Hjorth, Poul G.

Karamehmedović, Mirza

This technical note deals with light scattering measurements for sizing of micrometer-scale particles in a suspension

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Downloaded from orbit.dtu.dk on: Dec 20, 2017Sizing of Microparticles from Angular Scattering RatioHjorth, Poul G.; Karamehmedovic, MirzaPublication date:2013Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Hjorth, P. G., & Karamehmedovic, M. (2013). Sizing of Microparticles from Angular Scattering Ratio. Paperpresented at Foodtech Bazar, Roskilde, Denmark.Sizing of Microparticles from Angular Scattering RatioP.G. Hjorth, M. Karamehmedovic´, DTU Compute28. October 2013.This technical note deals with light scattering measurements for sizing of micrometer-scaleparticles in a suspension.Angular Scattering. The intensity of light scattered from a single spherical particle, Fig1(a), has strong angular dependence, as illustrated in Fig 1(b). Notice that θ is measuredclockwise.LASERparticlelight(a) (b)Figure 1. (a),(b): laser light scattered from a spherical particle has a strong depen-dence on angle θ. The ratio of intensities for two fixed angle values (c) is a stronglyvarying function of particle size.This effect is also seen for a suspension of particles, provided the average interparticledistance is much larger than the particle diameter d, that is, provided dρ1/3  1, whereρ is the particle density.The ratio σ = I(25◦)/I(90◦) of scattered light intensity measured at two fixed anglesθ = 25◦ and θ = 90◦ is strongly dependent on the electrical size d/λ of the particle. Here,λ is the wavelength of the incoming monochromatic light. Fig 1(c) is from reference [2],and it shows an example of the intensity ratio σ as function of particle diameter. Forparticles with the size parameter dpi/λ in the approximate range from 0.1 to 100, Mietheory is applicable in the description and the numerical computation of the scatteredlight.In certain intervals of particle diameter the intensity ratio σ is a monotone function ofparticle size, and it can therefore be used as an accurate and unambiguous measure ofthe diameter of the suspended particles.12Fig 2(a) shows the numerically computed intensity ratio σ in the restricted range ofparticle diameter from d = 0.8µm to d = 1.45µm. We used Scott Prahl’s online Miescattering calculator [3].The illumination is unpolarised and with a fixed free-space wavelength λ = 650nm.The spherical particles have refractive index 1.4, and are suspended in tap water (refractiveindex 1.0114). The particle concentration is on the order of ρ = 1017 spheres/m3. It is seenthat this mode of measurement allows the unique determination of particle diameter in thedynamical range 800nm to 1.45µ, and also that the numerically simulated intensity ratioσ approximately attains the value 1 at particle diameter 1µm, as observed experimentallyby TurbiSense.Sizing particulates in a plasmaFigure 1. Variation of scattering ratio   with particle radius a. The scattering ratio   is the ratio of parallel (Ik) andperpendicular (I?) polarized scattered intensities. The size measurement involves measuring Ik and I? experimentally andthen comparing their ratio with the theoretical curve (as shown by the broken lines). Above a radius of 0.1 , the curve ismulti-valued and it is difficult to determine the particle size. Below this limit, the curve is single-valued and   / a4. TheseMie scattering calculations are for   = 0.488 µm and a homogeneous sphere with refractive index N = 2  i.the particles suspended in a plasma. We test the sensitivityof the scattering ratio method to particulate parametersincluding the refractive index, shape and size distribution inthe small particle size regime (diameter less than one-fifththe optical wavelength). This is important, because in manycases particles in plasmas are non-spherical, polydisperse,or have an unknown refractive index. We also quantify theerrors in size measurements and a limit of the smallest sizethat can be measured due to optical imperfections. Basedon our results, we provide a few suggestions for choosingan acceptable detector solid angle and polarizer extinctionratio. We also compute the signal-to-noise ratio that canbe expected and discuss how it restricts the successful useof this method to particulates larger than about 0.02 µmradius.2. The scattering ratio methodHere we briefly review the scattering ratio method (Sinclairand La Mer 1949). The particle size is determined from theratio   = Ik/I? of the intensities of the parallel (Ik) and theperpendicular (I?) polarized components of the scatteredlight.For a system of monosize spherical particulates, Ikand I? are functions of only three parameters: relativerefractive index m = N/Nm, scattering angle ✓ and sizeparameter x = 2⇡Nma/ . Here N and Nm are therefractive indices of the particle and medium, a is theparticulate radius and   is the wavelength of incidentradiation. The scattering ratio   is also a function of m, ✓and x. For given values of m and ✓ ,   depends only onthe size parameter x; hence polarization measurements fora given m and ✓ can be used to determine the particle size.After determining the particle size, the number density canbe readily computed using Mie scattering theory for eitherIk or I?.The particle size is deduced by comparing the measuredvalue of   to a theoretical plot of   versus particulate size.This plot can be prepared using a Mie scattering code forhomogeneous spheres, such as the one presented by Bohrenand Huffman (1983), which we used for this paper. Figure1 is a representative plot of   versus a for 90  scattering.This assumes a sphere suspended in a plasma with Nm = 1and illuminated by an argon laser (  = 0.488 µm). Thecomplex refractive index N = Nr + Ni is assumed to be2.0   1.0i, which is typical of carbon in graphite form,although there is an uncertainty of this value (Hodkinson1964).In figure 1, note that   is a single-valued monotonicfunction of a/  < 0.1, whereas for larger particle sizes itis multi-valued. For the monotonic region, the scatteringratio scales with particle size according to   / a4. Itis in this region that straightforward and unambiguousparticulate sizing measurements are possible. For largerparticles, where   becomes a multi-valued function of a,accurate particulate sizing is more complicated, requiringfor example combining the   -measurement with anotherlight scattering measurement or making   measurementsat three different wavelengths (Heller and Tabibian 1962).In this paper, we concentrate on using the method in themonotonic region, a/  < 0.1.85Figure 2. (a) Intensity ratio σ = I(25◦/I(90◦ for particle diameter from 0.8µm to1.45µm and unpolarised illumination. The intensity ratio is a clear indicator of particlesize. (b) Intensity ratio Iparallel(90◦)/Iperpendicular(90◦) for particle diameter from 0 to0.2λ.For broader range sizing electrically small particles, we recommend workingwith polarised light. Fig 2(b) is from [4] and it shows an example of the ratio of t eparallel and perpendicularly p larised scattered light intensity measured at one singleangle, θ = 90◦. Here, the particle diameter is reconstructible in the range from 0 toapprox. 0.2λ, which in our case would be he interval 0nm to 130nm. The equipmentcurrently used by TurbiSense should be easily modifiable to use polarised light.References[1] W. Heller, R. Tabibian Experimental Investigations of the Light Scattering f Colloid l Spheres, IV:Scattering Ratio, J. Phys. Chem. 66(10), 1962.[2] M. Neuman, P. Edstro¨m Anisotropic Reflectance from turbid media II. Measurements, J. Opt. Soc.Am. 27 1041, 2010.[3] S. Prahl, Mie Scattering Calculator, http://omlc.ogi.edu/calc/mie_calc.html accessed25.10.2013[4] G. Praburam, J. Goree A scattering atio method for sizing pa ticulat s in a plasma, Plas a SourcesSci. Technol. 5, 1996.

Sizing of Microparticles from Angular Scattering Ratio

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Sizing of Microparticles from Angular Scattering Ratio

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