Retrieval of Aerosol Complex Refractive Index by Combining Cavity Ring Down Aerosol Spectrometer Measurements with Full Size Distribution Information

Abstract

Cavity ring down aerosol extinction measurements are combined with size distribution measurements to provide a multi-parameter basis for the retrieval of the aerosol complex refractive index. We show that two distinct size distributions of small particles (< 300 nm) suffice to obtain robust convergence of the Mie theory fit of the extinction function. Experiments are performed both for purely scattering and for absorbing aerosol. Thus this method provides a perspective to use cavity ring down aerosol spectroscopy in field and laboratory measurements that often suffer from low particle concentrations and a lack of large particles.

INTRODUCTION

Atmospheric aerosol particles play a major role in the regulation of Earth's radiation balance. The effect of aerosols is both direct by absorption and scattering of incoming shortwave and outgoing longwave radiation (Bates et al. 2006; Bellouin et al. 2005) and indirect by serving as cloud condensation nuclei and thereby contributing to changes in cloud microphysical properties and the albedo of the planet (Hansen et al. 2005; Lohmann and Feichter 2005). Determination of the direct effect requires knowledge of the interaction of the aerosol with radiation. The quantity describing the optical properties of a substance is its complex refractive index (RI). We focus in this study on the determination of the RI of two model aerosol species by combining simultaneous extinction and size distribution measurements.

The wavelength of light in the visible and UV spectral regions is comparable to the size of most common atmospheric particles. The framework describing the interaction of radiation with such particles is Mie theory and its subsequent modifications (Huffman 1983). The cavity ring down aerosol spectrometer (CRD-AS) was developed for measuring the extinction coefficient of atmospheric particulate matter in both laboratory and field conditions (Smith and Atkinson 2001; Strawa et al. 2003; Thompson et al. 2002). Recently, this method was used for the retrieval of aerosol complex refractive index (Abo Riziq et al. 2007; Baynard et al. 2006; Bulatov et al. 2006; Bulatov et al. 2002; Dinar et al. 2007; Lack et al. 2006; Pettersson et al. 2004). Aerosol RI can be obtained with a CRD-AS by measuring the extinction of light passing through a size-selected monodisperse aerosol sample and mapping out the Mie scattering curve of the aerosol. The RI is then retrieved by fitting a Mie curve to the measured extinction efficiencies by varying the real and imaginary components of the RI to obtain the best fit. This method has been successfully applied to the determination of the RI of both absorbing and non-absorbing single and multi-component aerosols in laboratory experiments (Abo Riziq et al. 2007; Baynard et al. 2007; Dinar et al. 2007; Lack et al. 2006). Recently the method has also been adopted for field applications (Baynard et al. 2007).

In field measurements and in chamber studies, in contrast to laboratory conditions, this method may suffer from a number of limitations. First, the number of sampled particles is often too low to perform an entire set of optical measurements for different particle sizes. Second, large particle sizes may be needed in order to sample the important domains of the Mie extinction curve and to obtain a robust fit. Third, due to variations in the atmospheric conditions occurring on short time scales, the properties of the sampled aerosols may not be constant throughout the required measurement time interval.

Here we test a modification of the CRD-AS method for fast retrievals of aerosol complex refractive index (RI, m = n + ik) with less measurement points and shorter sampling times, with a motivation to overcome the above-mentioned limitations of low particle number, small particle sizes, and temporal variability of the atmospheric sample. Therefore, we do not restrict the data processing to the modal diameter midpoint of the sampled particles. Instead, optical extinction measurements and determination of the size distribution are performed simultaneously. The entire aerosol size distribution is included in the calculation and different distributions are used to provide a data set for a Mie fit. This approach is compared to the “standard” approach used in previous studies (Abo Riziq et al. 2007; Baynard et al. 2006; Bulatov et al. 2006; Bulatov et al. 2002; Dinar et al. 2007; Lack et al. 2006; Pettersson et al. 2004).

Two model aerosols are investigated in this study: ammonium sulfate (AS), which is a purely scattering aerosol with well known optical properties (Abo Riziq et al. 2007); and the water soluble dye nigrosin, which was also examined in several previous studies (Bond et al. 1999; Dinar et al. 2007; Garvey and Pinnick 1983; Lack et al. 2006). The nigrosin represents an aerosol species with a strong absorption at a wavelength of 532 nm.

METHODS

Experimental Design

A scheme of the experimental setup is shown in Figure 1. Experiments are carried out as following: DMA-1 selects a narrow particle size distribution with modal diameter D _i . This size distribution is characterized with the scanning mobility particle sizer (SMPS). Simultaneously, the extinction resulting from this particle distribution is determined with the CRD-AS and the total particle number density inside the CRD cavity is counted with CPC-2. These measurements are then repeated several times. After that, another modal diameter D _{i + 1} and a new size distribution and extinction data are acquired.

FIG. 1 Schematic diagram of the experimental setup.

The extinction of AS aerosol and the corresponding size distributions were measured for size distributions centered between 175 nm and 300 nm in steps of 25 nm, and in addition for 350 nm and 450 nm to investigate the retrieval accuracy for larger particles.

For nigrosin, measurements were performed for particle diameters from 150 nm to 300 nm in steps of 25 nm and for 350 nm and 400 nm.

Experimental Details

Aqueous solutions of ammonium sulphate or nigrosin (0.02–1 mg/ml) were nebulized using a constant output atomizer (TSI-3076) with dry particle-free nitrogen flow. The solution concentrations were varied based on the size of the investigated aerosol to reduce the size of the aerosol formed and to minimize contributions from multiply charged large particles. The generated particles were dried using two silica gel column dryers (RH < 3%) yielding a polydisperse aerosol flow. The aerosol was neutralized (TSI 3012A) to obtain an equilibrium charge distribution.

A narrow aerosol size distribution (σ ≈ 1.05) was generated using DMA-1. Following DMA-1, the aerosol flow was split into two flows. One flow was directed to a scanning mobility particle sizer (SMPS) to determine the size distribution. The second flow was directed to a dilution apparatus for precise control of particle number concentration and total flow (0.8 SLM) and then to the cavity ring down aerosol spectrometer (CRD-AS) operating at 532 nm. The obtained aerosol size distributions are corrected for the contribution of multiply charged particles by an internal routine of the SMPS measurement software. Typical number concentrations used in the experiments are between 200 and 1000 cm^{− 3}. A full measurement takes between 10 and 15 minutes.

The CRD-AS consists of two highly reflective plano-concave mirrors (curvature radii of 1 m and 99.995% reflectivity at 532 nm ([Los Gatos, USA]) mounted at the two ends of a 93 cm 3/4^″ stainless steel tube. A small purge flow of dry particle-free nitrogen (0.05 and 0.1 SLM) is introduced in front of each mirror to prevent mirror contamination by particle deposition. The aerosol flow enters the cavity through four tubes at 45° designed to ensure good mixing and homogenous concentration of the particles. The particles exit the cavity at a flow rate of 0.95 SLM in a similar configuration. The length of the cavity occupied by particles is about 68 cm. The particle concentration in the cavity is determined by a second condensation particle counter (CPC-2). It was verified that the particle size distribution at the exit of the cell matches the one measured by the SMPS.

The 532 nm laser light is obtained from the second harmonic generation of a Nd:YAG laser (10 Hz, 3–6 ns) which is coupled with an Optical Parametric Oscillator laser (OPO, EKSPLA, NT 342C/3/UVE, tunable 0.2–2 μ m). The laser beam is directed through a spatial filter consisting of two lenses with focal length of 5 cm and 10 cm, and a 100 μm-pinhole in the common focus of the lenses. The beam diameter in front of the cavity is about 1 mm, with energy of 1–1.5 mJ/pulse.

The laser intensity emerging from the CRD cell is measured by a photomultiplier (Hamamatsu H6780-02), and the resulting signal is fed into a digital oscilloscope (LeCroy, model 9361, 300 MHz). The decay time for a cavity filled with particle-free dry nitrogen (τ₀) is about 60 μs resulting in a detection limit of the order of α_min = 1.26 × 10^{− 9} cm^{− 1} (Brown et al. 2002; Dinar et al. 2007). 1000 laser shots were averaged for each point.

Refractive Index Retrieval

In order to relate the extinction coefficients to the respective size distributions, both measurements are normalized. For that purpose, the extinction coefficients obtained by the CRD measurements were divided by the particle number density in the cavity, measured with CPC-1. The results of the 3–6 repeated measurements at a specific modal diameter D _i were averaged in order to obtain a mean α _emeasured,i and a standard error ϵ _i .

The aerosol size distributions obtained with the SMPS are processed in a similar way. Each measured size distribution n _i (D _P ) is also normalized by dividing the raw distribution by the total number concentration, _i,0 (D _P ) = n _i (D _P )/∑ _{D P} n _i (D _P ). Distributions that correspond to the same modal diameter D _i were averaged to a mean distribution n _i,0(D _P ). Total extinction was calculated for this distribution and was compared to the measured extinction. As a result of the normalizations, the calculated and the measured extinction coefficients are directly comparable and can be combined to retrieve the complex RI of the particles.

The method used in previous studies (Abo Riziq et al. 2007; Bulatov et al. 2006; Bulatov et al. 2002; Dinar et al. 2007; Lack et al. 2006) was to approximate the aerosol size distribution by the mean diameter and to map out the Mie curve of these particles. The RI in these experiments was retrieved using a set of extinction efficiencies at several different mean diameters. This approach is called “the diameter midpoint method” in the following discussion. It is compared in this article with our new approach that takes the entire aerosol size distribution into account. The extinction coefficients of all contributing particle sizes (obtained from the SMPS measurement) are calculated and summed up for comparison with the measured extinction coefficients. This method is described below in detail.

The extinction efficiency depends on the size parameter x = π D _P /λ and therefore on the wavelength of the light (λ) used in the extinction experiment. It further depends on the unknown complex RI m = n + ik of the aerosol particles. The RI is retrieved by independently varying the real and complex parts of the refractive index and minimizing the difference between the calculated and measured extinction. The RI of the particles is the one which leads to the minimal difference. To guarantee a fast and robust convergence of the search algorithm, we restrict the imaginary part of the RI to k ≥ 0. This is not a limitation of the method since negative values of k represent unphysical solutions. We apply a Mie theory algorithm for homogeneous spheres (Huffman 1983) to calculate the extinction efficiency Q _e (x,m) of each individual particle size D _i . Weighting each size bin with the respective concentration and the geometrical cross section gives the extinction coefficient depending on the particle diameter within the size distribution i:

The total calculated extinction coefficient for a normalized size distribution is then the sum over all particle diameters, α _i,0(m) = ∑ _{D P} α _i,0(D _P ,m). Since inversion of the extinction efficiency Q _e (x,m) is nontrivial, we use an optimization strategy to obtain the complex RI of the aerosol particles. Starting from an initial guess, the algorithm varies the real and imaginary part of the RI simultaneously and compares the resulting extinction coefficient with the measured extinction coefficient (i.e., α _i,e ) in the form of the least-squares deviation χ²:

The sum runs over all N particle size distributions j. ϵ _j are the errors of the measured extinction coefficients for different measurements of one size distribution, as outlined above. χ _i ² varies with the tested RI (m) and the best fit value m ₀ results in a minimal χ _io ². The search is performed with the built-in MATLAB function “fminsearch” based on a direct simplex search algorithm (J. C. Lagarias 1998). It was verified that the results do not depend on the initial guess for the RI.

RESULTS

The extinction of AS aerosol and the corresponding size distributions were measured for 8 size distributions centered between 175 nm and 300 nm, and also for distributions centered at 350 nm and 450 nm to investigate the retrieval accuracy for larger particles. All possible subsets of this data series can be used in the calculation of the RI. We show that just few measurement points (two or three points were used in the following examples) suffice to obtain values of the RI in good agreement with literature values. The results of the calculations are shown in Figure 2. The RIs for all possible combinations of three out of the eight measurement points are shown as squares in Figure 2a. The circles indicate the results for all possible combinations of two data points out of eight. (The combinations [175 nm, 200 nm, 225 nm] (squares) and [200 nm, 225 nm] (circles) were excluded since no close convergence of the search algorithm was found in these cases). These two data sets were obtained by using the entire size distributions measured with the SMPS system. In contrast, the triangular points were obtained by taking only the diameter midpoint of the size distribution and combining two sizes for each RI. In Figure 2b only the results from combinations of particle distributions with mean diameters smaller or equal to 275 nm are shown. The results for combinations of three distributions were excluded for clarity.

FIG. 2 Refractive indices of AS. In (a) all particle sizes are included in the retrieval procedure. The retrieved RIs of all possible combinations of 3 (squares) and 2 (circles) size distributions and of 2 diameter midpoints (triangles) are shown. (b) shows only the results for small particle diameters up to 275 nm. In both panels, the cross shows the literature value reported by Abo Riziq et al. (2007). The deviation of the average of the circles in b from the reference is –0.7 % for n. Since all k are close to 0, giving a relative deviation for k has no meaning.

The same information as in Figure 2 is shown for nigrosin in Figure 3. For this substance, measurements were performed for particle diameters from 150 nm to 300 nm in steps of 25 nm and for 350 nm and 400 nm. Figure 3a shows combinations of all particle sizes, while Figure 3b shows only combinations of small particles up to 250 nm.

FIG. 3 Refractive indices of nigrosin. As in Figure 2 the panels show the search results for all particle sizes (a) and for small particles up to 250 nm (b). In both panels, the crosses show literature values value reported by Dinar et al (2007) and references therein. The deviation of the average of the circles in (b) from the reference is –2.2 % and +2.5 % for n and k, respectively.

For both aerosol species, the retrieved RI depends on the particular combination of particle sizes included in the optimization. To test whether the investigated method is stable and reliable, we average the data sets of Figures 2 and 3 and compare the respective standard errors. This deviation is not a measurement error, but rather a statistical variation of the retrieved RI for different data sets. Figure 4 shows the average value of the RI and the respective standard errors of n and k for the five scenarios investigated in Figures 2 and 3. The results are shown for AS in Figure 4a and for nigrosin in Figure 4b. Note that the extent of the error bars in Figure 4a to k < 0 has no physical meaning and results only from statistics.

FIG. 4 Mean RIs for AS (a) and nigrosin (b) obtained by using different subsets of measurement points. The crosses correspond to literature values reported by Abo Riziq et al. (2007) and by Dinar et al. (2007) and references therein.

DISCUSSION

Considering the low number of data points, a good agreement exists between the retrieved RIs with the literature values for all the tested scenarios. Even in the simplest case, with knowledge of the diameter midpoints of two measured size distributions, the deviations for AS at the upper boundary of the error bar are as small as Δ n = 0.075 and Δ k = 0.046. For nigrosin, the largest deviations are Δ n = 0.033 and Δ k = 0.023. This suggests that the Mie extinction function can be predicted using a very limited number of measurement points.

However, the quality of the retrieved RI can be further increased by taking the entire size distribution into account as explained above. The principal improvement resulting from using entire distributions is seen in the more confined, and therefore more reliable, range of the imaginary part of the RI. For all particle sizes of AS (Figure 2a, 4a), the majority of the retrieved values of k are 0 when using three or two different distributions, while the algorithm converges more frequently to slightly positive values with two diameter midpoints (this was found also by the Abo Riziq et al. (2007) and may be attributed to some absorption by residuals in the water or some surfactants). There is also a smaller range in the real part of the RI, and furthermore, a shift toward values closer to the literature values. The deterioration that occurs if only two size distributions instead of three are used is very small. Therefore, we use the advantage of less measurement points in our discussion of the results for small particles (Figure 2b) and do not further consider sets of three distributions.

In the small-particle limit, the size distribution method is clearly advantageous. Taking only two diameter midpoints does not lead to consistent results, while all combinations of two size distributions lead to k = 0 and a very small range of n. This difference is obvious by comparing the inverted triangle and the diamond data point in Figure 4a. The relative deviation of the real part of the RI of AS from the literature value obtained with the same experimental system (Abo Riziq et al. 2007) is only –0.7 % when using two small-size distributions. The imaginary part of the RI is 0 when using two small-size distributions, therefore a calculation of the relative deviation from literature is meaningless. However, a value of 0 lies within the error bar of the literature data, and is very close to the true value since AS has little measurable absorbance at 532 nm.

The results are in better agreement in the case of nigrosin. The RI retrieval is better when employing particles smaller than 250 nm. In Figure 3a, the points at high values of n belong to combinations of large particle sizes. k has a especially high variability in that region. When including only the small particle sizes (Figure 3b), the variability decreases both for the size distributions and for the diameter midpoints. However, as in the AS case, evaluating the entire size distributions leads to smaller variations in the individual combinations (comp. Figure 4b, reversed triangles and diamonds). In comparison with the literature value of the RI of nigrosin, the size distribution method is closer to k and the midpoint method is closer to n. However, the relative deviations of the small-size distribution n and k from the literature (Abo Riziq et al. 2007) are –2.2% and +2.5%, respectively. The precision obtained with the few data points used makes this method suited for field and chamber studies, and enables the derivation of climate-relevant parameters such as the single scattering albedo of the studied particles (data not shown).

For both aerosol species we were able to retrieve the RI in good agreement with the previously reported values (Abo Riziq et al. 2007; Bond et al. 1999; Dinar et al. 2007; Garvey and Pinnick 1983; Lack et al. 2006). It is therefore suggested that it is not necessary to map the extinction function over a large range of particle sizes. A few measurements of two size distributions at small particle diameters and the respective extinction coefficient are sufficient to obtain the RI. This method provides a way to overcome the need to use the large particles required by the “diameter midpoint method.” Therefore, this new method may be better suited for field and simulation chamber measurements when large particles in the atmosphere are scarce. The approach presented here can also provide information about whether the optical properties of the particles are constant throughout the entire size range or vary with size. This information cannot be directly obtained by “the diameter midpoint method.” It is noted that the CRD-AS system used in this study is not as compact as some other optical measurement instruments. However, it can easily be used in simulation chamber studies. Moreover, a field instrument based on similar instrumentation was recently developed and employed (Baynard et al. 2007).

The conclusion of this study fits well with results from validation measurements presented in (Abo Riziq et al. 2007) (data not shown). Several subsets of the extinction data from that study were considered. Various subsets of the extinction data from that study were evaluated. The subsets varied in both the number of data points and the distribution of the points within the range of the data series. For example, the RI fitting results obtained with a small number of points ranging from the smallest to the largest particle sizes were compared with the results obtained with the same number of points covering only a narrow range of the measured sizes. No characteristic particle sizes were identified; in particular it was shown that it is not obligatory to perform many measurements of the extinction of particles with sizes in the oscillating part of the extinction function. However, such measurements add to the fit's robustness. With the constraint to measure at a maximum of four different diameter midpoints the best strategy was to choose three small sizes (size parameter x _AS < 2.3, x _Nigrosin < 1.3) and one large size (x _AS > 3, x _Nigrosin > 2), but also four evenly spread points for a large range of sizes resulted in very close RIs.

Additional experiments were conducted using different size distributions at a single aerosol mode. In these studies the particles were size selected with DMA-1 at a fixed diameter setting, but the sheath flow was varied so that the resulting size distribution after DMA-1 broadened significantly with decreasing flow velocity. Combinations of different size distributions were tested with the RI retrieval algorithm. This method works partly with several narrow distributions, but fails if the geometric standard deviation increases strongly. Therefore we recommend using narrow, well resolved aerosol size distributions for extinction measurements.

CONCLUSIONS

The results presented here suggest that the RI of aerosols can be retrieved by simultaneous measurement of the optical extinction and the size distribution of the aerosol sample. We explored this technique for two model aerosols, purely scattering ammonium sulfate and strongly absorbing nigrosin. In both cases, measurements at only two particle sizes were sufficient to guarantee a convergence of the retrieved RI to values comparable with the literature. The best results were obtained for particle sizes between 150 nm and 275 nm. The small number of required measurement points, the faster acquisition times and the preference for small particle sizes makes this method a fast and reliable technique suited for field and simulation chamber studies.

Acknowledgments

The authors thank Dr. Carynelisa Erlick for the helpful discussions. This work was partly funded by the German Israeli Science Foundation (GIF), contract no. I-899-228.10/2005 and by the Minerva Foundation of the Max Planck society.