Optics of Heterogeneous Media. Comparison of Some Light Scattering Model Calculations

1993 ◽  
Vol 58 (10) ◽  
pp. 2272-2281 ◽  
Author(s):  
Jaroslav Holoubek
Keyword(s):  
Heterogeneous Media ◽  
Incident Light ◽  
Mie Theory ◽  
Polystyrene Latex ◽  
Asymmetry Factor ◽  
Good Correspondence ◽  
Model Calculations ◽  
Surrounding Matrix ◽  
Media Comparison ◽  
Scattering Correction

Typical dependences of turbidity as a function of diameter of scattering elements and their volume fractions as well as a function of the wavelength of the incident light were calculated, based both on the Lorenz-Mie theory and the fluctuation theory of Debye and Bueche. Such dependences calculated for the polyethylene, polypropylene and polyamide inclusions differing slightly in their reactive index from the surrounding matrix of the same material were compared. The multiple scattering correction of the Lorenz-Mie theory based on the asymmetry factor affects the turbidity similarly as the use of mixing rule for refractive indices of multicomponent systems. A good correspondence between both theories was found only for small scattering inclusions fulfilling the approximate condition for diameter d < 0.3 λ. Only approximate agreement of the turbidity and refractive index fluctuations up to the diameters d < 5 λ can be observed for the present systems using both theories. The results obtained for the solid polymers were compared with model calculations for polystyrene latex under identical conditions: the latter are in a reasonable agreement with the expected trends (more pronounced dispersion and larger turbidity).

Stress Whitening in Polypropylene. I. Light Scattering Theory and Model Experiments

1995 ◽  
Vol 60 (11) ◽  
pp. 1875-1887 ◽  
Author(s):  
Jaroslav Holoubek ◽  
Miroslav Raab
Keyword(s):  
Refractive Index ◽  
Light Scattering ◽  
Incident Light ◽  
Polymeric Materials ◽  
Wavelength Dependence ◽  
Theoretical Background ◽  
Surrounding Matrix ◽  
Embedded Particles ◽  
The One ◽  
Stress Whitening

Theoretical background for an optical method is presented which makes it possible to distinguish unambiguously between voids and particles as light scattering sites in polymeric materials. Typical dependences of turbidity as a function of diameter of scattering elements, their volume fractions and also turbidity curves as a function of the wavelength of the incident light were calculated, based both on the Lorenz-Mie theory and the fluctuation theory. Such dependences calculated for polypropylene-containing voids on the one hand and particles, differing only slightly from the surrounding matrix in their refractive index, on the other hand, are markedly different. The most significant results are: (i) Turbidity is at least by two orders of magnitude larger for voids in comparison to embedded particles of ethylene-propylene (EPDM) rubber of the same size, concentration and at the same wavelength. (ii) The wavelength dependence of turbidity for EPDM particles and the inherent refractive index fluctuations in the polypropylene matrix is much steeper as compared to voids for all considered diameters (0.1-10 μm). Thus, the nature of stress whitening in complex polymeric materials can be determined from turbidity measurements.

scholarly journals On the scattering behaviour of bullet-rosette and bullet-shaped ice crystals

1996 ◽  
Vol 14 (5) ◽  
pp. 566-573
Author(s):  
B. Strauss
Keyword(s):  
Ray Tracing ◽  
Ice Crystals ◽  
Asymmetry Factor ◽  
Model Calculations ◽  
Geometrical Features ◽  
The Asymmetry ◽  
Particle Length ◽  
Phase Functions ◽  
Tracing Method ◽  
Factor G

Abstract. The scattering behaviour of bullet-rosette and bullet-shaped ice particles is investigated using model calculations (ray tracing method) with special emphasis on the asymmetry factor g. Because the variability of the geometrical features of these particles is very large, some representative shapes are used in the calculations. The model is based on geometrical optics, and particles are assumed to be oriented randomly; a wavelength of 0.56 μm is considered; absorption is neglected. The scattering behaviour of bullet rosettes is compared to that of single branches out of the bullet rosette. It turns out that there are slight differences in the asymmetry factor values, depending on the lengths of the branches (∆g~0.02) and on the angles between the branches (∆g~0.01). Bullets show some special features in their phase functions due to the pyramid. The length of the particle influences the asymmetry factor (∆g~0.10), as does the shape of the pyramid (∆g~0.07). The influence of the pyramidal shape decreases with increasing particle length. Bullets were compared to hexagonally shaped columns. This was done for two columns, one as long as the columnar part of the bullet (length without pyramid), and one for a column as long as the bullet including the pyramid. Asymmetry factor values of bullets with a pyramidal angle of 28° deviate less than ∆g~0.01 from the range given by the two values of the columns.

Quantification of the backscatter coefficient in heterogeneous media: Comparison of attenuation compensation methods

2020 ◽  
Vol 148 (4) ◽  
pp. 2559-2559
Author(s):  
Laura Casta ñeda-Martinez ◽  
Timothy J. Hall ◽  
Noushin Jafarpisheh ◽  
Hayley Whitson ◽  
Hassan Rivaz ◽  
...  
Keyword(s):  
Heterogeneous Media ◽  
Backscatter Coefficient ◽  
Attenuation Compensation ◽  
Media Comparison ◽  
Compensation Methods

A study of Mie scattering modelling for external mixtures of NAT and STS Polar Stratospheric Clouds

2021 ◽  
Author(s):  
Francesco Cairo ◽  
Marcel Snels ◽  
Luca Di Liberto ◽  
Terry Deshler ◽  
Andrea Scoccione ◽  
...  
Keyword(s):  
Refractive Index ◽  
Incident Light ◽  
Mie Theory ◽  
Threshold Value ◽  
Mie Scattering ◽  
Optical Parameters ◽  
Polar Stratospheric Clouds ◽  
Ground Based Lidar ◽  
Factor C ◽  
Stratospheric Clouds

&lt;p&gt;Mie scattering codes have long been used to study the optical properties of Polar Stratospheric Clouds, once the particle size distribution (PSD) is known and a suitable refractive index is assumed. However, PSCs are often composed as external mixtures of STS and NAT, making questionable the use of Mie theory with a single refractive index. Furthermore, the NAT particles are non-spherical, while strictly speaking the applicability of Mie theory is limited to particles with circular symmetry along the direction of propagation of the incident light.&amp;#160;&lt;br&gt;Here we consider a set of 15 coincident measurements of polar stratospheric clouds above McMurdo Station, Antarctica, by ground-based lidar (backscatter and depolarization) and balloon-borne Optical Particle Counters (PSD), and apply Mie theory to the measured PSD, to seek matching with the observed optical parameters.&lt;br&gt;In our model, we consider the PSD particles as STS if their radius is below a certain threshold value R and NAT if above it, assuming the corresponding refractive indexes known from literature. Moreover, we reduce the Mie calculation for the NAT part of the PSD by multiplying it by a factor C &lt;1, which takes into account the backscattering depression expected from aspheric particles. Finally, we consider the fraction X of the backscattering contribution of the NAT part of the PSD as polarized, and the remaining (1-X) as depolarized.&lt;br&gt;The three parameters R, C and X of our model are then chosen to provide the best match with the observed lidar backscattering and depolarization.&lt;/p&gt;

Polarization property of light scattered on dielectric nanorods at oblique incident angle

2019 ◽  
Vol 28 (04) ◽  
pp. 1950041
Author(s):  
Suhandoko D. Isro ◽  
Alexander A. Iskandar ◽  
May On Tjia
Keyword(s):  
Incident Angle ◽  
Incident Light ◽  
Mie Theory ◽  
Grazing Angle ◽  
Light Polarization ◽  
Polarization Property ◽  
Main Axis ◽  
Numerical Work ◽  
Resonance Modes ◽  
Different Characteristics

We report the study of light polarization property upon scattering off a dielectric nanorod in which the direction of the incident light is at an angle with respect to the cylinder main axis. The numerical work is done on the basis of the cylindrical Mie theory. It is shown that for incident light with different polarization, the resulted scattering cross-section spectra will also show different characteristics with varying incident angles. For TE case, resonance splitting is observed due to excitation of a new resonance mode, while for TM case, resonance merging is observed. An interference effect between different resonance modes due to variation of incident angle is then resulted in suppression of backward scattering intensity for TM case. Meanwhile, for TE case, at illumination angle approaching grazing angle, a spectral range exists whereby the scattered wave’s angular intensity profile forms a perpendicular dipolar feature with different polarization. The reported results may be useful for aplication of nanoantenna, photovoltaic, and polarization conversion.

RADIATION BOUNDARY CONDITIONS FOR VERTICALLY HETEROGENEOUS ACOUSTIC MEDIA

1993 ◽  
Vol 01 (03) ◽  
pp. 321-333 ◽  
Author(s):  
GONGQIN LI ◽  
JOSEPH E. MURPHY ◽  
STANLEY A. CHIN-BING
Keyword(s):  
Boundary Conditions ◽  
Heterogeneous Media ◽  
Plane Waves ◽  
Reflection Coefficients ◽  
Radiation Boundary Conditions ◽  
Media Comparison ◽  
Acoustic Media ◽  
Radiation Boundary ◽  
Radiation Conditions ◽  
Effective Reflection Coefficient

Several radiation boundary conditions for inhomogeneous acoustic media are investigated. Previous investigators have developed various approximate radiation conditions and have studied their accuracy by calculating an effective reflection coefficient for plane waves incident on such radiating boundaries. In this paper, it is shown that effective reflection coefficients can be calculated for a class of parabolic approximations to the Helmholtz equation. These results are valid for vertically heterogeneous media. Comparison of these radiation conditions is given through numerical examples.

scholarly journals An optical particle size spectrometer for aircraft-borne measurements in IAGOS-CARIBIC

2015 ◽  
Vol 8 (11) ◽  
pp. 11597-11642
Author(s):  
M. Hermann ◽  
A. Weigelt ◽  
D. Assmann ◽  
S. Pfeifer ◽  
T. Müller ◽  
...  
Keyword(s):  
Particle Size ◽  
Size Distribution ◽  
Particle Number ◽  
Counting Efficiency ◽  
Polystyrene Latex ◽  
Particle Size Range ◽  
Model Calculations ◽  
Number Size Distribution ◽  
Particle Number Size Distribution ◽  
Earth’S Climate

Abstract. The particle number size distribution is an important parameter to characterize the atmospheric aerosol and its influence on the Earth's climate. Here we describe a new Optical Particle Size Spectrometer (OPSS) for measurements of the accumulation mode particle number size distribution in the tropopause region onboard a passenger aircraft (IAGOS-CARIBIC observatory (In-service Aircraft for a Global Observing System – Civil Aircraft for Regular Investigation of the Atmosphere Based on an Instrument Container)). A modified "KS93 particle sensor" from RION Co., Ltd. together with a new airflow system and a dedicated data acquisition system are the key components of the CARIBIC OPSS. The instrument records individual particle pulses in the particle size range 130–1110 nm diameter (for a particle refractive index of 1.47-i0.006 for an upper tropospheric (UT) aerosol particle) and thus allows the post-flight choice of the time resolution and the size distribution bin width. The CARIBIC OPSS has a 50 % particle detection diameter of 152 nm and a maximum asymptotic counting efficiency of 98 %. The instruments measurement performance shows no pressure dependency and no coincidence for free tropospheric conditions. The size response function of the CARIBIC OPSS was obtained by a polystyrene latex calibration in combination with model calculations. Particle number size distributions measured with the new OPSS in the lowermost stratosphere agreed within a factor of two in concentration with balloon-borne measurements over western North America. Since June 2010 the CARIBIC OPSS is deployed once per month in the IAGOS-CARIBIC observatory.

scholarly journals An optical particle size spectrometer for aircraft-borne measurements in IAGOS-CARIBIC

2016 ◽  
Vol 9 (5) ◽  
pp. 2179-2194 ◽  
Author(s):  
Markus Hermann ◽  
Andreas Weigelt ◽  
Denise Assmann ◽  
Sascha Pfeifer ◽  
Thomas Müller ◽  
...  
Keyword(s):  
Particle Size ◽  
Size Distribution ◽  
Particle Number ◽  
Pulse Signal ◽  
Counting Efficiency ◽  
Polystyrene Latex ◽  
Particle Size Range ◽  
Model Calculations ◽  
Number Size Distribution ◽  
Particle Number Size Distribution

Abstract. The particle number size distribution is an important parameter to characterize the atmospheric aerosol and its influence on the Earth's climate. Here we describe a new optical particle size spectrometer (OPSS) for measurements of the accumulation mode particle number size distribution in the tropopause region on board a passenger aircraft (IAGOS-CARIBIC observatory: In-service Aircraft for a Global Observing System – Civil Aircraft for Regular Investigation of the Atmosphere Based on an Instrument Container). A modified KS93 particle sensor from RION Co., Ltd., together with a new airflow system and a dedicated data acquisition system, is the key component of the CARIBIC OPSS. The instrument records individual particle pulse signal curves in the particle size range 130–1110 nm diameter (for a particle refractive index of 1.47-i0.006) together with a time stamp and thus allows the post-flight choice of the time resolution and the size distribution bin width. The CARIBIC OPSS has a 50 % particle detection diameter of 152 nm and a maximum asymptotic counting efficiency of 98 %. The instrument's measurement performance shows no pressure dependency and no particle coincidence for free tropospheric conditions. The size response function of the CARIBIC OPSS was obtained by a polystyrene latex calibration in combination with model calculations. Particle number size distributions measured with the new OPSS in the lowermost stratosphere agreed within a factor of 2 in concentration with balloon-borne measurements over western North America. Since June 2010 the CARIBIC OPSS is deployed once per month in the IAGOS-CARIBIC observatory.

scholarly journals The HIP 79977 debris disk in polarized light

2017 ◽  
Vol 607 ◽  
pp. A90 ◽  
Author(s):  
N. Engler ◽  
H. M. Schmid ◽  
Ch. Thalmann ◽  
A. Boccaletti ◽  
A. Bazzon ◽  
...  
Keyword(s):  
Surface Brightness ◽  
Rayleigh Scattering ◽  
Broad Band ◽  
Contrast Ratio ◽  
Asymmetry Factor ◽  
Debris Disks ◽  
Infrared Excess ◽  
Model Calculations ◽  
Diagnostic Potential ◽  
Debris Disk

Context. Debris disks are observed around 10 to 20% of FGK main-sequence stars as infrared excess emission. They are important signposts for the presence of colliding planetesimals and therefore provide important information about the evolution of planetary systems. Direct imaging of such disks reveals their geometric structure and constrains their dust-particle properties. Aims. We present observations of the known edge-on debris disk around HIP 79977 (HD 146897) taken with the ZIMPOL differential polarimeter of the SPHERE instrument. We measure the observed polarization signal and investigate the diagnostic potential of such data with model simulations. Methods. SPHERE-ZIMPOL polarimetric data of the 15 Myr-old F star HIP 79977 (Upper Sco, 123 pc) were taken in the Very Broad Band (VBB) filter (λc = 735 nm, Δλ = 290 nm) with a spatial resolution of about 25 mas. Imaging polarimetry efficiently suppresses the residual speckle noise from the AO system and provides a differential signal with relatively small systematic measuring uncertainties. We measure the polarization flux along and perpendicular to the disk spine of the highly inclined disk for projected separations between 0.2′′ (25 AU) and 1.6′′ (200 AU). We perform model calculations for the polarized flux of an optically thin debris disk which are used to determine or constrain the disk parameters of HIP 79977. Results. We measure a polarized flux contrast ratio for the disk of (Fpol)disk/F∗ = (5.5 ± 0.9) × 10-4 in the VBB filter. The surface brightness of the polarized flux reaches a maximum of SBmax = 16.2 mag arcsec-2 at a separation of 0.2′′–0.5′′ along the disk spine with a maximum surface brightness contrast of 7.64 mag arcsec-2. The polarized flux has a minimum near the star <0.2′′ because no or only little polarization is produced by forward or backward scattering in the disk section lying in front of or behind the star. The width of the disk perpendicular to the spine shows a systematic increase in FWHM from 0.1′′ (12 AU) to 0.3′′−0.5′′, when going from a separation of 0.2′′ to >1′′. This can be explained by a radial blow-out of small grains. The data are modelled as a circular dust belt with a well defined disk inclination i = 85( ± 1.5)° and a radius between r0 = 60 and 90 AU. The radial density dependence is described by (r/r0)α with a steep (positive) power law index α = 5 inside r0 and a more shallow (negative) index α = −2.5 outside r0. The scattering asymmetry factor lies between g = 0.2 and 0.6 (forward scattering) adopting a scattering-angle dependence for the fractional polarization such as that for Rayleigh scattering. Conclusions. Polarimetric imaging with SPHERE-ZIMPOL of the edge-on debris disk around HIP 79977 provides accurate profiles for the polarized flux. Our data are qualitatively very similar to the case of AU Mic and they confirm that edge-on debris disks have a polarization minimum at a position near the star and a maximum near the projected separation of the main debris belt. The comparison of the polarized flux contrast ratio (Fpol)disk/F∗ with the fractional infrared excess provides strong constraints on the scattering albedo of the dust.

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