Negative Polarization Branch Research Articles

Polarimetric properties of asteroids

Quite frequently astronomic polarimetric observations of different celestial bodies do not guarantee a proper phase angle coverage that is required for estimating all of the attributes of their polarization phase curves with a high accuracy. To approximate the phase dependences of polarization observed for particulate surfaces, we use a simple empiric formula recently suggested by Shestopalov (2004). The efficiency of the approximating function in a wide range of phase angles is illustrated with the use of the results of polarimetric measurements of lunar areas, lunar samples, and near-Earth asteroids. For asteroids of various types, we can reproduce their negative polarization branches with adequate accuracy and roughly estimate a probable value of the maximum polarization degree at an appropriate phase angle. From the polarimetric database available at NASA PDS [Asteroid Polarimetric Database V7.0 (2012)] we calculated the main parameters of 153 polarimetric curves of asteroids in various spectral bands with the accuracy comparable to the observation errors. One more purpose of our analysis was to find correlations between the polarimetric and photometric properties of asteroids. For C-, M-, S-, E-type asteroids, the characteristics of the negative branch of polarization curves turned out to correlate closely with the phase coefficient of the photometric function of asteroids and the photometric roughness of asteroid surfaces. This implies that the complex geometry of the surface microrelief affects the polarization properties of asteroids. In particular, the data scattering around regression lines on the plots of the albedo versus the depth of negative polarization branch and the slope of the polarimetric function at inversion angle strongly depends on the differences in the photometric roughness of asteroid surfaces.

Polarimetry of major Uranian moons at the 6-m telescope

We present the results of polarimetric observations of the icymoons of Uranus (Ariel, Titania, Oberon, and Umbriel) performed at the 6-m BTA telescope of the SAO RAS with the SCORPIO-2 focal reducer within the phase angle range of $$0_.^ \circ 06 - 2_.^ \circ 37$$ . The parameters of the negative polarization branch (referred to the scattering plane) are obtained in the V filter: for Ariel the maximum branch depth of P min ≈ −1.4% is reached at the phase angle of α min ≈ 1°; for Titania P min ≈ −1.2%, $$\alpha _{\min } \approx 1_.^ \circ 4$$ ; for Oberon P min ≈ −1.1%, $$\alpha _{\min } \approx 1_.^ \circ 8$$ . For Umbriel the polarization minimum was not reached: for the last measurement point at $$\alpha _{\min } \approx 2_.^ \circ 4$$ , polarization amounts to −1.7%. The declining P min and shifting αmin towards larger phase angles correlate with a decrease of the geometric albedo of the Uranian moons. There is no longitudinal dependence of polarization for the moons within the observational errors which indicates a similarity in the physical properties of the leading and trailing hemispheres. The phase-angle dependences of polarization for the major moons of Uranus are quite close to those observed in the group of small trans-Neptunian objects (Ixion, Huya, Varuna, 1999 DE9, etc.), which are characterized by a large gradient of negative polarization, about −1% per degree in the phase-angle range of $$0_.^ \circ 1 - 1^ \circ$$ .

HUBBLE SPACE TELESCOPE PRE-PERIHELION ACS/WFC IMAGING POLARIMETRY OF COMET ISON (C/2012 S1) AT 3.81 AU

We present polarization images of Comet ISON (C/2012 S1) taken with the Hubble Space Telescope (HST) on UTC 2013 May 8 (rh = 3.81 AU, Delta = 4.34 AU), when the phase angle was alpha = 12.16 degrees. This phase angle is approximately centered in the negative polarization branch for cometary dust. The region beyond 1000 km from the nucleus shows a negative polarization amplitude of p% -1.6%. Within 1000 km of the nucleus, the polarization position angle rotates to be approximately perpendicular to the scattering plane, with an amplitude p% +2.5%. Such positive polarization has been observed previously as a characteristic feature of cometary jets, and we show that Comet ISON does indeed harbor a jet-like feature. These HST observations of Comet ISON represent the first visible light, imaging polarimetry with sub-arcsecond spatial resolution of a Nearly Isotropic Comet (NIC) beyond 3.8 AU from the Sun at a small phase angle. The observations provide an early glimpse of the properties of the cometary dust preserved in this Oort-cloud comet.

Comparing the differential capacitance of two ionic liquid electrolytes: Effects of specific adsorption

The differential capacitance/potential curves of two ionic liquid (IL) electrolytes, 1-butyl-3-methyl-imidazolium hexafluorophosphate (BMIM+/PF6−) and N-butyl-N-methyl-pyrrolidinium hexafluorophosphate (Pyr14+/PF6−) on a glassy carbon (GC) electrode were measured experimentally. The differential capacitance of BMIM+/PF6−/GC is higher in the negative polarization, while the differential capacitance of Pyr14+/PF6−/GC is higher in the positive polarization, although both ILs are composed of common anions, with cations of similar ionic structures and diameters. Such an opposite trend may be understood in terms of the specific adsorption between BMIM+ and the GC electrode, caused by the π-stacking interaction between the aromatic imidazolium ring and the sp2 graphite surface. The specific adsorption effectively shortens the electric double layer (EDL) thickness on the negatively charged electrode but elongates the EDL thickness on the positively charged electrode. Such an effect is manifested in the differential capacitance, with a higher value on the negative polarization branch than on the positive polarization branch. The impact of the specific adsorption is also seen from the positive shift of the potential of zero charge of BMIM+/PF6−/GC in comparison with that of Pyr14+/PF6−/GC.

Coherent backscattering by discrete random media composed of clusters of spherical particles

The approximate method of accounting for the weak localization effect in discrete random media makes it possible to calculate the intensity and the degree of linear polarization of radiation reflected by a semi-infinite layer containing randomly oriented clusters of identical nonabsorbing spherical particles. The paper is focused on the analysis of the influence of the medium properties – the concentration of the clusters, their structure, the sizes and the number of constituent monomers – on the phase dependence of the characteristics of the interference (coherent) component of radiation. Three types of clusters were chosen for the analysis: a fractal-like cluster and two random clusters with different packing densities of monomers. Three values of the size parameters of monomers were considered: 0.5, 1.0, and 1.5. The chosen values of the refractive index of monomers correspond to that of magnesium oxide in the visible spectral range. This allowed us to compare the theoretical phase curves of the degree of linear polarization of light reflected by the medium with the data of measurements by Lyot. For all of the considered cluster types, starting from some minimal number of constituent monomers, which is typical of the specified cluster's type and the monomer's size, the characteristics of the coherent component were found to be practically independent of the number of constituents. In particular, in the phase-angle range from 0° to 15°, the branch of negative polarization measured for a layer of magnesium oxide by Lyot can be well described with several models of the media containing either the fractal-like clusters or the random clusters with the packing density larger than 30%. In these models, the number and sizes of constituent monomers vary. To select from the whole set of “suitable” clusters those the optical characteristics of which actually correspond to characteristics of an elementary volume of the specified medium, additional information is required. For example, this can be the results of polarization measurements in a wider phase interval that includes a zone of the dominating influence of incoherent (diffuse) scattering.

Light scattering by cometary dust: Large-particle contribution

Using the discrete dipole approximation (DDA) and a model of agglomerated debris particles, we study the contribution of large particles on the light scattering by cometary dust. The numerical simulations show that moderately and highly absorbing particles larger than 3 µm do not significantly affect the backscattering phenomena observed at visible wavelengths in comets at phase angles α ≤ 30°, such as the brightness surge and the negative polarization branch. Weakly and non-absorbing particles may play some role even if they are larger than 3 µm; but they are not abundant species in comets. However, the contribution of large particles on polarizations at phase angles α > 30° can be significant, even though they are highly absorbing; simultaneously, the phase dependence of brightness remains insensitive to the contribution of large particles.

Interpretation of similarity in the negative polarization of comets and C-type asteroids in terms of common properties of asteroidal and cometary dust

At small phase angles, the whole coma aperture-averaged linear polarization of comets nearly coincides with that of C-type asteroids. However, the experimental study of light scattering by independent dust particles and regoliths, consisting of exactly the same particles, shows that their negative polarization branches are substantially different. Therefore, the similarity in the linear polarization of comets and C-type asteroids has to be interpreted in terms of a random coincidence rather than evidence for common properties of dust particles. Imaging polarimetry of comets shows two features with a distinctive behavior of the linear polarization: jets and circumnucleus haloes. Dust particles in jets produce only positive polarization through all the phase angles; whereas, dust particles in the halo reveal a significant negative polarization branch with Pmin = −6%. By comparison with the experimental study of light scattering, such a difference in the negative polarization could indicate common properties of dust in the circumnucleus haloes and C-type asteroids. The high negative polarization can be confidently attributed to weakly absorbing particles. The real part of the refractive index Re(m) is 1.5–1.6, and the imaginary part is limited to Im(m) ≤ 0.02. The morphology of dust particles in the circumnucleus haloes can be rather fluffy with a material density of about 0.8 g/cm3. The power-law index for the size distribution is estimated to be about a = 1.5–2.

Modelling the polarization properties of Comet 1P/Halley using a mixture of compact and aggregate particles

Recently, the result obtained from `Stardust' mission suggests that the overall ratio of compact to aggregate particles is 65:35 (or 13:7) for Comet 81P/Wild 2 (Burchell et al. 2008). In the present work, we propose a model which considers cometary dust as a mixture of compact and aggregate particles, with composition of silicate and organic. We consider compact particles as spheroidal particles and aggregates as BCCA and BAM2 aggregate with some size distribution. For modeling Comet 1P/ Halley, the power-law size distribution n(a)= a^{-2.6}, for both compact and aggregate particles is taken. We take a mixture of BAM2 and BCCA aggregates with a lower and upper cutoff size around 0.20$\mu m$ and 1$\mu m$. We also take a mixture of prolate, spherical and oblate compact particles with axial ratio (E) from 0.8 to 1.2 where a lower and upper cutoff size around 0.1$\mu m$ and 10$\mu m$ are taken. Using T-matrix code, the average simulated polarization curves are generated which can best fit the observed polarization data at the four wavelengths $\lambda$ = 0.365$\mu m$, 0.485$\mu m$, 0.670$\mu m$ and 0.684$\mu m$. The suitable mixing percentage of aggregates emerging out from the present modeling corresponds to 50% BAM2 and 50% BCCA particles and silicate to organic mixing percentage corresponds to 78% silicate and 22% organic in terms of volume. The present model successfully reproduces the observed polarization data, especially the negative branch, more effectively as compared to other work done in the past. It is found that among the aggregates, the BAM2 aggregate plays a major role, in deciding the cross-over angle and depth of negative polarization branch.

Model for cometary grains to explain optical polarization

The observed optical polarizations for comets have been explained in past assuming cometary grains to be compact spheres, such that Mie theory could be applied to simulate the observed polarizations. However, recently other shapes like spheroids and then more realistic shapes like aggregates of monomers have been considered for cometary grains, to explain the observed polarizations. For this purpose T-matrix or DDA based light scattering technique was mostly used to simulate the observed polarizations. A number of authors have used T-matrix, DDA and various other techniques along with aggregate grain model to explain the polarizations of comets like 1P/Halley, C 1995/O1 Hale–Bopp, C/1990 K1 (Levy) and C/1996 B2 Hyakutake, etc. Recent STARDUST mission had suggested cometary grains to be mixtures of compact and porous aggregates. Accordingly, attempts have been made recently to reproduce the cometary polarization with mixtures of various compositions, shapes and porosity. The work presented here considers a model for cometary grains which contains (1) solid grains of pyroxene (silicate) and organic with various sizes of spheres, prolates and oblates and (2) aggregates with monomers of various sizes, with composition of pyroxene (silicate) and organic, having structures (shapes) defined by BCCA and BAM2 codes. It was found that the present model can explain the observed polarization data, especially the negative branch, for comet 1P/Halley at 0.485 μ m , more effectively as compared to other work done in past. Among the aggregates the BAM2 structure was found to play a key role, in deciding the cross-over angle and depth of negative polarization branch.

Interpretation of photo-polarimetric observations of comet 17P/Holmes

We present multispectral photo-polarimetric observations of comet 17P/Holmes taken at three different dates. These observations show the evolution of the negative polarization branch (NPB) as a function of time and wavelength. We perform discrete-dipole approximation (DDA) simulations on agglomerated debris particles of various sizes and refractive indices. Our simulations show that the observations are consistent with the cloud being composed of agglomerated debris particles having refractive indices of approximately m=1.5–1.6+0.1 i. Our results are also consistent with the particles obeying a power-law size distribution r – a and having a lower particle-radius cut-off of approximately 0.6 μm, where the index a∼3.5 for the early observations and shrinks to a∼1.5 for the later observations. This is consistent with the smaller, more accelerated particles in the distribution being propelled out of the field of view.

Light scattering by aggregates of varying porosity and the opposition phenomena observed in the low-albedo particulate media

The rule that the opposition phenomena in brightness and linear polarization observed in many regolith surfaces usually accompany each other is violated in the cases of very dark asteroids and particulate samples: practically no nonlinear surge of brightness to opposition is observed while the branch of negative polarization at small phase angles exists. To explain this fact, we model the light scattering by particulate media with ensembles of spherical particles (with size comparable to the wavelength) of varying packing density and refractive index. The superposition T-matrix method is used. The increase in the absorption and/or packing density diminishes the amplitude of the brightness opposition peak, and its profile becomes wider. The influence on the branch of negative polarization is more complex and depends on the relation between the size parameters of the constituents, the refractive index, and the porosity. However, the feature common to all considered cases is that the negative branch changes its shape and the polarization minimum moves to the inversion point. This behavior radically differs from that observed in nonabsorbing ensembles of particles and reflects the fact that the efficiency of the coherent backscattering, which mainly determines these characteristics in nonabsorbing ensembles (to the packing density of about 30%), decreases. Moreover, since the angular profiles are not simply damped, but the polarization minimum changes its angular position, we may conclude that the near-field interaction of the constituents becomes important: the shielding of particles by each other eliminates many constituents from the scattering and the near-field effects promote the negative polarization and smooth the backscattering brightness surge. Due to this, when the packing density exceeds 10–20%, the opposition phenomena in absorbing ensembles are caused not only by the coherent backscattering, and situations, when the opposition brightness surge is practically suppressed, but the negative branch of polarization still survives, are possible. This may explain the fact that the dark regolith surfaces show no brightness opposition effect, but produce the branch of negative polarization with the minimum shifted from opposition.

Single‐scattering modeling of thin, birefringent mineral‐dust flakes using the discrete‐dipole approximation

The morphology and composition of mineral‐dust particles in two surface samples collected in the Sahara desert are investigated by electron microscope imaging, X‐ray diffractography, and energy‐dispersive spectroscopy. Most submicron particles in the samples are found to be flake‐like and thin, and appear to be composed of either calcite or dolomite. The single‐scattering properties of these flake‐like particles are modeled using the discrete‐dipole approximation for size parameters from 1 to 10. For simplicity, the particles are assumed to be composed of calcite, as the properties of dolomite are very similar. The birefringence of calcite is fully accounted for in the simulations, but to assess the importance of birefringence on scattering, two equivalent, isotropic cases analogous to internal and external mixing also are considered. The results show that both isotropic analogs scatter similarly, whereas birefringence affects the light scattering considerably. In particular, the asymmetry parameter is systematically smaller for birefringent than for isotropic flakes. The birefringence also weakens the negative‐polarization branch (NPB) near the backscattering direction. Flakes are found to scatter light very differently from volume‐equivalent spheroids, spheres, or roundish irregularly shaped particles: their asymmetry parameters tend to be much higher, and their backscattering enhancement and their NPBs are much weaker. The results demonstrate that the single‐scattering properties of different mineral‐dust types can be remarkably different. Whether the findings have a significant impact on the assessment of the radiative impact of atmospheric dust depends on the abundance of flake‐like particles in the atmosphere, which is not known.

Polarization and brightness opposition effects for the E-type Asteroid 44 Nysa

We present new polarimetric and photometric observations of high-albedo E-type Asteroid 44 Nysa in the BVRI wavebands at phase angles ranging from 0.41° to 7.49° during the 2005 opposition. A bimodal phase-angle dependence of polarization was found for Nysa in the V band. The polarization opposition effect was revealed in the form of a secondary minimum of negative polarization with amplitude ∼0.3% centered at a phase angle ∼0.8°. It is superimposed on the regular negative polarization branch with minimal polarization −0.30% at a phase angle 5.8°. We analyzed all available polarimetric data for E-type Asteroids 44 Nysa, 64 Angelina, and 214 Ashera and confirmed the presence of the polarization opposition effect for high-albedo asteroids at phase angle ∼1° with an amplitude ∼0.35%. The magnitude–phase curves reveal the presence of spike-like opposition effect of brightness for 44 Nysa in the BVRI spectral bands. 44 Nysa is the second high-albedo asteroid after 64 Angelina for which both the polarization opposition effect and the brightness opposition effect are detected. The differences between the parameters of the opposition effects for silicate surfaces (44 Nysa, 64 Angelina, Io) and icy surfaces (Europa, Ganymede, Iapetus, Saturn's rings) are discussed. The specific morphological parameters of opposition effects, in particular the angular width of the polarization opposition effect is comparable to that of the brightness opposition effect, provide almost unequivocal evidence that they are caused by coherent backscattering. One of unexpected results of our investigation is that 44 Nysa becomes bluer with increasing phase angle, while 64 Angelina shows phase reddening.

Effect of absorption on light scattering by agglomerated debris particles

We study the influence of material absorption on light scattering by agglomerated debris particles whose sizes are comparable with the wavelength. We find that the angular profile of linear polarization is extremely sensitive to the imaginary part of refractive index, and there are some unique features that may assist in the retrieval of physical properties of particles using remote-sensing techniques. Most notably, the position of the positive polarization maximum α max changes monotonically with the imaginary part of refractive index, allowing it to be used to characterize this property. In addition, the amplitude of the negative polarization branch (NPB) is significantly greater for dielectric particles than for non-dielectric particles. It disappears in the transition region between dielectric and conducting particles before reappearing as the imaginary part of the refractive index is increased further. Further increasing the imaginary part of the refractive index may see the NPB disappearing and reappearing in quasi-periodic fashion. This recurrent NPB has a much smaller amplitude than that of dielectric particles. This suggests that the cometary circumnuclear haloes, which have significant NPBs, cannot contain significant quantities of absorbing particles. In addition, combined observations suggest that the polarization maximum of circumnuclear haloes are relatively small P max∼12%, and occur at relatively small phase angles α max∼60°, which is also consistent with dielectric particles.

Polarimetric mapping of the Moon at a phase angle near the polarization minimum

At small phase angles the light scattered by the Moon reveals a negative polarization branch whose average amplitude is 1%. We present results of polarimetric mappings of the Moon in P min at a phase angle near 11°. The observations were carried out with the Kharkov 50-cm telescope at the Maidanak Observatory (Middle Asia) using a polarizing filter. A thorough calibration of the camera array allows for the reliable detection of significant variations of | P min | over the lunar surface, from 0.2 to 1.6%, at a wavelength of 0.52 μm. The smallest | P min | are characteristic of young bright craters, while the | P min | are the highest for the lunar highland and bright mare areas. The horse-shoe shape of the correlation dependence P min (albedo) is treated with data of our laboratory measurements of powdered surfaces and computer modeling of light scattering by small particles with the DDA (discrete dipole approximation) technique.

Extended calculation of polarization and intensity of fractal aggregates based on rigorous method for light scattering simulations with numerical orientation averaging

The intensity and polarization of fractal aggregates have been investigated using both rigorous and approximate methods for light scattering simulations. However, previous studies using the analytical orientation averaging version of the rigorous method were generally limited to a few hundred monomers when the monomer size parameter was around 1.7. In this study, we propose using numerical orientation averaging instead of analytical orientation averaging. The numerical averaging is performed together with a fixed orientation version of the rigorous T-matrix method for clusters of spheres. This approach enables increasing the number of monomers by a factor of 2–7 or the size of monomers by a factor of 8–10 compared to the analytical orientation averaging version. We investigated the influence of monomer size and the number of monomers on the light scattering of silicate aggregates (refractive index m = 1.68 + 0.03 i ) for incident light with a wavelength of 0.6 μ m . We considered ballistic particle–cluster aggregates (BPCA) and ballistic cluster–cluster aggregates (BCCA) composed of 128, 256, 512, and 1024 monomers with radii between 0.11 and 0.17 μ m . Our results show that the size of monomers plays an important role in reproducing the negative polarization branch for all the BPCA and BCCA. Silicate aggregates with the monomer radius of less than 0.17 μ m contribute to reproducing the negative polarization branch, while aggregates with monomers larger than 0.17 μ m do not have the negative polarization branch. Polarization oscillation with scattering angle occurs for larger monomers (i.e., monomer radius ⩾ 0.3 μ m ). The maximum polarization decreases for increasing monomer radius between 0.11 and 0.17 μ m . However, the negative polarization branch is generally enhanced for monomer radii up to around 0.15 μ m , and reduced for further increase of monomer size. The number of monomers also has a large influence on the negative polarization branch in the case of BPCA. The increase in the number of monomers from 128 to 1024 shifts the scattering angle of minimum polarization to larger angles for BPCA. In addition, the increase in the number of monomers reduces the values of negative polarization for BPCA while the variation with the number of monomers for BCCA is small and is not monotonic.

Interrelating scattering characteristics to internal electric fields for Gaussian-random-sphere particles

We investigate the single-scattering interference mechanism related to the negative polarization branch (NPB) and intensity enhancement branch (IEB) near the backscattering direction for wavelength-scale Gaussian-random-sphere particles. Previously, we showed that for wavelength-scale spherical particles there is a two-part mechanism related to the longitudinal and the transverse components of the internal electric fields that are responsible for producing both the NPB and IEB near the backscattering direction. For comparison with the previous study, we have chosen the ensemble-averaged parameters of the Gaussian-random-sphere particles to be equivalent to those for spherical particles. We conclude that the same mechanism also can explain the NPB and IEB for non-spherical particles and that the mechanism seems to be stronger inside spherical particles, mainly because of stronger interference, and becomes weaker as the particle becomes more non-spherical.

Comment on “Modeling of opposition effects with ensembles of clusters: Interplay of various scattering mechanisms” by Elena V. Petrova, Victor P. Tishkovets, Klaus Jockers, 2007 [Icarus 188, 233–245

We show that the mechanism called “near-field effect” [e.g., Petrova, E.V., Tishkovets, V.P., Jockers, K., 2007. Icarus 188, 233–245], which is used to explain wide-phase-angle negative polarization branch observed for planetary regoliths and cometary comas, is not realistic as it contradicts laboratory experiments and results of modeling with discrete dipole approximation calculations.

The scattering matrix of random media consisting of large opaque spheres calculated using ray tracing and accounting for coherent backscattering enhancement

Phase curves of the scattering Mueller matrix elements are calculated for light scattering in media randomly packed with large, non-transparent spheres ( X = 125 ) , the surfaces of which reflect light according to the Fresnel equations. We here consider three values of the refractive index: m = 0.73 + 5.93 i (metal Al), 1.6 + 1.72 i (metal Fe), and 1.5 + 0.1 i (black glass). We use a Monte Carlo ray-tracing approach, taking into account the coherent backscattering effects. The ray-tracing procedure is based on calculation of the Jones matrix for each ray originating from a random starting point with a given incident direction. When the ray leaves the medium after n reflections, we try to found the so-called reciprocal ray, which is reflected by the same subset of particles, but in the reverse order. If such a ray exists, we calculate the corresponding Jones matrix and sum this with the Jones matrix of the initial ray coherently. Then the Mueller matrix is calculated. We find that the main contributions to the coherent opposition spike are the second and third orders of reflection. Higher reflection orders make only a minor contribution to the total intensity even for highly reflective materials like Al. For these media we detect weak negative polarization branches at small phase angles. Their depth and width are about 0.5% and 7 ∘ , respectively. The iron shows a deeper negative polarization branch, and aluminum (bright metal) demonstrates almost zero polarization; whereas, dark glass takes an intermediate position. We find that for the second scattering order, the normalized elements of the scattering matrix, M 22 / M 11 , M 33 / M 11 , and M 44 / M 11 , depend noticeably on density at small phase angles. All elements on the main diagonal of the scattering matrix are sensitive to the angle of incidence; whereas, those on the secondary diagonals are sensitive to the phase angle. Phase dependencies of the elements - M 21 / M 11 , - M 12 / M 11 , - M 43 / M 11 , and - M 34 / M 11 for oblique illumination shift relative to the case of normal illumination. In the case of - M 21 / M 11 this shift has been observed experimentally.

Photopolarimetric properties of analytic models of some biological particles with irregular shape

We provide analytic descriptions of the morphologies of some biological particles: Sporisorium cruentum spores, Aspergillus terreus spores, and erythrocytes. We use the T-matrix extended-boundary-condition method to calculate the scattering properties of these particles. It is found that the morphology of A. terreus spores reveals an unusually wide negative polarization branch with two minima near large scattering angles, and that of S. cruentum spores do not display a negative polarization branch at all. We show that for unrealistically small size parameters, a simple cylinder has many of the same qualitative scattering properties of the much more complicated model of erythrocytes; however, as the particle size is made more realistic, very large differences appear in the scattering from these particle systems.