Polarized Imaging Nephelometer for in situ airborne measurements of aerosol light scattering Gergely Dolgos1,2,* and J. Vanderlei Martins1,2 1

Department of Physics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, Maryland 21250, USA 2 Joint Center for Earth Systems Technology, University of Maryland Baltimore County, 5523 Research Park Drive, Baltimore, Maryland 21228, USA * [email protected]

Abstract: Global satellite remote sensing of aerosols requires in situ measurements to enable the calibration and validation of algorithms. In order to improve our understanding of light scattering by aerosol particles, and to enable routine in situ airborne measurements of aerosol light scattering, we have developed an instrument, called the Polarized Imaging Nephelometer (PI-Neph). We designed and built the PI-Neph at the Laboratory for Aerosols, Clouds and Optics (LACO) of the University of Maryland, Baltimore County (UMBC). This portable instrument directly measures the ambient scattering coefficient and phase matrix elements of aerosols, in the field or onboard an aircraft. The measured phase matrix elements are the P11, phase function, and P12. Lasers illuminate the sampled ambient air and aerosol, and a wide field of view camera detects scattered light in a scattering angle range of 3° to 176°. The PI-Neph measures an ensemble of particles, supplying the relevant quantity for satellite remote sensing, as opposed to particle-by-particle measurements that have other applications. Comparisons with remote sensing measurements will have to consider aircraft inlet effects. The PI-Neph first measured at a laser wavelength of 532nm, and was first deployed successfully in 2011 aboard the B200 aircraft of NASA Langley during the Development and Evaluation of satellite ValidatiOn Tools by Experimenters (DEVOTE) project. In 2013, we upgraded the PI-Neph to measure at 473nm, 532nm, and 671nm nearly simultaneously. LACO has deployed the PI-Neph on a number of airborne field campaigns aboard three different NASA aircraft. This paper describes the PI-Neph measurement approach and validation by comparing measurements of artificial spherical aerosols with Mie theory. We provide estimates of calibration uncertainties, which show agreement with the small residuals between measurements of P11 and –P12/P11 and Mie theory. We demonstrate the capability of the PI-Neph to measure ambient aerosol with two data sets from the Deep Convective Clouds and Chemistry (DC3) field campaign, from flights over Colorado in June 2012. ©2014 Optical Society of America OCIS codes: (010.1110) Aerosols; (010.1310) Atmospheric scattering; (280.3420) Laser sensors; (120.4640) Optical instruments; (120.5820) Scattering measurements; (290.5855) Scattering, polarization.

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#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21972

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1. Introduction Aerosols and clouds interacting with them play important roles in the climate of our planet [1]. Aerosol may be solid or liquid with respect to phase, or a mixture of both. Measureable diameters of aerosols potentially include 3 nm at the lower limit [2] and tens of micrometers at the upper limit [3]. Sources of aerosols are numerous, and their spatial and temporal distribution is highly variable on the scale of tens of kilometers and hours [4]. In all practical circumstances, aerosols seed cloud droplets, and largely determine the properties of clouds. Direct and indirect radiative forcings of aerosols are the largest obstacles to understanding and predicting climate change [5], since these forcings have the largest uncertainties among forcing agents, and are highly variable spatially and temporally [6]. Therefore, aerosols and their effects on clouds must be understood globally, which is only possible through satellite remote sensing [1,5,7,8]. We need to know how aerosol particles scatter light in each direction, in order to be able to detect aerosol characteristics from space [9,10], and to calculate their direct radiative forcing [11]. For describing the scattering process, we use the Stokes vector [12] to quantify both the polarization and irradiance [13] of light. This formalism is able to represent partially polarized light and fully elliptically polarized light. The Stokes vector consists of the irradiance I, and the Q, U, and V Stokes parameters. Figure 1 illustrates the scattering geometry. The illuminating light propagates in the positive z-axis direction; the aerosol ensemble is in the origin. The dashed green-gray arrow ending at point M denotes the scattered light. θ is the polar scattering angle, the angle between the propagation directions of the illuminating and scattered light.

Fig. 1. Scattering geometry and notation of the measurement equation. Panels (a) and (b) show the same geometry, from nearly perpendicular views. We employ the view of panel (b) because it is an advantageous orientation for Fig. 2. The incident light travels in the positive z direction. The scattering event takes place in the ΔV volume, while point M is the center of the detection. The projection of point M onto the ‘xy’ plane is point N. The scattering plane lies on points M, N, and O, and on the z-axis. The scattering plane includes the propagation directions of the incident laser beam and the scattered light.

The angle η is the rotation of the scattering plane with respect to the ‘xz’ plane, and around the z-axis, which is the same as the azimuthal scattering angle in our notation. We refer to θ simply as the scattering angle. The phase matrix is the scattering angle dependent operator that transforms the polarization Stokes vector of the incident light to that of the scattered light. The phase matrix is dependent on microphysical properties such as the shape, size and refractive index distributions of aerosols in an ensemble [14]. The aerosol refractive index, and therefore the

#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21975

phase matrix, vary spectrally, requiring multi-wavelength measurements for particle characterization [15]. The Stokes vector of incident light has to be expressed in the rotated coordinate system of the scattering plane. In that case, the aerosol phase matrix, P (θ ) , produces the scattered light Stokes vector, according to the measurement equation [12]:  I sca (θ )   I in      Q θ  sca ( )  = β sca ⋅ ΔV ⋅ P (θ ) ⋅  Qin   U sca (θ )   U in  4π ⋅ r 2      Vin   Vsca (θ ) 

(1)

The phase matrix depends explicitly on θ, and implicitly on the type of aerosol present and the wavelength of light. The scattering angle resolution of the measurement is Δθ, and the corresponding scattering volume is ΔV. In Eq. (1), the distance of detection from the scattering event is r. The scattering coefficient of the scatterer, in this case aerosol, is βsca [12]. The phase matrix will be independent of the azimuthal scattering angle when the scattering medium is macroscopically isotropic and mirror symmetric [13]. This necessitates the assumption that the particles are randomly oriented. Additionally we have to assume that the dominant scattering contribution is not from helical structures like biogenic sugar molecules with a predominant handedness. Therefore, η only denotes the scattering plane rotation angle, and Eq. (2) is the form of the phase matrix that we seek to measure:  P11 (θ ) P12 (θ ) 0 0    P12 (θ ) P22 (θ ) 0 0   P (θ ) =  0 0 P33 (θ ) P34 (θ )    0 − P34 (θ ) P44 (θ )   0

(2)

The phase function, P11(θ), is the top left element of the phase matrix, and it expresses the directional distribution of the irradiance of scattered light. Satellite remote sensing retrieves the microphysical properties of aerosols by matching measured radiances (and potentially polarizations) with modeled signals, by adjusting aerosol types, quantities, and optical properties in the forward model [16]. Elements of the phase matrix may be used in the forward model at a single scattering angle per scene [10], or at multiple scattering angles for the same scene [16]. The relevant scattering angle depends on the relative position of the Sun, the satellite, and the volume of dependence or scene. Passive remote sensing detects backscattered sunlight. Passive retrievals of aerosol microphysics often rely on assumptions like a-priori aerosol models, surface properties, cloudiness and hygroscopicity [10]; assumptions must be validated by in situ airborne measurements of the retrieved quantities. Aircraft measurements are especially crucial for instruments with a narrow ground track making it difficult to achieve statistically significant collocation with ground based sensors of aerosol microphysical properties [17,18]. A nephelometer is a device that measures light scattering, in situ. The Glory science team called for a “high accuracy airborne polarization nephelometer” [9], such an instrument has been unavailable so far. The accuracy of data products of airborne and space-based polarimeters will benefit crucially from employing such a polarization nephelometer in the calibration and validation efforts. Airborne polarimetric instruments include the: 1. Airborne Multiangle SpectroPolarimetric Imager (AirMSPI) [19], 2. Research Scanning Polarimeter (RSP) [20], and

#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21976

3. Passive Aerosol and Cloud Suite (PACS) [21]. Future space-based instruments include the 1. Multi-viewing, Multi-channel, Multi-polarization imaging (3MI) ESA mission [22], 2. HyperAngular Rainbow Polarimeter HARP-CubeSat [23,24] funded by NASA. The most common type of nephelometer is the integrating nephelometer [25], which measures the scattering coefficient. In contrast, polar nephelometers measure the directional distribution of scattered light [26]. Polar nephelometers often lack sensitivity at the ambient aerosol loading or Rayleigh scattering level of about 10 Mm−1, and they often do not measure calibrated scattering coefficient at all. Phase matrix elements of aerosols have been measured in the laboratory through a variety of ways, including instruments with rotating detectors [27– 30], and via elliptical mirrors used to capture light scattered in different directions [31–33], and in various other ways. Instruments may measure resuspended aerosols, deagglomerated in the laboratory, or individual particles one at a time, and on the ground only. These measurements are therefore liable to artificial biases in size distributions and particle shapes and produce scattering properties that are not representative of the volume of dependence of a satellite pixel. The large vertical and horizontal extent of satellite volumes of dependence [10] and the large natural variability of aerosols justifies the need for airborne in situ measurements [34], which is a promising and feasible approach to obtaining representative and accurate scattering data for natural aerosol ensembles. The great investment in current aerosol remote sensing instruments, both airborne and space based, justifies the need for continuous in situ measurements for validation. In situ airborne measurements [35] of aerosol phase matrix elements are not available today. Comparisons of in situ and remote sensing measurements will have to account for instrument characteristics and aircraft inlet effects, including rejection of large particles and drying [36,37]. This motivates inlet free measurement development. In order to perform accurate size distribution retrievals from scattering data, it is important to be able to measure at scattering angles as close to forward scattering (θ = 0°) as possible. In situ determination of the LIDAR ratio requires estimation of the phase function (P11) at the exact backscattering direction, θ = 180°. Spherical and non-spherical particles likely exhibit very different signatures in P11 and P12 near backscattering [15]. These are the main motivations to measure as close to θ = 180° as possible. The degree of linear polarization of scattered light is -P12/P11, if the incident light is unpolarized, for example in case of sunlight. This fact illustrates the applicability of P12 to atmospheric remote sensing. In case of single scattering (which is a frequently applicable approximation on clear days) the satellite signal will be primarily sensitive to P11 and P12 [38]. Therefore, aerosol remote sensing and climate science stands to benefit from an airborne instrument that can measure in situ P11 and P12 of aerosols. Development of such an instrument is a justified investment in light of the polarimetric remote sensing instruments for aerosols, which currently are in use or are under development. Therefore, the Laboratory for Aerosols Clouds and Optics (LACO) at the University of Maryland, Baltimore County (UMBC) has decided to fill this need, and develop a “high accuracy airborne polarization nephelometer” [9], called the Polarized Imaging Nephelometer (PI-Neph). 2. The imaging nephelometer concept The PI-Neph is a portable instrument designed and built at UMBC. The PI-Neph measures the scattering coefficient and the directional distribution of the scattered light, with polarization. The PI-Neph uses an imaging technique to measure scattered light at more than a hundred scattering angles simultaneously, without moving parts. This technique was first #214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21977

proven the LACO laboratory in 2007, and was first reported in 2009 [39], then on January 25, 2010 [40]. Preliminary geophysical results from an airborne deployment were presented in 2013 [41]. The measured phase matrix elements are P11, phase function, and P12, in a wide scattering angle range of 3° to 176°. The PI-Neph first measured at a laser wavelength of 532nm, and the LACO group upgraded it in 2013 to measure at 473nm, 532nm, and 671nm nearly simultaneously. The PI-Neph uses three lasers of different wavelengths combined into a common beam to illuminate the aerosol sample, together with a liquid crystal modulator that controls the orientation of linear polarization of the laser beam. A wide field of view imager detects scattered light. The system captures the P11 and P12 matrix elements by taking two sequential pictures one after another, with two different polarizations, parallel and perpendicular to the scattering plane. The duration of a single measurement primarily depends on the laser beam power, the aerosol loading, and the pupil setting of the lens (detector area), and can typically vary from a fraction of a second, to tens of seconds. The PI-Neph data applies to an ensemble of particles, which is the relevant quantity for satellite remote sensing, as opposed to particle-by-particle measurements that are relevant for theoretical studies and for in situ monitoring. The PI-Neph data will also be applicable to studies on the effects of humidity on aerosol scattering and in verification of light scattering models and microphysical retrieval algorithms. LACO has deployed the PI-Neph instrument aboard aircraft, in trailers, and in the field. In case of ambient measurements with the PI-Neph, it is important to quantify the inlet size cutoff, and the humidity conditions inside the measurement chamber relative to ambient humidity. The next section introduces the imaging nephelometer concept, first implemented in the PI-Neph. This design provides the large angular range in P11 and P12 measurements of ambient aerosol sampled through an inlet, and enables technology development toward inlet free measurements. Figure 2 illustrates the imaging nephelometer concept of the PI-Neph. The imaging system is a lens coupled to a camera that is a cooled charge coupled device (CCD). The lens is a commercial objective with a horizontal field of view (FOV) greater than 100°. The laser beam first falls on the mirror, for precision alignment, then passes through a sealed window entering the interaction volume with ambient aerosol, the sample chamber. Aerosols enter near the beam trap, flow along the laser beam and exit the chamber after passing in front of the lens. Apart from the mirror prior to the chamber window, all components in Fig. 2 are inside the pressure tight measurement chamber of the PI-Neph. Inside the PI-Neph, random orientation of particles is a reasonable assumption due to the turbulent flow at the inlet.

Fig. 2. Schematic of the imaging arrangement employed in the scattering chamber of the Polarized Imaging Nephelometer (PI-Neph). Panel (a) shows the arrangement of the instrument in a view approximating the orientation of Fig. 1. panel (b), looking in the positive x direction. The coordinate systems are the same in Fig. 1 and Fig. 2.

The beam passes in front of the camera twice, as illustrated in Fig. 2(a). On the first pass, the forward scattered light reaches the camera in the scattering angle range of 3° to approximately 100°, while on the second pass the backscattered light reaches the camera in the scattering angle range of approximately 80° to 176 °. To achieve this, the lens optical axis is oriented at approximately 45° with respect to the laser beam direction. In Fig. 2(a) the setup is displayed in the ‘xy’ plane, while in Fig. 2(b) it is displayed in the ‘xz’ plane (laser beams #214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21978

are overlapping), the coordinate system is the same as in Fig. 1. The corner cube mirror reflects the laser beam after the first pass in front of the camera, and after the second pass, it reaches a beam trap, which is sustained dust free by filtered air circuits. In Fig. 1 point M is the center of the detection area (center of entrance pupil corresponding to a few pixels of the CCD). Figure 3 shows image data from the PI-Neph. Forward and backward scattering portions of the laser beam correspond to bottom and top halves of the images, respectively.

Fig. 3. Panel (a) shows raw grayscale format data acquired from CO2 scattering. Scattering angles associated with a select few pixel locations appear next to perpendicular profile locations. The top and bottom beam boundaries are in blue and yellow color. Panel (b) is a single raw data image of 903nm diameter PS (polystyrene) spheres suspended in clear air, showing the Mie scattering pattern. The streaks of single particles average out for longer than a minute data acquisition times. Panels (c), (d), (e), and (f) are illustrations of the background subtraction procedure, two examples of CO2 and two from PS.

#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21979

Figure 3(a) shows 30-minute data of CO2 scattering in grayscale format. This data is a sum of many image pairs; each pair consists of two images with perpendicular laser polarizations. Figure 3(b) shows a single debayered image, with 3 seconds of exposure time, of 903 nm diameter PS (polystyrene) spheres suspended in otherwise particle free air, with the expected Mie pattern. Figure 3 images were taken with green (λ = 532nm) laser light. Figure 3(a) illustrates a few scattering angles along the laser beam images. Along the beams it also shows the result of our beam finding algorithm that automatically locates the center and boundaries (top and bottom) of the laser beams in the images, and generates the locations of perpendicular profiles. In order to extract a signal that is proportional to the scattered irradiance, we compute profiles across the beam image, according to panels (c), (d), (e), and (f). The profile locations are much denser than shown in panel (a); they are spaced apart by one pixel, and are fixed for a data set of aerosol data and Rayleigh scattering calibration data. The single pixel along-beam separation of profiles results in an approximate scattering angle resolution, Δθ, of 0.1°. The 0.1° resolution raw data is correlated; the point spread function of the lens results in an effective Δθ of approximately 0.4° near the 3° (forward) and 176° (backward) scattering angles. Δθ gradually increases to about 2° at the 90° (side) scattering angles on both the forward and backward scattering beams. In the direction perpendicular to the beam, the portion of the profile used for signal integration is marked green, while the portions of the profile used to find the background level are marked light red, on each ends of the central green profile. Stray light in the images is minimal and stable; therefore, we exclude the few contaminated background profile locations, and interpolate the background from neighboring locations. Panels (c) and (d) are profiles of CO2 data corresponding to 12° and 45° scattering angles. Panel (e) and (f) are profiles of PS data at the same scattering angles. Camera data is proportional to scattered irradiance falling on the lens entrance pupil from a scattering angle range, in the first order, while polarization effects play a role in second order modeling of the signal. Adjustments of the exposure time can accommodate variability of ambient scattering coefficient, which can reach more than four orders of magnitude. In order to capture all the angular scattering data in a single image, the CCD well depth has to provide the dynamic range at a fixed scattering coefficient and a fixed exposure time. Phase functions determine the dynamic range required to capture the scattered irradiance from 3° to the lows of side scattering. Measuring through an inlet limits particles to below 5μm of diameter. This size cutoff typically limits the dynamic range required for detecting the phase function to below three orders of magnitude, which is possible to achieve with our cooled Sony CCD, model ICX285AQ. 3. Instrument description and measurement scheme Figure 4 shows the optical and sensor layout of the PI-Neph. The lasers and the beam combining optics produce the multi wavelength beam that goes through the W1 window and the PO polarizer. Then the W2 beam pick-off feeds the PD1 power reference photodiode. The following liquid crystal variable retarder and the Fresnel rhomb act together as an achromatic polarization rotator. The M3 and M4 mirrors allow the independent positioning and orientation of the laser beam that enters the through the W3 window into the measurement chamber. Collimator series C1 and C2 reduce stray light to below the extremely low levels required for scattering measurements at βsca = 10 Mm−1 aerosol loading, or Rayleigh scattering. The collimators, camera and lens, and the BT beam trap are all located inside the pressure boundary, in an atmosphere filled with ambient air and aerosol. Therefore, it was necessary to construct a filtered air delivery system that recycles sample air at the ambient pressure, and fills the beam trap and corner cube assemblies with particle free air. The accumulation of ambient aerosols on these surfaces would lead to unacceptable stray light levels otherwise. A separate clean air pumping system maintains the components in the laser module free of particles; this system operates at cabin pressure. Heaters and temperature

#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21980

sensors stabilize instrument components near room temperature, mainly in order to avoid potential condensation on steep descents, and in order to ensure consistent performance, in case of the liquid crystal variable retarder and other electro-optics.

Fig. 4. The optical and sensor layout of the PI-Neph instrument. Components inside the pressure boundary and the M4 mirror are in the chamber module, other components reside in the laser module.

Measurements with different polarization orientations and different wavelengths are made sequentially. Figure 5 illustrates a measurement scheme for the case of a three-wavelength measurement. A single wavelength measurement requires taking images with two different polarizations. Thus far, we have measured sequentially in time for different wavelengths due to the differing liquid crystal retardance settings required to set the optimal polarizations at each wavelength. The hardware control and data acquisition program was written in C + + and we can configure instrument behavior by a custom set of commands in a text file. We can change the exposure start and stop time, laser on and off time, laser wavelength and polarization, among others.

Fig. 5. A common measurement scheme, employing a pair of perpendicular polarizations, one pair per each wavelength in a temporal sequence. A three-wavelength measurement takes 36 seconds in this case.

The sample chamber of the instrument has a volume of 10 liters, therefore at usual flow rates of 20 liters per minute it takes 30 seconds to exchange the aerosol sample. Therefore, we have usually collected data at 36 or 12 seconds intervals. The measurement frequency was 12 seconds when the instrument only employed a single wavelength, for example during the Deep Convective Clouds and Chemistry (DC3) field campaign in 2012. Longer exposure times reduce the number of acquired images, reducing the volume of image data that must be stored and analyzed. Figure 6 shows the external structure of the PI-Neph instrument, with the locations of the inlet and outlet, and the figure locates the sample chamber, laser module, camera, and electronics box. The PI-Neph is a modular instrument, the backbone is the sample chamber, and the laser module and the electronics box attach to it. The scattering chamber houses all the components inside the pressure boundary in Fig. 4 and the M4 mirror. During airborne deployments, the PI-Neph is sampling through an inlet that is specially engineered pipe, which draws aerosol laden ambient air from outside the aircraft. The sample air is at ambient pressure, which can be less than half of sea level pressure during high legs of a flight. On

#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21981

aircrafts, the PI-Neph is inside the fuselage at cabin pressure, which typically is at 80% or more of sea level pressure, therefore the sample chamber has to be pressure tight. The laser module houses the multi-wavelength lasers, the polarization control optics, and a power reference photodiode. Dimensions are in millimeters in panel (a). Panel (b) shows the PINeph installed on the NASA DC8 aircraft next to TSI integrating nephelometers, before the SEAC4RS (Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys) field mission.

Fig. 6. Panel (a) shows the drawing of the external structure of the instrument. Dimensions are in millimeters. The photo in panel (b) shows the PI-Neph inside the DC8 aircraft at the NASA Dryden Aircraft Operations Facility, August 2013.

4. Validation and errors of P11 and –P12/P11 data products The raw data from the photodiodes, the temperature and pressure sensors, and the camera require substantial post-processing. We independently and mechanically measure the scattering angle, the scattering plane rotation angle of Fig. (1), and the laser beam polarizations (with a Thorlabs PAX5710VIS-T polarimeter). Then we model the expected signal via Eq. (1) for Rayleigh scattering gases, air and CO2. The model input Rayleigh scattering properties follow the review of Hansen and Travis [12], with scattering coefficients interpolated to the PI-Neph wavelengths from Anderson et al. [42]. Due to its configuration, the PI-Neph does not measure phase matrix elements other than P11 and P12; therefore, only the scattered irradiance is modeled at this stage in the data reduction. The measured signals for particle free air and CO2 establish a linear relationship between the image data illustrated in Fig. 3 and the model of the scattered irradiance based on Eq. (1) and (2), at each scattering angle. The offsets of the linear fits between the image signal and modeled scattered irradiances are very small and consistent, on the level of a few percent of the air signal, and mostly eliminate stray light. Slopes of the fits calibrate for lens transmission at different incidence angles. We call this procedure the Rayleigh calibration; the results are fixed for a particular alignment or campaign data set. Rayleigh calibration linear fits, polarimetric, and angle calibration data allow the reduction of image data (sum of carrier air and aerosol data), illustrated by profiles of PS

#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21982

image data in Fig. 3. Subsequent subtraction of modeled signal contribution of carrier air yields aerosol parameters (βsca·P11) and (βsca·P12) We obtain the scattering coefficient βsca by extrapolating (βsca·P11)to the unmeasured scattering angles with a nearest neighbor method, and using the normalization condition for the integral of P11 over 4·π steradians [12]. In order to estimate the angular truncation related error in βsca, we consider the usual situation of sampling through the aircraft inlet employed by the LARGE group (Langley Aerosol Research Group Experiment), which has a particle size cutoff around 5μm diameter [36,37]. We used a Mie code [13] to estimate the truncation error in the specific case of a monomodal modified lognormal size distribution with rg = 2.00 μm and σg = 1.62, rg and σg are defined in chapter 5.10.1 of [13]. This size distribution has a surface weighed diameter mean and standard deviation of 3.56μm and 1.82μm, respectively. We computed the phase functions for refractive indices on (nr, ni) grid points with nr = (1.4, 1.6, 1.8) and ni = (0.001, 0.01, 0.1), where nr and ni are the real and imaginary part of the refractive index. Resulting truncation error estimates for the PI-Neph angular range of 3° to 176° were between 4.4% and 8.4%. For submicron particles, truncation error will be significantly smaller. We expect negligible truncation errors in the future by fitting (βsca·P11) directly with scattering models. Truncation error does not affect the shape of derived P11. The data product –P12/P11 is the ratio of –(βsca·P12) and (βsca·P11), therefore, truncation error in βsca does not influence it. We call the resulting P11 and –P12/P11 as initial data products. In order to gain confidence in the data reduction procedure and the instrument, we measured spherical artificial aerosols and compared the data to Mie simulations. During the DC3 campaign, the PI-Neph was integrated to the NASA DC8 aircraft, together with the suite of instrument of the LARGE group. Using the aerosol nebulizer in the LARGE suite, we collected 10 minutes of data on PS spheres suspended in clear air. The manufacturer of the PS solution, Thermo Scientific Inc., specifies the mean diameter of the size distribution to be 903 ± 12 nm (two sigma confidence level), NIST traceable. The manufacturer gives the size distribution full width at the 67th percentile (FW67, two standard deviations) as 8.2nm, not NIST traceable. Figure 7 shows the time average of the PS data over 10 minutes. P11 and –P12/P11 are independent scattering properties of the aerosols. We built a lookup table of Mie scattering phase matrix elements using our Matlab wrapper to the [13] Mie code over a grid of varied mean diameters and FW67. The imaginary refractive index of PS spheres was set to the value measured by Ma et al. [43], while for the real part we used the bulk value measured by Kasarova et al. [44]. We have confidence in applying the bulk dispersion formula of real refractive index to small particles, because it agrees within the measurement errors with measurements on PS spheres by Marx and Mulholland [27] at 441.6nm laser wavelength, for particles with 300nm diameter or larger. The mean diameter and FW67 ranges were first set to (903–65, 903 + 65) and (6, 46), respectively and measured in nm. The grid was 81 x 81 points in size. We computed the residuals between the Mie simulations for each grid point and the averaged PS initial data. We made separate residual maps for P11 and –P12/P11. Both residual maps showed clear global minima, very close to the manufacturer specified parameters. We checked the results with a finer grid of mean diameters and FW67 between (903–12, 903 + 12) and (2, 14), respectively and measured in nm, and found very closely the same results. The results of the finer grid are showed on Fig. 7, the fit to only P11 (red line) is able to reproduce the pattern of the –P12/P11 data. The fit to only –P12/P11 (black dashed line) is able to reproduce the pattern of the P11 data. The two matrix elements therefore are consistent measurements of the aerosol. Additionally, the initial data products and Mie fits result in size distribution parameters of PS spheres that are consistent between the two fits and the specification of the manufacturer. For a population of 59 measurements and corresponding fits, uncertainties given in Table 1

#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21983

are population standard deviations, the precision of the measurement. Due to the lack of sensitivity to FW67 in noisy data, for the FW67 result Table 1, we filtered 27 outlier cases of P11 and 20 of –P12/P11 measurements that resulted in either lower than 2nm or higher than 14nm full width. These points are also more than two standard deviations away from the mean of the rest of the time series in FW67. In all 59 cases there was a much higher sensitivity to the central diameter than to FW67, we found no outliers in central diameter. Table 1. Size Distribution Fit Results for Polystyrene Spheres central diameter [nm] FW67, full width, 67th percentile [nm]

Manufacturer 903 ± 12 8.2

fit to P11 904.4 ± 1.4 8.0 ± 3.4

fit to –P12/P11 903.5 ± 1.0 9.6 ± 2.6

The agreement of retrieval results within uncertainties in Table 1 supports that PI-Neph measurements of independent particle parameters, P11 and –P12/P11, are consistent. Further measurements of other test particles and natural aerosols, and numerical studies will be necessary to quantify and attribute accuracy of particle size, and refractive index retrievals to measurement errors, which is possible, based on prior experience [15,27,30,45,46].

Fig. 7. Measured initial P11 and –P12/P11 data products (10-minute average of 59 samples) for PS spheres are the green circles. Panel (a) shows P11, while panel (b) shows –P12/P11 data. Time averages of best fitting Mie simulations selected from a lookup table are the red solid and black dashed lines, representing the mean of fits to P11 only, and the mean of fits to –P12/P11 only, respectively.

#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21984

The data reduction that produced initial P11 and –P12/P11 did not use the full aerosol phase matrix. We devised an improved data reduction procedure that starts from raw aerosol and calibration data and incorporates the Mie fits presented in Fig. 7, and employs a more detailed model of the instrument. This results in improved agreement of the data product and its Mie fit beyond that of the initial data in Fig. 7. The improved data reduction takes into account all polarimetric effects, including the full phase matrix of the aerosols, and of the Rayleigh scattering gases, and the calibration measurement of the Mueller matrix of the lens and CCD. In order to be able to apply the detailed polarimetric model (second order effects) of the instrument, it is necessary to obtain the full aerosol phase matrix to the first order. In case of the PI-Neph, fitting a scattering model to the initial P11 and –P12/P11 data products must provide the full phase matrix. In case of PS data, the Mie fit of Fig. 7 to the initial data products provides the unmeasured elements of the aerosol phase matrix with sufficient accuracy. In addition, we reevaluate the Rayleigh calibration parameters with the lens and CCD Mueller matrix. Then a modified data reduction takes into account the unmeasured aerosol phase matrix elements from the Mie fit as corrections, to obtain the final aerosol data products for P11 and –P12/P11, plotted in Fig. 8. The same routine that reevaluates the calibration and incorporates the Mie fit of unmeasured phase matrix elements is the tool to estimate calibration uncertainties. A Monte Carlo simulation takes into account errors stemming from: 1. Rayleigh calibration measurements of gases, 2. laser polarization and angle calibration measurements, 3. measurements of the Mueller matrix of the lens and CCD, 4. modeling of scattering coefficients of gases (related to temperature, pressure and photodiode data, laser power stability), 5. uncertainties in the Rayleigh scattering depolarization parameter [12], 6. uncertainty of the Mie fit that provides the unmeasured phase matrix elements of the aerosol (PS in this case). Products of the Monte Carlo simulation are the systematic i.e. calibration errors (Δsys) of P11 and –P12/P11, stemming from all quantified calibration uncertainties. Additionally, we derived the covariance matrices of P11 and –P12/P11, CV1sys and CV2sys, due to systematic errors. In the Monte Carlo simulation, we used a population of 104 data instances, with randomly varied calibration errors. Resulting systematic errors showed less than 1% relative change upon increasing the population size to 105. Calibration parameters are fixed during a particular measurement; therefore, systematic errors do not manifest in temporal variations of P11 and –P12/P11. Next, we revisit the Mie fit. We derive the covariance matrices of P11 and –P12/P11 PS sphere data due to random errors, CV1r and CV2r, from the population of 59 subsequent measurements. Then the full covariance matrix is the sum of random measurement error and systematic error terms: CV1 = CV1r + CV1sys, CV2 = CV2r + CV2sys. However, in case of P11 data, the covariance matrix was ill conditioned even after screening at slightly stray light contaminated scattering angles, therefore we achieved stable fits by using only the diagonal of the covariance matrix. χ2 of –P12/P11 defined with the only the diagonal versus the full covariance matrix yielded 30% lower residuals, which are between P11 data and the prediction of P11 by the –P12/P11 fit. Therefore, in both cases we only used the diagonal elements of the covariance matrices. We calculated lookup tables of χ2 versus central diameter and FW67 at each temporal sample, on the same finer grid as when fitting the initial data. Global minima of monotonic χ2 at each time point gave the Mie fits. After a first round of fitting, we eliminated both angular and temporal points where the absolute value of residuals was above

#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21985

the mean by 1.5 times the standard deviation. The second round fitting provided the results in Fig. 8, representing 50 temporal samples. Figure 8 shows the temporal mean and standard deviation of the mean, for both the fit to P11 data and to –P12/P11 data. Both fits resulted in an estimate of the other quantity, for example the fit to P11 predicts a –P12/P11. Figure 8 also gives 95% confidence intervals for the final data products for P11 and –P12/P11 due to random errors (blue dashed lines) and total errors (green ribbon, both random and systematic errors). The mean of measurements (P11 and –P12/P11) and the mean Mie fits agree at nearly all scattering angles within their 95% confidence intervals. Residuals between Mie fit and PS data (angular mean and population standard deviation) are: 1. P11 data versus P11 of fit to –P12/P11 (relative residuals): –0.015 ± 0.055 2. –P12/P11 data versus –P12/P11 of fit to P11 (absolute residuals): 0.018 ± 0.056

Fig. 8. P11 and –P12/P11 data are in panels (a) and (b), respectively. Blue dashed lines are above and below the mean of final PS data by two standard deviations of the mean, σD (59 samples), showing the extent of random errors. Systematic (calibration) error of PS data is Δsys. The green ribbon is centered on the mean of final PS data, it shows the extent of random and systematic measurement errors. The largely overlapping red and black lines are fits to P11 and –P12/P11, respectively. The pink and grey ribbons show the standard deviations of the mean of the Mie fits, σM1 or σM2 (50 samples); the ribbons closely follow the Mie fits and are only clearly visible in –P12/P11.

#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21986

The angular statistics of total measurement errors (calibration and random errors) are: 1. P11 (relative total error): 0.028 ± 0.015 2. –P12/P11 (absolute total error): 0.046 ± 0.034 The residual levels agree with total error at aerosol loading, or scattering coefficient of 300 Mm−1 of the measurement, this gives confidence in the Monte Carlo model of systematic error. In Fig. 8, in panel (a), there are two Mie P11 curves, one derived by fitting to P11 data, the other by fitting to –P12/P11 data, but they largely overlap, so only the top red curve is visible (the fit to P11). In the same way, there are two –P12/P11 fit curves in panel (b), and they overlap. Agreement between the two fits to the final data products and the similar agreement between the two fits to the initial data products show that peculiarities of data evaluation methods do not play a role in proving the consistency of P11 and –P12/P11 data products. The small difference between the final PS data in Fig. 8 and the initial PS data in Fig. 7, expressed as angular average and standard deviation: 1. Final minus initial P11, divided by final P11, vs. scattering angle: –0.0072 ± 0.0395. 2. Final minus initial –P12/P11 vs. scattering angle: 0.0364 ± 0.0358. The difference of final and initial data, i.e. with polarimetric or only radiometric detection is on the order of the systematic error estimated for the final data. Therefore, the initial data is a reliable approximation, and it will enable microphysical fits. Upon measuring ambient aerosol, the systematic error of PI-Neph data will depend primarily on aerosol loading, and on the aerosol type, i.e. angular patterns of P11 and –P12/P11. However, we use the error model to give a rough estimate of expected calibration errors at other aerosol loadings, using PS aerosol characteristics. It will be possible to study performance in case of other aerosol types. The temporal average value of ground scattering coefficient in the eastern continental USA is approximately 100 Mm−1, in the western part it is between 15 and 40 Mm−1 [47,48], in Saharan dust clouds it can be over 100 Mm−1 [37], and in case of Chinese urban pollution 300 Mm−1 is possible [49]. At aerosol scattering coefficients of 100 and 30 Mm−1, we estimate the angular average calibration uncertainty of the PI-Neph, assuming 903 nm diameter PS spherical aerosol, respectively: 1. relative systematic error of phase functions (P11): 0.023 and 0.068, 2. absolute systematic error of polarized phase functions (–P12/P11): 0.033 and 0.079. As the aerosol loading decreases, the relative weight of subtracted signal contribution of carrier air increases, while the modeled relative error stays the same. This effect contributes most to increasing calibration error with decreasing aerosol loading. At 100 Mm−1 the averaging time required to obtain random error values similar to the systematic error will be on the order of minutes. The resulting accuracy of PI-Neph measurements will be sufficient for sensitivity to variations in particle morphology and shape, in addition to size and refractive index, based on simulations in [14,46]. Stray light errors are not included in the calibration error estimates. The forward scattering peak and the small deviations from the Mie fit at troughs near 70° and 100° scattering angle resemble the multiple scattering contributions simulated in [50]. Scattering simulation errors due to polystyrene refractive index uncertainty, deviation from spherical shape, presence of dimers [51], or the potential presence of residual water droplets past the drier were not included in the derivation of systematic errors, and should be quantified in future studies.

#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21987

We quantify the accuracy of the angle calibration by comparing the angular location of maxima and minima in the PS data (θPS) and the Mie fit (θMie). The average of θPS – θMie differences is –0.22°, the population standard deviation of 19 data points is 0.83°. 5. An airborne measurement example The following measurements are from the DC3 field campaign, based in Salina, KS, during May and June of 2012. The PI-Neph flew in the cabin of the NASA DC8 aircraft, in a manner similar to the SEAC4RS integration in Fig. 6. The PI-Neph sampled ambient air through the inlet installed by the LARGE group [36,37], and a temperature-controlled drier, ensuring that relative humidity was always below 40%. The data examples of Fig. 9 are from flights over the state of Colorado, and they illustrate the capability of the PI-Neph to measure ambient levels of aerosols. Calibration procedures and parameters were the same as for the initial data products, such as the PS data in Fig. 7, since the PS data was taken on 6/18/2012.

Fig. 9. Airborne measurements of ambient aerosol P11 and –P12/P11 are in panels (a) and (b), respectively. These are examples from the Deep Convective Clouds and Chemistry campaign, from two flights over the state of Colorado, demonstrating the capability of the PI-Neph to measure at ambient scattering coefficient, βsca, levels. Measurements of phase functions have low enough random errors that make the cases from 6/15 and 6/22 distinguishable. The random errors given for asymmetry parameters, g, are the population standard deviations. Assuming the dominant factor in variability of g is instrumental noise, the resulting standard deviations of the means for the two cases are: 0.0023 and 0.0017.

#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21988

Ambient aerosols have much lower concentration and thus scattering coefficient, βsca, than the artificially nebulized PS spheres. The ranges of scattering coefficients on Fig. 9, panel (a) are due to natural variability and measurement uncertainty. The range limits are one population standard deviation below and above the mean. Natural variability was likely negligible in the asymmetry parameter, g, defined in [13], since the observed variability was random, without a significant trend. Therefore, the mean g values are given with population standard deviation as uncertainties. The two cases highlight the sensitivity of the PI-Neph to slight variations in phase function, while show the larger errors in polarized phase function. The phase functions are clearly distinguishable in a statistically significant way, while the polarized phase functions are similar, within their random errors. Further studies, like the work of Boesche et al. [46], will be necessary to establish the achievable accuracies of retrieved microphysical parameters. The random errors in g are remarkably low. Assuming that the variability is from instrumental random errors, while the physical aerosol is uniform, gives us an upper bound on the random error in the asymmetry parameter. In the first case from 6/15/2012, to calculate the standard deviation of the mean, σm, from the standard deviation of the population, we have to divide by the square root of the number of samples, 77. The result is σm = 0.0023. In the second case from 6/22/2012, the resulting standard deviation of the mean asymmetry parameter is σm = 0.0017. In case of the 6/15/2012 data set, one measurement of P11 and –P12/P11 was removed, since it was deemed an outlier due to its unique asymmetry parameter of 0.386, which is more than ten population standard deviations below the mean of the rest of the time series. During DC3, the PI-Neph only measured at a laser wavelength of 532nm. In a way similar to the three wavelength scheme of Fig. 5, the measurement scheme involved three repeated polarization pairs, but at a single wavelength. Out of the three experimental polarization pairs, one provided a significantly smaller systematic error in –P12/P11 than the other two, due to it consisting of polarizations closer to being perpendicular to or parallel to the scattering plane. Accurate measurement of the scattering plane rotation angle, of polarization, acquisition and fabrication of related tools, and software development were required to shed light on the specific ways instrument parameters affect systematic errors. In later field campaigns, we only used this optimal polarization pair. However, in DC3, we filtered out those –P12/P11 measurements that correspond to less optimal polarization pairs. The polarization pairs not optimal for –P12/P11 still yielded useful P11 measurements, therefore only the corresponding –P12/P11 data was filtered. Therefore, the number of samples in the –P12/P11 measurements of Fig. 9 panel (b) are lower than the respective number of P11 samples in panel (a), by nearly a factor of three. Therefore, in future measurements under the same conditions, the uncertainty of the mean of –P12/P11 is expected to be lower by a factor of 3 . In Fig. 9, the data from 6/22/2012 was measured with the optimal polarization pair, while the data from 6/15/2012 with a sub-optimal pair, which resulted in higher noise, but still produced a measurement. Future work will provide microphysical retrievals by fitting Mie or spheroid phase matrices to the PI-Neph data. That will enable refinement of initial data (assuming scattered irradiance is proportional image signal), such as in Fig. 9, to produce final data, taking into account the full phase matrix of aerosols and Mueller matrix of the lens and CCD. The promising aspect of the PI-Neph is that the difference between PS data in Fig. 7 (initial) and Fig. 8 (final) is small enough to raise confidence in initial data of aerosol measurements, and to allow a single step correction. 6. Conclusion We presented the Polarized Imaging Nephelometer instrument, designed and built at the Laboratory for Aerosols, Clouds, and Optics (LACO) at the University of Maryland,

#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21989

Baltimore County (UMBC). We summarized the measurement approach and the instrument operation. Measurements of polystyrene sphere phase functions (P11) and polarized phase functions (–P12/P11) compare exceptionally well with fitted Mie simulations. At an ambient aerosol scattering coefficient of 100 Mm−1, the PI-Neph is expected to measure P11 with relative systematic error of approximately 2.3%, and to measure –P12/P11 with absolute systematic error of approximately 0.033. Future work will document details of calibration and data processing. We demonstrated the capability of the PI-Neph to measure ambient levels of aerosols, by examples from flights over Colorado from the Deep Convective Clouds and Chemistry campaign, in June 2012. It is our expectation that geophysical results from PINeph field measurements will enable tests of scattering models and provide comprehensive insights on the scattering properties of ambient aerosols. In cases when the sampling inlet effects are minimal, the PI-Neph data products are expected to be helpful in constraining radiative transfer models and aid in calibration and validation of satellite remote sensing. Acknowledgments Reed Espinosa from UMBC has been very helpful in streamlining the data reduction program, while working on data sets of SEAC4RS and DISCOVER-AQ (Deriving Information on Surface Conditions from Column and Vertically Resolved Observations Relevant to Air Quality). The team members of LACO at UMBC have been essential in fabrication, integration and testing of the PI-Neph instrument. The principal investigator, Johnathan Hair, and all members of the DEVOTE project (Development and Evaluation of Satellite ValidatiOn Tools by Experimenters), and the LARGE group at NASA, particularly Luke Ziemba, Andreas Beyersdorf, and Bruce Anderson, and James Crawford, the principal investigator of DISCOVER-AQ, are gratefully acknowledged for their extensive support in flying the PI-Neph. The DEVOTE project also funded the initial development of the PI-Neph. NASA Headquarters, under the NASA Earth and Space Science Fellowship Program, Grant NNX-10AN85H, supports Gergely Dolgos. We acknowledge funding support from the NASA Glory Mission Project and the SEAC4RS Mission, both administered by Hal Maring. We are grateful to all those who made the DC3 field campaign possible, in particular to the principal investigators Mary Barth, Christopher Cantrell, Steven Rutledge, and William Brune.

#214519 - $15.00 USD Received 23 Jun 2014; revised 24 Aug 2014; accepted 25 Aug 2014; published 3 Sep 2014 (C) 2014 OSA 8 September 2014 | Vol. 22, No. 18 | DOI:10.1364/OE.22.021972 | OPTICS EXPRESS 21990