The skylight degree of linear polarization (DoLP) was previously shown to vary primarily with aerosol optical depth and underlying surface reflectance for visible-to-near-infrared (VNIR) wavelengths. This paper extends the study of skylight polarization to 2.5 μm in the short-wave infrared (SWIR). A successive-orders-of-scattering radiative transfer code was used to model skylight polarization with measured inputs that included aerosol properties retrieved from a ground-based solar radiometer (extrapolated into the SWIR) and spectral surface reflectance from a handheld spectrometer. The modeled DoLP depended heavily on the aerosol size distribution at SWIR wavelengths and on the aerosol optical depth at VNIR wavelengths. Once the aerosol optical depth became greater than the Rayleigh optical depth, the predicted polarization deviated significantly from Rayleigh scattering theory. The SWIR polarization spectrum generally decreased at wavelengths beyond 1 μm at a rate dependent on the aerosol size distribution. The surface reflectance affected the polarization in the same manner throughout the visible (VIS)–SWIR spectrum, with higher reflectance decreasing the skylight polarization. Validation measurements of SWIR skylight polarization in a 1.5–1.8 μm band are also shown. These measurements were made on clean and smoky days using a SWIR imaging polarimeter. In both simulations and measurements, the SWIR skylight polarization was greater in the smoky atmosphere than in the clean atmosphere.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The added dimension of polarization in remote sensing  is being increasingly used in applications that include aerosol and cloud measurements [2–12], ocean sensing [13–21], surveillance [22–24], navigation [25–28], telescope calibration [29,30], and exoplanet detection [31–33]. This has increased the need for information about sky polarization, including its spectral distribution. Visible (VIS) and long-wave infrared (LWIR) polarimeters have been used widely in these studies, but short-wave infrared (SWIR) polarimeters are now increasingly being used to take advantage of improving detector quantum efficiency and dark current for applications such as enhanced long-range visibility, haze penetration, forest fire monitoring, and low-light night imaging [34–37]. Therefore, a more complete understanding of how skylight polarization changes from the VIS-to-SWIR is needed.
In cloud-free environments, skylight polarization in the visible-to-near-infrared (VNIR) spectral region depends on atmospheric aerosols, wavelength, underlying surface reflectance, and solar elevation angle [38–41]. Atmospheric scattering is a significant source of skylight polarization in the VIS-to-SWIR, whereas in the LWIR, thermal emission dominates and atmospheric radiation is randomly polarized [14,15,42]. Molecular scattering in the visible (VIS) spectrum can be described with Rayleigh scattering theory, which for a single scattering event predicts 100% linearly polarized light at angles 90° from the sun, with a polarization vector oriented orthogonal to the scattering plane (defined by the incident and scattered rays). Across the VIS spectrum, the degree of polarization for Rayleigh-scattered skylight generally increases with wavelength since the scattered radiance is inversely proportional to the fourth power of the wavelength, reducing multiple scattering at longer wavelengths. However, larger aerosols and multiple scattering tend to decrease skylight polarization. Clouds also reduce skylight polarization , but this study is focused on how aerosols alter the polarization spectrum in cloud-free skies.
By using a measurement-driven successive orders of scattering (SOS) radiative transfer model , validated with an all-sky imaging polarimeter , Pust and Shaw  found skylight polarization to vary over the VNIR spectrum in a complex but predictable manner that depended on aerosol and surface properties. They also observed discontinuities in the skylight polarization spectrum at gaseous absorption lines, consistent with previous reports [2,3]. However, that study was limited to wavelengths below 1 μm by a lack of long-wavelength surface reflectance data, and the individual contributions of aerosol content and surface reflectance were also not determined.
In this paper, we have expanded our previous modeling efforts [41,44,45] to explore how maximum skylight polarization varies independently with aerosols and surface reflectance, from the VIS to the SWIR. We explored realistic environments using our previously validated model with measurements of aerosol parameters and surface reflectance. We also varied the aerosol optical depth, aerosol size distribution, aerosol refractive index, and surface reflectance independently. In some cases, one or more of these parameters was fixed to a constant value to gain insight into how skylight polarization is affected by individual aerosol and surface reflectance properties. In Section 2 we outline our modeling methods, in Section 3 we discuss how maximum skylight polarization changes with different aerosol and surface reflectance parameters, in Section 4 we show preliminary validation measurements, and in Section 5 we offer conclusions.
2. MODELING METHODS
A. Model Overview
We modeled the VIS–SWIR skylight polarization spectrum using Lenoble’s SOS radiative transfer model  embedded within a Matlab code . The model was modified to include spectral extrapolations of aerosol properties retrieved from an Aerosol Robotic Network (AERONET) ground-based solar radiometer [46,47] and surface reflectance spectra from a handheld spectrometer. Our measurements were taken in Bozeman, Montana (45.7°N, 111.0°W; elevation 1507 m).
We used aerosol data from a clean atmosphere on 19 October 2014, a moderately hazy atmosphere on 18 August 2014, and a smoky atmosphere on 3 August 2014. For visual reference, Fig. 1 shows aerial photographs of Bozeman on days similar to the clean and smoky atmospheric cases. For consistency, the modeled solar zenith and azimuth angles were kept constant at 49° and 118°, respectively, matching our chosen reference measurement time of 18 August 2014 at 16:34:22 (UTC). An aerosol scattering phase matrix, which describes the changes of direction, intensity, and polarization of a light beam caused by a single scattering event, was computed for spherical particles using a Mie code , and the aerosol refractive index and volume size distribution were obtained from AERONET retrievals . Molecular absorption spectra were obtained from standard-atmosphere transmission calculated with MODTRAN5  for aerosol-free and cloud-free environments. An outline of our model is shown in Fig. 2.
To retrieve the VIS–SWIR skylight polarization, the model computed a Stokes vector containing the four Stokes parameters , , , and , where is the total radiance, is the difference between the 0° and 90° linearly polarized components, is the difference between the and linearly polarized components, and is the difference between right- and left-hand circularly polarized components (in our calculations, 0° represented a linear polarizer orientated orthogonal to the scattering plane defined by the incident and scattered rays). The Stokes parameters were used to calculate the degree of linear polarization (DoLP):
B. Molecular Absorption Parameters Simulated with MODTRAN
The molecular optical depth and the molecular single-scattering albedo were found using MODTRAN atmospheric transmission models. The 1976 U. S. standard atmosphere containing no aerosols or clouds was simulated using MODTRAN default constituents (nitrogen, oxygen, ozone, nitrogen dioxide, etc.) and AERONET-retrieved precipitable water vapor and ozone. The molecular optical depth was calculated as the log of the atmospheric transmission spectrum (Fig. 3).
The molecular single-scattering albedo was calculated as the Rayleigh optical depth divided by the molecular optical depth. The atmospheric absorption bands in the SWIR spectral range were mainly from water vapor (), and Fig. 4 shows some isolated atmospheric absorption bands from 0.35 to 2.5 μm. The vertical extinction distribution was exponential with an 8 km scale height.
C. Aerosol Parameters Retrieved from AERONET
The aerosol, Rayleigh, and total optical depths were retrieved using the AERONET ground-based solar radiometer located in Bozeman. The optical depth quantifies the path-integrated extinction by aerosol and gaseous scattering and absorption, as described by the Beer–Bouguer–Lambert law describing zenith atmospheric transmission,
The solar radiometer measured optical depths at wavelengths of 0.340, 0.380, 0.440, 0.500, 0.675, 0.870, 1.020, and 1.640 μm. To model skylight polarization out to 2.5 μm, optical depths were extrapolated using Angstrom’s turbidity formula . The Angstrom exponent,47]. The particles residing in the accumulation mode are from primary emissions created from forest fires, automobiles, and power plants. The particles in the coarse mode are produced by mechanical processes, such as wind or erosion, which stir up dust and pollens. The fine and coarse effective radii were 0.155 and 3.164 μm for the smoke-filled day, 0.154 and 2.341 μm for the moderately hazy day, and 0.146 and 1.754 μm for the clean day.
To reach out to 2.5 μm, the aerosol real refractive index was also extrapolated with a linear fit. The extrapolated real refractive index increased slightly with wavelength for smoky days and decreased slightly with wavelength for clean and hazy days, which matches the trends in . Beyond 2.5 μm, the aerosol refractive index begins to fluctuate significantly from rotational and vibrational absorption bands, which, if not modeled correctly, would lead to variations in the refractive index and errors in the modeled DoLP. Because the imaginary index extrapolation produced unrealistic negative values, we used the imaginary refractive indices at 1.018 μm for all longer wavelengths, which were 0.015 for the clean day, 0.011 for the moderately hazy day, and 0.010 for the smoke-filled day.
Figures 5–7 show the aerosol optical depth, index of refraction, and volume size distribution used in the model for the clean atmosphere on 19 October 2014, moderately hazy atmosphere on 18 August 2014, and smoky atmosphere on 3 August 2014, respectively. To resolve the line structure of molecular absorption, the aerosol optical depth and refractive index were interpolated to have a spectral resolution of 0.012 nm, matching the MODTRAN spectral transmission. However, to reduce the computation time by a significant amount, linear interpolation was performed with a spectral resolution of 1 nm for most simulations. In this approach, no major differences were observed outside the atmospheric absorptions bands.
D. Measured Surface Reflectance Spectra
A handheld portable spectrometer was used to measure surface reflectance spectra from 0.4 to 2.5 μm. Surface parameters were interpolated across strong atmospheric absorption features where accurate measurements could not be obtained. The surface was modeled as a uniformly reflective Lambertian surface. A more exact approach would take viewing geometries and the bidirectional reflectance distribution function (BRDF) into account; however, we focused on the general trend of skylight polarization with Lambertian surface reflectance.
3. MODELED VIS–SWIR SKYLIGHT POLARIZATION
To study the amount by which aerosol and surface reflectance parameters contribute individually to skylight polarization across the VIS–SWIR spectrum, we explored a variety of environments containing both measured and fixed surface parameters with constant aerosols, and a variety of environments containing both measured and fixed aerosol parameters with no surface reflectance. The subsection titles reflect which parameters were changed in the model at each step in the study. Unless stated otherwise, measured aerosol parameters (optical depth, size distribution, and refractive index) from the moderately hazy atmosphere on 18 August 2014 were used as input parameters, with solar zenith and azimuth angles of 49° and 118°, respectively. Input parameters are given in the corresponding figure captions, as well. All curves are shown for the maximum DoLP, which occurred between scattering angles of 86° and 106°.
A. Realistic Environments with Measured Aerosol Parameters and Surface Reflectance
In our first simulation (Fig. 8), we compared three models that included measured aerosol parameters from the clean, moderately hazy, and smoke-filled atmospheres using measured green grass surface reflectance (a comparison with no surface reflectance is given in Fig. 9). Input parameters were interpolated to match the MODTRAN transmission spectra with finer spectral resolution in Fig. 8. In this realistic simulation, we observed the skylight polarization spectra to be different in the VIS and SWIR. Maximum DoLP in the VIS occurred on the clean day, while maximum DoLP in the SWIR occurred on the smoky day. The primary feature attributed to the green grass surface reflectance in Fig. 8 is the drop in DoLP near the 0.7 μm wavelength, which arises because of the increased multiple scattering caused by the sharp increase of surface reflectance [40,41]; however, the variation among the three curves suggests that further investigation would be required to understand more completely how skylight polarization is affected separately by aerosols and surface reflectance. Such further study is described in the next sections.
B. Environments with Constant Aerosols and Fixed Surface Reflectance
In this part of the study we turned our attention to the question of how maximum SWIR skylight polarization changes with the underlying surface reflectance. For each model, the surface reflectance was spectrally fixed and the aerosol parameters remained constant. For the remainder of this paper, input parameters were spectrally interpolated with 1 nm resolution, limiting the amount of modeled DoLP detail observed in the absorption bands near 1.38, 1.88, and 2.4 μm (gaps in Fig. 10 and future figures occur where water vapor absorption is high). This made the spectral resolution coarser, but did not change the modeled DoLP results outside the absorption bands.
Figure 10 shows how skylight polarization changed when surface reflectance was fixed at 0%, 10%, 50%, 90%, and 100% at all wavelengths (100% represents a white surface and 0% represents a black surface). These results show that a highly reflective surface resulted in reduced sky polarization and vice versa (across the VIS–SWIR spectrum) because of the increased amount of randomly or differently polarized light contributed by the surface reflection [the primary effect of which is to increase the denominator in Eq. (1)]. This agrees with our previous findings for the VIS-NIR [40,41] but extends the result to say that the underlying surface reflectance has a similar effect on skylight polarization from the VIS through the SWIR spectral range.
C. Environments with Constant Aerosols and Measured Surface Reflectance
Realistic surfaces generally do not have spectrally constant reflectance; therefore, this section of the study looks at how skylight polarization changed with different types of surfaces. We used a handheld spectrometer to measure VIS–SWIR reflectance spectra for green grass and sand surfaces. The measured reflectance spectra and constant aerosols from the clean day on 19 October 2014 were used as model input parameters to produce Fig. 11.
Spectral features in the surface reflectance create differences in the skylight polarization spectrum, as can be seen specifically with green grass in Fig. 11. For green vegetation, the absorption bands of chlorophyll are responsible for the low reflectance  in the VIS spectrum, which results in small amounts of upwelling surface-reflected light to alter the skylight polarization. Near the red edge at approximately 0.7 μm, a sharp increase in surface reflectance results in a rapid decrease of DoLP. Absorption by liquid water in the leaves causes changes in reflectance at wavelengths beyond , leading to opposite effects in the SWIR DoLP. The sand surface reflectance increased from the VIS to SWIR, leading to a continual decay of DoLP with wavelength.
D. Environments with Fixed Aerosol Parameters and Zero Surface Reflectance
Surface reflectance was shown to change the maximum DoLP and to create similar characteristics within each spectrum of the realistic environments (Section 3.A). In this section we focused on the effects of varying aerosols by exploring a variety of environments containing both measured and fixed aerosol parameters with no surface reflectance.
1. No Aerosols: Rayleigh Scattering Case
An atmosphere with pure Rayleigh scattering produces high DoLP values at angles 90° from the sun, and an atmosphere with nearly pure Rayleigh scattering has been shown to exhibit polarization that increases with wavelength across the VIS spectrum [38,41]. This is because scattering is inversely proportional to the inverse fourth power of the wavelength, which increases multiple scattering at shorter wavelengths. To model a Rayleigh atmosphere, the aerosol optical depth was fixed to for all wavelengths, making it essentially zero. In this model, surface reflectance also was set to zero.
For the simulated Rayleigh environment (with aerosol optical depth much smaller than the Rayleigh optical depth), the maximum DoLP increased with wavelength to an upper limit of 95% (Fig. 12). The polarization rise in Fig. 12 is caused by the decreasing effect of multiple scattering as wavelength increases, while the flattening at long wavelengths is because of asymmetries in the shapes of the scattering molecules [54–57].
2. Spectrally Fixed Aerosol Optical Depths
Our next step was to look at what happens to skylight polarization in the VIS–SWIR spectrum when the fixed aerosol optical depth increased. All-sky polarimeter observations  and simulations in the VIS spectrum [41,44] have found that the increased multiple scattering causes skylight polarization to decrease when the aerosol optical depth increases. In this study, simulations were run with the aerosol optical depth spectrally fixed to 0.001, 0.1, and 1.0.
Skylight polarization at all modeled wavelengths decreased when the aerosol optical depth increased in this simulation (Fig. 13). An interesting feature of the spectra in Fig. 13 is that skylight polarization decayed with wavelength between approximately 1.5 and 2.5 μm, even for the very clean atmosphere with an aerosol optical depth of 0.001. The difference between this simulation and the previous one (Fig. 12) is that, in Fig. 13, the aerosol optical depth was greater than the Rayleigh optical depth at SWIR wavelengths. Under this condition, aerosol scattering dominated, and skylight polarization decreased at all longer wavelengths.
3. Spectrally Fixed Aerosol Optical Depth with Different Aerosol Size Distributions
Expanding upon the previous section, here we explore how skylight DoLP changed when a fixed aerosol optical depth () was combined with the AERONET-retrieved aerosol volume size distributions for the clean day (19 October 2014), moderately hazy day (18 August 2014), and the smoky day (3 August 2014). In Fig. 14 we see how the maximum DoLP varied with the aerosol volume size distribution for a fixed aerosol optical depth. It is important to observe that, while the polarization falls off at longer wavelengths because the aerosol optical depth is greater than the SWIR Rayleigh optical depth, it does so at different rates that are controlled by the size distribution. A particularly surprising example was that the DoLP curve for the smoky atmosphere remained higher than the others, which appears to be a result of the very different aerosol size distributions. Most of the particles on the smoky day were found within the accumulation (fine) mode of the volume distribution plot of Fig. 7, indicating that these particles had a much smaller scattering cross section than the predominantly larger particles (coarse mode) that were present on the other days. This shows that small smoke aerosols can be highly polarizing.
E. Environments with Measured Aerosols and Zero Surface Reflectance
To observe skylight polarization trends in the SWIR with completely realistic aerosol parameters, but in the absence of surface reflection effects, we next changed our model to incorporate extrapolated AERONET-retrieved aerosol optical depths rather than fixed values. This portion of the study emphasizes variations of skylight polarization with aerosol optical depth, aerosol volume size distribution, and aerosol index of refraction.
1. Measured Aerosol Optical Depth and Refractive Index Paired with Different Aerosol Size Distributions
In this section, we simulated nine different environments using actual AERONET-retrieved aerosol properties. To compare how the aerosol volume size distribution influences skylight polarization in the SWIR, the measured aerosol optical depths and refractive indices from each day were fixed and paired respectively with the three aerosol size distributions from the smoke-filled, moderately hazy, and clean days.
With different combinations of aerosol parameters used in the simulations, common skylight polarization trends were observed in Fig. 15. For example, skylight polarization in the VIS spectrum was distinctly related to the aerosol optical depth, with the aerosol parameters from the clean day producing the greatest DoLP. Conversely, in the SWIR, skylight polarization depended primarily on the aerosol size distribution, as indicated by the separation in DoLP curves and the smoky aerosols giving rise to the greatest modeled maximum DoLP.
To further analyze skylight polarization in the SWIR, Fig. 16 shows the spectral scattering cross section and phase matrix element (at a 90° scattering angle) from the clean, moderately hazy, and smoke-filled days. Both the scattering cross section and phase matrix element vary spectrally. The element generates scattering from randomly polarized radiation into the linear polarization states described by the Stokes parameter. Figure 16 indicates that the modeled SWIR DoLP in Fig. 15 was greatest for environments simulated with smoky aerosol volume size distributions as a result of the accumulation-mode particles (smoke) having a smaller scattering cross section than the larger particles on the clean and moderately hazy days (Fig. 16). This caused the smoke particles to become more Rayleigh-like (and therefore more polarizing) as wavelength increased.
2. Measured Aerosol Optical Depth and Volume Size Distribution Paired with Different Aerosol Indices of Refraction
In this section, we looked at how sky polarization varies with aerosol index of refraction. Aerosol parameters from 18 August 2014 were paired with different aerosol refractive indices from the clean, hazy, and smoke-filled environments. The maximum modeled skylight polarization (Fig. 17) was similar for all three sets of refractive indices, with slight differences observed throughout the spectrum. Although skylight polarization depends on the aerosol index of refraction, from these simulations we can conclude that the aerosol index of refraction did not create the differences observed between the realistic environments in Fig. 8.
The overall general trend observed in this comprehensive aerosol study shows skylight polarization in the VIS to depend primarily on the aerosol optical depth, whereas skylight polarization in the SWIR depends primarily on the aerosol volume size distribution and aerosol scattering cross sections (Figs. 15 and 16). When modeling or interpreting skylight polarization in the VIS–SWIR, it is important to understand how different aerosols contribute to the overall polarization signature.
4. VALIDATION MEASUREMENTS
Our modeled results showed that spectral patterns of skylight polarization existed from the VIS to the SWIR and that SWIR polarization was greater for smoky air than for clean air. The latter was a surprising result, and in this section we describe the use of a SWIR rotating polarimeter (Polaris Sensor Technologies, Huntsville, Alabama), shown in Fig. 18, to measure skylight polarization in a single band from 1.5 to 1.8 μm to validate our modeling efforts. We measured clean-sky polarization on 28 April 2015 at 16:18 (UTC) and a sky containing thick wildfire smoke on 20 August 2015 at 19:57 (UTC) in Bozeman, Montana (45.7°N, 111.0°W; elevation 1507 m). The passive polarimeter captured radiance images  at 0°, 45°, 90°, and 135° sequentially in time through a polarizer rotating continuously at a spin rate of 60 revolutions per second. A non-uniformity correction was applied to the measured images and a post-processing algorithm was used to compute a Stokes vector representing the polarization state and the DoLP for each pixel in the image.
For comparing measured and modeled results, the maximum DoLP for each day was calculated using the AERONET-retrieved aerosol optical depth, size distribution, and refractive index as inputs to the SOS model. The aerosol optical depths, volume size distributions, and indices of refraction from 28 April 2015 and 20 August 2015 are shown in Figs. 19–21, respectively. Thick wildfire smoke was observed on 20 August 2015, resulting in the large aerosol optical depth shown in Fig. 19.
The surface was modeled with a green-grass reflectance spectrum measured with a handheld spectrometer (Fig. 22). The adequacy of this simple approach is indicated by the excellent agreement between this spectrum and the average reflectance measured in the MODIS 1.628–1.652 μm band, also plotted on Fig. 22 for 28 April, 29 April, 1 August, 19 August, and 20 August (all dates in the year 2015). The MODIS surface reflectance measurements were spatially averaged over a radius of 50 km from our measurement site.
A. Measured Skylight Polarization with Simulated Fisheye Models
The field of view of the SWIR polarimeter was 9.1° wide by 7.3° high. The instrument could not be pointed at elevation angles larger than approximately 30° because of the liquid-nitrogen-cooled focal plane array. This meant that we could not make measurements exactly at the point of maximum DoLP. Therefore, to align our measurement locations with the simulated results, we used an image of a grid pattern to map the angles of each pixel in the SWIR polarimetric images. The reference horizon was taken as the roofline in the reference images. To aid visualization and interpretation of our measured and simulated results, we also created simulated fisheye all-sky images of the polarization across the entire sky, averaged over the 1.5–1.8 μm SWIR polarimeter band. The top of each fisheye image represents north and the right side represents east.
1. Clear-Sky Measurement
On 28 April 2015 we measured skylight polarization on a mostly clear day with a few small clouds near the horizon. A reference image of our measurement is given in Fig. 23, where the instrument was looking northeast with the sun behind and to the right of the imager. The solar azimuth and elevation angles were 114° and 41°, respectively. The maximum band of polarization was centered at an azimuth angle of 294°, approximately 49° above the horizon. In the simulation, the clean-air maximum DoLP varied between 17% and 27% across the validation measurement band of 1.5–1.8 μm. The simulated band-averaged DoLP in a 1.5–1.8 μm rectangular bandpass was 21% (Fig. 24).
The top image of Fig. 25 is the actual SWIR DoLP measurement, which shows the skylight DoLP decreasing top-down from 13% to 8%. The polarimeter’s field of view covered elevation angles from 9.1° to 1.8° with respect to the horizon, and in between these angles the DoLP was modeled to be approximately 8%. The modeled data averaged over 1.5–1.8 μm are represented in the bottom fisheye image of Fig. 25. The red arrow indicates the viewing direction of the polarimeter.
2. Smoky Sky Measurement
A sky filled with thick wildfire smoke was measured on 20 August 2015. A reference image of our measurement is shown in Fig. 26. The polarimeter was directed northwest with the sun to the left of the imager. The solar azimuth and elevation angles were 193° and 56°, respectively. The maximum band of polarization was centered at an azimuth angle of 13°, approximately 34° from the horizon. Across the spectral band of 1.5–1.8 μm where our SWIR validation measurements were made, the maximum DoLP for the smoky atmosphere simulations varied between 45% and 54%, with a band-average value of 48% (Fig. 24).
In the top image of Fig. 27, the skylight DoLP was observed to decrease top-down from 45% to 36%, approximately 22° to 15° above the horizon. The modeled DoLP was 46%–44% between these angles. A simulated all-sky fisheye DoLP image averaged over the 1.5–1.8 μm band is shown in the bottom of Fig. 27. The red arrow indicates the viewing direction of the polarimeter.
For both clean and smoky situations, our measurements and simulations agreed to within the measurement and modeling uncertainties, indicating that as the aerosol optical depth becomes greater than the Rayleigh optical depth, changes in the SWIR skylight polarization are driven primarily by the aerosol volume size distribution and scattering cross sections. Because of this, the smoky atmosphere was found to have higher DoLP than a clean atmosphere in both simulation and measurement.
This study provides insight into how aerosol and surface parameters separately and together control skylight polarization in the VIS to SWIR spectral range (0.35–2.5 μm). Once the aerosol optical depth became greater than the Rayleigh optical depth, the degree of linear polarization in the SWIR spectrum was found to depend strongly on the aerosol size distribution, whereas the VIS polarization depended most strongly on the aerosol optical depth. Most of the particles on the smoke-filled day were found within the accumulation mode of the volume distribution plot (Fig. 3), indicating that these smaller and more polarizing particles had a much smaller scattering cross section than the predominantly larger particles found on the clear day. The surface reflectance spectrum influenced skylight polarization in the same manner from the VIS through the SWIR, with a higher surface reflectance decreasing the sky polarization. Measurements of skylight polarization made on a clean day and a smoky day were used to verify that the degree of linear polarization in the SWIR spectrum was indeed higher for smoky air than for clean air.
Additional refinements in future studies could include considering both spherical and non-spherical particles, more complete models of aerosol complex refractive index, and more realistic models of surface BRDF. For simplicity, the current model uses only Mie scattering with spherical particles; however, real aerosols are generally aspheric, and a more accurate model of the real atmospheric environment could result from this modification.
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