Journals > > Topics > Scattering
Scattering|139 Article(s)
Machine Learning-Based Inversion Algorithm for Particle Size Distribution of Non-Spherical Particle System
Jiaxing Xu, Min Xia, Kecheng Yang, Yinan Wu, and Wei Li
ObjectiveIn the measurement of particle size distribution, light scattering methods have the advantages of a wide measurement range, high speed, and non-contact measurement. Among them, the dynamic light scattering technique is an important method to measure the size distribution of nanometer to micron particles.In medical testing, the analysis of red blood cells is a common method for disease diagnosis. The variation coefficient of the red cell volume distribution width (RDW) is generally used to characterize the uniformity in size and shape of red blood cells in blood samples, whose increment often indicates diseases. The variation coefficient of RDW can be calculated by inversion of the particle size distribution of blood cells, which can provide reliable support in the early detection and diagnosis of some major diseases.Current particle size inversion algorithms are mostly based on the regularization method, but the traditional regularization algorithm lacks the inversion model and algorithm for the particle size distribution of non-spherical particle systems. Moreover, its performance on narrowly distributed particle systems and the multi-angle scattered light analysis are not satisfying, which limits its application in biomedical fields.Therefore, the corresponding model and algorithm for particle size distribution analysis based on machine learning are developed in this study, and the simulation results are provided.MethodsIt has been shown that neural networks have advantages in expressing complex objective functions such as particle size distribution, which can hierarchically describe effective data characteristics from a large amount of input data. Of the neural networks, generalized regression neural networks have been proven to be effective for function approximation. Thus, it can be widely used in various research fields requiring parameter inversion of nonlinear pathological equations without a priori knowledge of the complex arithmetic relations involved in the problem model.In this paper, the idea of introducing generalized regression neural networks into the inversion of particle size distribution is adopted. A generalized regression neural network based on the inversion model and algorithm for the particle size distribution of particle systems is designed, which can be applied to the particle size analysis by the multi-angle dynamic light scattering method. The proposed algorithm is tested by simulations using biconcave-disk and ellipsoidal red blood cells as typical non-spherical particle models in the biomedical field.Results and DiscussionsThe evaluation indexes selected in the training process of the inversion model are clarified, and the particle size distributions of non-spherical particle systems such as biconcave-disk red blood cells (Fig. 4) and ellipsoidal red blood cells (Fig. 7) are retrieved by the neural network. The optimization method for the training matrix expansion is proposed in the training process of the network (Table 1 and Table 3). During the inversion of the particle size distribution curves of biconcave-disk and ellipsoidal models, the use of 20 sets of training matrices to jointly train the neural network can result in evaluation indexes with mean values as small as 1.0027 and 0.6568, respectively.The network (Table 2 and Table 4) is tested, and the result reveals that it has a significant advantage over the conventional regularized Tikhonov algorithm (Fig. 5 and Fig. 8) using at least two scattering angles. The use of only two scattering angles means that it is easier to build and debug a multi-angle dynamic light scattering measurement system for practical applications, which can reduce the systematic errors introduced by the consistency of concerned devices.ConclusionsThe experimental results show that compared with the conventional regularized Tikhonov algorithm, the inversion algorithm designed in this paper is more accurate and less time-consuming, and the neural network model can be well adapted to biconcave-disk and ellipsoidal models. The number of scattering angles in the multi-angle dynamic light scattering method is also considered, and the results show that the accurate inversion of the particle size distribution of non-spherical particle systems can still be achieved with data obtained at only two scattering angles. As long as the shape of the particles in the particle system to be measured can be clearly expressed, such as a mathematical expression for the particle shape, the network model can be extended to many other cases of non-spherical particle systems.As an example of analyzing a non-spherical particle system, if the RDW-CV is to be further calculated after the inversion of the particle size distribution of the red blood cells, it is required that the particle size distribution curve obtained from the inversion is as close as possible to the actual particle size distribution curve at each particle size. The evaluation indexes used in this study can precisely characterize the difference between the two particle size distribution curves. Hence, it is expected that if the accuracy step of particle size inversion is appropriately reduced, it can be applied to rapid clinical detection of the particle size distribution of red blood cells for early detection and diagnosis of some major diseases. ObjectiveIn the measurement of particle size distribution, light scattering methods have the advantages of a wide measurement range, high speed, and non-contact measurement. Among them, the dynamic light scattering technique is an important method to measure the size distribution of nanometer to micron particles.In medical testing, the analysis of red blood cells is a common method for disease diagnosis. The variation coefficient of the red cell volume distribution width (RDW) is generally used to characterize the uniformity in size and shape of red blood cells in blood samples, whose increment often indicates diseases. The variation coefficient of RDW can be calculated by inversion of the particle size distribution of blood cells, which can provide reliable support in the early detection and diagnosis of some major diseases.Current particle size inversion algorithms are mostly based on the regularization method, but the traditional regularization algorithm lacks the inversion model and algorithm for the particle size distribution of non-spherical particle systems. Moreover, its performance on narrowly distributed particle systems and the multi-angle scattered light analysis are not satisfying, which limits its application in biomedical fields.Therefore, the corresponding model and algorithm for particle size distribution analysis based on machine learning are developed in this study, and the simulation results are provided.MethodsIt has been shown that neural networks have advantages in expressing complex objective functions such as particle size distribution, which can hierarchically describe effective data characteristics from a large amount of input data. Of the neural networks, generalized regression neural networks have been proven to be effective for function approximation. Thus, it can be widely used in various research fields requiring parameter inversion of nonlinear pathological equations without a priori knowledge of the complex arithmetic relations involved in the problem model.In this paper, the idea of introducing generalized regression neural networks into the inversion of particle size distribution is adopted. A generalized regression neural network based on the inversion model and algorithm for the particle size distribution of particle systems is designed, which can be applied to the particle size analysis by the multi-angle dynamic light scattering method. The proposed algorithm is tested by simulations using biconcave-disk and ellipsoidal red blood cells as typical non-spherical particle models in the biomedical field.Results and DiscussionsThe evaluation indexes selected in the training process of the inversion model are clarified, and the particle size distributions of non-spherical particle systems such as biconcave-disk red blood cells (Fig. 4) and ellipsoidal red blood cells (Fig. 7) are retrieved by the neural network. The optimization method for the training matrix expansion is proposed in the training process of the network (Table 1 and Table 3). During the inversion of the particle size distribution curves of biconcave-disk and ellipsoidal models, the use of 20 sets of training matrices to jointly train the neural network can result in evaluation indexes with mean values as small as 1.0027 and 0.6568, respectively.The network (Table 2 and Table 4) is tested, and the result reveals that it has a significant advantage over the conventional regularized Tikhonov algorithm (Fig. 5 and Fig. 8) using at least two scattering angles. The use of only two scattering angles means that it is easier to build and debug a multi-angle dynamic light scattering measurement system for practical applications, which can reduce the systematic errors introduced by the consistency of concerned devices.ConclusionsThe experimental results show that compared with the conventional regularized Tikhonov algorithm, the inversion algorithm designed in this paper is more accurate and less time-consuming, and the neural network model can be well adapted to biconcave-disk and ellipsoidal models. The number of scattering angles in the multi-angle dynamic light scattering method is also considered, and the results show that the accurate inversion of the particle size distribution of non-spherical particle systems can still be achieved with data obtained at only two scattering angles. As long as the shape of the particles in the particle system to be measured can be clearly expressed, such as a mathematical expression for the particle shape, the network model can be extended to many other cases of non-spherical particle systems.As an example of analyzing a non-spherical particle system, if the RDW-CV is to be further calculated after the inversion of the particle size distribution of the red blood cells, it is required that the particle size distribution curve obtained from the inversion is as close as possible to the actual particle size distribution curve at each particle size. The evaluation indexes used in this study can precisely characterize the difference between the two particle size distribution curves. Hence, it is expected that if the accuracy step of particle size inversion is appropriately reduced, it can be applied to rapid clinical detection of the particle size distribution of red blood cells for early detection and diagnosis of some major diseases.
Acta Optica Sinica
- Publication Date: May. 10, 2023
- Vol. 43, Issue 9, 0929002 (2023)
Study on Raman Enhancement of Silver/Paper Composite Structure Using Inkjet Printing
Zhimou Tang, Ning Sun, and Jie Zhang
ObjectiveSurface enhanced Raman scattering (SERS) is a multifunctional detection technology widely used in chemical and biological molecules. It has the advantages of high detection sensitivity, no sample treatment, nondestructive testing, etc. SERS technology can realize ultra-low concentration molecular detection or even single molecule detection. As a flexible substrate material, paper is different from the traditional rigid substrate. The rigid substrate is fragile, which greatly limits the application of plasma nanostructures. The flexible substrate can be easily cut into different shapes and sizes to meet the needs of non-planar, flexible, and other applications. At the same time, as paper has the characteristics of easy access and low cost, there are many explorations in the preparation of paper-based SERS substrates, and there are various preparation methods for paper-based SERS substrates, such as pen on paper, spray preparation, and other preparation methods. However, the preparation process of these paper-based SERS substrates is relatively cumbersome, and it is difficult to meet the different pattern design requirements under different environmental conditions. In this paper, the Ag-paper-based SERS substrate is prepared by inkjet printing, and the high-performance paper-based SERS substrate is prepared by selecting the optimal parameters.MethodsIn this study, an Ag-paper-based SERS substrate is prepared by inkjet printing on hydrophobic A4 paper. Firstly, a brown-green silver sol solution with an average particle size of 58.6 nm is prepared by the Lee preparation method, and the parameters of silver nitrate, sodium citrate, and heating time are set. Silver ink is prepared as follows. Silver sol is centrifuged and ultrasonically operated, the supernatant is removed, and the silver sol washing process is repeated twice. According to the silver sol concentration multiples of 10, 20, 33, and 50, supernatants of 50, 53, 54, and 55 mL on the surface are removed, respectively. The absolute ethanol and glycerin are added according to the configuration scheme of silver ink, and the silver ink is filtered with a polytetrafluoroethylene (PTFE) membrane filter (with a pore size of 0.2 mm), so as to ensure the working fluency of the silver ink. After that, the paper receives hydrophobic treatment with a 20% mixed hexanol solution of dodecene succinic anhydride (DDSA). Next, the silver ink is put into the ink cartridge for a few minutes and printed on the hydrophobic A4 paper. Finally, the prepared Ag-paper-based SERS substrate is used for Raman detection of probe molecules.Results and DiscussionsThe prepared Ag-paper-based SERS substrate can be mass-produced rapidly. At the same time, it is cheap, and the preparation scheme is simple. The operator can quickly start to prepare and apply and thus realize multi-molecule detection. Through the optimal selection of silver ink multiples and the number of printing layers (Fig. 2), when the silver ink concentration is 50 times, and the number of printing layers is 7, the prepared Ag-paper-based SERS substrate has high Raman enhancement performance, with the maximum enhancement factor of about 1.92×109 and the relative standard deviation (RSD) of 14.3% (Fig. 3). After hydrophobic treatment of A4 paper, Raman detection sensitivity is greatly improved (Fig. 4). This is because after hydrophobic treatment, the contact angle of liquid droplets on the paper surface has been greatly improved, which leads to more silver nanoparticles per unit surface area. Therefore, Raman detection intensity has been enhanced. Paper is a flexible material. The flexible characteristic experiment (Fig. 5) shows that the prepared Ag-paper-based SERS substrate also shows excellent uniformity after bending, which proves that the Ag-paper-based SERS substrate has strong stability.ConclusionsIn this paper, the silver ink is printed on the hydrophobic A4 paper surface by an inkjet printing method, so as to serve as a flexible SERS substrate. By studying the influence of different silver ink multiples and printing layers on Raman detection sensitivity, it can be found that when the silver ink concentration is 50 times, and the number of printing layers is 7, the detection concentration of R6G molecules on SERS substrate is as low as 10-10 mol/L, and the maximum enhancement factor is about 1.92×109. At the same time, the SERS substrate has excellent uniformity, and the optimal RSD calculation result is 14.3%. The flexibility of Ag-paper-based SERS substrate is studied on the apple surface, and the detection of multi-molecules is realized. The method has the advantages of low price and mass production. Finally, according to the scanning electron microscope (SEM) results of the SERS substrate, the electromagnetic field enhancement characteristics of the SERS substrate are calculated by using finite-difference time-domain (FDTD) software. According to the numerical simulation and experimental results, the optimal number of printing layers is 7. ObjectiveSurface enhanced Raman scattering (SERS) is a multifunctional detection technology widely used in chemical and biological molecules. It has the advantages of high detection sensitivity, no sample treatment, nondestructive testing, etc. SERS technology can realize ultra-low concentration molecular detection or even single molecule detection. As a flexible substrate material, paper is different from the traditional rigid substrate. The rigid substrate is fragile, which greatly limits the application of plasma nanostructures. The flexible substrate can be easily cut into different shapes and sizes to meet the needs of non-planar, flexible, and other applications. At the same time, as paper has the characteristics of easy access and low cost, there are many explorations in the preparation of paper-based SERS substrates, and there are various preparation methods for paper-based SERS substrates, such as pen on paper, spray preparation, and other preparation methods. However, the preparation process of these paper-based SERS substrates is relatively cumbersome, and it is difficult to meet the different pattern design requirements under different environmental conditions. In this paper, the Ag-paper-based SERS substrate is prepared by inkjet printing, and the high-performance paper-based SERS substrate is prepared by selecting the optimal parameters.MethodsIn this study, an Ag-paper-based SERS substrate is prepared by inkjet printing on hydrophobic A4 paper. Firstly, a brown-green silver sol solution with an average particle size of 58.6 nm is prepared by the Lee preparation method, and the parameters of silver nitrate, sodium citrate, and heating time are set. Silver ink is prepared as follows. Silver sol is centrifuged and ultrasonically operated, the supernatant is removed, and the silver sol washing process is repeated twice. According to the silver sol concentration multiples of 10, 20, 33, and 50, supernatants of 50, 53, 54, and 55 mL on the surface are removed, respectively. The absolute ethanol and glycerin are added according to the configuration scheme of silver ink, and the silver ink is filtered with a polytetrafluoroethylene (PTFE) membrane filter (with a pore size of 0.2 mm), so as to ensure the working fluency of the silver ink. After that, the paper receives hydrophobic treatment with a 20% mixed hexanol solution of dodecene succinic anhydride (DDSA). Next, the silver ink is put into the ink cartridge for a few minutes and printed on the hydrophobic A4 paper. Finally, the prepared Ag-paper-based SERS substrate is used for Raman detection of probe molecules.Results and DiscussionsThe prepared Ag-paper-based SERS substrate can be mass-produced rapidly. At the same time, it is cheap, and the preparation scheme is simple. The operator can quickly start to prepare and apply and thus realize multi-molecule detection. Through the optimal selection of silver ink multiples and the number of printing layers (Fig. 2), when the silver ink concentration is 50 times, and the number of printing layers is 7, the prepared Ag-paper-based SERS substrate has high Raman enhancement performance, with the maximum enhancement factor of about 1.92×109 and the relative standard deviation (RSD) of 14.3% (Fig. 3). After hydrophobic treatment of A4 paper, Raman detection sensitivity is greatly improved (Fig. 4). This is because after hydrophobic treatment, the contact angle of liquid droplets on the paper surface has been greatly improved, which leads to more silver nanoparticles per unit surface area. Therefore, Raman detection intensity has been enhanced. Paper is a flexible material. The flexible characteristic experiment (Fig. 5) shows that the prepared Ag-paper-based SERS substrate also shows excellent uniformity after bending, which proves that the Ag-paper-based SERS substrate has strong stability.ConclusionsIn this paper, the silver ink is printed on the hydrophobic A4 paper surface by an inkjet printing method, so as to serve as a flexible SERS substrate. By studying the influence of different silver ink multiples and printing layers on Raman detection sensitivity, it can be found that when the silver ink concentration is 50 times, and the number of printing layers is 7, the detection concentration of R6G molecules on SERS substrate is as low as 10-10 mol/L, and the maximum enhancement factor is about 1.92×109. At the same time, the SERS substrate has excellent uniformity, and the optimal RSD calculation result is 14.3%. The flexibility of Ag-paper-based SERS substrate is studied on the apple surface, and the detection of multi-molecules is realized. The method has the advantages of low price and mass production. Finally, according to the scanning electron microscope (SEM) results of the SERS substrate, the electromagnetic field enhancement characteristics of the SERS substrate are calculated by using finite-difference time-domain (FDTD) software. According to the numerical simulation and experimental results, the optimal number of printing layers is 7.
Acta Optica Sinica
- Publication Date: May. 10, 2023
- Vol. 43, Issue 9, 0929001 (2023)
Simulation of Light Scattering and Imaging of Relay Wall in Non-Line-of-Sight Imaging
Yujie Fang, Xia Wang, Zhibin Sun, and Binghua Su
Results and Discussions In computational imaging of out-of-sight targets by virtue of reflective relay walls, the scattering characteristics of the relay wall and the measured target surface directly affect the imaging results. However, it is difficult to find a relay wall material with standardized scattering characteristics in reality. Therefore, this paper firstly proposes a scattering characteristic description method, namely describing with the composition of specular reflection, Lambert scattering and Gaussian scattering, abstracting the scattering characteristics of materials as scattering components, and simulating the scattering characteristics of different materials through computer simulation. Secondly, by tracking a large number of rays and observing the scattered light spots on the relay walls, it is found that the subjective visual effect of NLOS results is poor when the scattering characteristics of the target and the relay wall are similar. Finally, the images of scattered spots are measured by standard deviation, and a multi-factor analysis of variance is used to analyze the relationship between the scattering composition and the standard deviation of the NLOS image. The experiment suggests that the size of the Gaussian scattering angle has a significant effect on the NLOS imaging quality under low specular reflection composition conditions (≤5%).ObjectiveApplying computational imaging to behind the obstruction or other out-of-sight targets by virtue of relay walls is called non-line-of-sight imaging (NLOS). NLOS technology has great application potential in the fields of medical care, national defense, road safety, and scientific research. It can extend the range of human observation in scenarios where devices or human eyes cannot see. The existing NLOS technologies mainly include transient imaging, range-gated imaging, and passive NLOS imaging. These methods are mostly dedicated for Lambert reflector relay walls, featuring complex system structure, low imaging speed and high cost. However, the common materials in application scenarios are all non-Lambert reflectors. To this end, based on the bidirectional reflection distribution theory on relay wall materials, this paper proposes a material scattering characteristic description method, which realizes light intensity signal tracking and simulation of targets out of sight by configuring different scattering components of the relay wall and conducting massive ray tracing. The simulation work can provide a theoretical basis and experimental basis for the practical application of passive NLOS technologies, and provide a reference for relay wall selection, so it is of practical application significance.MethodsSince there are many kinds of relay walls actually used for NLOS, with quite different scattering characteristics, it is difficult to find a standardized material. Therefore, this paper proposes a material scattering description model based on the traditional bidirectional reflectance distribution function (BRDF) to define the scattering characteristics by composition. Firstly, it is assumed that the scattering characteristics of relay wall materials are described by a combination of specular reflection, Lambert scattering, and Gaussian scattering, with transmission light and superficial stochastic scattering ignored. Then, different combinations of the scattering components are set separately to image the scattered light spots on relay walls, and the imaging results are evaluated by the standard deviations of the images. Finally, the scattering composition is taken as the independent variable and the standard deviation of the image is taken as the dependent variable, multi-factor analysis of variance is used to quantitatively analyze the impact of the scattering compositions of relay walls on the light signals of targets out of sight.ConclusionsNLOS imaging technology for targets out of sight via relay walls has received wide attention in recent years. This paper proposes a material scattering characteristics description method for non-Lambert scattering relay walls in passive NLOS imaging scenarios and an NLOS simulation method, and analyzes the simulation results by variance analysis. Firstly, based on the material scattering principle, the optical scattering characteristics of some materials in nature are expressed as a combination of diffuse reflection, specular reflection and Gaussian scattering. Secondly, computer simulation is used to simulate the effect of different scattering characteristics of the relay wall and the target surface on the quality of NLOS imaging. Finally, multi-factor analysis of variance suggests a significant effect of Gaussian scattering in the scattering characteristics of the material on the standard deviation of the NLOS images. The proposed analysis method can provide prior knowledge for passive NLOS imaging algorithm under the condition that the scattering characteristics of the relay wall are certain. Besides, it can give an ideal transmission result of the optical signals of an out-of-sight target to compare with the actual result, reconstruct ideal NLOS signals to verify the effectiveness of actual reconstruction algorithm, provide a relay wall material selection scheme for NLOS imaging, and provide an analysis method for passive NLOS imaging conditions. Results and Discussions In computational imaging of out-of-sight targets by virtue of reflective relay walls, the scattering characteristics of the relay wall and the measured target surface directly affect the imaging results. However, it is difficult to find a relay wall material with standardized scattering characteristics in reality. Therefore, this paper firstly proposes a scattering characteristic description method, namely describing with the composition of specular reflection, Lambert scattering and Gaussian scattering, abstracting the scattering characteristics of materials as scattering components, and simulating the scattering characteristics of different materials through computer simulation. Secondly, by tracking a large number of rays and observing the scattered light spots on the relay walls, it is found that the subjective visual effect of NLOS results is poor when the scattering characteristics of the target and the relay wall are similar. Finally, the images of scattered spots are measured by standard deviation, and a multi-factor analysis of variance is used to analyze the relationship between the scattering composition and the standard deviation of the NLOS image. The experiment suggests that the size of the Gaussian scattering angle has a significant effect on the NLOS imaging quality under low specular reflection composition conditions (≤5%).ObjectiveApplying computational imaging to behind the obstruction or other out-of-sight targets by virtue of relay walls is called non-line-of-sight imaging (NLOS). NLOS technology has great application potential in the fields of medical care, national defense, road safety, and scientific research. It can extend the range of human observation in scenarios where devices or human eyes cannot see. The existing NLOS technologies mainly include transient imaging, range-gated imaging, and passive NLOS imaging. These methods are mostly dedicated for Lambert reflector relay walls, featuring complex system structure, low imaging speed and high cost. However, the common materials in application scenarios are all non-Lambert reflectors. To this end, based on the bidirectional reflection distribution theory on relay wall materials, this paper proposes a material scattering characteristic description method, which realizes light intensity signal tracking and simulation of targets out of sight by configuring different scattering components of the relay wall and conducting massive ray tracing. The simulation work can provide a theoretical basis and experimental basis for the practical application of passive NLOS technologies, and provide a reference for relay wall selection, so it is of practical application significance.MethodsSince there are many kinds of relay walls actually used for NLOS, with quite different scattering characteristics, it is difficult to find a standardized material. Therefore, this paper proposes a material scattering description model based on the traditional bidirectional reflectance distribution function (BRDF) to define the scattering characteristics by composition. Firstly, it is assumed that the scattering characteristics of relay wall materials are described by a combination of specular reflection, Lambert scattering, and Gaussian scattering, with transmission light and superficial stochastic scattering ignored. Then, different combinations of the scattering components are set separately to image the scattered light spots on relay walls, and the imaging results are evaluated by the standard deviations of the images. Finally, the scattering composition is taken as the independent variable and the standard deviation of the image is taken as the dependent variable, multi-factor analysis of variance is used to quantitatively analyze the impact of the scattering compositions of relay walls on the light signals of targets out of sight.ConclusionsNLOS imaging technology for targets out of sight via relay walls has received wide attention in recent years. This paper proposes a material scattering characteristics description method for non-Lambert scattering relay walls in passive NLOS imaging scenarios and an NLOS simulation method, and analyzes the simulation results by variance analysis. Firstly, based on the material scattering principle, the optical scattering characteristics of some materials in nature are expressed as a combination of diffuse reflection, specular reflection and Gaussian scattering. Secondly, computer simulation is used to simulate the effect of different scattering characteristics of the relay wall and the target surface on the quality of NLOS imaging. Finally, multi-factor analysis of variance suggests a significant effect of Gaussian scattering in the scattering characteristics of the material on the standard deviation of the NLOS images. The proposed analysis method can provide prior knowledge for passive NLOS imaging algorithm under the condition that the scattering characteristics of the relay wall are certain. Besides, it can give an ideal transmission result of the optical signals of an out-of-sight target to compare with the actual result, reconstruct ideal NLOS signals to verify the effectiveness of actual reconstruction algorithm, provide a relay wall material selection scheme for NLOS imaging, and provide an analysis method for passive NLOS imaging conditions.
Acta Optica Sinica
- Publication Date: Feb. 25, 2023
- Vol. 43, Issue 4, 0429001 (2023)
Electromagnetic Scattering of Dual Gaussian Beams by an Anisotropic Coated Sphere
Jing Bai, Yu Gao, Chengxian Ge, and Zhensen Wu
ObjectiveSince Lorenz-Mie theory was put forward, the scattering and absorption of electromagnetic waves by tiny particles have been widely studied. In recent years, coated media spheres have caught extensive attention from scholars due to their wide applications in various fields, including radar cross section (RCS), nanomaterials, and spectroscopy. Owing to different values of dielectric constants and magnetic permeability in various directions of anisotropic materials, significant changes occur in the internal electromagnetic field of a uniaxial anisotropic coated (UAC) sphere when a laser is incident from different directions, which significantly influences its surface RCS. The previous literature mainly studies the electromagnetic scattering of a single planar wave and a single Gaussian beam on coated spheres. However, in the optical manipulation of small particles, it is easier to employ two or more beams to capture and manipulate the particles than adopting only one laser beam. Therefore, it is essential to investigate the electromagnetic scattering problem of a UAC sphere by dual focused Gaussian beams for achieving optical manipulation of coated spheres.MethodsBased on the generalized Lorenz-Mie theory (GLMT), we study the scattering characteristics of a UAC sphere which is induced by two focused Gaussian beams with arbitrary directions. According to the orthogonality of spherical vector wave functions (SVWFs), the expression of dual Gaussian beam in terms of SVWFs is derived. By introducing the Fourier transform, the electromagnetic field expansion in the anisotropic coated area is obtained. The electromagnetic fields in each region of the UAC sphere are expanded in terms of the SVWFs, and by combining the boundary conditions, the scattering coefficients and the radar scattering crosssection of uniaxial anisotropic coated sphere illuminated by two Gaussian beams are obtained.Results and DiscussionsThe effects of the incident angle of dual beams, particle inner diameter, the ratio of coating thickness to the inner diameter, electrical anisotropy, and magnetic anisotropy on scattering intensity are analyzed. The results indicate that when the two Gaussian beams irradiate the coated sphere along different directions, the RCS will exhibit two maxima in the incident direction. Meanwhile, when the two beams propagate in opposite directions, the RCS of the E plane always exhibits a symmetrical distribution, while the RCS of the H plane exhibits two minima at ±90°, but the angular distribution does not show any significant changes (Fig. 3). As the waist width of the dual beams increases, both the E plane and H plane RCS will continuously rise due to the larger illuminated area on the UAC sphere (Fig. 4). The RCS increases with the rising inner radius of the particle around 0° and 180°, but becomes oscillatory around ±90°. When the inner radius is larger than the wavelength, the RCS value will increase slowly and tend to be stable if the inner radius increases continuously (Fig. 5). The variation of thickness, dielectric constant, and magnetic permeability of the anisotropic coating can bring significantly changed electromagnetic field in the coated region, leading to more complex scattering phenomena. Changing the ratio of coating to internal radius shows that with different angles, different variations occur in RCS (Fig. 6). When the electrical anisotropy is equal to 1, the coating material is isotropic and the RCS reaches the maximum at 90°. However, with the anisotropy increase or decrease, the RCS will reduce. The angular distribution of the whole E plane RCS will become more oscillatory with the rising electrical anisotropy. Contrary, the electrical anisotropy changes do not affect the RCS angular distribution on the H plane (Fig. 7). By varying the magnetic anisotropy of the UAC sphere, the magnetic anisotropy changes have a much greater influence on the RCS angular distribution of H plane than that of E plane (Fig. 8).ConclusionsBased on the GLMT, we provide a method to calculate the RCS of the UAC sphere irradiated by dual beams. Theoretically, this method is suitable for spherical particles with arbitrary coating thickness and inner radius, and the spherical shell particles made of different anisotropic materials can be simulated and analyzed by changing the particle parameters. By comparing the RCS angular distribution of a degenerate UAC sphere under the illumination of dual Gaussian beams with the results in literature, it is confirmed that our theory and program are accurate. The theory and numerical analysis are expected to provide a theoretical basis for the scattering and optical operations of anisotropic coated particles by multiple lasers. ObjectiveSince Lorenz-Mie theory was put forward, the scattering and absorption of electromagnetic waves by tiny particles have been widely studied. In recent years, coated media spheres have caught extensive attention from scholars due to their wide applications in various fields, including radar cross section (RCS), nanomaterials, and spectroscopy. Owing to different values of dielectric constants and magnetic permeability in various directions of anisotropic materials, significant changes occur in the internal electromagnetic field of a uniaxial anisotropic coated (UAC) sphere when a laser is incident from different directions, which significantly influences its surface RCS. The previous literature mainly studies the electromagnetic scattering of a single planar wave and a single Gaussian beam on coated spheres. However, in the optical manipulation of small particles, it is easier to employ two or more beams to capture and manipulate the particles than adopting only one laser beam. Therefore, it is essential to investigate the electromagnetic scattering problem of a UAC sphere by dual focused Gaussian beams for achieving optical manipulation of coated spheres.MethodsBased on the generalized Lorenz-Mie theory (GLMT), we study the scattering characteristics of a UAC sphere which is induced by two focused Gaussian beams with arbitrary directions. According to the orthogonality of spherical vector wave functions (SVWFs), the expression of dual Gaussian beam in terms of SVWFs is derived. By introducing the Fourier transform, the electromagnetic field expansion in the anisotropic coated area is obtained. The electromagnetic fields in each region of the UAC sphere are expanded in terms of the SVWFs, and by combining the boundary conditions, the scattering coefficients and the radar scattering crosssection of uniaxial anisotropic coated sphere illuminated by two Gaussian beams are obtained.Results and DiscussionsThe effects of the incident angle of dual beams, particle inner diameter, the ratio of coating thickness to the inner diameter, electrical anisotropy, and magnetic anisotropy on scattering intensity are analyzed. The results indicate that when the two Gaussian beams irradiate the coated sphere along different directions, the RCS will exhibit two maxima in the incident direction. Meanwhile, when the two beams propagate in opposite directions, the RCS of the E plane always exhibits a symmetrical distribution, while the RCS of the H plane exhibits two minima at ±90°, but the angular distribution does not show any significant changes (Fig. 3). As the waist width of the dual beams increases, both the E plane and H plane RCS will continuously rise due to the larger illuminated area on the UAC sphere (Fig. 4). The RCS increases with the rising inner radius of the particle around 0° and 180°, but becomes oscillatory around ±90°. When the inner radius is larger than the wavelength, the RCS value will increase slowly and tend to be stable if the inner radius increases continuously (Fig. 5). The variation of thickness, dielectric constant, and magnetic permeability of the anisotropic coating can bring significantly changed electromagnetic field in the coated region, leading to more complex scattering phenomena. Changing the ratio of coating to internal radius shows that with different angles, different variations occur in RCS (Fig. 6). When the electrical anisotropy is equal to 1, the coating material is isotropic and the RCS reaches the maximum at 90°. However, with the anisotropy increase or decrease, the RCS will reduce. The angular distribution of the whole E plane RCS will become more oscillatory with the rising electrical anisotropy. Contrary, the electrical anisotropy changes do not affect the RCS angular distribution on the H plane (Fig. 7). By varying the magnetic anisotropy of the UAC sphere, the magnetic anisotropy changes have a much greater influence on the RCS angular distribution of H plane than that of E plane (Fig. 8).ConclusionsBased on the GLMT, we provide a method to calculate the RCS of the UAC sphere irradiated by dual beams. Theoretically, this method is suitable for spherical particles with arbitrary coating thickness and inner radius, and the spherical shell particles made of different anisotropic materials can be simulated and analyzed by changing the particle parameters. By comparing the RCS angular distribution of a degenerate UAC sphere under the illumination of dual Gaussian beams with the results in literature, it is confirmed that our theory and program are accurate. The theory and numerical analysis are expected to provide a theoretical basis for the scattering and optical operations of anisotropic coated particles by multiple lasers.
Acta Optica Sinica
- Publication Date: Dec. 10, 2023
- Vol. 43, Issue 23, 2329001 (2023)
Deep Learning-Based Particle Shape Classification Using Low-Bit-Depth Speckle Patterns in Interferometric Particle Imaging
Yushi Fu, Hongxia Zhang, Jinghui Hou, Dagong Jia, and Tiegen Liu
ObjectiveParticle shape is an important parameter in irregular particle measurement, which has scientific and practical significance for studying environmental climate changes and ensuring engineering production safety. The interferometric particle imaging (IPI) technique has been widely employed in recent years to measure the sizes and shapes of irregular particles. Irregular particles form complex speckle patterns at defocused planes, which have been utilized to retrieve size and shape features such as 2D auto-correlation estimation and particle orientation. However, there are still two main problems during processing defocused speckles detected in IPI measurement. On one hand, the existing methods in IPI have slower processing time and thus incur significant time costs when processing large amounts of speckle data. On the other hand, a large amount of speckle data also brings enormous pressure to the storage and transmission of detected datasets. Therefore, we propose a method for rapid shape analysis of a large number of defocused speckles to reduce the memory cost brought by the dataset through data compression.MethodsWe apply a deep learning method to rapidly analyze large amounts of defocused speckle data of ice crystal particles collected by the IPI system. The proposed method includes two steps of data collection and network training. In data collection, we build an experimental particle IPI system to obtain a sufficient number of defocused speckles of ice crystal particles and provide different particle shapes in the dataset with unique speckle fields through the diffuser update strategy. In network training, we adopt the DenseNet network structure to classify the shapes corresponding to the speckle patterns, input the speckle data of the training set into the untrained DenseNet, and output the prediction category. After completing the training step, trained DenseNet is leveraged to classify the shape of the test set speckle data to test the ability to distinguish particle speckle patterns of different shape categories. Furthermore, we utilize bit-depth compression to compress the speckle dataset to eliminate information redundancy in DenseNet classification. Meanwhile, the original speckle dataset is segmented by a grayscale threshold strategy to generate a low bit-depth speckle dataset, and DenseNet is trained for shape classification and feasibility verification.Results and DiscussionsBy comparing three different network structures (Fig. 10 and Table 1), we choose the DenseNet structure for speckle classification. Firstly, we compare the classification accuracy of DenseNet under defocused speckle dataset from different defocused distances. The experimental results (Fig. 11) show that the classification accuracy exceeds 90% at all four different defocused distances, with the highest accuracy up to 92.7%. Our experimental results on low bit-depth speckle datasets (Fig. 13) show that the classification accuracy of DenseNet decreases with the reducing speckle data bit-depth, while the lowest classification accuracy still exceeds 85% when the information compression ratio reaches 12.5%. For the 1 bit-depth speckle data with the lowest information compression ratio, the classification results of the dataset (Fig. 14) indicate that the threshold near the average grayscale threshold could achieve the highest classification accuracy. Moreover, the speckle sparsity increases with the rising binarization threshold. Finally, the size analysis of the defocused speckle (Fig. 15) indicates that the size of the defocused speckle pattern cannot be too small to ensure that the neural network can recognize the hidden particle shape features in the speckle pattern.ConclusionsThe proposed deep learning-based method can rapidly analyze the shape information of a large number of defocused speckle patterns detected in IPI measurement. The experimental results show that compared with traditional methods, our method has an average processing time of only 0.06 s for each defocused speckle pattern to greatly reduce the time cost of speckle processing. Meanwhile, the trained DenseNet network has high classification accuracy on the collected ice crystal particle speckle dataset with a maximum of 92.7%. Furthermore, DenseNet trained on low bit-depth speckle datasets still maintains classification accuracy of over 85% with a minimum information compression ratio of 12.5%, significantly reducing the data storage and transmission pressure. Thus, this method is of significance for rapidly analyzing a large amount of speckle data in IPI measurement and could facilitate low-cost storage and efficient transmission of speckle data. ObjectiveParticle shape is an important parameter in irregular particle measurement, which has scientific and practical significance for studying environmental climate changes and ensuring engineering production safety. The interferometric particle imaging (IPI) technique has been widely employed in recent years to measure the sizes and shapes of irregular particles. Irregular particles form complex speckle patterns at defocused planes, which have been utilized to retrieve size and shape features such as 2D auto-correlation estimation and particle orientation. However, there are still two main problems during processing defocused speckles detected in IPI measurement. On one hand, the existing methods in IPI have slower processing time and thus incur significant time costs when processing large amounts of speckle data. On the other hand, a large amount of speckle data also brings enormous pressure to the storage and transmission of detected datasets. Therefore, we propose a method for rapid shape analysis of a large number of defocused speckles to reduce the memory cost brought by the dataset through data compression.MethodsWe apply a deep learning method to rapidly analyze large amounts of defocused speckle data of ice crystal particles collected by the IPI system. The proposed method includes two steps of data collection and network training. In data collection, we build an experimental particle IPI system to obtain a sufficient number of defocused speckles of ice crystal particles and provide different particle shapes in the dataset with unique speckle fields through the diffuser update strategy. In network training, we adopt the DenseNet network structure to classify the shapes corresponding to the speckle patterns, input the speckle data of the training set into the untrained DenseNet, and output the prediction category. After completing the training step, trained DenseNet is leveraged to classify the shape of the test set speckle data to test the ability to distinguish particle speckle patterns of different shape categories. Furthermore, we utilize bit-depth compression to compress the speckle dataset to eliminate information redundancy in DenseNet classification. Meanwhile, the original speckle dataset is segmented by a grayscale threshold strategy to generate a low bit-depth speckle dataset, and DenseNet is trained for shape classification and feasibility verification.Results and DiscussionsBy comparing three different network structures (Fig. 10 and Table 1), we choose the DenseNet structure for speckle classification. Firstly, we compare the classification accuracy of DenseNet under defocused speckle dataset from different defocused distances. The experimental results (Fig. 11) show that the classification accuracy exceeds 90% at all four different defocused distances, with the highest accuracy up to 92.7%. Our experimental results on low bit-depth speckle datasets (Fig. 13) show that the classification accuracy of DenseNet decreases with the reducing speckle data bit-depth, while the lowest classification accuracy still exceeds 85% when the information compression ratio reaches 12.5%. For the 1 bit-depth speckle data with the lowest information compression ratio, the classification results of the dataset (Fig. 14) indicate that the threshold near the average grayscale threshold could achieve the highest classification accuracy. Moreover, the speckle sparsity increases with the rising binarization threshold. Finally, the size analysis of the defocused speckle (Fig. 15) indicates that the size of the defocused speckle pattern cannot be too small to ensure that the neural network can recognize the hidden particle shape features in the speckle pattern.ConclusionsThe proposed deep learning-based method can rapidly analyze the shape information of a large number of defocused speckle patterns detected in IPI measurement. The experimental results show that compared with traditional methods, our method has an average processing time of only 0.06 s for each defocused speckle pattern to greatly reduce the time cost of speckle processing. Meanwhile, the trained DenseNet network has high classification accuracy on the collected ice crystal particle speckle dataset with a maximum of 92.7%. Furthermore, DenseNet trained on low bit-depth speckle datasets still maintains classification accuracy of over 85% with a minimum information compression ratio of 12.5%, significantly reducing the data storage and transmission pressure. Thus, this method is of significance for rapidly analyzing a large amount of speckle data in IPI measurement and could facilitate low-cost storage and efficient transmission of speckle data.
Acta Optica Sinica
- Publication Date: Nov. 25, 2023
- Vol. 43, Issue 22, 2229001 (2023)
Measurement of Polarized Volume Scattering Function of Particles in Water in a Wide Angle Range
Yaorui Pan, Bangyi Tao, Chaofan Wu, Zhihua Mao, and Haiqing Huang
Results and discussions A new type of exit prism with simpler processing was designed in this paper. The prism was developed by bonding a neutral density filter with a prism cut into a specific shape. The new prism designed could effectively reduce the influence of stray light on the measurement of large-angle backscattering and small-angle forward scattering. In Fig. 3, the measurement accuracy of the new prism is verified by comparing the measurement results of the old and new prisms. Fig. 5 compares the measured results of 3-μm diameter polystyrene standard particles with the theoretically calculated values and reveals that they are in good agreement with each other, which proves the reliability of the system in measuring the polarized volume scattering function. Finally, the system was tested in the natural water body of the Qiandao Lake, and the 3×3 scattering Mueller matrix of particles in water within the range of 10°-170° was obtained for the first time in China, as shown in Fig. 7 and Fig. 8. A comparison with the spectral shapes measured by HS6 indicates that the particle types at different depths at the same station are different, and the surface particle types at different stations are also different. The results show that polarized scattering characteristics can provide more abundant information of particle characteristics.ObjectiveThe polarized volume scattering function of particles in water is the most basic and complete parameter describing their scattering characteristics as it reflects the types, particle size spectra, shapes, and refractive indexes of the molecules and large particles in water. Therefore, the polarized volume scattering function of particles in water is of great research significance. This function is the most critical inherent optical parameter in the study of active and passive ocean optical remote sensing. Nevertheless, it is also the inherent parameter most difficult to measure. To solve the problem that no instrument is currently available in China for measuring the polarized volume scattering function of particles in water in a large angle range, this paper develops a measurement system for the polarized volume scattering characteristics of particles in water on the basis of a periscope-like optical path structure and the detection method of the rotating polarization detector. It further verifies the applicability of an output prism obtained by the half attenuation bonding method to the measurement of the polarized volume scattering characteristics in a large angle range and achieves the measurement of the 3×3 scattering Mueller matrix of particles in water in the range of 10°-170°.MethodsIn this study, pure water was used for baseline measurements, and the scattering characteristics of particles were determined by removing the contribution of the pure water signal to the total signal. According to the characteristics of standard particles in the Mie scattering theory, a standard particle (diameter of 0.2 μm) with relatively gentle Mie scattering results was used for amplitude calibration and calibration coefficient determination, and another one (diameter of 2 μm) with salient angle characteristics was used for angle calibration. Polarization was performed with a Stokes meter. The scattered light received by the detector suggests that the scattering optical paths detected at all angles are not the same, and the attenuation transmission distances in water are also different, which necessitates the normalization of the scattering optical path and the correction of the attenuation optical path.ConclusionsIn this study, a measurement system based on a periscope-like optical path structure and the rotating polarization detector was designed to measure the polarized volume scattering function of particles in water, and the measurement of the 3×3 polarized volume scattering function in the range of 10°-170° was thereby achieved. Moreover, a new type of exit prism with simpler processing was designed, and the measurement accuracy of the new prism was verified. To obtain accurate measurement results, this paper proposes strict methods for data processing and calibration procedures of the instrument, including baseline measurement, angle and amplitude calibration, polarization calibration, and data correction. An accurate theoretically calculated value of the polarized volume scattering function was obtained by applying the Mie scattering theory and compared with the measurement results of the experimental instrument. The measurement results are in good agreement with the theoretically calculated value. The accuracy of the measurement results of the experimental prototype is thus ensured. The system was further tested in the Qiandao Lake, and a 3×3 scattering Muller matrix of particles in water was obtained in the range of 10°-170° in this lake. Results and discussions A new type of exit prism with simpler processing was designed in this paper. The prism was developed by bonding a neutral density filter with a prism cut into a specific shape. The new prism designed could effectively reduce the influence of stray light on the measurement of large-angle backscattering and small-angle forward scattering. In Fig. 3, the measurement accuracy of the new prism is verified by comparing the measurement results of the old and new prisms. Fig. 5 compares the measured results of 3-μm diameter polystyrene standard particles with the theoretically calculated values and reveals that they are in good agreement with each other, which proves the reliability of the system in measuring the polarized volume scattering function. Finally, the system was tested in the natural water body of the Qiandao Lake, and the 3×3 scattering Mueller matrix of particles in water within the range of 10°-170° was obtained for the first time in China, as shown in Fig. 7 and Fig. 8. A comparison with the spectral shapes measured by HS6 indicates that the particle types at different depths at the same station are different, and the surface particle types at different stations are also different. The results show that polarized scattering characteristics can provide more abundant information of particle characteristics.ObjectiveThe polarized volume scattering function of particles in water is the most basic and complete parameter describing their scattering characteristics as it reflects the types, particle size spectra, shapes, and refractive indexes of the molecules and large particles in water. Therefore, the polarized volume scattering function of particles in water is of great research significance. This function is the most critical inherent optical parameter in the study of active and passive ocean optical remote sensing. Nevertheless, it is also the inherent parameter most difficult to measure. To solve the problem that no instrument is currently available in China for measuring the polarized volume scattering function of particles in water in a large angle range, this paper develops a measurement system for the polarized volume scattering characteristics of particles in water on the basis of a periscope-like optical path structure and the detection method of the rotating polarization detector. It further verifies the applicability of an output prism obtained by the half attenuation bonding method to the measurement of the polarized volume scattering characteristics in a large angle range and achieves the measurement of the 3×3 scattering Mueller matrix of particles in water in the range of 10°-170°.MethodsIn this study, pure water was used for baseline measurements, and the scattering characteristics of particles were determined by removing the contribution of the pure water signal to the total signal. According to the characteristics of standard particles in the Mie scattering theory, a standard particle (diameter of 0.2 μm) with relatively gentle Mie scattering results was used for amplitude calibration and calibration coefficient determination, and another one (diameter of 2 μm) with salient angle characteristics was used for angle calibration. Polarization was performed with a Stokes meter. The scattered light received by the detector suggests that the scattering optical paths detected at all angles are not the same, and the attenuation transmission distances in water are also different, which necessitates the normalization of the scattering optical path and the correction of the attenuation optical path.ConclusionsIn this study, a measurement system based on a periscope-like optical path structure and the rotating polarization detector was designed to measure the polarized volume scattering function of particles in water, and the measurement of the 3×3 polarized volume scattering function in the range of 10°-170° was thereby achieved. Moreover, a new type of exit prism with simpler processing was designed, and the measurement accuracy of the new prism was verified. To obtain accurate measurement results, this paper proposes strict methods for data processing and calibration procedures of the instrument, including baseline measurement, angle and amplitude calibration, polarization calibration, and data correction. An accurate theoretically calculated value of the polarized volume scattering function was obtained by applying the Mie scattering theory and compared with the measurement results of the experimental instrument. The measurement results are in good agreement with the theoretically calculated value. The accuracy of the measurement results of the experimental prototype is thus ensured. The system was further tested in the Qiandao Lake, and a 3×3 scattering Muller matrix of particles in water was obtained in the range of 10°-170° in this lake.
Acta Optica Sinica
- Publication Date: Sep. 25, 2023
- Vol. 43, Issue 18, 1829002 (2023)
Forward Transmission into Scattering Media by an Improved Polarized Monte Carlo Program
Xiangwei Zeng, Yan Zhang, and Junxiu Yang
ObjectiveVector radiation transport in scattering media is a research hotspot. The exact analytical solution to the vector radiative transfer equation cannot be obtained without the simplified treatment, and it needs to be calculated by numerical calculation methods. The polarized Monte Carlo program simulates the transmission of mass photons. As it does not lead to computational errors due to finite dispersion, the program is usually employed as a standard to verify the computational accuracy of other methods. At present, this method can obtain the outgoing polarization state of each light wave after the solution is obtained, but it is difficult to know the photon transmission situation. This limits the analysis of the polarization state retention of scattering light. However, photons with good retention characteristics of the polarization state usually have a small information loss and a long transmission distance. The study and analysis of these photons can be potentially applied to extract good transmission signals.MethodsThis paper proposes a method to count the photon polarization states during forward transmission into scattering media on the basis of the polarization meridian Monte Carlo program. The original algorithm and improved algorithm are shown in Fig. 1. The white part is required for calculating both the original algorithm and the improved algorithm, and the blue part is the additional flow for calculating the improved algorithm. One hundred thousand parallelly polarized photons or right-handed circularly polarized photons are sent into a slab represented by one particular particle distribution for each environment, and photons are transmitted at a given distance. Then, the aggregated polarization is calculated from the photons that arrive in a given area, and photons on the front face of the slab are considered the transmitted photons. This process continues for all the launched photons, and the result is calculated. For the original algorithm, a photon completes forward transmission when it passes through a specific forward distance. The improved algorithm adds a link to output the polarization state of each photon. Moreover, the improved algorithm can count the total number of received photons and the number of photons similar to the polarization state of the initial photon.Results and DiscussionsThis paper uses an example to compare the original algorithm and the improved algorithm. The following simulations are performed in the polystyrene suspension with a mass concentration of 2.08 μg/μm3. The wavelength of incident light is 532 nm, and polystyrene's refractive index is 1.597. The particle diameter of the polystyrene suspension is 1 μm in simulation, and the transmission distance is 10 cm. One hundred thousand parallelly polarized photons or right-handed circularly polarized photons are launched for simulations of the original algorithm and the improved algorithm separately. There are 66358 received photons after the transmission of parallelly polarized photons and 66367 after the transmission of right-handed circularly polarized photons. After that, the first 100 received photons are selected as samples (Figs. 3 and 4). Calculations show that for the sample data of parallelly polarized photons, the NRoPS is 0.13, and for the sample data of right-handed circularly polarized photons, the NRoPS is 0.53. The calculation results are both similar to the overall situation. The simulated calculation of polarized light transmission in the polystyrene suspension demonstrates that the optimized method can not only reflect the change in the photon polarization state but also count the percentage of photons with good retention characteristics of the polarization state. The comparison between the original results and the optimization results shows that the results of the optimized algorithm are less than the polarization degree value. This is because the optimized algorithm not only avoids the error introduced in the calculation of the intensity difference in the orthogonal component but also excludes photons that are not similar to the polarization state of the initial photon.ConclusionsCompared with the polarized Monte Carlo program, the improved method can not only reflect the change in the photon polarization state but also count the percentage of photons with good retention characteristics of the polarization state. It reflects the change in the polarization state of the transmitted photons in multiple dimensions. This study can provide technical support for research on the extraction of excellent transmission signals. ObjectiveVector radiation transport in scattering media is a research hotspot. The exact analytical solution to the vector radiative transfer equation cannot be obtained without the simplified treatment, and it needs to be calculated by numerical calculation methods. The polarized Monte Carlo program simulates the transmission of mass photons. As it does not lead to computational errors due to finite dispersion, the program is usually employed as a standard to verify the computational accuracy of other methods. At present, this method can obtain the outgoing polarization state of each light wave after the solution is obtained, but it is difficult to know the photon transmission situation. This limits the analysis of the polarization state retention of scattering light. However, photons with good retention characteristics of the polarization state usually have a small information loss and a long transmission distance. The study and analysis of these photons can be potentially applied to extract good transmission signals.MethodsThis paper proposes a method to count the photon polarization states during forward transmission into scattering media on the basis of the polarization meridian Monte Carlo program. The original algorithm and improved algorithm are shown in Fig. 1. The white part is required for calculating both the original algorithm and the improved algorithm, and the blue part is the additional flow for calculating the improved algorithm. One hundred thousand parallelly polarized photons or right-handed circularly polarized photons are sent into a slab represented by one particular particle distribution for each environment, and photons are transmitted at a given distance. Then, the aggregated polarization is calculated from the photons that arrive in a given area, and photons on the front face of the slab are considered the transmitted photons. This process continues for all the launched photons, and the result is calculated. For the original algorithm, a photon completes forward transmission when it passes through a specific forward distance. The improved algorithm adds a link to output the polarization state of each photon. Moreover, the improved algorithm can count the total number of received photons and the number of photons similar to the polarization state of the initial photon.Results and DiscussionsThis paper uses an example to compare the original algorithm and the improved algorithm. The following simulations are performed in the polystyrene suspension with a mass concentration of 2.08 μg/μm3. The wavelength of incident light is 532 nm, and polystyrene's refractive index is 1.597. The particle diameter of the polystyrene suspension is 1 μm in simulation, and the transmission distance is 10 cm. One hundred thousand parallelly polarized photons or right-handed circularly polarized photons are launched for simulations of the original algorithm and the improved algorithm separately. There are 66358 received photons after the transmission of parallelly polarized photons and 66367 after the transmission of right-handed circularly polarized photons. After that, the first 100 received photons are selected as samples (Figs. 3 and 4). Calculations show that for the sample data of parallelly polarized photons, the NRoPS is 0.13, and for the sample data of right-handed circularly polarized photons, the NRoPS is 0.53. The calculation results are both similar to the overall situation. The simulated calculation of polarized light transmission in the polystyrene suspension demonstrates that the optimized method can not only reflect the change in the photon polarization state but also count the percentage of photons with good retention characteristics of the polarization state. The comparison between the original results and the optimization results shows that the results of the optimized algorithm are less than the polarization degree value. This is because the optimized algorithm not only avoids the error introduced in the calculation of the intensity difference in the orthogonal component but also excludes photons that are not similar to the polarization state of the initial photon.ConclusionsCompared with the polarized Monte Carlo program, the improved method can not only reflect the change in the photon polarization state but also count the percentage of photons with good retention characteristics of the polarization state. It reflects the change in the polarization state of the transmitted photons in multiple dimensions. This study can provide technical support for research on the extraction of excellent transmission signals.
Acta Optica Sinica
- Publication Date: Sep. 25, 2023
- Vol. 43, Issue 18, 1829001 (2023)
Titanium Dioxide/Silver Composite Structure Prepared and Raman Enhancement Experiment
Mu Jiang, Yong Zhu, and Jie Zhang
Silver nanoparticles are grown on the surface of TiO2 nanorods by ultraviolet irradiation and used as surface-enhanced Raman scattering substrate. The effect of ultraviolet irradiation time on Raman sensitivity is studied, and samples of TiO2 nanorods/silver composite structure are prepared under different irradiation time. COMSOL Multiphysics simulation software is used to calculate the electromagnetic distribution and theoretical enhancement factors on the surface of TiO2 nanorods/silver composite structure. The experimental results show that the detection concentration of rhodamine is lower than 10 -10 mol/L and the maximum enhancement factor is about 1.84×10 8 after 10 min of ultraviolet irradiation, indicating that the substrate has good self-cleaning function. Silver nanoparticles are grown on the surface of TiO2 nanorods by ultraviolet irradiation and used as surface-enhanced Raman scattering substrate. The effect of ultraviolet irradiation time on Raman sensitivity is studied, and samples of TiO2 nanorods/silver composite structure are prepared under different irradiation time. COMSOL Multiphysics simulation software is used to calculate the electromagnetic distribution and theoretical enhancement factors on the surface of TiO2 nanorods/silver composite structure. The experimental results show that the detection concentration of rhodamine is lower than 10 -10 mol/L and the maximum enhancement factor is about 1.84×10 8 after 10 min of ultraviolet irradiation, indicating that the substrate has good self-cleaning function.
Acta Optica Sinica
- Publication Date: Jan. 28, 2022
- Vol. 42, Issue 4, 0429001 (2022)
Simultaneous Inversion of Seawater Temperature and Salinity Based on Stimulated Brillouin Scattering
Ning Xu, Bo Zhang, Ningning Luo, Jinjun Xu, Xingdao He, and Jiulin Shi
To realize the synchronous measurement of temperature and salinity of seawater, we study a data inversion method by combining frequency shift and line width of stimulated Brillouin scattering (SBS) theoretically and experimentally. Theoretically, the variations of frequency shift and line width of SBS with the changes in temperature and salinity are fitted by empirical formulas. Experimentally, the frequency shift and line width of SBS in seawater with different temperatures and salinity are measured, and then the temperature and salinity of seawater are analyzed by the theoretical inversion model. The results indicate that the simultaneous inversion of seawater temperature and salinity can be realized by the combination of frequency shift and line width of SBS. The minimum and maximum temperature inversion errors are 0.04 ℃ and 0.41 ℃, respectively, and the minimum and maximum salinity inversion errors are 0.09‰ and 0.65‰, respectively. To realize the synchronous measurement of temperature and salinity of seawater, we study a data inversion method by combining frequency shift and line width of stimulated Brillouin scattering (SBS) theoretically and experimentally. Theoretically, the variations of frequency shift and line width of SBS with the changes in temperature and salinity are fitted by empirical formulas. Experimentally, the frequency shift and line width of SBS in seawater with different temperatures and salinity are measured, and then the temperature and salinity of seawater are analyzed by the theoretical inversion model. The results indicate that the simultaneous inversion of seawater temperature and salinity can be realized by the combination of frequency shift and line width of SBS. The minimum and maximum temperature inversion errors are 0.04 ℃ and 0.41 ℃, respectively, and the minimum and maximum salinity inversion errors are 0.09‰ and 0.65‰, respectively.
Acta Optica Sinica
- Publication Date: Jan. 01, 2022
- Vol. 42, Issue 24, 2429001 (2022)
Particle Size Distribution Inversion of Cuckoo Search Algorithm Using Weber Distribution
Liang Shan, Tingting Zha, Ming Kong, and Bo Hong
Weber distribution has better optimization accuracy and global search ability in nonlinear optimization problems. For this reason, a cuckoo search (WCS) algorithm based on Weber distribution is proposed to solve the problem of particle size distribution inversion. The WCS algorithm is used to invert the particle size distribution of unimodal and bimodal particle systems which follow Johnson’s SB distribution, Rosin-Rammler distribution, and normal distribution, and the results are compared with those of other traditional algorithms. The results show that the overall performance of the WCS algorithm is better than that of the artificial fish swarm algorithm and the artificial bee colony algorithm, and the standard deviation of the improved four heavy-tailed distribution CS algorithm is 2-3 orders of magnitude higher than the original CS algorithm. Compared with the other three heavy-tailed distributions, the relative root mean square error of the WCS algorithm can be reduced by at least 1/2 when the scattering light energy of the objective function is added into the noise. The small angle forward scattering measurement system is used to study the unimodal particle system and bimodal mixed particle system. It is found that the relative root mean square error of the WCS algorithm is about 40% lower than that of the original CS algorithm. Weber distribution has better optimization accuracy and global search ability in nonlinear optimization problems. For this reason, a cuckoo search (WCS) algorithm based on Weber distribution is proposed to solve the problem of particle size distribution inversion. The WCS algorithm is used to invert the particle size distribution of unimodal and bimodal particle systems which follow Johnson’s SB distribution, Rosin-Rammler distribution, and normal distribution, and the results are compared with those of other traditional algorithms. The results show that the overall performance of the WCS algorithm is better than that of the artificial fish swarm algorithm and the artificial bee colony algorithm, and the standard deviation of the improved four heavy-tailed distribution CS algorithm is 2-3 orders of magnitude higher than the original CS algorithm. Compared with the other three heavy-tailed distributions, the relative root mean square error of the WCS algorithm can be reduced by at least 1/2 when the scattering light energy of the objective function is added into the noise. The small angle forward scattering measurement system is used to study the unimodal particle system and bimodal mixed particle system. It is found that the relative root mean square error of the WCS algorithm is about 40% lower than that of the original CS algorithm.
Acta Optica Sinica
- Publication Date: Dec. 27, 2021
- Vol. 42, Issue 2, 0229001 (2022)
Topics
© Copyright 2018-2021 | Chinese Laser Press. All Rights Reserved 沪ICP备15018463号-20