The Optics and Lidar Laboratories
Group of Hans Hallen and Russell Philbrick, Physics Department, North Carolina State University
Aerosols are generated by many sources (wind spallation, water bubbles breaking, burning, volcanic, condensation of organics, etc.) at different sizes, and can further evolve by accumulation, particularly of water, but also smaller particles and organic vapors. Usually these factors result in an aerosol particle distribution that can be modelled by three lognormal distributions. The aerosols have several impacts: on visibility and light transmission by scattering (and to a lesser extent, absorption), on climate by changing the radiation balance, and on health because they are inhaled along with the air. The impacts depend strongly upon the size, composition and wavelength of light. The scattering from very small particles scales as the fourth power of the size/wavelength, reaches a maxima with resonances (for symmetric particles) at size/wavelength ~ 1, and becomes more forward, small angle scattering and geometric Snell's law refracting for particles large compared to the wavelength. Absorption also influences the extinction. The primary non-obvious effect occurs for particles large compared to the absorption length, for which part of the volume is shielded from the incident light by the material before. The absorption increases when these particles are ground, then re-suspended (we refer to it as an increase in absorption efficiency for small particles.).
Remote measurement of aerosols with lasers can use several of the properties noted above, and we will describe them in detail and give examples below. Aerosols both scatter and absorb light, together the effect is called extinction. Absolute extinction can be measured by Raman lidar. The Raman part is required so that the nitrogen density can be used as a reference for the signal level to make the measurement absolute. If different wavelengths are used, then information about particle size can be obtained via the dependence as a function of size/wavelength . The laser used for Raman lidar, or another laser (even a CW laser), can also be used in a multistatic measurement configuration to measure the angular dependent scattering, the scattering phase function. It is useful to take two measurements at each angle with the laser polarized in two perpendicular directions and form the polarization ratio scattering phase function to render the measurement independent of the laser power and path loss of the laser beam. Several cameras spaced at different distances from the laser can provide a large range of large angle scattered light measurements in the lidar-like configuration. If the aerosol size distribution is uniform over a distance and the aerosols are nearly circular (see below) such as will be the case in moist air, the size distribution parameters assuming three lognormal distributions can be determined  . Information about the size distributions and index of refraction can also be determined by looking at the nearly forward scattered light, the scattering aureole. This frontal lobe narrows for larger aerosols. If one wants to know the scattering properties of a dust sample, then one can aerosolize it or, as we also show, press it into a pellet and measure leisurely . The aureole scattering region is also a good place to identify the substance that makes up the aerosol by measuring the scattering at one angle as a function of wavelength and identifying index-related signatures . Finally, we have shown that the aureole scattering angles produce a scattering profile which is compatible with spherical (Mie) calculations for quantitative analysis of aerosol size even for nonspherical particles, in particular, for spheroids with aspect ratios up to two . Thus, the aureole scattering region is practical for straightforward analysis of aerosol size and index. The problem is that it is near forward scattering, so is not possible to use in combination with an upward pointing lidar laser. Our study of the literature has shown us that many studies that measure aerosol index do so by fitting to only a particular quantity (that varies with the paper). The results of these analyses often have nonphysical results, so we have developed a few ways of accurately measuring the index of refraction of aerosols. Of particular importance is that the proper use of the particle index imbedded in air, calculated by effective medium theory or Mie calculations, is required for artifact-free results. Our methods use ellipsometry or careful infrared absorption .
We refer here to the use of a lidar-like laser configuration, where the scattering from a CW or pulsed laser is measured at relatively large scattering angles: greater than 90 degrees and up to 180 degrees. A summary of measurements taken in conjunction with a Raman lidar can be found in Ref . Here, we describe a set of experiments using a variety of measurement modalities with CW laser light of several wavelengths. This document contains a brief overview; the details can be found in , . Arizona Road Dust (ARD) was disbursed into an atmospheric environment with air motion to keep it aloft and relatively uniform. The experiments investigate the effects of dust particle size on the scattering using sifted ARD to produce seven size cuts. Each size cut was studied at three different density distributions. An Aerodynamic Particle Sizer (APS) unit monitored the size distribution as a function of time while the larger, and then the smaller, particles settle out of the air. Studies of the combination of particle distributions cover a wide range of particle sizes. We use data from the size-selected samples to examine extinction due to small, medium, and larger particles in the ARD samples. The utility of this approach is tested by predicting the extinction from a distribution with a range of sizes and by combining data from seven size-cut ranges (0-3, 0-5, 0-10, 5–10, 0-20, 10-20, and the Ultrafine size, <15, microns, as sold by Powder Technologies, Inc.) and three densities (20, 100, and 200 grams of dust into a volume of about 80 m3), and comparing with simulations. Three laser wavelengths in the visible (532 nm), the near infrared (1064 nm), and the long wave infrared (LWIR, 10.6 microns), are used to study the effects of the lofted dust on scattering and transmission. Each dust sample is injected into the test chamber to produce a cloud, which scatters the beams, and the two polarized components are measured in the forward and backward directions for each wavelength. The trials are of short time duration due to settling speed of the dust and a time sequence of measurements records the optical scattering as a function of the changing size distribution.
The polarization-dependent measurements enable an examination of the scattering contributions of irregular shaped particles and multiple scattering by ARD dust particles. The polarized laser beams experience a measureable degree of depolarization when the scatters are non-spherical in nature, and when the density is high enough that multiple scattering occurs. The depolarization measurement is performed by comparing the cross-polarized signal with the signal in the laser polarization plane. The cross-polarized signal would remain at zero for the case of spherical aerosols under single-scattering conditions. Any significant variance from zero indicates a non-spherical particle and/or multiple scattering. The data are normalized by the reference levels to eliminate the need for full detector calibration and correction for the laser power, thus allowing a direct comparison of depolarization amplitude at each wavelength. The data from the 532 nm beam show evidence for non-spherical particles in ARD. In Figure 1 we compare depolarization measurements at a 100 gram loading in different size cuts. The figure displays runs of (a) 0-5 µm, (b) 5-10 µm, and (c) 10-20 µm. The 0-5 µm shows a peak at 0.03. The 5-10 µm shows a peak near 0.017. The 10-20 µm shows a peak at 0.0315. A run at 0-3 µm. We see a peak in the depolarization at 0.17. We see an inverse relationship with particle size for the smaller sizes. This is indicative of a particle shape property and not a population property. The increase in the peak for the largest particle size may be due to multiple scattering for this mass loading. We also learn from the seemingly uniform data of Figure 1 that the dusts of the different size cuts seem to be equally efficient at generating depolarized light. If, for example, the small dust was spherical and the larger dust eccentric, then the smaller dust would produce no depolarization while the larger dust would produce a significant amount. The uniformity suggests that the different sizes of dust are equally eccentric.
(a) (b) (c)
Figure 1. These three plots show the depolarization measurement for 532 nm at size cuts of (a) 0-5 µm, (b) 5-10 µm, and (c) 10-20 µm at a mass loading of 100 grams. Indications of non-spherical particles develop from the consistency of the depolarization curve for the changing conditions at smaller size cuts. In the largest size cut we see evidence for multiple scattering due to the mass density.
We now examine the forward extinction patterns that develop during various trials. Size cut selection has an effect, as does the concentration level in the aerosol cloud. The concentration of the particles determines the optical depth of the chamber for a particular test. Larger particles have a short suspension time, even for a large chamber, considering the measurement for the 10 micron diameter particle size cut. The following plots, Figures 2-4, compare the transmission levels of three wavelengths for different concentration levels and size cuts of Arizona Road Dust. We list the size-cuts used in each test. One key to understanding the features are the particle size relative to the wavelength. If the particle is much smaller than the wavelength, the scattering will be Rayleigh, and as stated above, weak but strongly dependent upon size. If the two are nearly the same, then Mie scattering is required for spheres (it always works, but isn't always needed). The scattering is strong and oscillates in direction and wavelength. If the particle is large, then a more geometric limit is approached, and scattering becomes strongly forward directed. The other key point is that larger particles settle out of the air faster than smaller ones. This impacts the time dependence.
Measurement results are shown in Fig. 2 for a 0-5 µm sample of ARD at a concentration of 200 grams, which was the highest mass loading of dust for the series of tests. The higher loading and larger particles cause a much stronger response for the 10.6 µm beam than observed in a similar test but with 0-3 µm dust at 20 gram loading. The visible and near infrared beams show almost complete extinction (scattering of all wavelengths and absorption at LWIR) since the loading is heavy and the particles small, the number densities are very high. The small particles take a long time to settle out of the chamber, so this run is long, about 1.5 times longer than with 0-3 µm dust at 20 gram loading
Figure 2. A loading of 200 g in the 0–5 µm size cut presents an optical thickness to all three beams that causes extinction over a longer interval. The density of the loading produces saturation in the 532 nm and the 1064 nm and exhibits the whitening characteristic of multiple scattering during injection.
Figure 3 shows the same types of results as shown in Figure 2 for the size cuts 5-10. These are larger particles, and the extinction in the long wave now contains scattering as well as significant absorption. The extinction in the long wave exceeds that in the visible and near infrared in both cases, at least at times not long after injection. This is due to the combination absorption at LWIR with multiple scattering for heavy loadings, as discussed above. The larger particles drop out of the distribution quite quickly, leaving only the smaller particles and reducing the component of multiple scattering. In fact, at later times during the run, the particle distribution begins to look more like the 0-5 micron distribution. Perhaps many of these particles are generated during the injection process by a break-up of a conglomerate or shed from the surface of a larger particle, but they settle out so slowly compared to the larger particles that they are still present at the end of a trial. Note the length of these runs is considerably shorter than for the smaller particles, even with the larger (100 or 200 gram) loadings, reflecting the faster dropout rate.
Figure 3. At the size cut of 5–10 µm, 100 g loading, the 10.6 µm beam undergoes significant scattering as well as absorption. The size of the particles ensures a short suspension time.
Figure 4 shows an example of optical measurements of a 0-10 µm particle size distribution. This size distribution causes the 10.6 µm to strongly scatter and absorb when there are large particles present in the distribution. As the larger particles rapidly settle out, the 10.6 µm signal recovers, while the visible and near infrared, 532 nm and 1064 nm signals, continue to be depressed by scattering from the smaller, longer-lived airborne particles. Wide particle distributions undergo the most dramatic changes during the settling process.
Figure 4. A sample with a particle size cut of 0-10 µm and 100 g loading causes the 10.6 µm wavelength to scatter much less when the only particles left are smaller than the wavelength.
It is useful to be able to predict the extinction of an arbitrary size distribution. Since we have several size cuts that are almost non-overlapping, 0-5, 5-10, and 10-20 µm, we can estimate the extinction of an arbitrary distribution by decomposing it into a sum of these three distributions. This would be mathematically sound if they were orthogonal and formed a basis, neither of which is true but both of which are approximately true. We take the number of particles in each distribution, and combine them as I = I0 exp (-[N1C1 + N2C2 + N3C3] z), (2) where Nj are the number per volume for each distribution, I the extinction of optical irradiance for I0 the input irradiance, z the length of the scattering volume, and Cj the extinction coefficients for each of our three size ranges that we calculate here. The C's can be measured on pure distributions. We obtain:
Table 1: The values of the effective per-particle extinction coefficient C in inverse square microns are calculated by inverting Equation 2 and selecting for the desired mode as a function of time. Mode Size range, loading 532 nm 1064 nm 10.6 µm 0-3 µm, 100 g 10.093 6.432 1.223 5-10 µm, 100 g 158.66 164.11 272.10 10-20 µm, 100 g 790.49 846.35 1190
We test the utility of the coefficients of extinction from Table 1 by comparing measured extinction data to that calculated by breaking up the number distribution from the APS into 3 segments, counting particles, then predicting the extinction using Equation (2) and the values from Table 1. This process is repeated for many time steps during a trial. An example is shown in Figure 5, for a trial of 0-20 microns particles at 200 g loading. The results show reasonably good performance of the prediction method.
(a) (b) (c)/p>
Figure 5. A comparison of a measured optical extinction for a broad distribution: 0-20 µm with the predicted extinction from a sum, Equation 2, of three modes, and scaled to approximate the actual size distribution as a function of time. We see close correlations between the measured optical extinction (designated F) and the predicted extinction (designated C) for: (a) 532 nm, (b) 1064 nm, and (c) 10.6 µm.
The qualitative aspects of extinction are observed for the wide range of size distributions studied. Small particles scatter the shorter wavelengths, the visible and near infrared, much more strongly than the long wave laser source. For larger particles, the long wave also scatters and its extinction is because both scatter and absorption are active at the long wave, while scattering is the important process for the shorter wavelengths studied. The larger particles settle faster, thus changing the size distribution as a function of time. The greatest change in the optical properties is observed when the initial distributions contain a wide range of particle sizes.
We find evidence of multiple scattering during the maximum number density of several heavy load trials, just after the injection process completes. This can be seen in Figure 4, which are data for both medium and large particles at high dust loading. Near the maximum density when the transmission is near minimum, the visible and near IR data lie on top of each other, illustrating whitening. The LWIR data exhibit a transmission lower than the visible and near IR at these times. This is due to a combination of whitening plus additional extinction from the absorption present at LWIR wavelengths but absent at the other wavelengths. In fact, when single scattering dominates and there is no whitening, the LWIR signals show less normalized transmission than the visible or near IR wavelengths. It is likely that multiple scattering is also observed at the visible and near-IR wavelengths near the maximum loading of the small particles in Figure 3, just as it does in Figure 4. The LWIR does not show whitening (plus absorption) since it is scattered by these particles much more weakly than the shorter wavelengths. We do not detect multiple scattering for the trails with smaller loading or after a significant fraction of the particles have fallen out during any trial. Eccentric particles account for the most or all of the measured depolarization signals at lower densities. We have studied the eccentricity of the particles using microscopy and analyzed the effects of these eccentricities on extinction measurements, see below. These results suggest that Mie calculations are valid for the optical extinction of particles found in ARD. The impact of these eccentricities, which have values less than 2 (few are greater than 1.5), is observed only at angles beyond the forward scattering lobe, and those are only strong for angles beyond the first secondary peak of the scattering phase function. Finally, we have shown that we can predict extinction of a complex distribution from analysis of simpler distributions that make it up. This is important as it shows that we can predict what the extinction of a known dust aerosolized will be as a function fo time and differential settling.
Aerosol optical scattering experiments are often large, expensive, and provide poor control of dust uniformity and size distribution. The size distribution of such suspended atmospheric aerosols varies rapidly in time, since larger particles settle quickly. Even in large chambers, 10 micron particles settle in tens of seconds. We describe lab-scale experiments with stable particle distributions. A viscous colloidal solution can stabilize the particles for sufficient time to measure optical scattering properties. Colloids with different concentrations or size distributions enable nearly time independent studies of prepared distributions. Details can be found in .
We perform laser aureole scattering from a colloid containing a few percent by volume of Arizona Road Dust (ARD) in mineral oil and glycerin, and 1-micron polystyrene spheres in water. We discuss aureole analysis, the differences expected in scattering properties due to the index of refraction of the mineral oil medium versus air, and the impact of non-spherical shape on the scattering. This research demonstrates that particles suspended in a viscous medium can be used to simulate aerosol optical scattering in air, while enabling signal averaging, offering reproducibility, and easing problems resulting from parameter variations in studies of dust properties. Combined with the last section techniques and analysis of settling, this will permit lab based measurements to predict extinction of a dust over time without need for any aerosol measurements.
For a colloid or air, the settle time needs to be calculated from the Stokes flow around a sphere result, including buoyancy, for the terminal velocity: v_t=gd/18μ (ρ_s-ρ) where g is gravitational acceleration, d is the diameter, ρ is the density of the fluid, ρ_sis the density of the sphere, and μ is the viscosity of the medium. The chamber or sample height divided by this yields the time. The time is 2-5 orders of magnitude longer for water and glycerin, respectively, than for air. It becomes not important. Trapping the dust in KBr pellets makes it completely unimportant, but requires careful pellet fabrication to avoid fogging or imperfections in the crystal that scatter light. To calculate the fraction of dust needed in the colloid or pellet, it is the same as in a chamber in terms of the number of aerosol particles that a beam of light will pass as it goes through the chamber. That gives a thickness over the laser area, and the thickness will be the same in the colloid or pellet. It is uniformly distributed throughout the sample volume, before pressing pellets and with overnight agitation for colloids. Water was found to wash the particles, leach metal ions from the dust particles, and otherwise change the particles, so we do not use it for ARD.
We used two colloids to study the ARD scattering properties; a mineral oil colloid 0.00105 % bV ARD, and a glycerin colloid 0.001285% bV ARD. Both sets of data agreed very closely, as shown in Figure 6, which indicates that the system was working as intended. Specifically, it indicates both samples are structured the same, despite the different ways of getting the dust into a colloid. In particular, these solvents do not tear apart the complex structure of the particles, as water does. Both data sets are compared with silica sphere forward calculation, and the poor agreement probably indicates that the index of refraction of the ARD cannot be approximated by that of silica. The fit is calculated by varying nARD. Here, nARD=1.56. This indicates that we can retrieve the index of refraction of the particles from the aureole scattering measurments.
Figure 6. The ARD colloids plotted with equivalent size silica sphere Mie scattering calculations and Mie fit to get the actual refractive index.
Figure 7 shows KBr scatter compared to both glycerin and mineral oil scatter. The differences are likely due to the difference in index of refraction of the medium. The size parameter in Mie calculations, ka = 2πa/λ for λ the wavelength of light in the medium and a the sphere radius, depends linearly on the medium’s index of refraction through the inverse wavelength. Thus, a higher index for the medium KBr compared to mineral oil and glycerin (with nearly the same index) should result in a narrower scattering lobe for the KBr sample. This is qualitatively observed in the plots. The scattering angles are those inside the material and are calculated from the physical angle outside the material using Snell's Law.
Figure 7. The scattering data for glycerin and mineral oil colloids, and KBr pellet plotted together. Note that the KBr scatter differs from the scatter of the colloids due to the larger difference in medium index.
Identification of atmospheric aerosol species and their chemical composition may help to trace their source and better estimate their impact on climate and environment. Optical scattering of aerosols depends primarily on aerosol chemical composition, size distribution, particle shape and the wavelength used. Extraction of features due to the aerosol complex refractive index from scattering spectroscopy at a single angle of observation allows composition identification via the spectral fingerprint, as shown computationally with Mie calculations of the optical scattering. Size-dependent scattering effects are eliminated by using near-forward scattering, such as in the scattering aureole. The only features of the aerosol aureole scattering spectra that very rapidly with wavelength are associated with the composition, so the aureole can give a reliable identification of aerosol composition. The central idea is to create a ‘background-free’ or ‘high frequency’ spectral fingerprints can be stored in a library and used to identify an unknown by matching the spectral fingerprint with a measurement that has also had background features, which vary slowly in wavelength, removed. Our optical technique that does not require any knowledge of the particle sizes or distribution, so fewer assumptions about particle distributions are required, and the types of efforts required by other techniques are not needed. Details can be found in .
The criterion for choice of angle is selected so that the particle size effects should not be a strong. It is known that the width of the forward scattering lobe of the scattering aureole depends on the particle size and on the wavelength [next section], but that the wavelength dependence is relatively weak, so it will only create features that can be removed as a slowly varying background in the measured spectra (we subtract a best-fit third order polynomial from the data using the ‘detrend’ function in the freely available Octave environment then scale so that a large deviation from zero has unit magnitude to create our spectral fingerprint). Further, the aureole has been shown to be weakly dependent upon particle shape [next section]. Finally, the scattering intensity is usually large near the forward scattering direction, so the signal level will be intense within the aureole. These factors suggest that the best angle to use is within the aureole. This section presents the simulations that support this assertion. An angle of 1.8 degrees is chosen for the aureole observation angle. This is large enough that the signal should be separable from the incident beam, yet close enough to the center of the forward lobe that the signal will not be dramatically affected by a change in angle, integration over a small range of angles by the detector, or by possible Mie angle resonances at larger angles. The paper shows that the 1.8 degrees is nearly optimal in many cases.
Figure 8 shows an example of spectral fingerprints compared to refractive indices using a typical lognormal particle distribution: CMD = 10 micron and σg = 1.3 in Mie simulations.
Figure 8. The scattering radiant intensity of (a) oleic acid, (b) nitric acid, (c) silica glass, (d) silica type α(crystalline), and (e) ammonium nitrate show that the signatures reflect the respective complex indices, and thus can be used for identification.
An important characteristic of the technique that we wish to demonstrate is the independence from particle size. Figure 9 shows the scattering calculation for several different particle size distributions within the aureole, at 1.8 degrees. The calculation shows that for a wide range of particle distributions, when varying both the peak size from 5-20 µm and the width of the distribution, σg, all of the features that would become part of a normalized spectral fingerprint are preserved. In particular, although the scattering intensity is found to scale with the particle size, and the strength of the features depends upon both particle size and (more weakly) the distribution width, these spectral features remain the same. This is what is required for a robust fingerprint, so these data indicate the practicality of the proposed technique. The excellent agreement for smaller wavelengths is such that the different signatures can hardly be identified from one another. There is some deviation at larger wavelengths that is likely due to the simple 3rd order polynomial de-trending. The signatures are expected to be in better agreement with an optimal de-trending technique. Some difference for the smaller particles result from the larger relative influence of air scattering in the case of the smaller particles compared to the larger particles. We did not change the density of the particles to account for less scattering by smaller particles
Figure 9. Ammonium nitrate with different size distributions has different scattering intensities (a), but similar spectral fingerprints (b), showing the robust fingerprint technique.
The small shifts observed between the spectral signature and the refractive index features that you may have noticed can be explained by the small particles: the presence of nearby air that alters the strength of the electric field compared to that when the material is everywhere, so the material's index of refraction, that describes this internal field strength, is not accurate. Effective medium theory can provide an index that describes the internal electric field of this complex air/particle combination. The section ofter next shows more examples of this.
The index of refraction of the materials that compose aerosols are wavelength-dependent. In particular, there are characteristic, sharp spectral features at particular, material-dependent, wavelengths. These features determine a material’s spectral fingerprint, which will cause scattering calculations in the material to have ‘high frequency’ features at those wavelengths. These can be isolated, by removal of low frequency components and normalizing, to provide a spectral fingerprint, which can be used to identify the composition of the aerosols. We have shown calculations that predict measurements of the scattering intensity expected within the aureole region, which occurs near forward scattering. These calculations predict a large signal that is independent of particle shape or size (after removal of low frequency background). Density variations change the magnitude of the signal, but not the spectral fingerprint. The technique does not require assumptions about the particle size distribution or extensive measurements to identify it in addition to extracting the particle refractive index from the scattering data; thus, this approach makes analysis easier. The method does require measurements over a large wavelength range when the samples are completely unknown. It can be used for remote detection-in a real time system, with speed limited primarily by signal strength, path resolution, geometry, and detectors. Effective medium theory analysis will be required to identify complex mixtures of materials.
Lidar is a powerful tool for measuring the vertical profiles of aerosols in the atmosphere using Rayleigh and Raman lidar techniques. Bistatic lidar can be used to obtain the angular structure of the scattered light. When the aerosols are uniformly distributed, this information can be analyzed to provide particle size distribution information. However, dusts tend to be irregularly shaped particles with varied composition. We investigate the impact of the irregular shape using optical scattering at several wavelengths, scanning electron microscopy, and T-matrix calculations. In particular, we study the rapid loss of Mie scattering resonances as the particle shape departs from spherical. This is due to the angular resonances resulting from electric field standing wave resonances in the particle, which are destroyed by scattering by sharp edges or small asperities or by distortion of the particle. Different size distributions produced by different size-cuts of Arizona Road Dust (ARD) are studied. Details can be found in .
We begin with a microscopy study of Arizona Road Dust (ARD), as it is selected to be a reference material, to identify the range of eccentricity that is expected. Images of dust samples from the Arizona Sonoran Desert are similar in shape, despite being significantly larger in size. Examination of several different samples shows that the results we find are more general. We then perform a model study using T-matrix calculations of optical scattering. The front scattering lobe is found to be almost independent of the particle eccentricity, but does vary with effective size of the particle, for the range of common values found in ARD. This indicates that an approach to measure particle sizes based upon the scattering aureole can be based upon a simple Mie scattering analysis. It will not be sensitive to particle shape, nor is it expected to, since the aureole is dominated by bulk scattering. The advantage is that the eccentricity parameter need not be extracted from the data, so the inversion problem is more tractable. Another situation that we identify as tractable occurs when particles have a size comparable or large relative to the wavelength of the light used. We find that the scattering is independent of particle eccentricity and there is close agreement between T-matrix and Mie calculated results. Scanning electron microscopy provides a higher resolution than optical microscopy (also shown in paper), so the decoration of the larger particles by smaller ones can be studied in more detail, as can the shapes of the smaller particles. Whereas the particle height apparently stretches due to the short focal distance of the optical microscope, the SEM flattens the particles in the images due to its long focal length compared to the particle height. Figure 10(a) shows a large area view of a sample of ultrafine ARD. It is typical, and gives a good indication of the range of particle shapes that are found. A few of the particles have eccentricities close to 2, but most are smaller. Sharp corners are again a more prevalent departure from a spherical form, as was observed in the optical micrographs. Although the ultrafine particle size distribution is supposed to include sizes up to 15 microns, we observe very few close to that. The number distribution peak of Ultrafine ARD, according to its documentation, is ~2-4 microns, and agrees qualitatively with what we observe here. A higher resolution image at a different location is shown in Figure 10(b). Besides the same general features noted in conjunction with Figure 10(a), the decoration of the larger particles by smaller ones is easily observed. The smaller particles adhered to the tape between the larger particles are also more easily observed.
Figure 10. Scanning electron micrographs of ultrafine ARD appear flattened by the long focal length of the SEM. The eccentricity of the particles is consistent with the optical microscopy, with most less than 1.5 and a few outliers near 2. Sharper features are also observed with the additional resolution of the SEM. Again, the larger particles are decorated by smaller ones: (a) A large area view gives statistics on the particle shapes. (b) A zoom-in illustrates the decoration and smaller particles between larger ones. Although some particles appear ‘layered,’ this is a long focal length ‘flattening’ artifact, as can be seen on the tilted particle at the center right, the ‘ledges’ are really foreshortened decorating particles.
Figure 11 reminds us that care is always needed when viewing objects in SEM, since the long focal length compared to the object size flattens the particles, so lengths measured are projected, not necessarily actual sizes.
Figure 11. Two SEM micrographs of the same particles: (a) The top-down view shows the edge and two sides. (b) Once the sample is tilted 35 degrees so that the face on the left is seen more head-on, the apparent layers are observed to be really foreshortened smaller particles on the face. It is also seen that the two particles beneath the larger are actually separate from it.
Now that we hava n idea of what types of deviations from spherical particles are found in a typical dust, we can see the effects on the measurements. In practice, the scattering as a function of angle will be measured. The T-matrix calculation method is used with a range of wavelengths and particle sizes. Our simulations use a fixed particle size of 2-micron area-equivalent spherical particle diameter. The reason for choosing an area-equivalent diameter is to keep the overall scattering cross section reasonably constant (although variations in scattering efficiency occur). Four wavelengths are simulated: 0.532 microns, which has a size parameter ka~12, with k = 2π/wavelength and a the particle radius, and is somewhat smaller than the particle size; 1.064 microns or ka~6, about the radius of the particle, 4-microns or ka ~ 1.5, and 10 microns or ka ~ 0.6, small but not yet in the Rayleigh regime. The eccentricity values examined are between 1.0 (spheres) and 2.0 (approximately the largest value observed in SEM images), with more values chosen closer to 1.0, consistent with more particles having those values. An index of refraction of 1.5 + 0.0001i is selected for the particles.
The calculation results for the scattering phase function with the selected values of eccentricity are shown in Fig. 12. Many of the curves lie on top of each other. The shorter wavelength, larger size parameter, results in part (a) do show a significant decrease in the amplitude of the magnitude of the resonance peaks versus angle, when compared to particles with even a small eccentricity. However, they do not go to zero, but saturate at a new level until the new resonances in the perpendicular directions become significantly different, and the resonance locations shift to other angles. Since we are using particles with constant area-equivalent spheres, the sizes change, and so do the resonance locations as expected. The onset is more abrupt than naively may be expected. The longer wavelength, smaller size parameter, results are shown in part (b). The dependence is again weaker than those at a larger size parameter, and it is in fact largely independent of particle eccentricity. This is not surprising for size parameters close to 1.0, where the scattering lacks peaks due to particle resonances. The data for 1.064 microns is rather striking, with significant deviations only for eccentricities above ~1.5. Not shown in the figure is the height of the forward lobe, which for the x ~ 12 sphere case is marginally above the non-spheres, which are all virtually identical. At the smaller size parameters studied, the forward lobe peak is independent of eccentricity and agrees with the spherical result. In summary, the forward lobe is almost independent of particle eccentricity for all eccentricity and size parameters studied. For large size parameters, there is a significant change at all other angles, including backscatter. For smaller size parameters, ka~ 6, the scattering phase function is almost independent of eccentricity until the eccentricity is on the tail of the observed eccentricities for ARD. This implies applicability of Mie based analysis for these data.
Figure 12. Scattering phase functions versus angle. The wavelengths and eccentricities (in parentheses) are given in the legend: (a) The resonances decrease slowly with eccentricity after an initial drop, for a size parameter near 12, but remain qualitatively the same until the eccentricity reaches ~2, which was rarely observed in ARD Ultrafile samples. (b) The dependence is increasingly weak for longer wavelengths, or smaller size parameters (~ few to less than one), until there is none at all. Notice the lack of dependence on eccentricity begins long before the particles enter the Rayleigh regime. This occurs even before symmetry in the front and back scattering is approached, and well before a value of zero is reached at 90 degrees.
The effects of an imaginary part to the index of refraction, which leads to absorption, is also investigated in the paper, and similar conclusions are reached.
For experiments we use Arizona Road Dust, ARD, for which we know the size distributions and have an good idea of the eccentricity ranges. Incident light at 532 nm and the 0-5 micron sieved ARD are measured and modeled. As expected from the above computations, the non-spherical nature of the particles results in a decrease of the oscillation magnitude of the phase function compared to the spherical assumption. As time passes, two properties of the particle size distribution change. The first is an overall decrease due to settling. The second is a trend towards smaller particles on average, since the large particles will drop out more quickly according to the same Stokes law reasoning presented earlier (but here in air). Smaller particle are expected to have a broader aureole, and it is observed to be so. The aureole is expected to retain agreement with the spherical assumption of the Mie calculation, according to the above computational analysis. Figure 12 shows a plot of the measured aureole at 500 seconds and a Mie calculation that uses the size distribution given above. It has only one free parameter, a scaling due to the detector sensitivity. The agreement is quite good. The discrepancy between the calculation and the measured data is likely due to a wrong index of refraction for ARD used in the calculation. Since a value could not be found in the literature, we simply used the value for silica, a major component. Use of a higher index would steepen the curve and provide better agreement.
Figure 13. Scaled scattering phase function versus angle at small angles, the scattering aureole, is measured and plotted along with the a Mie calculation based upon the measured particle size distribution and using silica’s index of refraction for the ARD.
An experimental study with both optical and electron microscopy has revealed the range of particle eccentricities to be small (eccentricity <2.0 and mostly less than 1.1) for ARD and Sonoran Desert dusts. We use these limits to choose bounds for a computational study on the effects of particle asymmetry on the polarization ratio and scattering phase functions. These two useful quantities that can be inverted to obtain information about the particle size distribution and particle concentration when the background air Rayleigh scatter is also measured. We find that a spherical analysis, based upon Mie scattering calculations, is valid when the particle size parameters are close to or smaller than 1.0. For larger size parameter, the forward lobe is still almost independent of the eccentricity, indicating that scattering aureole measurements may also be analyzed by a Mie scattering based inversion. The introduction of significant imaginary index of refraction does not change the aureole width, but does damp the forward scattering intensity. Backscatter is also found to be strongly damped. Measurements of scattering from ARD display features similar to those modeled.
Dusts are irregularly-shaped particles with varied composition and strong variations in index of refraction in the LWIR. The irregular shape (scattering enters to confuse optical measurements) and proximity to the surrounding air (the particle effective index differs from the index of the material making up the particle) make measurement of the material index difficult. Assumptions that are not always correct are made, and errors result. We present a few methods to attain accurate refractive index results. We measure dust indices using ellipsometry and transmission through KBr pellets. Milling makes the ellipsometry data less dependent on incidence angle (a good sanity check), and the results of measurements on milled materials agree with those from transmission measurements. Measurements show that the spectrum of a milled Arizona Road Dust (ARD) approaches that of pure quartz (whereas that of unmilled is dominated by clay-like features), indicating (1) that the decrease of absorption efficiency for particles larger than the absorption length substantially affects the results, i.e., the structure of the particle matters, and (2) that the average index of the entire particle is attained only when it is milled. Details can be found in .
Milling the particles until they are small, and more uniform, relative to the wavelength can minimize the effects of particle scattering in the sample. The magnitude of the scattering from individual particles in a pellet sample is minimized by choosing a host material with a real index of refraction similar to that of the particulate to be studied. However, it does not completely eliminate scattering in the regions of very large gradients in the indices of refraction, such as near a sharp absorption resonance, or for measurements at wavelengths near or below the size of the smallest particulates after milling. When we claim to measure the index of refraction, we mean the bulk index. This is the quantity used in scattering calculations, but the (bulk) index of refraction is only a valid concept deep inside a large volume of material. Near the surface, the particular atom or molecule reacts to the bound surface charge at the interface between the materials, as required by Maxwell’s equations. Thus, the effective local index of refraction is changed. We show that it can shift the wavelength at which sharp absorption features are observed, thereby precluding the use of a simple linear combination of material dielectric constants in determining the particle refractive index. Using this sort of analysis to determine indicies of refraction of complex materials is a common mistake. Instead, the effects of the proximity to the surface of nearly all atoms in a small particulate must be corrected as part of the data analysis. The technique used for the refractive index correction is based upon effective medium theory. It is valid when the sizes of the particles are less than about 1/10 the wavelength of the light. Calculations require that the volume fraction of the components of a mixture be determined to obtain the correct optical properties (including air, if it is the host medium for the particles). Several possible variants of effective medium theory have been devised for different scenarios. Maxwell-Garnett theory is useful for single constituent particles embedded in a medium but well separated from each other. The Bruggeman effective medium approximation is useful for coated particles or material mixtures in which there is no clear choice of host material over inclusions. The limits of the possible dielectric constants can be evaluated with minimum and maximum shielding effective medium models. We show here that use of effective medium theory is required for accurate determination of the index of refraction. We also show that Mie scattering calculations include effective medium corrections, as they must, since they are based directly on solutions to Maxwell’s equations.
The ellipsometric measurements of the real and imaginary parts of the refractive index at different angles are compared in Fig. 14, and there is excellent agreement. We found, but do not show, that the particles must be milled prior to making ellipsometry measurements; otherwise, the indices determined by ellipsometry are dependent upon the angle of incidence of the light, which is obviously not physically correct.
Figure 14. Ellipsometry determined n and k for Ultrafine ARD that is milled prior to being pressed; (a) the real index of a milled ARD pellet the data shows low noise and excellent agreement at various incidence angles; (b) the imaginary index once again it shows low noise and no apparent angular dependence. Unmilled ARD shows angular dependence and other artifacts.
We evaluate the usefulness of transmission measurements for obtaining the complex index of refraction of particles. By taking the ratio of the transmission of two pellets with the same composition but different thicknesses (being very careful about the pellet quality), we can eliminate most of the uncertainties of sample reflectivity, the absorption of surface films, and greatly simplify the data analysis. The imaginary index is easily obtained from the ratio of data obtained with different thickness pellets, and the real index follows from a Kramers-Kronig analysis. Effective medium theory is then used to determine the complex index of refraction of the particles. The results from transmission data should be the same as those indices of refraction determined by ellipsometry, and they are close.
An intermediate result is shown in Fig. 15, obtained from a Beer's law inversion for keff. = (λ/(4π(d1-d2))ln(T1/T2) with d's the thickness of and T's the transmission of pellets with the same composition but different thickness; and a Kramer's Kronig analysis to obtain neff.. It is the effective index of the ARD aerosols in KBr. Note that the real effective index barely deviates from that of KBr, and the imaginary effective index barely deviates from zero. The 0.5 volume percent of ARD means that the material is mostly KBr, so this is not surprising.
Figure 15. Indices of refraction of 0.5% ARD in KBr pellets from transmission the low concentration of ARD in KBr causes only a slight variation in the real index from that of KBr itself, and a very small absorption index.
What is surprising is that the peaks are shifted away from what they would be in a pure material. As a demonstration of the effect on the measured indices of refraction by an interaction between a matrix and its inclusions an effective medium calculation of 0.005 v/v silica suspended in air is shown in Figures 16 (a) and (b), which compare the effective real and imaginary indices of the mixture, with those of silica. As can be seen from the figures, the peaks and transitions of the effective indices are shifted to the left from those of pure silica --- this has important implications. The common method of using a volume fraction weighted linear combinations of the component indices cannot be used to retrieve (in this case) silica’s indices from the observed effective indices. A linear volume mixing model for a surrounding medium, such as air or KBr, that have a constant or slowly varying real index and no significant imaginary index over the observed wavelengths, cannot produce a left or right shift in features in the effective refractive index. Air was chosen in this demonstration to amplify the peak shift. If KBr had been chosen, the peak shift would still exist; however, it would be only ~4% because of the better index match between KBr and silica.
Figure 16. Comparison of n and k of 0.005 v/v silica (right axis, narrow range) in air versus pure silica (left axis); (a) the transitions in n associated with the peaks in the imaginary index are shifted to the short wavelength side by approximately 10%; (b) the effective imaginary index of silica in air also shows a significant peak shift, and the absorption bands of this composite material would therefore be shifted to shorter wavelengths than would be observed for pure silica.
With this in mind, we need to correctly extract the particle index from the medium index. This is done here with Maxwell Garnet effective medium theory, which relates the medium dielectric constant (index squared) ε to the host dielectric constant εh and the volume fraction f of the spherical particles with dielectric constant εp as: (ε-εh)/(ε+2εh) = f(εp-εh)/(εp+2εh). Solving (with complex math) for each wavelength point, we obtain the result in Fig. 17. The figure also contains the ellipsometer-measured indices for comparison. Very good agreement is seen between the imaginary indices above 8 microns. The disagreement below 8 microns is likely due to particle size effects and scattering. There is a larger discrepancy, on the order of 10%, between the real indices measured with ellipsometry and those derived from transmission. These errors can arise from scattering, imperfections in the KBr pellet, and errors in the assumption of n at small wavelengths (part of the Kramers-Kronig process).
Figure 17. Comparison of transmission derived indices of milled ARD with those derived from ellipsometry; (a) the real index as a function of wavelength; (b) the imaginary index as a function of wavelength. Very good agreement is seen between the imaginary indices above 8 microns however a 10% difference is seen for the real component.
An experimental study of two methods of determining the optical properties of Arizona Road Dust has revealed that, when treated correctly, transmission measurements of sparse dust in a matrix of KBr and ellipsometry measurements of pure dust pressed in pellets do agree quantitatively. Transmission measurements are faster to conduct, require far less dust to make samples than ellipsometry, and use cheaper equipment; however, transmission measurements require small particles and a Kramers-Kronig analysis to retrieve an effective n. It also requires an effective medium analysis to isolate the dust inclusion indices from those of the KBr/dust mixture to find the effective index. Ellipsometry measures both the real and imaginary index at the same time, but it requires milling of dust to produce uniform pellets with optically flat surfaces so that the results are independent of incidence angle. Ellipsometry is also highly susceptible to surface imperfections and films, requires exceptionally expensive equipment, and requires a long time to make a low noise measurement of dust in the infrared. Our analysis approach demonstrates that accurate measurements of the refractive indices of single component particulate distributions can be made via transmission with a standard FTIR instrument, for ranges of wavelengths several times larger than the diameter of the milled particulates.
More info is in the papers.
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