We present both a computational and an experimental approach to the problem of biological aerosol characterization, joining the expertises reached in the field of theoretical optical scattering by complex, arbitrary shaped particles (multipole expansion of the electromagnetic fields and Transition Matrix), and a novel experimental technique based on two-dimensional angular optical scattering (TAOS). The good agreement between experimental and computational results, together with the possibility for a laboratory single-particle angle-resolved investigation, opens a new scenario in biological particle modelling, and might have major implications for a rapid discrimination of airborne particles.
©2006 Optical Society of America
In the last years there has been a growing interest in methods for the analysis and characterization of biological aerosols. The main aim is to achieve differentiation between various types of airborne particles so that the presence of biowarfare agents can be rapidly detected from a safe distance. Although important advances have been made in determining the properties of biological particles, a definitive characterization is still elusive. Both the infrared extinction spectra  and the fluorescence spectra  of aerosolized biological spores are relatively smooth and devoid of any sharp identifiable line structure. The most characteristic features associated with the presence of certain spore proteins occur in the range between 5.6 and 6.6 μm wavelength. Unfortunately, this highly characteristic region lies in the middle of the most opaque portion of the atmosphere and is probably of little value when we are considering possible remote detection techniques .
Methods involving optical or electron microscopy can change the shape and internal structure of the particles, and are also incapable of doing real-time particle-by-particle diagnosis. Methods and instruments have been developed using particle and fluorescence counters , and incorporating simultaneous measurement of aerodynamic size and intrinsic fluorescence [3, 4]. However, these monitoring systems are susceptible to the occurrence of false positives, due to the fact that non-biological particles may be present with similar size and fluorescence signature to biological particles. This implies the need for other methodologies, that are able to probe additional particle properties. To this aim, elastic light scattering appears to be a suitable tool, since it is dependent on the particle size, shape, surface roughness and complex index of refraction [1, 5, 6, 7].
Bioaerosols are typically inhomogeneous and often nonspherical, which makes even accurate predictive calculations extremely difficult. Holler et al. analyzed clusters of Bacillus subtilis var niger (BG) spores (a simulant for anthrax) through a two-dimensional angular optical scattering (TAOS) technique . Angle-resolved elastic light scattering opens a new window for single-particle investigation and may be developed into a new technology for a fast, highly sensitive, and reliable discriminatory instrument.
Two research groups, headed by P. H. Kaye and R. K. Chang respectively, have been working intensely over the past few years to develop and refine elastic scattering technologies for aerosol characterization, particularly as an optical diagnostic tool for rapid discrimination of biowarfare agents. In this paper we describe a system that can simultaneously obtain TAOS patterns of aerosol particles (1-10 μm in diameter) in both the forward and the backward hemispheres in real time, and with a single laser pulse. Scattering in the forward and backward hemispheres contain information about particle size, morphology, surface roughness and complex index of refraction. TAOS patterns of ambient aerosols and laboratory generated simulants allowed particle discrimination between B. subtilis spores and aerosol particles found in the ambient atmosphere . We notice that a recent paper  has pointed out that B. Subtilis var. niger should actually be reclassified as Bacillus Atrophaeus. Nevertheless, in this paper we stick to the denomination B. Subtilis that is perhaps more known to non specialists.
In the next section, we will describe a system to simultaneously acquire TAOS patterns in the forward and backward hemispheres of single particles on-the-fly. The complete angle-resolved scattering information and data are ready for comparison with theoretical computations.
A theoretical approach that has proven to be suitable for comparison with measured TAOS patterns is the Multipole Expansion of the electromagnetic fields in the framework of the Transition Matrix (METM) method. Such approach allows us to calculate the scattering properties of particles with arbitrary size and to take proper account of asymmetries in the scatterer shape. The Transition Matrix method was found to be very useful and flexible in describing asymmetric particles in terms of aggregates of spheres [Borghese, Denti and Saija  and references therein]. The METM method can also be useful in modelling biological spores, as we will show in Section 3. An alternative computational approach, through the finite-difference time-domain, has been very recently used by Li et al. that model the spore as an ellipsoid with a centered core and one layer coat .
In Section 4 we will present our computational results, studying the effect of the refractive indices on the scattering behaviour of some spore simulants. A comparison will be done between experimental TAOS and theoretical patterns, computed through the METM approach. Finally, in Section 5 we will draw our main conclusions.
2. The Forward-Backward TAOS experimental set-up
The experimental setup used for simultaneously collecting TAOS patterns in the forward and backward hemispheres is illustrated in Fig. 1. The particle travels downward along the y-axis and is irradiated by a 50 ns pulse of a 532 nm Nd:YAG laser (Spectra Physics, X-30), propagating along the z-axis. The symmetry axis of the truncated ellipsoidal reflector is oriented along the x-axis and thus is perpendicular to the direction of laser propagation. The scattering event occurs at the first focal point of the truncated ellipsoid (F1). A large portion (63% of 4 sr) of the light scattered by the particle is intercepted by the reflector, and projected onto the ICCD detector (1024×1024 pixels, Andor iStar). The ICCD detector is positioned on the x-axis, after the second focus (F2) of the reflector. Half of the ICCD detector detects the forward-scattering pattern, and the other half detects the backward-scattering pattern.
TAOS is measured for the scattering angles in the range 15° < θ < 165° and for azimuthal angles covering as much as 360° in the near-forward and near-backward scattering. The full range of azimuthal angles (0° < ϕ < 360°) is collected for all θ except where the reflector has parts removed by truncation of the ellipsoid and five holes drilled through the reflector. The truncated hole will restrict 0° < ϕ < 270° at θ = 90°. The five drilled holes also caused a small amount of loss of ϕ. The reason and location for each of the five holes are explained below. The particles enter through the top hole at θ = 90°, ϕ = 270°, and exit through the bottom hole at θ = 90°, ϕ = 90°. The laser beam enters through a side hole centered at θ = 180 ° and exits through a side hole at θ = 0°. Lastly, there is the fifth hole in the back (θ = 90°, ϕ = 180°) used for the passage of the trigger laser diode beam. The particles are generated by putting acqueous solutions of polystyrene (PSL) microspheres or BG spores in an Ink-Jet Aerosol Generator .
It is quite instructive to transform the recorded patterns into the traditional spherical coordinate system. The resulting TAOS patterns were divided into forward and backward halves (Fig. 2) for easier comparison with the theoretical calculations. The dark shadows at the center, the left side, and the right side in both patterns are caused by the loss of the reflection from the open space and holes of the reflector. This loss of reflection restricts the range of angles ϕ collected for each θ.
3. A model for spore simulants
The choice of a suitable model for the spore simulants has been suggested by the electron microscope images. These images give quite accurate indication about size and shape of biological particles. From SEM microscopy BG spores appear to have a cylindrical-like shape. The model that we adopt in our computations for spore simulants consists of a cluster of two identical, mutually contacting, spheres. At the laser wavelenght used in the TAOS set-up, such model is appropriate. Indeed, as expected from the general scattering theory, the difference between the pattern from such a cluster and a cylindrical particle is not appreciable. This suggests that the binary cluster model is a reasonable choice. Our choice is further supported by the comparison between the measured TAOS patterns of a cluster of two PSL microspheres and the pattern of a single BG spore (Figs. 5 and 7). In the calculations, the radius of the spherical monomers is chosen so to reproduce, as best as possible, the actual size of the BG spore.
One of the problems with the characterization of bacteriological agents lies in determining their exact refractive index. This is a very relevant parameter for the correct reproduction of the features of the optical spectra. Thus, the refrative index plays an important role in the discrimination of biological spores. B. subtilis is generally considered the best simulant of the spores of anthrax. The refractive index of the B. subtilis spore has been published by Tuminello et al. , who reported four kinds of refractive indices corresponding to spores that were exposed (used) or not exposed (as-received) to water in preceding experiments. Values were reported for the refractive index measured both in water and in glycerol, in order to discriminate the effect of the chemico-physical nature of the environment on the measured spectra. The various forms of the refractive index reported for the B. subtilis spores differed rather little from each other. In our computations we use the values of the refractive index for the as-received B. subtilis spores in water. All the theoretical results presented in the following section are obtained through the METM method.
4. Results and discussion. A comparison between computational and experimental data
The sensitivity of the optical properties to the particle refractive index is shown in Fig. 3, where we present the scattering and extinction cross sections computed for a dispersion of spores in a random orientation. Results obtained using the refractive indices for B. subtilis and B. cereus, another spore belonging to the same family of anthrax, are shown. We model a single spore as a cluster of two spheres, each with a radius of 0.35 μm. This choice for the spore size follows the suggestion given by Katz et al.  relative to the radius of dry homogeneous spores. The results for random orientation are independent of the state of polarization.
No relevant differences appear in the reported extinction cross sections. More interesting is the comparison between the scattering cross sections: differences appear in the ultraviolet (between 0.2 and 0.4 μm) and near infrared regions (between 0.7 and 0.9 μm). These are the wavelength ranges in which the refractive indices of B. subtilis and B. cereus show the largest differences. The results in Fig. 3 suggest that a multi-wavelength analysis could be useful in discriminating between the B. subtilis and B. cereus spores. We are currently working to reach this goal with our instrumental set-up.
Figure 4 shows the the element Z 11 of the modified Stokes phase matrix for ϕ = 90° and as a function of θ . We present the results both in the forward and backward regions, for B. subtilis and B. cereus spores, and PSL particles. We model both the spores and the PSL particles as clusters of two spheres, keeping the monomer radius fixed at 0.35 μm. No relevant difference is observed in the forward scattering pattern. A difference only occurs in the backward region. The results in Fig. 4 confirm that the scattering pattern in the backward region may be more sensitive to the refractive index of the particle than the scattering pattern in the forward region. The symmetry axis of the cluster is along the z axis in Fig. 1. Here and hereafter we are considering the same polarization for incident and scattered field, that has been assumed to be linear and parallel to they axis (see Fig. 1).
Figure 5 shows the TAOS patterns for a cluster of two PSL spheres, illuminated by a single pulse of the second harmonic of a Nd:YAG laser, at 532 nm. The primary particle size is 1.44 μm in diameter. The relatively noisy appearance of the backward hemisphere portion of the pattern relative to the forward portion might be related to two factors: first, the scattered intensity in the near forward hemisphere is roughly one hundred times larger than the scattered intensity in the near backward hemisphere. Thus the two hemispheres are measured at two distinct regions of the ICCD’s efficiency curve. Second, the more intricate appearance of the backward hemisphere, as compared to the forward hemisphere, might follow from the considerations that scattering in the backward hemisphere is more sensitive to the particle refractive index than that in the forward hemisphere.
Figure 6 shows the computed forward and backward hemisphere scattering pattern, produced by a cluster of two PSL spheres with the same diameter as the ones used in the measurement shown in Fig. 5 (i.e. 1.44 μm). Here and hereafter, the computed scattering patterns represent the element Z 11 of the modified Stokes phase matrix. The computations were performed by slightly varying the orientation of the cluster around the z axis, aiming to best reproduce the asymmetry of the experimental patterns. In fact, the experimental setup does not guarantee the vertical orientation of the cluster. The computed pattern that we report in Fig. 6 is the one that, in our opinion, achieves the best agreement between experimental and theoretical results.
The encouraging agreement obtained for PSL spheres led us to extend the comparison to the case of BG spores. The experimental TAOS pattern is presented in Fig. 7. Concerning the computational results, some previous considerations are necessary. The scattering computed through the METM is strongly dependent on the particle size, so that even a slight variation can affect the results in a relevant way . This consideration, together with the uncertainty in the experimental determination of the actual spore size, led us to consider the monomer radius a free parameter, varying between 0.25 and 0.45 μm. Then we looked for the best fit of the experimental data. The best fit was obtained for a binary cluster with a monomer radius of 0.38 μm. The computed pattern is shown in Fig. 8. To better show the comparison between experimental and computed results, we extracted the intensity profiles from Figs. 7 and 8 along the direction indicated by the broken line in the computed patterns. The comparison between experimental (dotted line) and computational (solid line) results, shown in Fig. 9 for both the forward and backward zone, is very satisfactory.
The motivation of this work comes from the growing interest in the characterization of aerosolized biological particles. We propose a twofold approach to the problem, joining the theoretical experience reached in the field of optical scattering by complex particles, and a novel experimental method (TAOS) for aerosol characterization. The METM method, based on the multipole expansion of the electromagnetic field within the framework of the Transition Matrix approach, proved to be powerful and flexible in describing scattering of light by composite, arbitrary shaped particles , overcoming most of the rough approximations often used in the literature when dealing with non-spherical particles. A reliable model to simulate particles with complex morphology is the cluster of spheres, that proved to be successful also when modelling biological spores. Specifically, through a binary cluster with appropriate size, suggested by experimental evidences.
Angle-resolved elastic light scattering offers a great opportunity to the development of single-particle investigation techniques. In this context, the TAOS technique appears a very promising approach for a fast and highly sensitive aerosol characterization . The system that we described to simultaneously obtain the forward and backward scattering patterns allows to partially discriminate between biological spores and aerosol particles. Scattering in the forward direction mainly allows to reconstruct information about particle size and morphology; while the backward scattering gives more detailed information about internal structure, composition, and surface roughness. The joint examination of the forward and backward TAOS patterns, and the good comparison with the theoretical results opens a new window for a deep analysis of the optical properties of biological spores and will hopefully enable us to overcome many of the limits encountered in this field up today (structural changes induced on investigated particles, incapability to perform a real-time particle-by-particle analysis, occurrence of false positives).
The computational approach that we used enables us to carry out a complete angle-resolved analysis in terms of particle refractive index, size, and shape. The results presented also show the importance of a multi-wavelength analysis of the particle scattering behaviour to achieve differentiation between various types of airborne particles and/or spore simulants. This is the next goal that will be hopefully reached with the TAOS instrumental set-up.
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