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Research on Weighted Bayesian Inversion Algorithm with Non-negative Least Squares Constraint

Yi-zhuo LIANG, Ling LIU, Li PENG, Jian QIU, Kai-qing LUO, Dong-mei LIU, and Peng HAN

In the multi-angle dynamic light scattering for nanoparticle size analysis， the weighted Bayesian inversion algorithm is proved to have a good anti-noise capability. However， it suffers from initial value sensitivity and long time-consuming. This paper presents a method of non-negative least squares constrained weighted Bayesian inversion algorithm， in which the results of the non-negative least squares method are used as the prior value as well as the optimization range of the median diameter and peak width of the weighted Bayesian algorithm. The simulated and experimental results demonstrate that this method can improve significantly the convergence and the anti-noise performance of the unimodal particle system. When there is a big noise， the convergence speed is increased by more than 8 times and the distribution error is guaranteed to be within 0.070 9. In the multi-angle dynamic light scattering for nanoparticle size analysis， the weighted Bayesian inversion algorithm is proved to have a good anti-noise capability. However， it suffers from initial value sensitivity and long time-consuming. This paper presents a method of non-negative least squares constrained weighted Bayesian inversion algorithm， in which the results of the non-negative least squares method are used as the prior value as well as the optimization range of the median diameter and peak width of the weighted Bayesian algorithm. The simulated and experimental results demonstrate that this method can improve significantly the convergence and the anti-noise performance of the unimodal particle system. When there is a big noise， the convergence speed is increased by more than 8 times and the distribution error is guaranteed to be within 0.070 9.

Acta Photonica Sinica

- Publication Date: Oct. 15, 2020
- Vol. 49, Issue 10, 1029001 (2020)

Approximate Model of Three-dimensional Clouds Multiple Scattering Based on Finitely Adjacent-cloud Radiative Transfer

Yin ZHANG, Jun MA, Jun-hua YAN, Hao YAN, Xi-yang ZHI, and Jin-nan GONG

In view of the high computational cost of radiative transfer for three-dimensional clouds in high-resolution detections， an approximate model of multiple scattering based on finitely adjacent-cloud was proposed. According to the radiative coupling law between adjacent clouds in different spatial positions， the finitely adjacent-cloud was divided into horizontally and vertically adjacent fields of clouds. The equation of variation for horizontal flux density was introduced to calculate the horizontal radiation exchange， thus characterize the radiative effects between horizontally adjacent fields of clouds. Regarding the error of flux along vertical direction， the function of compensation for flux density was used to correct it to more accurately characterize the radiative effect caused by vertically adjacent fields of clouds. A three-dimensional field of cumulus was selected as experimental scene， and the independent pixel approximation and the multiple scattering （calculated by the Eddington’s approximation） which combined with standard single scattering were compared. Experimental results show that the proposed model can improve the accuracies of upward and downward source functions by up to 47.39% and 33.93%， and the improvements are more than 8% and 10% when solar zenith angle is less than 60°； under different illuminating and observing conditions， mean relative errors of intensity for the proposed model are less than 40%； in terms of computational efficiency， the proposed model has significant advantage， which is helpful to research the rapid solution of radiative transfer in large-scale scenarios. In view of the high computational cost of radiative transfer for three-dimensional clouds in high-resolution detections， an approximate model of multiple scattering based on finitely adjacent-cloud was proposed. According to the radiative coupling law between adjacent clouds in different spatial positions， the finitely adjacent-cloud was divided into horizontally and vertically adjacent fields of clouds. The equation of variation for horizontal flux density was introduced to calculate the horizontal radiation exchange， thus characterize the radiative effects between horizontally adjacent fields of clouds. Regarding the error of flux along vertical direction， the function of compensation for flux density was used to correct it to more accurately characterize the radiative effect caused by vertically adjacent fields of clouds. A three-dimensional field of cumulus was selected as experimental scene， and the independent pixel approximation and the multiple scattering （calculated by the Eddington’s approximation） which combined with standard single scattering were compared. Experimental results show that the proposed model can improve the accuracies of upward and downward source functions by up to 47.39% and 33.93%， and the improvements are more than 8% and 10% when solar zenith angle is less than 60°； under different illuminating and observing conditions， mean relative errors of intensity for the proposed model are less than 40%； in terms of computational efficiency， the proposed model has significant advantage， which is helpful to research the rapid solution of radiative transfer in large-scale scenarios.

Acta Photonica Sinica

- Publication Date: Dec. 25, 2020
- Vol. 49, Issue 12, 180 (2020)

Inversion of Multimodal Particle Size Distribution Based on the Artificial Bee Colony Algorithm

Liang SHAN, Hao-ran LI, Bo HONG, Dao-dang WANG, Ting-ting ZHA, and Ming KONG

This research proposes to use Artificial Bee Colony algorithm to realize the inversion of the multimodal distribution of the particle size of small angle forward scattering method based on Mie scattering theory. The inversions of uniform spherical particle systems which obeying normal distribution， Rosin-Rammler distribution or Johnson's SB distribution function were performed， and the particle group issimulated as unimodal， bimodal and trimodal distribution respectively. The particle size can be well inverted by the Artificial Bee Colony algorithm. In the case of unimodal distribution， the relative root mean square error of the particle weight frequency distribution curve can be as low as 3.53×10-8. The relative root mean square error of the particle weight frequency distribution curve of the wide bimodal distribution decreased from 3.38% and 2.70% to 1.53% when it's compared with the independent mode algorithm Philip-Twomey-NNLS and Chahine. The accuracy of the Artificial Bee Colony algorithm is higher， and as the number of peaks increases， the width of the distribution curve becomes narrower and the noise increases， the errors of the Philip-Twomey-NNLS algorithm and the Chahine algorithm increase to 44.99% and 24.36%， respectively， while the error of the Artificial Bee Colony algorithm is 18.22%. A particle measurement system based on small angle forward scattering method was constructed， and the scattering images of 35 μm particle group and 30μm and 51μm mixed particle group of national standard particles were collected for experimental study. The relative error of the characteristic particle diameter obtained by Artificial Bee Colony algorithm is within 5%， which is about 50% lower than that of Philip-Twomey-NNLS algorithm. This research proposes to use Artificial Bee Colony algorithm to realize the inversion of the multimodal distribution of the particle size of small angle forward scattering method based on Mie scattering theory. The inversions of uniform spherical particle systems which obeying normal distribution， Rosin-Rammler distribution or Johnson's SB distribution function were performed， and the particle group issimulated as unimodal， bimodal and trimodal distribution respectively. The particle size can be well inverted by the Artificial Bee Colony algorithm. In the case of unimodal distribution， the relative root mean square error of the particle weight frequency distribution curve can be as low as 3.53×10-8. The relative root mean square error of the particle weight frequency distribution curve of the wide bimodal distribution decreased from 3.38% and 2.70% to 1.53% when it's compared with the independent mode algorithm Philip-Twomey-NNLS and Chahine. The accuracy of the Artificial Bee Colony algorithm is higher， and as the number of peaks increases， the width of the distribution curve becomes narrower and the noise increases， the errors of the Philip-Twomey-NNLS algorithm and the Chahine algorithm increase to 44.99% and 24.36%， respectively， while the error of the Artificial Bee Colony algorithm is 18.22%. A particle measurement system based on small angle forward scattering method was constructed， and the scattering images of 35 μm particle group and 30μm and 51μm mixed particle group of national standard particles were collected for experimental study. The relative error of the characteristic particle diameter obtained by Artificial Bee Colony algorithm is within 5%， which is about 50% lower than that of Philip-Twomey-NNLS algorithm.

Acta Photonica Sinica

- Publication Date: Dec. 25, 2020
- Vol. 49, Issue 12, 191 (2020)

Study on Polarized Reflection Characteristics of Space Object Thermal Control Coatings

Kai WANG, Hong LIU, and Xiu-xing ZHANG

Focusing on the demand of polarized detection for space objects， the polarized characteristics of space object thermal control coatings are simulated based on three-component polarized Bidirectional Reflection Distribution Function （pBRDF）model， the reflected Stokes vector and Degree of Linear Polarization（DOLP） in passive illustration condition are given， and the pBRDF matrix in active polarized detection is presented. The simulation and measurement of polarized characteristics of two typical space object thermal control coatings SR107 and S781 show the accuracy of three-component pBRDF model. The polarized properties of space object thermal coatings are analyzed with simulated and measured data. The conclusion of this paper presents important references for space object polarized detection applications. Focusing on the demand of polarized detection for space objects， the polarized characteristics of space object thermal control coatings are simulated based on three-component polarized Bidirectional Reflection Distribution Function （pBRDF）model， the reflected Stokes vector and Degree of Linear Polarization（DOLP） in passive illustration condition are given， and the pBRDF matrix in active polarized detection is presented. The simulation and measurement of polarized characteristics of two typical space object thermal control coatings SR107 and S781 show the accuracy of three-component pBRDF model. The polarized properties of space object thermal coatings are analyzed with simulated and measured data. The conclusion of this paper presents important references for space object polarized detection applications.

Acta Photonica Sinica

- Publication Date: Dec. 25, 2020
- Vol. 49, Issue 12, 205 (2020)

Regulation of Hierarchical Structure on Surface-enhanced Raman Scattering Characteristics of Nanoporous Metals

Ronghui CAI, Ruirui SONG, and Ling ZHANG

Hierarchical nanoporous materials with high-density "hot spots" were obtained by constructing secondary mesopores on the single-stage nanoporous metal ligaments. The finite difference time domain method was used to simulate the local electromagnetic field intensity and distribution of hierarchical nanoporous structures， and the SERS characteristics of dealloyed hierarchical nanoporous metals were detected with the help of Raman spectroscopy. Combined experimental results with theoretical analysis， it can be seen that the local electromagnetic field intensity and hot spots density of the hierarchical nanoporous metals are higher than that of the single-stage nanoporous metals， resulting in better SERS activity. The detection limit of hierarchical nanoporous gold and hierarchical nanoporous copper for crystal violet molecules can reach 10-11 mol·L-1， and the SERS enhancement factor is about two orders of magnitude higher than that of single-stage nanoporous metals. The study indicates that the introduction of secondary structure can greatly improve the local electromagnetic field intensity of single-stage nanoporous metals， which provides a new method for preparing of high-performance SERS substrate. Hierarchical nanoporous materials with high-density "hot spots" were obtained by constructing secondary mesopores on the single-stage nanoporous metal ligaments. The finite difference time domain method was used to simulate the local electromagnetic field intensity and distribution of hierarchical nanoporous structures， and the SERS characteristics of dealloyed hierarchical nanoporous metals were detected with the help of Raman spectroscopy. Combined experimental results with theoretical analysis， it can be seen that the local electromagnetic field intensity and hot spots density of the hierarchical nanoporous metals are higher than that of the single-stage nanoporous metals， resulting in better SERS activity. The detection limit of hierarchical nanoporous gold and hierarchical nanoporous copper for crystal violet molecules can reach 10-11 mol·L-1， and the SERS enhancement factor is about two orders of magnitude higher than that of single-stage nanoporous metals. The study indicates that the introduction of secondary structure can greatly improve the local electromagnetic field intensity of single-stage nanoporous metals， which provides a new method for preparing of high-performance SERS substrate.

Acta Photonica Sinica

- Publication Date: Jun. 25, 2021
- Vol. 50, Issue 6, 217 (2021)

Surface Field Distribution and Composite Scattering Characteristics of Three-dimensional Micro-nano Hemispherical Periodic Structure Optical Surface

Lei GONG, Yanglin LIU, Jie YU, Haibin WANG, Liguo WANG, Linqiu TAN, and Zhensen WU

In order to further expand the functional characteristics of micro nano periodic superstructure and meet the high-precision design requirements of optical periodic superstructure，based on the Multi-resolution Time-domain Method（MRTD）， starting from Maxwell equation and deducing the surface composite scattering field of the micro-nano three-dimensional hemispheric optical periodic structure， a good agreement is presented when the calculation results are compared with the results of the FDTD method. The surface field distribution of the mico-nano three-dimensional hemispheric optical periodic structure is given and the differential scattering cross section of mico-nano three-dimensional hemispheric optical periodic structure is numerically calculated. The influence of the filling material， hemisphere size， hemispheric distance and other parameters on the surface scattering field is simulated and analyzed. The following conclusions are obtained： the electric field distribution under P polarization could highlight the surface structure unit profile of periodic structure； the scattering field increases with the incident angle， and gradually decreases in the direction of the mirror scattering angle； the peak number of the scattering field of filled unit is consistent with the number of filling units in the detection range when the radius and wavelength values are equivalent； with the increase of the filling hemisphere distance， the maximum value of the scattering field increases successively， and the angle interval corresponding to the maximum value decreases sequentially. In order to further expand the functional characteristics of micro nano periodic superstructure and meet the high-precision design requirements of optical periodic superstructure，based on the Multi-resolution Time-domain Method（MRTD）， starting from Maxwell equation and deducing the surface composite scattering field of the micro-nano three-dimensional hemispheric optical periodic structure， a good agreement is presented when the calculation results are compared with the results of the FDTD method. The surface field distribution of the mico-nano three-dimensional hemispheric optical periodic structure is given and the differential scattering cross section of mico-nano three-dimensional hemispheric optical periodic structure is numerically calculated. The influence of the filling material， hemisphere size， hemispheric distance and other parameters on the surface scattering field is simulated and analyzed. The following conclusions are obtained： the electric field distribution under P polarization could highlight the surface structure unit profile of periodic structure； the scattering field increases with the incident angle， and gradually decreases in the direction of the mirror scattering angle； the peak number of the scattering field of filled unit is consistent with the number of filling units in the detection range when the radius and wavelength values are equivalent； with the increase of the filling hemisphere distance， the maximum value of the scattering field increases successively， and the angle interval corresponding to the maximum value decreases sequentially.

Acta Photonica Sinica

- Publication Date: Jul. 25, 2021
- Vol. 50, Issue 7, 173 (2021)

Effect of Resonant Scattering on Photonic Jet of a Microsphere

Qian LIU, and Jianqi SHEN

The relationship between the characteristic parameters of photon jet and those of particles is studied， including the mechanism in the generation of photon jet under different polarization modes of resonant and non-resonant scattering. The dependence of the photonic jet characteristic parameters on the refractive index and particle parameters is numerically analyzed with the Lorenz-Mie theory calculation. The effect of resonant scattering on the photonic jet is studied， showing the contribution from the resonant partial wave. Besides， a comparison is made for the photonic jets in linearly- and circularly-polarized irradiations. The results show that resonant scattering affects the photonic jet by narrowing its transverse width， shifting the focus inward to the particle surface， shortening the longitudinal length， enhancing the intensity at the focus and making the field distribution more complex. The relative intensity of the radial and transverse components of the electric field is different under TE and TM resonances. The polarization state of the incident light affects the transverse distribution of the photonic jet only. By controlling the parameters of incident light and particles， the characteristic parameters and the field distribution of the photonic jet can be modulated. The study provides theoretical reference for the applications of photonic jet. The relationship between the characteristic parameters of photon jet and those of particles is studied， including the mechanism in the generation of photon jet under different polarization modes of resonant and non-resonant scattering. The dependence of the photonic jet characteristic parameters on the refractive index and particle parameters is numerically analyzed with the Lorenz-Mie theory calculation. The effect of resonant scattering on the photonic jet is studied， showing the contribution from the resonant partial wave. Besides， a comparison is made for the photonic jets in linearly- and circularly-polarized irradiations. The results show that resonant scattering affects the photonic jet by narrowing its transverse width， shifting the focus inward to the particle surface， shortening the longitudinal length， enhancing the intensity at the focus and making the field distribution more complex. The relative intensity of the radial and transverse components of the electric field is different under TE and TM resonances. The polarization state of the incident light affects the transverse distribution of the photonic jet only. By controlling the parameters of incident light and particles， the characteristic parameters and the field distribution of the photonic jet can be modulated. The study provides theoretical reference for the applications of photonic jet.

Acta Photonica Sinica

- Publication Date: Jul. 25, 2021
- Vol. 50, Issue 7, 182 (2021)

Multi-point Controllable Wavefront Shaping Based on Superpixel Method

Yang ZHAO, and Yingchun DING

A new algorithm for iterative optimization of wavefront shaping which is the combination of Nondominated Sorting Genetic Algorithm Ⅱ-Hybrid and the superpixel method is proposed， using digital micromirror devices for light field modulation. Multi-point controllable light focusing of reflective wavefront shaping is realized. Our method has two advantages. On the one hand， while increasing the enhancement factor， it also ensures that the uniformity of the intensity of multiple focal points is controllable， that is， all focal points have uniform intensity； on the other hand， the structure of reflective wavefront shaping is more conducive to application. In order to verify our algorithm， we use frosted glass as the scattering media in the experiment. The experimental results show that， compared with the genetic algorithm based on superpixel method， the enhancement factor of the focal point is increased by 24.12%， and the coefficient of variation is reduced from 13.3% to 4.2%. This research provides a new method for reflective wavefront shaping multi-point light focusing， and has potential application value in the field of optogenetics and light capture. A new algorithm for iterative optimization of wavefront shaping which is the combination of Nondominated Sorting Genetic Algorithm Ⅱ-Hybrid and the superpixel method is proposed， using digital micromirror devices for light field modulation. Multi-point controllable light focusing of reflective wavefront shaping is realized. Our method has two advantages. On the one hand， while increasing the enhancement factor， it also ensures that the uniformity of the intensity of multiple focal points is controllable， that is， all focal points have uniform intensity； on the other hand， the structure of reflective wavefront shaping is more conducive to application. In order to verify our algorithm， we use frosted glass as the scattering media in the experiment. The experimental results show that， compared with the genetic algorithm based on superpixel method， the enhancement factor of the focal point is increased by 24.12%， and the coefficient of variation is reduced from 13.3% to 4.2%. This research provides a new method for reflective wavefront shaping multi-point light focusing， and has potential application value in the field of optogenetics and light capture.

Acta Photonica Sinica

- Publication Date: Sep. 25, 2021
- Vol. 50, Issue 9, 0929002 (2021)

Dynamic Evolution of the Patically Coherent Circular Edge Dislocation Beams Propagating in Biological Tissues

Meiling DUAN, Jiao DU, Zhiguo ZHAO, Xiaodong HUANG, Yanqin GAO, and Chaoliang DING

The analytical expression for the cross spectral density function of partially coherent circular edge dislocation beams propagating in the deep dermis of mouse tissue is derived based on the generalized Huygens-Fresnel principle， the effects of the initial beam parameters （the beam wavelength λ and the number of circular edge dislocations n） and the propagation distance z on the normalized intensity distribution， phase evolution and propagation trajectory of the beam are investigated. The results show that the central intensity of the partially coherent circular edge dislocation beam with n dislocation number is the largest in the source plane， and 2n secondary peaks symmetrically distribute on both sides. With the increment of propagation distance， the intensity distribution gradually evolves from multi-peak to single-peak， the longer the wavelength is， the smaller the n is， the faster the intensity distribution evolution is. The more the number of dislocations is， the better the beam stability is. Additionally， in the source plane the radius of the innermost ring of n circular edge dislocations decreases as the number of dislocations increases. Owing to the combination of the biological tissue turbulence induction and diffraction effect， the n circular edge dislocation has split into n sets of coherent vortices whose topological charges are "+1" and "-1" from the beginning of the propagation， respectively. As the propagation proceeds， n sets of coherent vortices with topological charges of "+1" and "-1" will be generated. The bigger the wavelength is， the more the n is， the faster the evolution of the beam phase， the more the distribution of the coherent vortices tends to be concentrated， and finally all the coherent vortices are annihilated. The smaller the distance between the coherent vortices， the earlier the annihilation. The longer the wavelength is， the larger the value of n is， the earlier the annihilation of the initial coherent vortices pairs is， and the longer the propagation distance to the total annihilation is. The smaller the wavelength is， the larger the value of n is， the earlier the annihilation of the newly generated coherent vortices pairs is， and the longer the propagation distance to the total annihilation is. The analytical expression for the cross spectral density function of partially coherent circular edge dislocation beams propagating in the deep dermis of mouse tissue is derived based on the generalized Huygens-Fresnel principle， the effects of the initial beam parameters （the beam wavelength λ and the number of circular edge dislocations n） and the propagation distance z on the normalized intensity distribution， phase evolution and propagation trajectory of the beam are investigated. The results show that the central intensity of the partially coherent circular edge dislocation beam with n dislocation number is the largest in the source plane， and 2n secondary peaks symmetrically distribute on both sides. With the increment of propagation distance， the intensity distribution gradually evolves from multi-peak to single-peak， the longer the wavelength is， the smaller the n is， the faster the intensity distribution evolution is. The more the number of dislocations is， the better the beam stability is. Additionally， in the source plane the radius of the innermost ring of n circular edge dislocations decreases as the number of dislocations increases. Owing to the combination of the biological tissue turbulence induction and diffraction effect， the n circular edge dislocation has split into n sets of coherent vortices whose topological charges are "+1" and "-1" from the beginning of the propagation， respectively. As the propagation proceeds， n sets of coherent vortices with topological charges of "+1" and "-1" will be generated. The bigger the wavelength is， the more the n is， the faster the evolution of the beam phase， the more the distribution of the coherent vortices tends to be concentrated， and finally all the coherent vortices are annihilated. The smaller the distance between the coherent vortices， the earlier the annihilation. The longer the wavelength is， the larger the value of n is， the earlier the annihilation of the initial coherent vortices pairs is， and the longer the propagation distance to the total annihilation is. The smaller the wavelength is， the larger the value of n is， the earlier the annihilation of the newly generated coherent vortices pairs is， and the longer the propagation distance to the total annihilation is.

Acta Photonica Sinica

- Publication Date: Sep. 25, 2021
- Vol. 50, Issue 9, 0929001 (2021)

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