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Imaging theory of nonlinear second harmonic and third harmonic generations in confocal microscopy

science china(Physics,Mechanics & Astronomy) 2004年第1期47卷 8-16页

作者： tang zhilie1, XING Da2.& LIU Songhao2.1. Department of Physics,{2., guangzhou 510631, china 2. school for information and optoelectronic science and engineering,{2., guangzhou 510631, china correspondence should be addressed to tang zhilie (email: tangzhl@***) received april 2., 2003 Department of Physics South China Normal University Guangzhou China school for information and {2. science and engineering South China Normal University Guangzhou China

The imaging theory of nonlinear second harmonic generation (SHG) and third harmonic generation (THG) in confocal microscopy is presented in this paper. The nonlinear effect of SHG and THG on the imaging properties of confocal microscopy has been analyzed in detail by the imaging theory. It is proved that the imaging process of SHG and THG in confocal microscopy, which is different from conventional coherent imaging or incoherent imaging, can be divided into two different processes of coherent imaging. The three-dimensional point spread functions (3D-PSF) of SHG and THG confocal microscopy are derived based on the nonlinear principles of SHG and THG. The imaging properties of SHG and THG confocal microscopy are discussed in detail according to its 3D-PSF. It is shown that the resolution of SHG and THG confocal microscopy is higher than that of single- and two-photon confocal microscopy.

关键词： second harmonic generation, third harmonic generation, confocal microscopy, three-dimensional point spread function.

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On the new results of global attractive set and positive invariant set of the Lorenz chaotic system and the applications to chaos control and synchronization

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science in china(Series F) 2005年第3期48卷 304-321页

作者： LIAO Xiaoxin 1, 2, 3 , FU Yuli 4 & XIE Shengli 4 1. Department of Control science & Control engineering, Huazhong university of science & Technology, Wuhan 430074, china 2. school of Automation, Wuhan university of science & Technology, Wuhan 430070, china 3. school of information, Central south university of Economy, Politics and Law, Wuhan 430064, china 4. school of Electronics & information engineering, south china university of Technology, guangzhou 510640, china correspondence should be addressed to Liao Xiaoxin (email: xiaoxin_liao@***) Department of Control science & Control engineering Huazhong University of Science & Technology Wuhan China school of Automation Wuhan University of Science & Technology Wuhan China school of information Central South University of Economy Politics and Law Wuhan China school of Electronics & information {2. South China University of Technology Guangzhou China

Constructing a family of generalized Lyapunov functions, a new method is proposed to obtain new global attractive set and positive invariant set of the Lorenz chaotic system. The method we proposed greatly simplifies the complex proofs of the two famous estimations presented by the Russian scholar Leonov. Our uniform formula can derive a series of the new estimations. Employing the idea of intersection in set theory, we extract a new Leonov formula-like estimation from the family of the estimations. With our method and the new estimation, one can confirm that there are no equilibrium, periodic solutions, almost periodic motions, wandering motions or other chaotic attractors outside the global attractive set. The Lorenz butterfly-like singular attractors are located in the global attractive set only. This result is applied to the chaos control and chaos synchronization. Some feedback control laws are obtained to guarantee that all the trajectories of the Lorenz systems track a periodic solution, or globally stabilize an unstable (or locally stable but not globally asymptotically stable) equilibrium. Further, some new global exponential chaos synchronization results are presented. Our new method and the new results are expected to be applied in real secure communication systems.

关键词： Lorenz chaotic system global attractive set positive invariant set globally exponential tracking globally exponential synchronization.

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