owing to ACSMC would take environment disturbance, plant model variation into consideration and has better tracking precision. Next, the straightness error of PM+ACSMC is almost half than the other one due to that the phase signal is more sensitive to the tip-sample distance than the amplitude signal. Then the settling time of PM+ACSMC is smaller than the other one for the reason that the time constant of phase signal is smaller than the amplitude one. In next two sections, we scan two kinds of biological cell, Human red blood cells in air and HEK-293 cells in liquid. 3) Biological Cell in Air Fig. 3. Phase-distance curves. B. Sample Scanning 1) Phase Distance Curve (PDC) Before scanning, the sample approaching procedure is inevitable. Only when the cantilever amplitude and phase can be changed with tip-sample distance linearly and sensitively, this procedure is finished. Then, we can obtain the so-called PDC curve as shown in Fig. 3. The horizontal Fig. 5. 3D AFM image of human blood cells. 5492

6 In General, the appearance of human red blood cell is a cave in the center of the cell, and the range of the cell size can be from 6 6 to Here we would use trajectory to make sure we can obtain a complete cell. Owing to the side-walls effect [16], which is related to the nature of probe, the left side of cell is slightly higher than the right side. From Fig. 5, we would easily find a complete cell, then we would define the length, width and the height of the cell. First we take two lines to calculate the maximum values of length and width. Besides, we can also obtain the height information. The length, width and height are 6.54, 13.2 and 0.355, respectively, which belong to reasonable regions. From the reconstruction 3D image of red blood cell by our AFM system, the cave in the center of the cell is still obvious. The results can verify the proposed AFM system has the ability to scan biological cell without damage on the cell. 4) Biological Cell in Liquid (a) (b) Fig. 8. AFM image of HEK-293 cell (a) 3D view (b) 2D view. Human Embryonic Kidney 293 cell often referred as HEK-293, and the range of the cell size can be from 6 6 to 20 20, it is decided by the growth. And the 3D and 2D AFM images of HEK239 cell are shown in Fig. 8 (a) and Fig. 8 (b). From above figures, we would define the length, width and the height of the cell. First we take two lines to calculate the maximum values of length and width. Besides, we can also obtain the height information. The length, width and height are 7.24, 7.5 and 1.32, respectively, which belong to reasonable regions. From the figures we can find the AFM 3D image matches to the optical microscope one and it would ensures the credibility of the images. VI. CONCLUSION In this paper, a homemade phase-detection mode AFM system adopting CD/DVD pickup head in cantilever measuring system has been proposed to reconstruct 3D cell contour. To reduce the damage on cell, tip-sample distance control has been taken into consideration and an adaptive complementary sliding mode controller (ACSMC) is designed to make the z-axis scanner smoothly track the sample topography and reduce the tracking error. Besides, we design an MIMO adaptive double integral sliding mode controller (ADISMC) in xy-plane to overcome the system uncertainties, cross coupling, hysteresis effect, and disturbance, which improve the positioning accuracy and provide precision cell size. The scanning performances at roughness, flatness, straightness, settling time and hysteresis are 2 nm, 13 nm, 0.92%, 0.37 sec and 1.06%, respectively. Finally, we use the proposed AFM system to practically scan two kinds of biological cells under air and liquid environment. The calculated cell size from the AFM image corresponds to the range of the real cell size. The most important of all, the red blood cell and HEK-293 cell of AFM images can obtain the cave of the cell, and it mean the cells are well-protected in scanning process. Therefore, the proposed PM-AFM in this work will be helpful to life science field. REFERENCES [1] G. Binnig, C. F. Quate, and C. Gerber, "Atomic Force Microscope," Physical Review Letters, vol. 56, pp , [2] R. Garca and R. Pérez, "Dynamic atomic force microscopy methods," Surface Science Reports, vol. 47, pp , [3] T. Fukuma, J. I. Kilpatrick, and S. P. Jarvis, "Phase modulation atomic force microscope with true atomic resolution," Review of Scientific Instruments, vol. 77, pp , [4] R. Nishi, I. Houda, T. Aramata, Y. Sugawara, and S. Morita, "Phase change detection of attractive force gradient by using a quartz resonator in noncontact atomic force microscopy," Applied Surface Science, vol. 157, pp , [5] R. Nishi, K. Kitano, I. Yi, Y. Sugawara, and S. 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