Solutions of electromagnetic scattering problems are obtained by appropriate application of the M... more Solutions of electromagnetic scattering problems are obtained by appropriate application of the Maxwell electromagnetic equations to scattered of a specified geometry. Formal solutions for the scattering by cylinders and spheres are well-known, classic results of this approach. This paper presents a unified theory of electromagnetic scattering for infinite cylinders and spheres, in which the scattering coefficients have a common functional form with the geometry being determined by whether half-integer (sphere) or integer (cylinder) order Bessel functions are used. The application of the theory to the development of new scattering codes is also described.
Abstract : The objective of the work contained in this report was to develop techniques and instr... more Abstract : The objective of the work contained in this report was to develop techniques and instrumentation to measure the particle-size distribution in dye smokes. This report presents a method of determining the particle-size distribution of smokes utilizing the Battelle CI-S-8 impactor. A special long-path photometer, which was designed to determine the small amounts of dye collected on the impactor slides, is described in detail.
Abstract : The purpose of the work was to study the light scattered from a simple statistical med... more Abstract : The purpose of the work was to study the light scattered from a simple statistical medium that consisted of a monodispersed ensemble of spherical, Brownian particles. The light from a helium-neon laser operating at a wavelength of 632.8 nm was scattered from a dilute water suspension of the particles, which are polystyrene spheres of diameter 0.557 micrometers. The spectrum of the scattered light is a very narrow Lorentzian whose half width at half height is related to the diffusion constant of the particles. An experiment that employs the technique of pulse interval analysis to analyze the scattered light spectrum is described in detail. The results of this experiment yielded a spectral linewidth that is caused not only by the diffusive motion, but also by the convective motion of the particles.
Abstract : This report describes the ASCMIE subroutine for performing Mie scattering calculations... more Abstract : This report describes the ASCMIE subroutine for performing Mie scattering calculations by means of the downward recursion algorithm developed by J. V. Dave. ASCMIE is written in UNIVAC 1100 series ASCII FORTRAN language. The ASCII FORTRAN compiler is a modern, state-of-the-art compiler which implements the ANSI FORTRAN 77 standard; this compiler is intended as a future replacement for the UNIVAC 1100 series FORTRAN V compiler. Rather than carry out a straightforward conversion of the FORTRAN V Mie scattering routine to ASCII FORTRAN, the code was completely rewritten in order to incorporate new ASCII FORTRAN language elements. The result is a more structured, modular, Mie scattering code which executes faster than the FORTRAN V code. (Author)
Final Report Jan 1991 Jan 1994 Edgewood Research Development and Engineering Center Aberdeen Proving Ground Md, Oct 1, 1994
Abstract : In this report, relevant parts of the scattering theory for magnetic spheres are prese... more Abstract : In this report, relevant parts of the scattering theory for magnetic spheres are presented. Mass extinction coefficients, and the lognormal size distribution are defined. The theory and algorithms for integrating scattering parameters over size distributions are developed. The integrations are carried out in terms of dimensionless scattering, and size distribution parameters, which are simply related to the usual mass scattering coefficients. Fortran codes, which implement the algorithmic design, are presented, and examples of code use are given. Code listings are included. (AN)
It is generally accepted that, for a single sphere, the Lorenz-Mie efficiency factor for extincti... more It is generally accepted that, for a single sphere, the Lorenz-Mie efficiency factor for extinction Qe approaches 2 as the size parameter of the sphere X approaches infinity. We show that, for an ensemble of lognormally distributed spherical particles, the dimensionless extinction coefficient assumes a simple mathematical form when the particle-size distribution is dominated by particles for which Qe-2. The accuracy with which this asymptotic expression for the dimensionless extinction coefficient approaches an exact Lorenz-Mie calculation is examined when the complex refractive index is given by 1.10 S n S 3.00 and 0.0 S k • 4.0 and when the parameters of the lognormal particle-size distributions are given by mass median size parameters 0.01 S Xm • 100.0 and geometric standard deviations 1.1 • ag S 3.0.
When only two substances, m chemical equilibrium with each other, are responsible for all absorpt... more When only two substances, m chemical equilibrium with each other, are responsible for all absorption in a wavelength region, there must exist at least one wavelength m the spectrmn of this region where the absorption coefficient will be independent of the ratio of the concentrations of the two substances. This wavelength is called as the isosbestic point, or point of equal absorbance. Such points can also exist m the extraction spectra where at a particular wavelength the extraction coefficient becomes in&pendent of solution concentration. Mie theory has been applied to compute such extraction coefficients. This paper shows the occurrence of isosbestic points in the extraction spectra of liquid droplet aerosols of sizes ranging from O. 1 gm to 10 }am and comprising several concentrations each of hydrochloric, nitric, sulfuric, and orthophosphoric acids in water. Such isosbestic points can serve as reference wavelengths for aerosol spectrometry and also for estimation of liquid content in haze, fog, and nonraining clouds.
Abstract A functional scaling approach to computing the electromagnetic (em) scattering coefficie... more Abstract A functional scaling approach to computing the electromagnetic (em) scattering coefficients ( a n , b n ) is described and used to develop a unified theory of em scattering for infinite cylinders and spheres. Scattering algorithms based on the unified theory and scaled Bessel functions are described.
A rapid method is presented for the determination of vapor pressure/molecular weight correlations... more A rapid method is presented for the determination of vapor pressure/molecular weight correlations for homologous hydrocarbon mixtures. By comparing droplet evaporation data to discretizad theoretical continuum mass flux rates which employ two parameter expouential vapor prassure/molecular weight correlations, best fit pressure correlation parameters are determined. The present technique is applied to the multicomponent oil mixture, 100 pale oil, which is modeled as a fifteen component system. Postulating the mixture is tbermodynamlcally ideal, best fit pressure correlations are determined which result in less than 5% error between theory and experiment. It is shown the hydrocarbon vapor pressure calculated from the derived pressure corralation is in satisfactory agreement with pressures calculated from distillation data and the Clausius Clapayron relation.
<p>The reaction of elemental phosphorus with atmospheric oxygen and water vapor pro... more <p>The reaction of elemental phosphorus with atmospheric oxygen and water vapor produces a highly visible white smoke; extinction spectra in the 7-14-microm infrared have been measured for such phosphorus-derived smokes in varying environmental conditions. The extinction spectra show that the smoke particles are not homogeneous droplets of o-phosphoric acid. A descriptive model of the formation of the phosphorus-derived smoke particles is proposed; this model describes the smoke particles as chemically quasi-stable radially inhomogeneous layered spheres of condensed phosphoric acids. The dependence of phosphorus-derived smoke extinction on relative humidity is described, and extinction spectra taken over a 280-min time period show that the smoke evolves toward an o-phosphoric acid aerosol.</p> <p>The relative humidity and time-dependent smoke extinction spectra are compared with o-phosphoric acid extinction spectra computed from Lorenz-Mie theory. The optical constants of the phosphorus-derived smoke are found from the extinction spectra as functions of relative humidity and time.</p>
A method is described, and equations are developed for the determination of aerosol droplet size ... more A method is described, and equations are developed for the determination of aerosol droplet size and concentration based upon simple transmittance readings. Data and experimental results are presented for water, but the method is applicable to water solutions or other materials as well for which complex indices of refraction are known at specific wavelengths in the visible or the ir. An equation is given for transmittance at 0.63 Am (He:Ne laser) which allows the interrelationship between water cloud or fog droplet size and concentration to be determined. A second equation permits specific values of concentration and droplet size to be determined knowing transmittance values at one or more ir wavelengths located in regions of spectral absorption by the liquid comprising the droplets. For water, data are given for ir wavelengths of 8.5 im, 10.5 Am, and 12.57 ,um, and specific determinations of droplet size and concentration are tabulated based upon these observation wavelengths. In addition, a composite of wavelengths in the 8-13-um window is presented so that aerosol determinations, can be made simply by comparing transmittances at 0.63 gm to those taken broadband at 8-13 gm by devices operating in the latter region without wavelength-scanning capability. For water drops, the method produces results of about 410% precision. The method is based upon the constancy of the product of extinction coefficient and droplet diameter in Mie calculations for water at 0.63 gum and is applicable for droplet sizes of from 6 m to at least 30 gm. Determinations for droplets as small as 2 gm can be made at +30% precision.
The application in light scattering of the Mueller matrix ratio ͗S 34 ͗͘͞S 11 ͘ for determining a... more The application in light scattering of the Mueller matrix ratio ͗S 34 ͗͘͞S 11 ͘ for determining average particle size is extended to a large size parameter range for spherical or randomly oriented rod-shaped particles such as microorganisms. It is shown that combining the graph of this ratio with a Coulter counter measurement of particle volume gives results in agreement with microscopic measurements. Thus this combination provides a method to measure particle diameter and width simultaneously in real time for elongated particles such as bacteria, which are measured in vivo with this method. An approximate empirical formula is developed to estimate the motion of the extrema in the graph of the oscillating matrix ratio as size changes occur. This formula is also shown to be consistent with wavelength changes.
Infrared extinction spectra in the 3-5-,um and 7-13-gm atmospheric window regions have been obtai... more Infrared extinction spectra in the 3-5-,um and 7-13-gm atmospheric window regions have been obtained for smokes of petroleum oil, sulfuric acid, and phosphoric acid of varying droplet concentration and for water fogs. Spectra were also obtained at 0.36-2.35 gm for petroleum oil and sulfuric acid smokes. Experimental results were compared, for sulfuric acid and water aerosols, to calculated values obtained from the Mie theory. Agreement was as good as ±10%. When absorbing smoke droplets are small compared to wavelength, very useful approximations apply, and droplet clouds may be spectrally simulated by thin liquid films. In such cases, the imaginary component of refractive index may be approximated directly from aerosol spectra. At 12.5-gm wavelength, water fog extinction is nearly independent of droplet size distribution, suggesting a simple scheme for measurement of total liquid water content of an optical path.
Extinction spectra in the 3- to 5-, 8- to 13-, and 0.4 to 2.4-micrometer spectral region have bee... more Extinction spectra in the 3- to 5-, 8- to 13-, and 0.4 to 2.4-micrometer spectral region have been obtained for FS (Chlorosulfonic acid - Free SO3), red phosphorus, HC (Zinc oxide, Aluminum, Hexachloroethane), and fog oil smokes. A limited number of theoretical predictions based on Mie theory are also presented and compared with the experimental results. The experimental and computational
Solutions of electromagnetic scattering problems are obtained by appropriate application of the M... more Solutions of electromagnetic scattering problems are obtained by appropriate application of the Maxwell electromagnetic equations to scattered of a specified geometry. Formal solutions for the scattering by cylinders and spheres are well-known, classic results of this approach. This paper presents a unified theory of electromagnetic scattering for infinite cylinders and spheres, in which the scattering coefficients have a common functional form with the geometry being determined by whether half-integer (sphere) or integer (cylinder) order Bessel functions are used. The application of the theory to the development of new scattering codes is also described.
Abstract : The objective of the work contained in this report was to develop techniques and instr... more Abstract : The objective of the work contained in this report was to develop techniques and instrumentation to measure the particle-size distribution in dye smokes. This report presents a method of determining the particle-size distribution of smokes utilizing the Battelle CI-S-8 impactor. A special long-path photometer, which was designed to determine the small amounts of dye collected on the impactor slides, is described in detail.
Abstract : The purpose of the work was to study the light scattered from a simple statistical med... more Abstract : The purpose of the work was to study the light scattered from a simple statistical medium that consisted of a monodispersed ensemble of spherical, Brownian particles. The light from a helium-neon laser operating at a wavelength of 632.8 nm was scattered from a dilute water suspension of the particles, which are polystyrene spheres of diameter 0.557 micrometers. The spectrum of the scattered light is a very narrow Lorentzian whose half width at half height is related to the diffusion constant of the particles. An experiment that employs the technique of pulse interval analysis to analyze the scattered light spectrum is described in detail. The results of this experiment yielded a spectral linewidth that is caused not only by the diffusive motion, but also by the convective motion of the particles.
Abstract : This report describes the ASCMIE subroutine for performing Mie scattering calculations... more Abstract : This report describes the ASCMIE subroutine for performing Mie scattering calculations by means of the downward recursion algorithm developed by J. V. Dave. ASCMIE is written in UNIVAC 1100 series ASCII FORTRAN language. The ASCII FORTRAN compiler is a modern, state-of-the-art compiler which implements the ANSI FORTRAN 77 standard; this compiler is intended as a future replacement for the UNIVAC 1100 series FORTRAN V compiler. Rather than carry out a straightforward conversion of the FORTRAN V Mie scattering routine to ASCII FORTRAN, the code was completely rewritten in order to incorporate new ASCII FORTRAN language elements. The result is a more structured, modular, Mie scattering code which executes faster than the FORTRAN V code. (Author)
Final Report Jan 1991 Jan 1994 Edgewood Research Development and Engineering Center Aberdeen Proving Ground Md, Oct 1, 1994
Abstract : In this report, relevant parts of the scattering theory for magnetic spheres are prese... more Abstract : In this report, relevant parts of the scattering theory for magnetic spheres are presented. Mass extinction coefficients, and the lognormal size distribution are defined. The theory and algorithms for integrating scattering parameters over size distributions are developed. The integrations are carried out in terms of dimensionless scattering, and size distribution parameters, which are simply related to the usual mass scattering coefficients. Fortran codes, which implement the algorithmic design, are presented, and examples of code use are given. Code listings are included. (AN)
It is generally accepted that, for a single sphere, the Lorenz-Mie efficiency factor for extincti... more It is generally accepted that, for a single sphere, the Lorenz-Mie efficiency factor for extinction Qe approaches 2 as the size parameter of the sphere X approaches infinity. We show that, for an ensemble of lognormally distributed spherical particles, the dimensionless extinction coefficient assumes a simple mathematical form when the particle-size distribution is dominated by particles for which Qe-2. The accuracy with which this asymptotic expression for the dimensionless extinction coefficient approaches an exact Lorenz-Mie calculation is examined when the complex refractive index is given by 1.10 S n S 3.00 and 0.0 S k • 4.0 and when the parameters of the lognormal particle-size distributions are given by mass median size parameters 0.01 S Xm • 100.0 and geometric standard deviations 1.1 • ag S 3.0.
When only two substances, m chemical equilibrium with each other, are responsible for all absorpt... more When only two substances, m chemical equilibrium with each other, are responsible for all absorption in a wavelength region, there must exist at least one wavelength m the spectrmn of this region where the absorption coefficient will be independent of the ratio of the concentrations of the two substances. This wavelength is called as the isosbestic point, or point of equal absorbance. Such points can also exist m the extraction spectra where at a particular wavelength the extraction coefficient becomes in&pendent of solution concentration. Mie theory has been applied to compute such extraction coefficients. This paper shows the occurrence of isosbestic points in the extraction spectra of liquid droplet aerosols of sizes ranging from O. 1 gm to 10 }am and comprising several concentrations each of hydrochloric, nitric, sulfuric, and orthophosphoric acids in water. Such isosbestic points can serve as reference wavelengths for aerosol spectrometry and also for estimation of liquid content in haze, fog, and nonraining clouds.
Abstract A functional scaling approach to computing the electromagnetic (em) scattering coefficie... more Abstract A functional scaling approach to computing the electromagnetic (em) scattering coefficients ( a n , b n ) is described and used to develop a unified theory of em scattering for infinite cylinders and spheres. Scattering algorithms based on the unified theory and scaled Bessel functions are described.
A rapid method is presented for the determination of vapor pressure/molecular weight correlations... more A rapid method is presented for the determination of vapor pressure/molecular weight correlations for homologous hydrocarbon mixtures. By comparing droplet evaporation data to discretizad theoretical continuum mass flux rates which employ two parameter expouential vapor prassure/molecular weight correlations, best fit pressure correlation parameters are determined. The present technique is applied to the multicomponent oil mixture, 100 pale oil, which is modeled as a fifteen component system. Postulating the mixture is tbermodynamlcally ideal, best fit pressure correlations are determined which result in less than 5% error between theory and experiment. It is shown the hydrocarbon vapor pressure calculated from the derived pressure corralation is in satisfactory agreement with pressures calculated from distillation data and the Clausius Clapayron relation.
<p>The reaction of elemental phosphorus with atmospheric oxygen and water vapor pro... more <p>The reaction of elemental phosphorus with atmospheric oxygen and water vapor produces a highly visible white smoke; extinction spectra in the 7-14-microm infrared have been measured for such phosphorus-derived smokes in varying environmental conditions. The extinction spectra show that the smoke particles are not homogeneous droplets of o-phosphoric acid. A descriptive model of the formation of the phosphorus-derived smoke particles is proposed; this model describes the smoke particles as chemically quasi-stable radially inhomogeneous layered spheres of condensed phosphoric acids. The dependence of phosphorus-derived smoke extinction on relative humidity is described, and extinction spectra taken over a 280-min time period show that the smoke evolves toward an o-phosphoric acid aerosol.</p> <p>The relative humidity and time-dependent smoke extinction spectra are compared with o-phosphoric acid extinction spectra computed from Lorenz-Mie theory. The optical constants of the phosphorus-derived smoke are found from the extinction spectra as functions of relative humidity and time.</p>
A method is described, and equations are developed for the determination of aerosol droplet size ... more A method is described, and equations are developed for the determination of aerosol droplet size and concentration based upon simple transmittance readings. Data and experimental results are presented for water, but the method is applicable to water solutions or other materials as well for which complex indices of refraction are known at specific wavelengths in the visible or the ir. An equation is given for transmittance at 0.63 Am (He:Ne laser) which allows the interrelationship between water cloud or fog droplet size and concentration to be determined. A second equation permits specific values of concentration and droplet size to be determined knowing transmittance values at one or more ir wavelengths located in regions of spectral absorption by the liquid comprising the droplets. For water, data are given for ir wavelengths of 8.5 im, 10.5 Am, and 12.57 ,um, and specific determinations of droplet size and concentration are tabulated based upon these observation wavelengths. In addition, a composite of wavelengths in the 8-13-um window is presented so that aerosol determinations, can be made simply by comparing transmittances at 0.63 gm to those taken broadband at 8-13 gm by devices operating in the latter region without wavelength-scanning capability. For water drops, the method produces results of about 410% precision. The method is based upon the constancy of the product of extinction coefficient and droplet diameter in Mie calculations for water at 0.63 gum and is applicable for droplet sizes of from 6 m to at least 30 gm. Determinations for droplets as small as 2 gm can be made at +30% precision.
The application in light scattering of the Mueller matrix ratio ͗S 34 ͗͘͞S 11 ͘ for determining a... more The application in light scattering of the Mueller matrix ratio ͗S 34 ͗͘͞S 11 ͘ for determining average particle size is extended to a large size parameter range for spherical or randomly oriented rod-shaped particles such as microorganisms. It is shown that combining the graph of this ratio with a Coulter counter measurement of particle volume gives results in agreement with microscopic measurements. Thus this combination provides a method to measure particle diameter and width simultaneously in real time for elongated particles such as bacteria, which are measured in vivo with this method. An approximate empirical formula is developed to estimate the motion of the extrema in the graph of the oscillating matrix ratio as size changes occur. This formula is also shown to be consistent with wavelength changes.
Infrared extinction spectra in the 3-5-,um and 7-13-gm atmospheric window regions have been obtai... more Infrared extinction spectra in the 3-5-,um and 7-13-gm atmospheric window regions have been obtained for smokes of petroleum oil, sulfuric acid, and phosphoric acid of varying droplet concentration and for water fogs. Spectra were also obtained at 0.36-2.35 gm for petroleum oil and sulfuric acid smokes. Experimental results were compared, for sulfuric acid and water aerosols, to calculated values obtained from the Mie theory. Agreement was as good as ±10%. When absorbing smoke droplets are small compared to wavelength, very useful approximations apply, and droplet clouds may be spectrally simulated by thin liquid films. In such cases, the imaginary component of refractive index may be approximated directly from aerosol spectra. At 12.5-gm wavelength, water fog extinction is nearly independent of droplet size distribution, suggesting a simple scheme for measurement of total liquid water content of an optical path.
Extinction spectra in the 3- to 5-, 8- to 13-, and 0.4 to 2.4-micrometer spectral region have bee... more Extinction spectra in the 3- to 5-, 8- to 13-, and 0.4 to 2.4-micrometer spectral region have been obtained for FS (Chlorosulfonic acid - Free SO3), red phosphorus, HC (Zinc oxide, Aluminum, Hexachloroethane), and fog oil smokes. A limited number of theoretical predictions based on Mie theory are also presented and compared with the experimental results. The experimental and computational
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Papers by Merrill Milham