In this paper, the Geometric Optics (GO) method using the approximate ray paths coupled with the Computer Aided Tri-dimensional Interface Application (CATIA) meshing modeling are implemented to analyze the performance...In this paper, the Geometric Optics (GO) method using the approximate ray paths coupled with the Computer Aided Tri-dimensional Interface Application (CATIA) meshing modeling are implemented to analyze the performance of electric large three-dimensional dielectric radome-enclosed antenna of arbitrary contour shape. The surfaces of the radome are approximated by planar triangular patches, the influences of various number of patches on power transmission coefficient and Insertion Phase Delay (IPD) via an ogive and a conical radome are discussed by the hybrid method. The simulation results indicate that computational error from planar triangular patches can limit in one percent, meeting the engineering application requirements.展开更多
The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies f...The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies for computing profile equations are equivalent. We prove that if L generates an evolution on L2 the same is true of the profile equations. We prove that the characteristic polynomial of the profile equations is the localization of the characteristic polynomial of the background operator at （y, dφ（y）） where φ is the background phase. We prove that the propagation cones of the profile equations are subsets of the propagation cones of the background operator.展开更多
This article considers a family of 3D-Hartree-type equation with Coulomb potential ｜x｜^-1, whose initial data oscillates so that a caustic appears. In the linear geometric optics case, by using the Lagrangian integr...This article considers a family of 3D-Hartree-type equation with Coulomb potential ｜x｜^-1, whose initial data oscillates so that a caustic appears. In the linear geometric optics case, by using the Lagrangian integrals, a uniform description of the solution outside the caustic, and near the caustic are obtained.展开更多
This paper considers a family of Schroedinger-Poisson system in one dimension, whose initial data oscillates so that a caustic appears. By using the Lagrangian integrals, the authors obtain a uniform description of th...This paper considers a family of Schroedinger-Poisson system in one dimension, whose initial data oscillates so that a caustic appears. By using the Lagrangian integrals, the authors obtain a uniform description of the solution outside the caustic, and near the caustic.展开更多
Research on light scattering from a large chiral sphere shows that the rainbow phenomenon is different from that of an isotropic sphere. A chiral sphere with certain chirality generates three first-order rainbows. In ...Research on light scattering from a large chiral sphere shows that the rainbow phenomenon is different from that of an isotropic sphere. A chiral sphere with certain chirality generates three first-order rainbows. In this Letter,we present a geometric optics interpretation for the phenomenon and make a calculation of the rainbow angles.The ray traces inside the sphere are determined by the reflection and refraction laws of light at the achiral–chiral interface and the chiral–achiral interface. The calculated rainbow angles achieve good agreements with those obtained by the analytical solutions. The effects of chirality and the refractive index of the sphere on rainbow angles are analyzed.展开更多
Optical surface scattering analyses based on diffractive optics (DO) are typically applied to one surface;however, there is a need for simulating surface scattering losses for devices having many surface interactions ...Optical surface scattering analyses based on diffractive optics (DO) are typically applied to one surface;however, there is a need for simulating surface scattering losses for devices having many surface interactions such as light pipes. Light pipes are often simulated with geometric optics (GO) using ray tracing, where surface scattering is driven by the surface slope distribution. In the DO case, surface scattering analyses depend on the spatial frequency distribution and amplitude as well as wavelength, with the sinusoidal grating as a fundamental basis. A better understanding of the link, or transition, between DO and GO scattering domains would be helpful for efficiently incorporating scattering loss analyses into ray trace simulations. A formula for the root-mean-square (rms) scattered angle width of a sinusoidal reflection grating that depends only on the surface rms slope is derived from the nonparaxial scalar diffraction theory, thereby linking it to GO. The scatter angle’s mean and rms width are evaluated over a range of grating amplitudes and periods using scalar theory and full vector simulations from the COMSOL® wave optic module for a sinusoidal reflection grating. The conditions under which the diffraction-based solution closely approximates the GO solution, as predicted by the rms slope, are identified. Close agreement is shown between the DO and GO solutions for the same surface rms slope scattering loss due to angular filtering near the critical angle of a total internal reflection (TIR) glass-to-air interface.展开更多
The perturbed Riemann problem for a hyperbolic system of conservation laws arising in geometrical optics with three constant initial states is solved.By studying the interactions among of the delta-shock,vacuum,and co...The perturbed Riemann problem for a hyperbolic system of conservation laws arising in geometrical optics with three constant initial states is solved.By studying the interactions among of the delta-shock,vacuum,and contact discontinuity,fourteen kinds of structures of Riemann solutions are obtained.The compound wave solutions consisting of delta-shocks,vacuums,and contact discontinuities are found.The single and double closed vacuum cavitations develop in solutions.Furthermore,it is shown that the solutions of the Riemann problem for the geometrical optics system are stable under certain perturbation of the initial data.Finally,the numerical results completely coinciding with theoretical analysis are presented.展开更多
The searches for large-gap quantum spin Hall insulators are important for both practical and fundamental inter- ests. In this work, we present a theoretical observation of the two-dimensional fully fluorinated stanene...The searches for large-gap quantum spin Hall insulators are important for both practical and fundamental inter- ests. In this work, we present a theoretical observation of the two-dimensional fully fluorinated stanene （SnF） by means of density functional theory. Remarkably, a significant spin-orbit coupling is observed for the SnF monolayer in the valence band at the F point, with a considerable indirect band gap of 278 meV. The direct gap of the SnF monolayer is at the F point, which is slightly larger by as much as 381 meV. In addition, the elastic modulus of the SnF monolayer is about 20J/m^2, which is comparable with the in-plane stiffness of black phos- phorus monolayer along the x-direction （~28.94 J/m^2）. Finally, the optical properties of stanene, SnF monolayer and stanene/SnF bilayer are calculated, in which the stanene/SnF bilayer is supposed to be an attractive sunlight absorber.展开更多
We investigate a novel spatial geometric phase of hybrid-polarized vector fields consisting of linear, elliptical and circular polarizations by Young＇s two-slit interferometer instead of the widely used Mach-Zehnder ...We investigate a novel spatial geometric phase of hybrid-polarized vector fields consisting of linear, elliptical and circular polarizations by Young＇s two-slit interferometer instead of the widely used Mach-Zehnder interferometer. This spatial geometric phase can be manipulated by engineering the spatial configuration of hybrid polarizations, and is directly related to the topological charge, the local states of polarization and the rotational symmetry of hybrid-polarized vector optical fields. The unique feature of geometric phase has implications in quantum information science as well as other physical systems such as electron vortex beams.展开更多
Two-photon fluorescence microscopy,based on the principles of two-photon excited fluorescence and second harmonic generation,enables real-time non-invasive in vivo imaging of skin and cells,providing a means to assess...Two-photon fluorescence microscopy,based on the principles of two-photon excited fluorescence and second harmonic generation,enables real-time non-invasive in vivo imaging of skin and cells,providing a means to assess human health status.In this paper,a miniaturized two-photon imaging system is designed and fabricated to withstand extreme vibration and shock environments.The mechanical stability of the optical and structural components of the miniaturized probe is evaluated under random vibration and shock vibration tests using finite element simulation methods and ray tracing techniques.During the environmental testing,the maximum stress on the probe is 11.5 MPa,which is well below the threshold for structural failure.The largest structural displacement occurs at the collimator,where random vibrations produce an offset of 10.9μm.This offset is analyzed by using geometric optics and point spread functions.Under the maximum collimator offset,the theoretical resolution,as calculated by the point spread function,shifted from 463.28 nm to 463.48 nm.Additionally,a lateral offset of 127 nm is observed at the center position,which does not significantly impact the imaging performance.Finally,environmental and imaging performance tests are conducted.The system’s measured resolution after the environmental tests is 530 nm,consistent with its resolution prior to testing.Imaging tests are also performed on the skin’s stratum corneum,granular layer,spinous layer,and basal cell layer,revealing clear cellular structural information.These results confirm the device’s potential for applications in extreme shock and vibration environments.展开更多
We present an iterative surface-reconstruction approach based on vision rays that achieves not only higher reconstruction accuracy than the Delaunay/Möller–Trumbore method but also a significant reduction in com...We present an iterative surface-reconstruction approach based on vision rays that achieves not only higher reconstruction accuracy than the Delaunay/Möller–Trumbore method but also a significant reduction in computation time.The peak-to-valley value of the reconstruction error is decreased from 4.190 to 0.347 nm,while the time for a single iteration drops from 16 to 0.12 s.By aligning the camera’s optical axis with the z axis of the coordinate system,the need for the Delaunay/Möller–Trumbore surface-updating process is eliminated,preventing errors in surface-normal computation during reconstruction.This alignment leads to an iterative reconstruction method based on vision rays within the optical-axis-based coordinate system that is fast,accurate,and robust.The robustness of this technique is further evaluated by studying the effects of the angleθbetween the camera’s optical axis and the z axis,as well as the angleφof the initial iteration-plane normal.Experimental results show that reconstruction errors introduced by the angleθare typically in the nanometer range;however,asθapproaches a certain critical angle,reconstruction errors can increase to the micrometer level,potentially leading to reconstruction failure.In contrast,errors introduced by the angleφremain at the picometer level and can be considered negligible.These findings demonstrate that aligning the camera’s optical axis with the z axis not only ensures the robustness of the iterative process but also achieves the highest reconstruction accuracy.展开更多
Researchers have recently attempted to monitor pool oscillations using the three-dimensional laser vision method.However,the deficiency of simulation software will result in significant capital expenditure.Both simula...Researchers have recently attempted to monitor pool oscillations using the three-dimensional laser vision method.However,the deficiency of simulation software will result in significant capital expenditure.Both simulations and experiments are performed in this study,and the Bessel equation is used to analyze the oscillation mode of a weld pool.The laser dot matrix images of(0,1),(1,1),(2,1),and(0,2)oscillation modes at different times are obtained via structured laser optical measurement simulation.The oscillation mode of a stationary gas tungsten arc weld pool is analyzed based on laser dot matrix images obtained from a structure laser experiment.Results show that the simulated laser dot matrix images are consistent with the experiment results.The oscillation mode of the weld pool can be recognized based on the laser dot matrix image.This study not only provides conditions for assessing the penetrating state of a weld pool,but also enable a further understanding of the oscillation mode of a weld pool and the development of more effective observation methods and measurement tools to effectively control and improve welding quality.展开更多
For large spherical bubbles in water, geometrical optics approximation is considered a better method for calculating light scattering patterns. In this paper, the basic theory of geometrical optics approximation is cl...For large spherical bubbles in water, geometrical optics approximation is considered a better method for calculating light scattering patterns. In this paper, the basic theory of geometrical optics approximation is clarified. The change of phase for bubbles is calculated when total reflection occurs, which is different from particles with relative refractive indices larger than 1. Verification of the method was achieved by assuming a spherical particle and comparing present results to Mie scattering and Debye calculation. Agreement with the Mie theory was excellent in all directions when the dimensionless size parameter is larger than 50. Limitations of the geometrical optics approximation are also discussed.展开更多
Optoelectronic imaging equipment is easy to expose to active laser detection devices because of ＂cat eye＂ effect. In this paper, we propose a new structure of optical system to reduce the retroreflector effect of a ...Optoelectronic imaging equipment is easy to expose to active laser detection devices because of ＂cat eye＂ effect. In this paper, we propose a new structure of optical system to reduce the retroreflector effect of a cat eye target. Decentered field lens structure is adopted in the design without sacrificing imaging quality and clear aperture. An imaging system with±30° field of view is taken for example. The detailed design and simulation results are presented. The results indicate that this kind of optical system can reduce the retroreflection signal substantially and maintain acceptable imaging performance.展开更多
This letter reports an autostereoscopic three-dimensional （3D） fiat panel display system employing a newly designed LCD-pixel-associated parallax barrier （LPB）. The battler＇s parameters can be conveniently determ...This letter reports an autostereoscopic three-dimensional （3D） fiat panel display system employing a newly designed LCD-pixel-associated parallax barrier （LPB）. The battler＇s parameters can be conveniently determined by the LCD pixels and can help to greatly simplify the conventional design. The optical system of the proposed 3D display is built and simulated to verify the design. For further experimental demonstration, a 508-mm autostereoscopic 3D displayprototype is developed and it presents good stereoscopic images. Experimental results agree well wlth the simulation, which reveals a strong potential for 3D display applications.展开更多
Integral imaging is a 3D display technology without any additional equipment. A new system is proposed in this paper, which uses a lenticular lens array to replace the lens array in the conventional integral imaging s...Integral imaging is a 3D display technology without any additional equipment. A new system is proposed in this paper, which uses a lenticular lens array to replace the lens array in the conventional integral imaging system. The lenticular integral imaging system reduces the complexity and the price of integral imaging system. The positive characteristics of conventional integral imaging system, such as full parallax and quasi-continuous view points, are still kept on the proposed system in horizontal direction. Optical results show that the time for calculating the elemental images is reduced by 25% compared with the conventional one. The resolution of integrated image in vertical direction is 4 times higher than that of conventional system. This proposed system opens a new way on application of integral imaging.展开更多
The paper solves analytically the Riemann problem for a nonstrictly hyperbolic system of conservation laws arising in geometrical optics,in which the flux contains the nonconvex function possessing an infinite number ...The paper solves analytically the Riemann problem for a nonstrictly hyperbolic system of conservation laws arising in geometrical optics,in which the flux contains the nonconvex function possessing an infinite number of inflection points.Firstly,the generalized Rankine–Hugoniot relations and entropy condition of delta shock waves and left（right）-contact delta shock waves are proposed and clarified.Secondly,with the help of the convex hull,seven kinds of structures of Riemann solutions are obtained.The solutions fall into three broad categories with a series of geometric structures involving simultaneously contact discontinuities,vacuums and delta shock waves.Finally,numerical experiments confirm the theoretical analysis.展开更多
By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechan...By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.展开更多
We extend the theory of global geometrical optics method, proposed originally for the linear scalar high-frequency wave-like equations in [Commun. Math. Sci., 2013, 11（1）： 105-140], to the more general vector- valu...We extend the theory of global geometrical optics method, proposed originally for the linear scalar high-frequency wave-like equations in [Commun. Math. Sci., 2013, 11（1）： 105-140], to the more general vector- valued Schrodinger problems in the semi-classical regime. The key ingredient in the global geometrical optics method is a moving frame technique in the phase space. The governing equation is transformed into a new equation but of the same type when expressed in any moving frame induced by the underlying Hamiltonian flow. The classical Wentzel-Kramers-Brillouin （WKB） analysis benefits from this treatment as it maintains valid for arbitrary but fixed evolutionary time. It turns out that a WKB-type function defined merely on the underlying Lagrangian submanifold can be obtained with the help of this moving frame technique, and from which a uniform first-order approximation of the wave field can be derived, even around caustics. The general theory is exemplified by two specific instances. One is the two-level SchrSdinger system and the other is the periodic SchrSdinger equation. Numerical tests validate the theoretical results.展开更多
基金Supported by the National Natural Science Foundation of China (No. 61172024)
文摘In this paper, the Geometric Optics (GO) method using the approximate ray paths coupled with the Computer Aided Tri-dimensional Interface Application (CATIA) meshing modeling are implemented to analyze the performance of electric large three-dimensional dielectric radome-enclosed antenna of arbitrary contour shape. The surfaces of the radome are approximated by planar triangular patches, the influences of various number of patches on power transmission coefficient and Insertion Phase Delay (IPD) via an ogive and a conical radome are discussed by the hybrid method. The simulation results indicate that computational error from planar triangular patches can limit in one percent, meeting the engineering application requirements.
文摘The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies for computing profile equations are equivalent. We prove that if L generates an evolution on L2 the same is true of the profile equations. We prove that the characteristic polynomial of the profile equations is the localization of the characteristic polynomial of the background operator at （y, dφ（y）） where φ is the background phase. We prove that the propagation cones of the profile equations are subsets of the propagation cones of the background operator.
文摘This article considers a family of 3D-Hartree-type equation with Coulomb potential ｜x｜^-1, whose initial data oscillates so that a caustic appears. In the linear geometric optics case, by using the Lagrangian integrals, a uniform description of the solution outside the caustic, and near the caustic are obtained.
文摘This paper considers a family of Schroedinger-Poisson system in one dimension, whose initial data oscillates so that a caustic appears. By using the Lagrangian integrals, the authors obtain a uniform description of the solution outside the caustic, and near the caustic.
基金supported by the National Natural Science Foundation of China(Nos.61172031,61308025,61475123,and 61571355)the Fundamental Research Funds for the Central Universities
文摘Research on light scattering from a large chiral sphere shows that the rainbow phenomenon is different from that of an isotropic sphere. A chiral sphere with certain chirality generates three first-order rainbows. In this Letter,we present a geometric optics interpretation for the phenomenon and make a calculation of the rainbow angles.The ray traces inside the sphere are determined by the reflection and refraction laws of light at the achiral–chiral interface and the chiral–achiral interface. The calculated rainbow angles achieve good agreements with those obtained by the analytical solutions. The effects of chirality and the refractive index of the sphere on rainbow angles are analyzed.
文摘Optical surface scattering analyses based on diffractive optics (DO) are typically applied to one surface;however, there is a need for simulating surface scattering losses for devices having many surface interactions such as light pipes. Light pipes are often simulated with geometric optics (GO) using ray tracing, where surface scattering is driven by the surface slope distribution. In the DO case, surface scattering analyses depend on the spatial frequency distribution and amplitude as well as wavelength, with the sinusoidal grating as a fundamental basis. A better understanding of the link, or transition, between DO and GO scattering domains would be helpful for efficiently incorporating scattering loss analyses into ray trace simulations. A formula for the root-mean-square (rms) scattered angle width of a sinusoidal reflection grating that depends only on the surface rms slope is derived from the nonparaxial scalar diffraction theory, thereby linking it to GO. The scatter angle’s mean and rms width are evaluated over a range of grating amplitudes and periods using scalar theory and full vector simulations from the COMSOL® wave optic module for a sinusoidal reflection grating. The conditions under which the diffraction-based solution closely approximates the GO solution, as predicted by the rms slope, are identified. Close agreement is shown between the DO and GO solutions for the same surface rms slope scattering loss due to angular filtering near the critical angle of a total internal reflection (TIR) glass-to-air interface.
基金supported by the National Natural Science Foundation of China(12061084)the Natural Science Foundation of Yunnan Province(2019FY003007).
文摘The perturbed Riemann problem for a hyperbolic system of conservation laws arising in geometrical optics with three constant initial states is solved.By studying the interactions among of the delta-shock,vacuum,and contact discontinuity,fourteen kinds of structures of Riemann solutions are obtained.The compound wave solutions consisting of delta-shocks,vacuums,and contact discontinuities are found.The single and double closed vacuum cavitations develop in solutions.Furthermore,it is shown that the solutions of the Riemann problem for the geometrical optics system are stable under certain perturbation of the initial data.Finally,the numerical results completely coinciding with theoretical analysis are presented.
基金Supported by the Science Foundation of Nanjing University of Posts and Telecommunications under Grant No NY215064the China Postdoctoral Science Foundation under Grant No 2015M581824the Jiangsu Post-doctoral Foundation under Grant No1501070B
文摘The searches for large-gap quantum spin Hall insulators are important for both practical and fundamental inter- ests. In this work, we present a theoretical observation of the two-dimensional fully fluorinated stanene （SnF） by means of density functional theory. Remarkably, a significant spin-orbit coupling is observed for the SnF monolayer in the valence band at the F point, with a considerable indirect band gap of 278 meV. The direct gap of the SnF monolayer is at the F point, which is slightly larger by as much as 381 meV. In addition, the elastic modulus of the SnF monolayer is about 20J/m^2, which is comparable with the in-plane stiffness of black phos- phorus monolayer along the x-direction （~28.94 J/m^2）. Finally, the optical properties of stanene, SnF monolayer and stanene/SnF bilayer are calculated, in which the stanene/SnF bilayer is supposed to be an attractive sunlight absorber.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11534006,11674184 and 11374166the Natural Science Foundation of Tianjin under Grant No 16JC2DJC31300Collaborative Innovation Center of Extreme Optics
文摘We investigate a novel spatial geometric phase of hybrid-polarized vector fields consisting of linear, elliptical and circular polarizations by Young＇s two-slit interferometer instead of the widely used Mach-Zehnder interferometer. This spatial geometric phase can be manipulated by engineering the spatial configuration of hybrid polarizations, and is directly related to the topological charge, the local states of polarization and the rotational symmetry of hybrid-polarized vector optical fields. The unique feature of geometric phase has implications in quantum information science as well as other physical systems such as electron vortex beams.
基金supported by the National Natural Science Foundation of China(62475008,62305186).
文摘Two-photon fluorescence microscopy,based on the principles of two-photon excited fluorescence and second harmonic generation,enables real-time non-invasive in vivo imaging of skin and cells,providing a means to assess human health status.In this paper,a miniaturized two-photon imaging system is designed and fabricated to withstand extreme vibration and shock environments.The mechanical stability of the optical and structural components of the miniaturized probe is evaluated under random vibration and shock vibration tests using finite element simulation methods and ray tracing techniques.During the environmental testing,the maximum stress on the probe is 11.5 MPa,which is well below the threshold for structural failure.The largest structural displacement occurs at the collimator,where random vibrations produce an offset of 10.9μm.This offset is analyzed by using geometric optics and point spread functions.Under the maximum collimator offset,the theoretical resolution,as calculated by the point spread function,shifted from 463.28 nm to 463.48 nm.Additionally,a lateral offset of 127 nm is observed at the center position,which does not significantly impact the imaging performance.Finally,environmental and imaging performance tests are conducted.The system’s measured resolution after the environmental tests is 530 nm,consistent with its resolution prior to testing.Imaging tests are also performed on the skin’s stratum corneum,granular layer,spinous layer,and basal cell layer,revealing clear cellular structural information.These results confirm the device’s potential for applications in extreme shock and vibration environments.
基金supported by the National Natural Science Foundation of China(Grant No.52035009).
文摘We present an iterative surface-reconstruction approach based on vision rays that achieves not only higher reconstruction accuracy than the Delaunay/Möller–Trumbore method but also a significant reduction in computation time.The peak-to-valley value of the reconstruction error is decreased from 4.190 to 0.347 nm,while the time for a single iteration drops from 16 to 0.12 s.By aligning the camera’s optical axis with the z axis of the coordinate system,the need for the Delaunay/Möller–Trumbore surface-updating process is eliminated,preventing errors in surface-normal computation during reconstruction.This alignment leads to an iterative reconstruction method based on vision rays within the optical-axis-based coordinate system that is fast,accurate,and robust.The robustness of this technique is further evaluated by studying the effects of the angleθbetween the camera’s optical axis and the z axis,as well as the angleφof the initial iteration-plane normal.Experimental results show that reconstruction errors introduced by the angleθare typically in the nanometer range;however,asθapproaches a certain critical angle,reconstruction errors can increase to the micrometer level,potentially leading to reconstruction failure.In contrast,errors introduced by the angleφremain at the picometer level and can be considered negligible.These findings demonstrate that aligning the camera’s optical axis with the z axis not only ensures the robustness of the iterative process but also achieves the highest reconstruction accuracy.
基金Supported by National Natural Science Foundation of China(Grant No.51205197).
文摘Researchers have recently attempted to monitor pool oscillations using the three-dimensional laser vision method.However,the deficiency of simulation software will result in significant capital expenditure.Both simulations and experiments are performed in this study,and the Bessel equation is used to analyze the oscillation mode of a weld pool.The laser dot matrix images of(0,1),(1,1),(2,1),and(0,2)oscillation modes at different times are obtained via structured laser optical measurement simulation.The oscillation mode of a stationary gas tungsten arc weld pool is analyzed based on laser dot matrix images obtained from a structure laser experiment.Results show that the simulated laser dot matrix images are consistent with the experiment results.The oscillation mode of the weld pool can be recognized based on the laser dot matrix image.This study not only provides conditions for assessing the penetrating state of a weld pool,but also enable a further understanding of the oscillation mode of a weld pool and the development of more effective observation methods and measurement tools to effectively control and improve welding quality.
基金the Ministry of Education of the People's Republic of China(No.208041)the Shanghai Municipal Education Commission(No.07ZZ88).
文摘For large spherical bubbles in water, geometrical optics approximation is considered a better method for calculating light scattering patterns. In this paper, the basic theory of geometrical optics approximation is clarified. The change of phase for bubbles is calculated when total reflection occurs, which is different from particles with relative refractive indices larger than 1. Verification of the method was achieved by assuming a spherical particle and comparing present results to Mie scattering and Debye calculation. Agreement with the Mie theory was excellent in all directions when the dimensionless size parameter is larger than 50. Limitations of the geometrical optics approximation are also discussed.
基金Project supported by the National Natural Science Foundation of China(Grant No.61471039)
文摘Optoelectronic imaging equipment is easy to expose to active laser detection devices because of ＂cat eye＂ effect. In this paper, we propose a new structure of optical system to reduce the retroreflector effect of a cat eye target. Decentered field lens structure is adopted in the design without sacrificing imaging quality and clear aperture. An imaging system with±30° field of view is taken for example. The detailed design and simulation results are presented. The results indicate that this kind of optical system can reduce the retroreflection signal substantially and maintain acceptable imaging performance.
基金supported by the Scientific Research Starting Foundation for Fuzhou University,China(No.022538)
文摘This letter reports an autostereoscopic three-dimensional （3D） fiat panel display system employing a newly designed LCD-pixel-associated parallax barrier （LPB）. The battler＇s parameters can be conveniently determined by the LCD pixels and can help to greatly simplify the conventional design. The optical system of the proposed 3D display is built and simulated to verify the design. For further experimental demonstration, a 508-mm autostereoscopic 3D displayprototype is developed and it presents good stereoscopic images. Experimental results agree well wlth the simulation, which reveals a strong potential for 3D display applications.
基金supported by the National Natural Science Foundation of China(No.11474169)
文摘Integral imaging is a 3D display technology without any additional equipment. A new system is proposed in this paper, which uses a lenticular lens array to replace the lens array in the conventional integral imaging system. The lenticular integral imaging system reduces the complexity and the price of integral imaging system. The positive characteristics of conventional integral imaging system, such as full parallax and quasi-continuous view points, are still kept on the proposed system in horizontal direction. Optical results show that the time for calculating the elemental images is reduced by 25% compared with the conventional one. The resolution of integrated image in vertical direction is 4 times higher than that of conventional system. This proposed system opens a new way on application of integral imaging.
基金Supported by National Natural Science Foundation of China(Grant No.11361073)
文摘The paper solves analytically the Riemann problem for a nonstrictly hyperbolic system of conservation laws arising in geometrical optics,in which the flux contains the nonconvex function possessing an infinite number of inflection points.Firstly,the generalized Rankine–Hugoniot relations and entropy condition of delta shock waves and left（right）-contact delta shock waves are proposed and clarified.Secondly,with the help of the convex hull,seven kinds of structures of Riemann solutions are obtained.The solutions fall into three broad categories with a series of geometric structures involving simultaneously contact discontinuities,vacuums and delta shock waves.Finally,numerical experiments confirm the theoretical analysis.
文摘By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11371218, 91630205）.
文摘We extend the theory of global geometrical optics method, proposed originally for the linear scalar high-frequency wave-like equations in [Commun. Math. Sci., 2013, 11（1）： 105-140], to the more general vector- valued Schrodinger problems in the semi-classical regime. The key ingredient in the global geometrical optics method is a moving frame technique in the phase space. The governing equation is transformed into a new equation but of the same type when expressed in any moving frame induced by the underlying Hamiltonian flow. The classical Wentzel-Kramers-Brillouin （WKB） analysis benefits from this treatment as it maintains valid for arbitrary but fixed evolutionary time. It turns out that a WKB-type function defined merely on the underlying Lagrangian submanifold can be obtained with the help of this moving frame technique, and from which a uniform first-order approximation of the wave field can be derived, even around caustics. The general theory is exemplified by two specific instances. One is the two-level SchrSdinger system and the other is the periodic SchrSdinger equation. Numerical tests validate the theoretical results.
