Integral diffraction coefficients of the crystal are the essential data of a crystal spectrometer which is extensively used to measure quantitative x-ray spectra of high temperature plasmas in kilo-electron-volt regio...Integral diffraction coefficients of the crystal are the essential data of a crystal spectrometer which is extensively used to measure quantitative x-ray spectra of high temperature plasmas in kilo-electron-volt region. An experimental method has been developed to measure the integral diffraction coefficients of crystals on beamline 4B7 of Beijing Synchrotron Radiation Facility. The integral diffraction coefficients of several crystals including polyethylene terephthalate （PET）, thallium acid phthalate （T1AP） and rubidium acid phthalate （RAP） crystals have been measured in the x-ray energy range 2100-5600 eV and compared with the calculations of the ＇Darwin Prins＇ and the ＇Mosaic＇ models. It is shown that the integral diffraction coefficients of these crystals are between the calculations of the ＇Darwin Prins＇ and the ＇Mosaic＇ models, but more close to the ＇Darwin Prins＇ model calculations.展开更多
Silicon(Si)diffraction microlens arrays are usually used to integrating with infrared focal plane arrays(IRFPAs)to improve their performance.The errors of lithography are unavoidable in the process of the Si diffrac-t...Silicon(Si)diffraction microlens arrays are usually used to integrating with infrared focal plane arrays(IRFPAs)to improve their performance.The errors of lithography are unavoidable in the process of the Si diffrac-tion microlens arrays preparation in the conventional engraving method.It has a serious impact on its performance and subsequent applications.In response to the problem of errors of Si diffraction microlens arrays in the conven-tional method,a novel self-alignment method for high precision Si diffraction microlens arrays preparation is pro-posed.The accuracy of the Si diffractive microlens arrays preparation is determined by the accuracy of the first li-thography mask in the novel self-alignment method.In the subsequent etching,the etched area will be protected by the mask layer and the sacrifice layer or the protective layer.The unprotection area is carved to effectively block the non-etching areas,accurately etch the etching area required,and solve the problem of errors.The high precision Si diffraction microlens arrays are obtained by the novel self-alignment method and the diffraction effi-ciency could reach 92.6%.After integrating with IRFPAs,the average blackbody responsity increased by 8.3%,and the average blackbody detectivity increased by 10.3%.It indicates that the Si diffraction microlens arrays can improve the filling factor and reduce crosstalk of IRFPAs through convergence,thereby improving the perfor-mance of the IRFPAs.The results are of great reference significance for improving their performance through opti-mizing the preparation level of micro nano devices.展开更多
In this paper, Kirchhoff formula has been transformed from surface integral form into a line integral form. The new form of the formula can be applied to separate geometrical optical field from diffraction field, and ...In this paper, Kirchhoff formula has been transformed from surface integral form into a line integral form. The new form of the formula can be applied to separate geometrical optical field from diffraction field, and reduce the time of numerical computation greatly. Based on the new form, an analytical formula of diffraction field in the far zone has been presented for the polygonal aperture illuminated by a uniform plane wave.展开更多
A Fast Multipole Method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to...A Fast Multipole Method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to the boundary integral equation method (BIEM) for current diffraction from arbitrary 3D bodies. The boundary integral equation is discretized by higher order elements, the FMM is applied to avoid the matrix/vector product, and the resulting algebraic equation is solved by the Generalized Conjugate Residual method (GCR). Numerical examination shows that the FMM is more efficient than the direct evaluation method in computational cost and storage of computers.展开更多
Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line sourc...Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of ficti- tious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, and the comparison between the degenerated solutions and available results in single-phase case. Finally, the nature of diffraction of plane P waves around an alluvial valley in poroelastic half-space is investigated in detail through nu- merical examples.展开更多
Formulas of diffraction field of lossy wedges with less than 180?wedge angle are derived on the basis of the Fresnel-Kirchhoff wave theory and their numerical results are compared with those of the heuristic lossy wed...Formulas of diffraction field of lossy wedges with less than 180?wedge angle are derived on the basis of the Fresnel-Kirchhoff wave theory and their numerical results are compared with those of the heuristic lossy wedge diffraction coefficient given by Luebbers (1984), showing good agreement between the two types of numerical results which have different bases in theory. The agreement shows that the lossy wedge diffraction coefficient as an extension of UTD is quite reasonable.展开更多
This review analyzes following numerical methods of a solution of problems of a sound diffraction on ideal and elastic scatterers of a non-analytical form: a method of integral equations, a method of Green’s function...This review analyzes following numerical methods of a solution of problems of a sound diffraction on ideal and elastic scatterers of a non-analytical form: a method of integral equations, a method of Green’s functions, a method of finite elements, a boundary elements method, a method of Kupradze, a T-matrix method and a method of a geometrical theory of a diffraction.展开更多
Machine Hammer Peening(MHP)is an emergent treatment that induces high compressive Residual Stresses(RS)which can enhance the in-service performance of components.This paper studies the use of small diameter MHP tools ...Machine Hammer Peening(MHP)is an emergent treatment that induces high compressive Residual Stresses(RS)which can enhance the in-service performance of components.This paper studies the use of small diameter MHP tools to improve the Surface Integrity(SI)of the nickel-based alloy Inconel 718 used in critical aero-engine components.Complementarily,the relaxation of RS is analyzed by in-situ annealing tests at in-service temperature combined with X-ray diffraction measurement.For this purpose,age hardened Inconel 718 discs were turned as reference condition,and then a pneumatic MHP tool was used under different conditions:two tool diameters(4 mm and 12 mm),feed rates(2.5 m/min and 5.0 m/min)and stepover distances(0.07 mm and 0.35 mm).Subsequently,surface topography characterization,RS measurements,nanoindentation tests,and microstructural observations were conducted.The in-situ annealing tests were done in the X-ray diffractometer at 550°C for exposure periods from 0 to 20 h.The results demonstrate that 4 mm diameter tools generate smooth surfaces and induce significant compressive RS within a0.5 mm thick layer.Residual stresses are relaxed,but they remain compressive even after a long thermal exposure.The microstructure of the surface layer(<10–15μm)was affected by the preceding turning operation,but importantly,MHP did not induce additional damage.展开更多
The integral equation method for the simulation of the diffraction by optical gratings is an efficient numerical tool if profile gratings determined by simple crosssection curves are considered.This method in its rece...The integral equation method for the simulation of the diffraction by optical gratings is an efficient numerical tool if profile gratings determined by simple crosssection curves are considered.This method in its recent version is capable to tackle profile curves with corners,gratings with thin coated layers,and diffraction scenarios with unfavorably large ratio period over wavelength.We discuss special implementational issues including the efficient evaluation of the quasi-periodic Green kernels,the quadrature algorithm,and the iterative solution of the arising systems of linear equations.Finally,as an example we present the simulation of echelle gratings which demonstrates the efficency of our approach.展开更多
This paper is concerned with the problem of scattering of time-harmonic electromag- netic waves from penetrable diffraction gratings in the 2D polarization case. We propose a new, weakly singular, integral equation fo...This paper is concerned with the problem of scattering of time-harmonic electromag- netic waves from penetrable diffraction gratings in the 2D polarization case. We propose a new, weakly singular, integral equation formulation for the scattering problem which is proved to be uniquely solvable. A main feature of the new integral equation formula- tion is that it avoids the computation of the normal derivative of double-layer potentials which is difficult and time consuming. A fast numerical algorithm is also developed for the scattering problem, based on the NystrSm method for the new integral equation. Nu- merical examples are also shown to illustrate the applicability of the new integral equation formulation.展开更多
A novel method to generate a collimated hollow-laser-beam (HLB) by only a single axicon is proposed. With some reasonable assumptions, the radial light intensity distribution is calculated in detail by diffraction int...A novel method to generate a collimated hollow-laser-beam (HLB) by only a single axicon is proposed. With some reasonable assumptions, the radial light intensity distribution is calculated in detail by diffraction integral theory.The result of numerical simulation shows that this method is valid.Compared with other methods of generating HLB,this scheme is extraordinarily simple in principle and can be utilized experimentally to construct a light trap in atomic fountain for convenience.展开更多
In this letter, we propose a method for the numerical calculations of the femtosecond laser pulse passed through a subwavelength aperture. The time-dependent laser pulse is decomposed into a series of monochromatic si...In this letter, we propose a method for the numerical calculations of the femtosecond laser pulse passed through a subwavelength aperture. The time-dependent laser pulse is decomposed into a series of monochromatic simple harmonic waves. For the light field of the harmonic wave with a single frequency, the numerical calculation is made based on the solution of the Green's integral equation set of the electromagnetic waves. Such numerical solution is iterated for all the waves with different frequencies, and all the numerical solutions are transformed into the light fields in the time domain by inverse Fourier transform. The light intensity distributions transmitted the subwavelength aperture are calculated and the results show the propagation of the light field is along the direction of the medium interface.展开更多
In the integral imaging light field display, the introduction of a diffractive optical element (DOE) can solve the problem of limited depth of field of the traditional lens. However, the strong aberration of the DOE s...In the integral imaging light field display, the introduction of a diffractive optical element (DOE) can solve the problem of limited depth of field of the traditional lens. However, the strong aberration of the DOE significantly reduces the final display quality. Thus, herein, an end-to-end joint optimization method for optimizing DOE and aberration correction is proposed. The DOE model is established using thickness as the variable, and a deep learning network is built to preprocess the composite image loaded on the display panel. The simulation results show that the peak signal to noise ratio value of the optimized image increases by 8 dB, which confirms that the end-to-end joint optimization method can effectively reduce the aberration problem.展开更多
基金Project supported by the Foundation of National Key Laboratory of High Temperature and Density Plasma Physics(Grant No.9140C6804020704)the National Natural Science Foundation of China(Grant No.10874156)one of the authors,GanXin-Shi,was also partially supported by the School of Physical Science and Technology in Sichuan University,China
文摘Integral diffraction coefficients of the crystal are the essential data of a crystal spectrometer which is extensively used to measure quantitative x-ray spectra of high temperature plasmas in kilo-electron-volt region. An experimental method has been developed to measure the integral diffraction coefficients of crystals on beamline 4B7 of Beijing Synchrotron Radiation Facility. The integral diffraction coefficients of several crystals including polyethylene terephthalate （PET）, thallium acid phthalate （T1AP） and rubidium acid phthalate （RAP） crystals have been measured in the x-ray energy range 2100-5600 eV and compared with the calculations of the ＇Darwin Prins＇ and the ＇Mosaic＇ models. It is shown that the integral diffraction coefficients of these crystals are between the calculations of the ＇Darwin Prins＇ and the ＇Mosaic＇ models, but more close to the ＇Darwin Prins＇ model calculations.
基金Supported by the National Natural Science Foundation of China(NSFC 62105100)the National Key research and development program in the 14th five year plan(2021YFA1200700)。
文摘Silicon(Si)diffraction microlens arrays are usually used to integrating with infrared focal plane arrays(IRFPAs)to improve their performance.The errors of lithography are unavoidable in the process of the Si diffrac-tion microlens arrays preparation in the conventional engraving method.It has a serious impact on its performance and subsequent applications.In response to the problem of errors of Si diffraction microlens arrays in the conven-tional method,a novel self-alignment method for high precision Si diffraction microlens arrays preparation is pro-posed.The accuracy of the Si diffractive microlens arrays preparation is determined by the accuracy of the first li-thography mask in the novel self-alignment method.In the subsequent etching,the etched area will be protected by the mask layer and the sacrifice layer or the protective layer.The unprotection area is carved to effectively block the non-etching areas,accurately etch the etching area required,and solve the problem of errors.The high precision Si diffraction microlens arrays are obtained by the novel self-alignment method and the diffraction effi-ciency could reach 92.6%.After integrating with IRFPAs,the average blackbody responsity increased by 8.3%,and the average blackbody detectivity increased by 10.3%.It indicates that the Si diffraction microlens arrays can improve the filling factor and reduce crosstalk of IRFPAs through convergence,thereby improving the perfor-mance of the IRFPAs.The results are of great reference significance for improving their performance through opti-mizing the preparation level of micro nano devices.
文摘In this paper, Kirchhoff formula has been transformed from surface integral form into a line integral form. The new form of the formula can be applied to separate geometrical optical field from diffraction field, and reduce the time of numerical computation greatly. Based on the new form, an analytical formula of diffraction field in the far zone has been presented for the polygonal aperture illuminated by a uniform plane wave.
文摘A Fast Multipole Method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to the boundary integral equation method (BIEM) for current diffraction from arbitrary 3D bodies. The boundary integral equation is discretized by higher order elements, the FMM is applied to avoid the matrix/vector product, and the resulting algebraic equation is solved by the Generalized Conjugate Residual method (GCR). Numerical examination shows that the FMM is more efficient than the direct evaluation method in computational cost and storage of computers.
基金supported by National Natural Science Foundation of China (50978183)
文摘Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of ficti- tious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, and the comparison between the degenerated solutions and available results in single-phase case. Finally, the nature of diffraction of plane P waves around an alluvial valley in poroelastic half-space is investigated in detail through nu- merical examples.
文摘Formulas of diffraction field of lossy wedges with less than 180?wedge angle are derived on the basis of the Fresnel-Kirchhoff wave theory and their numerical results are compared with those of the heuristic lossy wedge diffraction coefficient given by Luebbers (1984), showing good agreement between the two types of numerical results which have different bases in theory. The agreement shows that the lossy wedge diffraction coefficient as an extension of UTD is quite reasonable.
文摘This review analyzes following numerical methods of a solution of problems of a sound diffraction on ideal and elastic scatterers of a non-analytical form: a method of integral equations, a method of Green’s functions, a method of finite elements, a boundary elements method, a method of Kupradze, a T-matrix method and a method of a geometrical theory of a diffraction.
基金the financial support given by EPSRC to the Grant LOFAMO(No.EP/X023281/1)the Basque Government for the financial support given from Elkartek Program to the Project FRONTIERS 2022—Superficies Multifuncionales en la Frontera del Conocimiento(No.KK2022/00109)。
文摘Machine Hammer Peening(MHP)is an emergent treatment that induces high compressive Residual Stresses(RS)which can enhance the in-service performance of components.This paper studies the use of small diameter MHP tools to improve the Surface Integrity(SI)of the nickel-based alloy Inconel 718 used in critical aero-engine components.Complementarily,the relaxation of RS is analyzed by in-situ annealing tests at in-service temperature combined with X-ray diffraction measurement.For this purpose,age hardened Inconel 718 discs were turned as reference condition,and then a pneumatic MHP tool was used under different conditions:two tool diameters(4 mm and 12 mm),feed rates(2.5 m/min and 5.0 m/min)and stepover distances(0.07 mm and 0.35 mm).Subsequently,surface topography characterization,RS measurements,nanoindentation tests,and microstructural observations were conducted.The in-situ annealing tests were done in the X-ray diffractometer at 550°C for exposure periods from 0 to 20 h.The results demonstrate that 4 mm diameter tools generate smooth surfaces and induce significant compressive RS within a0.5 mm thick layer.Residual stresses are relaxed,but they remain compressive even after a long thermal exposure.The microstructure of the surface layer(<10–15μm)was affected by the preceding turning operation,but importantly,MHP did not induce additional damage.
基金the German Federal Ministry of Education and Research under Grant number 13N8478.
文摘The integral equation method for the simulation of the diffraction by optical gratings is an efficient numerical tool if profile gratings determined by simple crosssection curves are considered.This method in its recent version is capable to tackle profile curves with corners,gratings with thin coated layers,and diffraction scenarios with unfavorably large ratio period over wavelength.We discuss special implementational issues including the efficient evaluation of the quasi-periodic Green kernels,the quadrature algorithm,and the iterative solution of the arising systems of linear equations.Finally,as an example we present the simulation of echelle gratings which demonstrates the efficency of our approach.
文摘This paper is concerned with the problem of scattering of time-harmonic electromag- netic waves from penetrable diffraction gratings in the 2D polarization case. We propose a new, weakly singular, integral equation formulation for the scattering problem which is proved to be uniquely solvable. A main feature of the new integral equation formula- tion is that it avoids the computation of the normal derivative of double-layer potentials which is difficult and time consuming. A fast numerical algorithm is also developed for the scattering problem, based on the NystrSm method for the new integral equation. Nu- merical examples are also shown to illustrate the applicability of the new integral equation formulation.
基金This work was supported by the National Natural Science Foundation of China (No. 60008002)the Key Oriental Project of Chinese Academy of Sciences (KGCX_2-SW-110)the Shanghai Optical-Tech Special Project (01DJGK015).
文摘A novel method to generate a collimated hollow-laser-beam (HLB) by only a single axicon is proposed. With some reasonable assumptions, the radial light intensity distribution is calculated in detail by diffraction integral theory.The result of numerical simulation shows that this method is valid.Compared with other methods of generating HLB,this scheme is extraordinarily simple in principle and can be utilized experimentally to construct a light trap in atomic fountain for convenience.
文摘In this letter, we propose a method for the numerical calculations of the femtosecond laser pulse passed through a subwavelength aperture. The time-dependent laser pulse is decomposed into a series of monochromatic simple harmonic waves. For the light field of the harmonic wave with a single frequency, the numerical calculation is made based on the solution of the Green's integral equation set of the electromagnetic waves. Such numerical solution is iterated for all the waves with different frequencies, and all the numerical solutions are transformed into the light fields in the time domain by inverse Fourier transform. The light intensity distributions transmitted the subwavelength aperture are calculated and the results show the propagation of the light field is along the direction of the medium interface.
基金supported by the National Natural Science Foundation of China(Nos.62175015,61905019,and 62075016)Fundamental Research Funds for the Central Universities(No.2021RC13)。
文摘In the integral imaging light field display, the introduction of a diffractive optical element (DOE) can solve the problem of limited depth of field of the traditional lens. However, the strong aberration of the DOE significantly reduces the final display quality. Thus, herein, an end-to-end joint optimization method for optimizing DOE and aberration correction is proposed. The DOE model is established using thickness as the variable, and a deep learning network is built to preprocess the composite image loaded on the display panel. The simulation results show that the peak signal to noise ratio value of the optimized image increases by 8 dB, which confirms that the end-to-end joint optimization method can effectively reduce the aberration problem.
