光學顯微鏡(Optical Microscope, OM)是一種利用光學透鏡來放大影像的觀察儀器，其影像解析度的觀測極限為光波長的二分之一。它的主要功能是將人眼不能辨認之物體放大檢視，並進一步來觀察物體之結構，為一般微米或次微米尺度研究不可或缺之二維(2D)影像觀測儀器。而壓電平台(Piezo-stage)是一種高精密定位的裝置，它可以透過壓電效應使壓電平台來產生微小的位移，定位的精密度可以到達奈米等級。
本論文將OM以及一個z軸壓電平台結合，藉由系統互補的方式，來建構一個新的三維(3D)光學影像量測系統。其中，所開發系統之技術包括壓電平台進階控制器的設計，OM影像資料的演算法建構。首先，z軸壓電平台採用倒傳遞類神經網路(BPNN)控制法則，藉由連續步階的行走方式，由低至高來移動待測樣本，在z軸壓電平台的步階動作達到一個微小之穩態誤差時，以OM來擷取每一步階位置的樣本影像。其次，以連通分量標記法針對每張2D的OM影像做去雜訊，再藉由影像處理技術將每張去雜訊後的2D OM影像轉換成3D的數據。最後，將每一層的3D數據堆疊並建構出一張精確的3D影像。

Optical microscope (OM) is an observation instrument that uses optical lenses to magnify images, and its resolution is limited to one-half of the wavelength of light. Its primary function is to inspect the structure of objects that human eyes cannot recognize. It is an indispensable two-dimensional (2D) image observation instrument for general micro or sub-micro scale research. Piezo-stage is a high-precision positioning device, which can generate tiny displacements of the piezoelectric stage through the piezoelectric effect, and the positioning precision can reach the nanometer level.
This thesis will combine an OM and a z-axis piezoelectric stage to construct a new three-dimensional (3D) optical image measurement system. The technology of the developed system includes the design of the advanced controller in the piezoelectric stage and the construction of the algorithm in the OM image data. First, the z-axis piezoelectric stage uses a back propagation neural network (BPNN) control strategy. The z-axis piezoelectric stage uses continuous steps to move the scanned sample from a low-to-high manner. When each step motion reaches a small steady-state error, the OM is used to capture the scanned sample image of each step position. Second, each 2D OM image with connected-component labeling for de-noise, and then the 2D OM images are converted into 3D data by image processing. Finally, stack the 3D data of each layer to construct an accurate 3D image.

[1] G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,” Phys. Rev. Lett., vol. 56, no. 9, pp. 930–933, Mar. 1986.
[2] S. K. Nayar and Y. Nakagawa, “Shape from Focus,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16. no. 8, pp. 824-831, 1994.
[3] G. Binnig and H. Rohrer, “Scanning tunneling microscopy,” Helvetica Phys. Acta, vol. 55, pp. 726–735, 1982.
[4] J. Liu, J. Wang, and Q. Zou, “Decomposition-learning-based output tracking to simultaneous hysteresis and dynamics control: high-speed large-range nanopositioning example,” IEEE Transactions on Control Systems Technology, vol. 29, no. 4, pp. 1775-1782, 2021.
[5] Y. K. A. Nadawi, X. Tan, and H. K. Khalil, “Inversion-free hysteresis compensation via adaptive conditional servomechanism with application to nanopositioning control,” IEEE Transactions on Control Systems Technology, vol. 29, no. 5, pp. 1922-1935, 2021.
[6] Y. Tao, L. Li, H. X. Li, and L. Zhu, “High-bandwidth tracking control of piezoactuated nanopositioning stages via active modal control,” IEEE Transactions on Automation Science and Engineering, pp. 1-9, 2021.
[7] C. Yang, Y. Wang, and K. Y. Toumi, “Hierarchical antidisturbance control of a piezoelectric stage via combined disturbance observer and error-based adrc,” IEEE Transactions on Industrial Electronics, vol. 69, no. 5, pp. 5060-5070, 2022.
[8] X. Huang, W. Zhou, X. Li, L. Zhu, and H. T. Zhang, “Online koopman operator learning to identify cross-coupling effect of piezoelectric tube scanners in atomic force microscopes,” IEEE Transactions on Industrial Informatics, vol. 18, no. 2, pp. 1111-1120, 2022.
[9] Z. Feng, J. Ling, M. Ming, W. Liang, K. K. Tan, and X. Xiao, “Signal-transformation-based repetitive control of spiral trajectory for piezoelectric nanopositioning stages,” IEEE/ASME Transactions on Mechatronics, vol. 25, no. 3, pp. 1634-1645, 2020.
[10] R. Erni, M. D. Rossell, C. Kisielowski, and U. Dahmen, “Atomic-resolution imaging with a sub-50-pm electron probe,” Physical Review Letters, pp. 096101-1- 096101-4, Mar. 2009.
[11] E. Abbe, “Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Archiv Für Mikroskopische Anatomie, vol. 9, pp.413-468, 1873.
[12] E. Betzig, A. Lewis, A. Harootunian, M. Isaacson, and E. Kratschmer “Near field scanning optical microscopy (nsom): development and biophysical applications,” Biophysical Journal, vol. 49, no. 1, pp. 269-279, 1986.
[13] S. Hell and E. H. K. Stelzer, “Properties of a 4pi confocal fluorescence microscope,” Journal of the Optical Society of America A, vol. 9, no. 12, pp. 2159-2166, 1992.
[14] J. M. Guerra, “Photon tunneling microscopy,” Applied Optics, vol. 29, no. 26, pp. 3741-3752, 1990.
[15] M. Saxena, G. Eluru, and S. S. Gorthi, “Structured illumination microscopy,” Advances in Optics and Photonics, vol. 7, no. 2, pp. 241-275, 2015.
[16] A. DiSpirito III, D. Li, T. Vu, M. Chen, D. Zhang, J. Luo, R. Horstmeyer, and J. Yao, “Reconstructing undersampled photoacoustic microscopy images using deep learning,” IEEE Transactions on Medical Imaging, vol. 40, no. 2, pp. 562-570, 2021.
[17] A. Shajkofci and M. Liebling, “Spatially-variant cnn-based point spread function estimation for blind deconvolution and depth estimation in optical microscopy,” IEEE Transactions on Image Processing, vol. 29, pp. 5848-5861, 2020.
[18] J. Curie and P. Curie, “Development, via compression, of electric polarization in hemihedral crystals with inclined faces,” Bulletin de la Société Minérologique de France, pp. 90-93, 1880.
[19] P. J. Chen and S. T. Montgomery, “A macroscopic theory for the existence of the hysteresis and butterfly loops in ferroelectricity,” Ferroelectric, vol. 23, pp. 199-207, 1980.
[20] F. Preisach, “Über die magnetische nachwirkung,” Zeitschrift für Physik, vol. 94, pp. 277-302, 1935.
[21] Y. K. Wen, “Method for random vibration of hysteretic systems,” Journal of the Engineering Mechanics Division, vol. 102, no. 2, pp. 249-263, 1976.
[22] M. Goldfarb and N. Celanovic, “Modeling piezoelectric stack actuators for control of micromanipulation,” IEEE Control Systems Magazine, vol. 17, no. 3, pp. 69-79, 1997.
[23] H. Jung and D. G. Gweon, "Creep characteristics of piezoelectric actuators," Review of Scientific Instruments, vol. 71, no. 4, pp. 1895-1900, 1999.
[24] Born and Wolf, “Principles of optics: electromagnetic theory of propagation, interference and diffraction of light (6th ed.),” Pergamon Press INC. pp. 37-38, 2013.
[25] https://www.microscopyu.com/microscopy-basics/resolution
[26] N. Rezeki, E. Utami, and I. Oyong, “Analysis on digital elevation model data for 3d modeling,” 2019 International Conference on Information and Communications Technology (ICOIACT), Yogyakarta, Indonesia, 24-25 July, pp. 147-152, 2019.
[27] L. Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philosophical and Journal of Magazine Science, vol. 8 no. 49, pp. 261-274, 1879.
[28] C. E. Shannon, “Communication in the presence of noise,” Proceedings of the IRE, vol. 37, no. 1, pp. 10-21, 1949.
[29] https://www.piezosystem.com/
[30] https://navitar.com/
[31] https://sentech.co.jp/cn/index.html
[32] A. Rosenfeld and A.C. Kak, “Digital picture processing, 2, second ed,” Academic Press, San Diego, CA, 1982.
[33] K. Suzuki, I. Horiba, and N. Sugie, “Linear-time connected-component labeling based on sequential local operations,” Computer Vision and Image Understanding, vol. 89, no. 1, pp. 1-23, 2003.
[34] L. He, Y. Chao, and K. Suzuki, “A linear-time two-scan labeling algorithm,” IEEE International Conference on Image Processing, TX, USA, Sep. 16 – Oct. 19, 2007.
[35] T. Goto, Y. Ohta, M. Yoshida, and Y. Shirai, “High speed algorithm for component labeling,” IEICE Transactions on Information and Systems, vol. 21, no. 5, pp. 247-255, 1990.
[36] C. Fiorio and J. Gustedt, “Two linear time union-find strategies for image processing,” Theoretical Computer Science, vol. 154, no. 2, pp. 165-181, 1996.
[37] Y. Chauvin and D. E. Rumelhard, “Backpropagation theory, architectures, and applications,” New York, 1995.
[38] S. Karsoliya, “Approximating number of hidden layer neurons in multiple hidden layer bpnn architecture,” International Journal of Engineering Trends and Technology, vol. 3, no. 6, pp. 741-717, 2012.
[39] G. Wang, X. Xu, Y. Yao, and J. Tong, “A novel bpnn-based method to overcome the gps outages for ins/gps system,” IEEE Access, vol. 7, pp. 82134-82143, 2019.
[40] F. M. Ham and I. Kostanic, “Principles of neurocomputing for science & engineering,” McGraw-Hill Education-Europ, Jan. 2001.
[41] G. Cui, B. Su, and B. Cai, “The design of levitation controller based on bpnn with quantization factors for maglev yaw system of wind turnines,” 2019 Chinese Automation Congress (CAC), 22-24 Nov, Hangzhou, China, no. 19394465, pp. 4645-4650, 2019.
[42] Y. Song, S. Wu, and Y. Yan, “Development of self-tuning intelligent pid controller based on bpnn for indoor air quality control,” International Journal of Emerging Technology and Advanced Engineering, vol. 3, no. 11, pp. 283-290, 2013.
[43] Q. Song, J. Xiao, and Y. C. Soh, “Robust backpropagation training algorithm for multilayered neural tracking controller,” IEEE Transactions on Neural Networks, vol. 10, no. 5, pp. 1133-1141, 1999.
[44] H. Chen, Z. Zouaoui, and Z. Chen, “A modified smith predictive scheme based back-propagation neural network approach for FOPDT processes control,” Journal of Process Control, vol. 23, no. 19, pp. 1261-1269, 2013.
[45] T. Yabuta and T. Yamada, “Learning control using neural networks,” IEEE International Conference on Robotics and Automation, Sacramento, California, USA, pp. 740-745, 1991.
[46] K. C. Chee and K.Y. Lee, “Diagonal recurrent neural networks for dynamic systems control,” IEEE Transactions on Neural Networks, vol. 6, no. 1, pp. 144-156, 1995.