Abstract

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

1. INTRODUCTION

The added dimension of polarization in remote sensing [1] is being increasingly used in applications that include aerosol and cloud measurements [212], ocean sensing [1321], surveillance [2224], navigation [2528], telescope calibration [29,30], and exoplanet detection [3133]. 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 [3437]. 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 [3841]. 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 [8], 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 [43], validated with an all-sky imaging polarimeter [44], Pust and Shaw [41] 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 [43] embedded within a Matlab code [45]. 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 [48], and the aerosol refractive index and volume size distribution were obtained from AERONET retrievals [49]. Molecular absorption spectra were obtained from standard-atmosphere transmission calculated with MODTRAN5 [50] for aerosol-free and cloud-free environments. An outline of our model is shown in Fig. 2.

 

Fig. 1. Photographs from 20 October 2014 and 10 August 2014, showing conditions similar to the “clean” (top) and “smoky” (bottom) aerosol cases, respectively. For the modeled smoky case on 3 August 2014, there would have been significantly more haze, as the aerosol content was higher (500 nm AOD of 1.03, compared with 0.3 on 10 August).

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Fig. 2. Outline of the radiative transfer model used to determine the DoLP for skylight viewed from the ground. The input parameters included AERONET aerosol parameters, MODTRAN transmission spectra, and measured surface reflectance spectra.

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To retrieve the VIS–SWIR skylight polarization, the model computed a Stokes vector S containing the four Stokes parameters S0, S1, S2, and S3, where S0 is the total radiance, S1 is the difference between the 0° and 90° linearly polarized components, S2 is the difference between the +45° and 45° linearly polarized components, and S3 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):

DoLP=S12+S22S0,
which expresses the fraction of the total radiance that is linearly polarized. In our study, the maximum DoLP occurred at scattering angles varying between 86° and 106°. As the wavelength increased from 0.35 to 2.5 μm, the maximum DoLP generally occurred at larger scattering angles.

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).

 

Fig. 3. MODTRAN simulated transmission spectrum for a zenith path through the 1976 U. S. Standard Atmosphere with no aerosols or clouds on 18 August 2014.

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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 (H2O), 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.

 

Fig. 4. MODTRAN simulation of molecular absorption bands for an atmosphere containing no aerosols or clouds.

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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,

T=e(τaer+τray+τmol),
where τaer is the aerosol optical depth, τray is the Rayleigh scattering optical depth, and τmol is the molecular absorption optical depth.

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 [51]. The Angstrom exponent,

α=ln(τ1τ2)ln(λ1λ2),
describes the linear slope of a log–log plot of optical depths measured at two wavelengths, in this case 1.020 and 1.640 μm. The calculated exponent was then used to calculate the optical depth at 2.5 μm from the value at 1.640 μm using Angstrom’s turbidity formula,
τλ=τ0(λλ0)α.
The aerosol volume size distribution and complex refractive indices were obtained from AERONET inversion algorithms for wavelengths of 0.440, 0.675, 0.871, and 1.018 μm. AERONET provides the columnar volume size distribution for particles measured in the entire air column (from the ground at 0 to the top of the atmosphere, effectively infinity). The aerosol size distribution contains two modes: the accumulation mode for particles with radius <0.6  μm and the coarse mode for particles with radius >0.6  μm [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 [52]. 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 57 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.

 

Fig. 5. Interpolated and extrapolated AERONET Rayleigh optical depths and aerosol optical depths for a clean atmosphere on 19 October 2014, a moderately hazy atmosphere on 18 August 2014, and a smoky atmosphere on 3 August 2014.

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Fig. 6. Interpolated AERONET complex indices of refraction for a clean atmosphere on 19 October 2014, a moderately hazy atmosphere on 18 August 2014, and a smoky atmosphere on 3 August 2014.

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Fig. 7. AERONET-retrieved aerosol volume size distributions (dV(r)/dln(r) [μm3/μm2]) for a clean atmosphere on 19 October 2014, a moderately hazy atmosphere on 18 August 2014, and a smoky atmosphere on 3 August 2014.

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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.

 

Fig. 8. Maximum skylight DoLP modeled using full measured aerosol parameters with green grass surface reflectance.

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Fig. 9. Maximum skylight DoLP modeled for the three test days using full measured aerosol parameters and zero surface reflectance.

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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.

 

Fig. 10. Maximum skylight DoLP modeled with five different spectrally constant surface reflectance values and measured aerosol parameters from 18 August 2014. Skylight polarization over the entire VIS–SWIR spectrum has a similar spectral shape for the different surface reflectance values.

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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.

 

Fig. 11. Green grass and sand surface reflectance measurements with their corresponding modeled maximum skylight DoLP. For green vegetation, the absorption bands of chlorophyll are responsible for low reflectance values in the VIS spectrum, leading to a higher polarization.

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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 [53] 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 λ=1.3  μm, 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 106 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 [5457].

 

Fig. 12. Modeled maximum skylight degree of linear polarization for a Rayleigh scattering environment with the aerosol optical depth spectrally fixed to 106 (essentially zero) and with zero surface reflectance. With no aerosols, maximum skylight polarization in the SWIR reached an upper limit of 95%.

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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 [58] 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.

 

Fig. 13. Modeled maximum skylight DoLP for three different values of spectrally fixed aerosol optical depth (τaer) with zero surface reflectance and AERONET data products (Rayleigh optical depth, aerosol volume size distribution, and aerosol index of refraction) from 18 August 2014. In the SWIR, with the aerosol optical depth greater than the Rayleigh optical depth, the skylight polarization decreased with wavelength.

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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 (τaer=0.001) 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.

 

Fig. 14. Modeled maximum skylight DoLP for a constant aerosol optical depth (τaer=0.001) greater than the SWIR Rayleigh optical depth, paired with different AERONET-retrieved aerosol volume size distributions from three varying environments: a clean atmosphere on 19 October 2014, a moderately hazy atmosphere on 18 August 2014, and a smoke-filled atmosphere on 3 August 2014.

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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.

 

Fig. 15. Maximum skylight DoLP modeled using AERONET-retrieved aerosol optical depths and index of refraction with zero surface reflectance for different volume size distributions.

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To further analyze skylight polarization in the SWIR, Fig. 16 shows the spectral scattering cross section and phase matrix P12 element (at a 90° scattering angle) from the clean, moderately hazy, and smoke-filled days. Both the scattering cross section and phase matrix P12 element vary spectrally. The P12 element generates scattering from randomly polarized radiation into the linear polarization states described by the S1 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.

 

Fig. 16. Spectral scattering cross section and the phase matrix P12 element from each day.

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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.

 

Fig. 17. Maximum skylight DoLP modeled with the aerosol optical depth and volume size distribution from 18 August 2014 paired with the different AERONET-retrieved refractive indices for the three test days.

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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 [W/(m2sr)] 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.

 

Fig. 18. SWIR rotating-polarizer imaging polarimeter.

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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. 1921, respectively. Thick wildfire smoke was observed on 20 August 2015, resulting in the large aerosol optical depth shown in Fig. 19.

 

Fig. 19. Interpolated and extrapolated AERONET aerosol optical depths for a clean atmosphere on 28 April 2015 and a smoky atmosphere on 20 August 2015.

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Fig. 20. AERONET-retrieved aerosol volume size distributions (dV(r)/dln(r) [μm3/μm2]) for a clean atmosphere on 28 April 2015 and a smoky atmosphere on 20 August 2015.

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Fig. 21. Interpolated AERONET complex indices of refraction for a clean atmosphere on 28 April 2015 and a smoky atmosphere on 20 August 2015.

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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.

 

Fig. 22. Measured green grass spectra and MODIS-retrieved surface reflectance in the 1.628–1.652 μm band and spatially averaged over a circle of 50 km radius centered on our observation site.

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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).

 

Fig. 23. Reference image of our measurement on 28 April 2015. The solar azimuth and elevation angles were 114° and 41°, respectively.

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Fig. 24. SOS modeled maximum skylight polarization across the 1.5–1.8 μm validation band for a clean sky on 28 April 2015 and a sky containing thick wildfire smoke on 20 August 2015.

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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.

 

Fig. 25. (Top) Measured DoLP on 28 April 2015. Skylight polarization was measured to decrease top-down from 13% to 8%. (Bottom) Fisheye modeled maximum DoLP dependence averaged over 1.5–1.8 μm. The red arrow indicates the polarimeter pointing direction, where the modeled maximum polarization was 8%.

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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).

 

Fig. 26. Reference image of our measurement on 20 August 2015. The solar azimuth and elevation angles were 193° and 56°, respectively.

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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.

 

Fig. 27. (Top) Measured DoLP on 20 August 2015. Skylight DoLP was measured to decrease top-down from 45% to 36%. (Bottom) Simulated all-sky fisheye DoLP image averaged over 1.5–1.8 μm. Across the band of maximum polarization, the modeled DoLP ranged from 45% to 54%, with a band-average value of 48%. The red arrow indicates the portion of sky the polarimeter was viewing, in which the modeled polarization was 46%–44%.

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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.

5. CONCLUSION

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.

Funding

Air Force Office of Scientific Research (AFOSR) (FA9550-14-1-0140).

Acknowledgment

The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Research Laboratory or the U.S. Government.

REFERENCES

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2. I. Aben, F. Helderman, D. M. Stam, and P. Stammes, “Spectral fine structure in the polarisation of skylight,” Geophys. Res. Lett. 26, 591–594 (1999). [CrossRef]  

3. D. M. Stam, J. F. De Haan, and J. W. Hovenier, “Degree of linear polarization of light emerging from the cloudless atmosphere in the oxygen A band,” J. Geophys. Res. 104, 16843–16858 (1999). [CrossRef]  

4. M. Herman, J. L. Deuzé, A. Marchand, B. Roger, and P. Lallart, “Aerosol remote sensing from POLDER/ADEOS over the ocean: improved retrieval using a nonspherical particle model,” J. Geophys. Res. 110, D10S02 (2005). [CrossRef]  

5. E. Bosche, P. Stammes, T. Ruhtz, R. Preusker, and J. Fischer, “Effect of aerosol microphysical properties on polarization of skylight: sensitivity study and measurements,” Appl. Opt. 45, 8790–8805 (2006). [CrossRef]  

6. Z. Li, P. Goloub, C. Devaux, X. Gu, J. Deuzé, Y. Qiao, and F. Zhao, “Retrieval of aerosol optical and physical properties from ground-based spectral, multi-angular, and polarized sun-photometer measurements,” Remote Sens. Environ. 101, 519–533 (2006). [CrossRef]  

7. D. J. Diner, A. Davis, B. Hancock, G. Gutt, R. A. Chipman, and B. Cairns, “Dual-photoelastic-modulator-based polarimetric imaging concept for aerosol remote sensing,” Appl. Opt. 46, 8428–8445 (2007). [CrossRef]  

8. N. J. Pust and J. A. Shaw, “Digital all-sky polarization imaging of partly cloudy skies,” Appl. Opt. 47, H190–H198 (2008). [CrossRef]  

9. F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. I. Mischenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206 (2009). [CrossRef]  

10. G. van Harten, J. de Boer, J. H. H. Rietjens, F. Snik, A. Di Noia, O. P. Hasekamp, J. Vonk, H. Volten, J. M. Smit, J. S. Henzing, and C. U. Keller, “Atmospheric aerosol characterization with a ground-based SPEX spectropolarimetric instrument,” Atmos. Meas. Tech. 7, 4341–4351 (2014). [CrossRef]  

11. K. Knobelspiesse, B. van Diedenhoven, A. Marshak, S. Dunagan, B. Holben, and I. Slutsker, “Cloud thermodynamic phase detection with polarimetrically sensitive passive sky radiometers,” Atmos. Meas. Tech. 8, 1537–1554 (2015). [CrossRef]  

12. L. M. Dahl, M. J. Tauc, and J. A. Shaw, “Cloud thermodynamic phase detection using an all-sky imaging polarimeter,” Proc. SPIE 10407, 104070O (2017). [CrossRef]  

13. F. J. Iannarilli, J. A. Shaw, S. H. Jones, and H. E. Scott, “Snapshot LWIR hyperspectral polarimetric imager for ocean surface sensing,” Proc. SPIE 4133, 270–283 (2000). [CrossRef]  

14. J. A. Shaw, “Degree of linear polarization in spectral radiances from water-viewing infrared radiometers,” Appl. Opt. 38, 3157–3165 (1999). [CrossRef]  

15. J. A. Shaw, “Polarimetric measurements of long-wave infrared spectral radiance from water,” Appl. Opt. 40, 5985–5990 (2001). [CrossRef]  

16. M. Chami, “Importance of the polarization in the retrieval of oceanic constituents from the remote sensing reflectance,” J. Geophys. Res. 112, C05026 (2007). [CrossRef]  

17. C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19, 055503 (2008). [CrossRef]  

18. J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, and H. Schultz, “Wave slope measurement using imaging polarimetry,” Proc. SPIE 7317, 73170B (2009). [CrossRef]  

19. K. J. Voss and N. Souaidia, “POLRADS: polarization radiance distribution measurement system,” Opt. Express 18, 19672–19680 (2010). [CrossRef]  

20. P. Bhandari, K. J. Voss, and L. Logan, “An instrument to measure the downwelling polarized radiance distribution in the ocean,” Opt. Express 19, 17609–17620 (2011). [CrossRef]  

21. B. A. Hooper, B. Van Pelt, J. Z. Williams, J. P. Dugan, M. Yi, C. C. Piotrowski, and C. Miskey, “Airborne spectral polarimeter for ocean wave research,” J. Atmos. Ocean. Technol. 32, 805–815 (2015). [CrossRef]  

22. F. Goudail, P. Terrier, Y. Takakura, L. Bigué, F. Galland, and V. DeVlaminck, “Target detection with a liquid-crystal-based passive Stokes polarimeter,” Appl. Opt. 43, 274–282 (2004). [CrossRef]  

23. S. Lin, K. M. Yemelyanov, E. N. Pugh, and N. Engheta, “Polarization enhanced visual surveillance techniques,” in IEEE International Conference on Networking, Sensing and Control (2004), Vol. 1, pp. 216–221.

24. D. A. Lavigne, M. Breton, G. Fournier, J. M. Charette, V. Rivet, and A. Bernier, “Target discrimination of man-made objects using passive polarimetric signatures acquired in the visible and infrared spectral bands,” Proc. SPIE 8160, 816007 (2011). [CrossRef]  

25. D. Lambrinos, M. Maris, H. Kobayashi, T. Labhart, R. Pfeifer, and R. Wehner, “An autonomous agent navigating with a polarized light compass,” Adapt. Behav. 6, 131–161 (1997). [CrossRef]  

26. J. Chu, K. Zhao, Q. Zhang, and T. Wang, “Construction and performance test of a novel polarization sensor for navigation,” Sens. Actuators A 148, 75–82 (2008). [CrossRef]  

27. S. B. Karman, S. Z. M. Diah, and I. C. Gebeshuber, “Bio-inspired polarized skylight-based navigation sensor: a review,” Sensors 12, 14232–14261 (2012). [CrossRef]  

28. T. Aycock, A. Lompado, T. Wolz, and D. Chenault, “Passive optical sensing of atmospheric polarization for GPS denied operations,” Proc. SPIE 9838, 98380Y (2016). [CrossRef]  

29. D. M. Harrington, J. R. Kuhn, and S. Hall, “Deriving telescope Mueller matrices using daytime sky polarization observations,” Publ. Astron. Soc. Pac. 123, 799–811 (2011). [CrossRef]  

30. D. M. Harrington, J. R. Kuhn, and A. L. Ariste, “Daytime sky polarization calibration limitations,” Proc. SPIE 9912, 99126S (2016). [CrossRef]  

31. D. M. Stam, “Spectropolarimetric signatures of Earth-like extrasolar planets,” Astron. Astrophys. 482, 989–1007 (2008). [CrossRef]  

32. C. U. Keller, H. M. Schmid, L. B. Venema, H. Hanenburg, R. Jager, M. Kasper, P. Martinez, F. Rigal, M. Rodenhuis, R. Roelfsema, F. Snik, C. Verninaud, and N. Yaitskova, “EPOL: the exoplanet polarimeter for EPICS at the E-ELT,” in Ground-based and Airborne Instrumentation for Astronomy III (SPIE, 2010), Vol. 7735, paper 77356G.

33. M. F. Sterzik, S. Bagnulo, and E. Palle, “Biosignatures as revealed by spectropolarimetry of Earthshine,” Nature 483, 64–66 (2012). [CrossRef]  

34. M. A. Miller, R. V. Blumer, and J. D. Howe, “Active and passive SWIR imaging polarimetry,” Proc. SPIE 4481, 87–99 (2011). [CrossRef]  

35. R. G. Driggers, V. Hodgkin, and R. Vollmerhausen, “What good is SWIR? Passive day comparison of VIS, NIR, and SWIR,” Proc. SPIE 8706, 87060L (2013). [CrossRef]  

36. M. P. Hansen and D. S. Malchow, “Overview of SWIR detectors, cameras, and applications,” Proc. SPIE 6939, 69390I (2008). [CrossRef]  

37. B. Stark, M. McGee, and Y. Chen, “Short wave infrared (SWIR) imaging systems using small Unmanned Aerial Systems (sUAS),” in International Conference on Unmanned Aircraft Systems (ICUAS) (2015), pp. 495–501.

38. K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak, 1988).

39. A. Kreuter, C. Emde, and M. Blumthaler, “Measuring the influence of aerosols and albedo on sky polarization,” Atmos. Res. 98, 363–367 (2010). [CrossRef]  

40. A. Dahlberg, N. J. Pust, and J. A. Shaw, “Effects of surface reflectance on skylight polarization measurements at the Mauna Loa Observatory,” Opt. Express 19, 16008–16021 (2011). [CrossRef]  

41. N. J. Pust and J. A. Shaw, “Wavelength dependence of the degree of polarization in cloud-free skies: simulations of real environments,” Opt. Express 20, 15559–15568 (2012). [CrossRef]  

42. J. A. Shaw, “Infrared polarization in the natural earth environment,” Proc. SPIE 4819, 129–138 (2002). [CrossRef]  

43. J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007). [CrossRef]  

44. N. J. Pust, A. Dahlberg, M. Thomas, and J. A. Shaw, “Comparison of full-sky polarization and radiance observations to radiative transfer simulations which employ AERONET products,” Opt. Express 19, 18602–18613 (2011). [CrossRef]  

45. L. M. Dahl and J. A. Shaw, “Visible-to-SWIR wavelength variation of skylight polarization,” Proc. SPIE 9613, 96130P (2015). [CrossRef]  

46. B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998). [CrossRef]  

47. Bozeman AERONET Site, https://aeronet.gsfc.nasa.gov/.

48. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

49. O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements,” J. Geophys. Res. 105, 20673–20696 (2000). [CrossRef]  

50. A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Godlen, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, “MODTRAN5: 2006 update,” Proc. SPIE 6233, 508–515 (2006). [CrossRef]  

51. A. Ångström, “The parameters of atmospheric turbidity,” Tellus 16, 64–75 (1964).

52. E. P. Shettle and R. W. Fenn, “Models for the aerosols for the lower atmosphere and the effects of humidity variations on their optical properties,” Environmental Research Papers, AFGL-TR-79-0214, No. 676 (1979).

53. J. R. Jensen, Remote Sensing of the Environment: An Earth Resource Perspective (Pearson, 2006).

54. D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32, 785–790 (1984). [CrossRef]  

55. J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41(271), 107–120 (1871). [CrossRef]  

56. L. Rayleigh, “On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue sky,” Philos. Mag. 47(287), 375–384 (1899). [CrossRef]  

57. J. Lenoble, “Scattering and polarization of the solar radiation in the Earth’s atmosphere: historical review and present applications,” in AIP Conference Proceedings (2009), pp. 7–10.

58. N. J. Pust and J. A. Shaw, “Dual-field imaging polarimeter using liquid crystal variable retarders,” Appl. Opt. 45, 5470–5478 (2006). [CrossRef]  

References

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  • |

  1. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
    [Crossref]
  2. I. Aben, F. Helderman, D. M. Stam, and P. Stammes, “Spectral fine structure in the polarisation of skylight,” Geophys. Res. Lett. 26, 591–594 (1999).
    [Crossref]
  3. D. M. Stam, J. F. De Haan, and J. W. Hovenier, “Degree of linear polarization of light emerging from the cloudless atmosphere in the oxygen A band,” J. Geophys. Res. 104, 16843–16858 (1999).
    [Crossref]
  4. M. Herman, J. L. Deuzé, A. Marchand, B. Roger, and P. Lallart, “Aerosol remote sensing from POLDER/ADEOS over the ocean: improved retrieval using a nonspherical particle model,” J. Geophys. Res. 110, D10S02 (2005).
    [Crossref]
  5. E. Bosche, P. Stammes, T. Ruhtz, R. Preusker, and J. Fischer, “Effect of aerosol microphysical properties on polarization of skylight: sensitivity study and measurements,” Appl. Opt. 45, 8790–8805 (2006).
    [Crossref]
  6. Z. Li, P. Goloub, C. Devaux, X. Gu, J. Deuzé, Y. Qiao, and F. Zhao, “Retrieval of aerosol optical and physical properties from ground-based spectral, multi-angular, and polarized sun-photometer measurements,” Remote Sens. Environ. 101, 519–533 (2006).
    [Crossref]
  7. D. J. Diner, A. Davis, B. Hancock, G. Gutt, R. A. Chipman, and B. Cairns, “Dual-photoelastic-modulator-based polarimetric imaging concept for aerosol remote sensing,” Appl. Opt. 46, 8428–8445 (2007).
    [Crossref]
  8. N. J. Pust and J. A. Shaw, “Digital all-sky polarization imaging of partly cloudy skies,” Appl. Opt. 47, H190–H198 (2008).
    [Crossref]
  9. F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. I. Mischenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206 (2009).
    [Crossref]
  10. G. van Harten, J. de Boer, J. H. H. Rietjens, F. Snik, A. Di Noia, O. P. Hasekamp, J. Vonk, H. Volten, J. M. Smit, J. S. Henzing, and C. U. Keller, “Atmospheric aerosol characterization with a ground-based SPEX spectropolarimetric instrument,” Atmos. Meas. Tech. 7, 4341–4351 (2014).
    [Crossref]
  11. K. Knobelspiesse, B. van Diedenhoven, A. Marshak, S. Dunagan, B. Holben, and I. Slutsker, “Cloud thermodynamic phase detection with polarimetrically sensitive passive sky radiometers,” Atmos. Meas. Tech. 8, 1537–1554 (2015).
    [Crossref]
  12. L. M. Dahl, M. J. Tauc, and J. A. Shaw, “Cloud thermodynamic phase detection using an all-sky imaging polarimeter,” Proc. SPIE 10407, 104070O (2017).
    [Crossref]
  13. F. J. Iannarilli, J. A. Shaw, S. H. Jones, and H. E. Scott, “Snapshot LWIR hyperspectral polarimetric imager for ocean surface sensing,” Proc. SPIE 4133, 270–283 (2000).
    [Crossref]
  14. J. A. Shaw, “Degree of linear polarization in spectral radiances from water-viewing infrared radiometers,” Appl. Opt. 38, 3157–3165 (1999).
    [Crossref]
  15. J. A. Shaw, “Polarimetric measurements of long-wave infrared spectral radiance from water,” Appl. Opt. 40, 5985–5990 (2001).
    [Crossref]
  16. M. Chami, “Importance of the polarization in the retrieval of oceanic constituents from the remote sensing reflectance,” J. Geophys. Res. 112, C05026 (2007).
    [Crossref]
  17. C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19, 055503 (2008).
    [Crossref]
  18. J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, and H. Schultz, “Wave slope measurement using imaging polarimetry,” Proc. SPIE 7317, 73170B (2009).
    [Crossref]
  19. K. J. Voss and N. Souaidia, “POLRADS: polarization radiance distribution measurement system,” Opt. Express 18, 19672–19680 (2010).
    [Crossref]
  20. P. Bhandari, K. J. Voss, and L. Logan, “An instrument to measure the downwelling polarized radiance distribution in the ocean,” Opt. Express 19, 17609–17620 (2011).
    [Crossref]
  21. B. A. Hooper, B. Van Pelt, J. Z. Williams, J. P. Dugan, M. Yi, C. C. Piotrowski, and C. Miskey, “Airborne spectral polarimeter for ocean wave research,” J. Atmos. Ocean. Technol. 32, 805–815 (2015).
    [Crossref]
  22. F. Goudail, P. Terrier, Y. Takakura, L. Bigué, F. Galland, and V. DeVlaminck, “Target detection with a liquid-crystal-based passive Stokes polarimeter,” Appl. Opt. 43, 274–282 (2004).
    [Crossref]
  23. S. Lin, K. M. Yemelyanov, E. N. Pugh, and N. Engheta, “Polarization enhanced visual surveillance techniques,” in IEEE International Conference on Networking, Sensing and Control (2004), Vol. 1, pp. 216–221.
  24. D. A. Lavigne, M. Breton, G. Fournier, J. M. Charette, V. Rivet, and A. Bernier, “Target discrimination of man-made objects using passive polarimetric signatures acquired in the visible and infrared spectral bands,” Proc. SPIE 8160, 816007 (2011).
    [Crossref]
  25. D. Lambrinos, M. Maris, H. Kobayashi, T. Labhart, R. Pfeifer, and R. Wehner, “An autonomous agent navigating with a polarized light compass,” Adapt. Behav. 6, 131–161 (1997).
    [Crossref]
  26. J. Chu, K. Zhao, Q. Zhang, and T. Wang, “Construction and performance test of a novel polarization sensor for navigation,” Sens. Actuators A 148, 75–82 (2008).
    [Crossref]
  27. S. B. Karman, S. Z. M. Diah, and I. C. Gebeshuber, “Bio-inspired polarized skylight-based navigation sensor: a review,” Sensors 12, 14232–14261 (2012).
    [Crossref]
  28. T. Aycock, A. Lompado, T. Wolz, and D. Chenault, “Passive optical sensing of atmospheric polarization for GPS denied operations,” Proc. SPIE 9838, 98380Y (2016).
    [Crossref]
  29. D. M. Harrington, J. R. Kuhn, and S. Hall, “Deriving telescope Mueller matrices using daytime sky polarization observations,” Publ. Astron. Soc. Pac. 123, 799–811 (2011).
    [Crossref]
  30. D. M. Harrington, J. R. Kuhn, and A. L. Ariste, “Daytime sky polarization calibration limitations,” Proc. SPIE 9912, 99126S (2016).
    [Crossref]
  31. D. M. Stam, “Spectropolarimetric signatures of Earth-like extrasolar planets,” Astron. Astrophys. 482, 989–1007 (2008).
    [Crossref]
  32. C. U. Keller, H. M. Schmid, L. B. Venema, H. Hanenburg, R. Jager, M. Kasper, P. Martinez, F. Rigal, M. Rodenhuis, R. Roelfsema, F. Snik, C. Verninaud, and N. Yaitskova, “EPOL: the exoplanet polarimeter for EPICS at the E-ELT,” in Ground-based and Airborne Instrumentation for Astronomy III (SPIE, 2010), Vol. 7735, paper 77356G.
  33. M. F. Sterzik, S. Bagnulo, and E. Palle, “Biosignatures as revealed by spectropolarimetry of Earthshine,” Nature 483, 64–66 (2012).
    [Crossref]
  34. M. A. Miller, R. V. Blumer, and J. D. Howe, “Active and passive SWIR imaging polarimetry,” Proc. SPIE 4481, 87–99 (2011).
    [Crossref]
  35. R. G. Driggers, V. Hodgkin, and R. Vollmerhausen, “What good is SWIR? Passive day comparison of VIS, NIR, and SWIR,” Proc. SPIE 8706, 87060L (2013).
    [Crossref]
  36. M. P. Hansen and D. S. Malchow, “Overview of SWIR detectors, cameras, and applications,” Proc. SPIE 6939, 69390I (2008).
    [Crossref]
  37. B. Stark, M. McGee, and Y. Chen, “Short wave infrared (SWIR) imaging systems using small Unmanned Aerial Systems (sUAS),” in International Conference on Unmanned Aircraft Systems (ICUAS) (2015), pp. 495–501.
  38. K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak, 1988).
  39. A. Kreuter, C. Emde, and M. Blumthaler, “Measuring the influence of aerosols and albedo on sky polarization,” Atmos. Res. 98, 363–367 (2010).
    [Crossref]
  40. A. Dahlberg, N. J. Pust, and J. A. Shaw, “Effects of surface reflectance on skylight polarization measurements at the Mauna Loa Observatory,” Opt. Express 19, 16008–16021 (2011).
    [Crossref]
  41. N. J. Pust and J. A. Shaw, “Wavelength dependence of the degree of polarization in cloud-free skies: simulations of real environments,” Opt. Express 20, 15559–15568 (2012).
    [Crossref]
  42. J. A. Shaw, “Infrared polarization in the natural earth environment,” Proc. SPIE 4819, 129–138 (2002).
    [Crossref]
  43. J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007).
    [Crossref]
  44. N. J. Pust, A. Dahlberg, M. Thomas, and J. A. Shaw, “Comparison of full-sky polarization and radiance observations to radiative transfer simulations which employ AERONET products,” Opt. Express 19, 18602–18613 (2011).
    [Crossref]
  45. L. M. Dahl and J. A. Shaw, “Visible-to-SWIR wavelength variation of skylight polarization,” Proc. SPIE 9613, 96130P (2015).
    [Crossref]
  46. B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
    [Crossref]
  47. Bozeman AERONET Site, https://aeronet.gsfc.nasa.gov/ .
  48. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  49. O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements,” J. Geophys. Res. 105, 20673–20696 (2000).
    [Crossref]
  50. A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Godlen, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, “MODTRAN5: 2006 update,” Proc. SPIE 6233, 508–515 (2006).
    [Crossref]
  51. A. Ångström, “The parameters of atmospheric turbidity,” Tellus 16, 64–75 (1964).
  52. E. P. Shettle and R. W. Fenn, “Models for the aerosols for the lower atmosphere and the effects of humidity variations on their optical properties,” (1979).
  53. J. R. Jensen, Remote Sensing of the Environment: An Earth Resource Perspective (Pearson, 2006).
  54. D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32, 785–790 (1984).
    [Crossref]
  55. J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41(271), 107–120 (1871).
    [Crossref]
  56. L. Rayleigh, “On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue sky,” Philos. Mag. 47(287), 375–384 (1899).
    [Crossref]
  57. J. Lenoble, “Scattering and polarization of the solar radiation in the Earth’s atmosphere: historical review and present applications,” in AIP Conference Proceedings (2009), pp. 7–10.
  58. N. J. Pust and J. A. Shaw, “Dual-field imaging polarimeter using liquid crystal variable retarders,” Appl. Opt. 45, 5470–5478 (2006).
    [Crossref]

2017 (1)

L. M. Dahl, M. J. Tauc, and J. A. Shaw, “Cloud thermodynamic phase detection using an all-sky imaging polarimeter,” Proc. SPIE 10407, 104070O (2017).
[Crossref]

2016 (2)

T. Aycock, A. Lompado, T. Wolz, and D. Chenault, “Passive optical sensing of atmospheric polarization for GPS denied operations,” Proc. SPIE 9838, 98380Y (2016).
[Crossref]

D. M. Harrington, J. R. Kuhn, and A. L. Ariste, “Daytime sky polarization calibration limitations,” Proc. SPIE 9912, 99126S (2016).
[Crossref]

2015 (3)

B. A. Hooper, B. Van Pelt, J. Z. Williams, J. P. Dugan, M. Yi, C. C. Piotrowski, and C. Miskey, “Airborne spectral polarimeter for ocean wave research,” J. Atmos. Ocean. Technol. 32, 805–815 (2015).
[Crossref]

K. Knobelspiesse, B. van Diedenhoven, A. Marshak, S. Dunagan, B. Holben, and I. Slutsker, “Cloud thermodynamic phase detection with polarimetrically sensitive passive sky radiometers,” Atmos. Meas. Tech. 8, 1537–1554 (2015).
[Crossref]

L. M. Dahl and J. A. Shaw, “Visible-to-SWIR wavelength variation of skylight polarization,” Proc. SPIE 9613, 96130P (2015).
[Crossref]

2014 (1)

G. van Harten, J. de Boer, J. H. H. Rietjens, F. Snik, A. Di Noia, O. P. Hasekamp, J. Vonk, H. Volten, J. M. Smit, J. S. Henzing, and C. U. Keller, “Atmospheric aerosol characterization with a ground-based SPEX spectropolarimetric instrument,” Atmos. Meas. Tech. 7, 4341–4351 (2014).
[Crossref]

2013 (1)

R. G. Driggers, V. Hodgkin, and R. Vollmerhausen, “What good is SWIR? Passive day comparison of VIS, NIR, and SWIR,” Proc. SPIE 8706, 87060L (2013).
[Crossref]

2012 (3)

M. F. Sterzik, S. Bagnulo, and E. Palle, “Biosignatures as revealed by spectropolarimetry of Earthshine,” Nature 483, 64–66 (2012).
[Crossref]

S. B. Karman, S. Z. M. Diah, and I. C. Gebeshuber, “Bio-inspired polarized skylight-based navigation sensor: a review,” Sensors 12, 14232–14261 (2012).
[Crossref]

N. J. Pust and J. A. Shaw, “Wavelength dependence of the degree of polarization in cloud-free skies: simulations of real environments,” Opt. Express 20, 15559–15568 (2012).
[Crossref]

2011 (6)

A. Dahlberg, N. J. Pust, and J. A. Shaw, “Effects of surface reflectance on skylight polarization measurements at the Mauna Loa Observatory,” Opt. Express 19, 16008–16021 (2011).
[Crossref]

N. J. Pust, A. Dahlberg, M. Thomas, and J. A. Shaw, “Comparison of full-sky polarization and radiance observations to radiative transfer simulations which employ AERONET products,” Opt. Express 19, 18602–18613 (2011).
[Crossref]

D. A. Lavigne, M. Breton, G. Fournier, J. M. Charette, V. Rivet, and A. Bernier, “Target discrimination of man-made objects using passive polarimetric signatures acquired in the visible and infrared spectral bands,” Proc. SPIE 8160, 816007 (2011).
[Crossref]

P. Bhandari, K. J. Voss, and L. Logan, “An instrument to measure the downwelling polarized radiance distribution in the ocean,” Opt. Express 19, 17609–17620 (2011).
[Crossref]

M. A. Miller, R. V. Blumer, and J. D. Howe, “Active and passive SWIR imaging polarimetry,” Proc. SPIE 4481, 87–99 (2011).
[Crossref]

D. M. Harrington, J. R. Kuhn, and S. Hall, “Deriving telescope Mueller matrices using daytime sky polarization observations,” Publ. Astron. Soc. Pac. 123, 799–811 (2011).
[Crossref]

2010 (2)

K. J. Voss and N. Souaidia, “POLRADS: polarization radiance distribution measurement system,” Opt. Express 18, 19672–19680 (2010).
[Crossref]

A. Kreuter, C. Emde, and M. Blumthaler, “Measuring the influence of aerosols and albedo on sky polarization,” Atmos. Res. 98, 363–367 (2010).
[Crossref]

2009 (2)

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, and H. Schultz, “Wave slope measurement using imaging polarimetry,” Proc. SPIE 7317, 73170B (2009).
[Crossref]

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. I. Mischenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206 (2009).
[Crossref]

2008 (5)

N. J. Pust and J. A. Shaw, “Digital all-sky polarization imaging of partly cloudy skies,” Appl. Opt. 47, H190–H198 (2008).
[Crossref]

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19, 055503 (2008).
[Crossref]

J. Chu, K. Zhao, Q. Zhang, and T. Wang, “Construction and performance test of a novel polarization sensor for navigation,” Sens. Actuators A 148, 75–82 (2008).
[Crossref]

D. M. Stam, “Spectropolarimetric signatures of Earth-like extrasolar planets,” Astron. Astrophys. 482, 989–1007 (2008).
[Crossref]

M. P. Hansen and D. S. Malchow, “Overview of SWIR detectors, cameras, and applications,” Proc. SPIE 6939, 69390I (2008).
[Crossref]

2007 (3)

M. Chami, “Importance of the polarization in the retrieval of oceanic constituents from the remote sensing reflectance,” J. Geophys. Res. 112, C05026 (2007).
[Crossref]

D. J. Diner, A. Davis, B. Hancock, G. Gutt, R. A. Chipman, and B. Cairns, “Dual-photoelastic-modulator-based polarimetric imaging concept for aerosol remote sensing,” Appl. Opt. 46, 8428–8445 (2007).
[Crossref]

J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007).
[Crossref]

2006 (5)

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Godlen, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, “MODTRAN5: 2006 update,” Proc. SPIE 6233, 508–515 (2006).
[Crossref]

N. J. Pust and J. A. Shaw, “Dual-field imaging polarimeter using liquid crystal variable retarders,” Appl. Opt. 45, 5470–5478 (2006).
[Crossref]

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
[Crossref]

E. Bosche, P. Stammes, T. Ruhtz, R. Preusker, and J. Fischer, “Effect of aerosol microphysical properties on polarization of skylight: sensitivity study and measurements,” Appl. Opt. 45, 8790–8805 (2006).
[Crossref]

Z. Li, P. Goloub, C. Devaux, X. Gu, J. Deuzé, Y. Qiao, and F. Zhao, “Retrieval of aerosol optical and physical properties from ground-based spectral, multi-angular, and polarized sun-photometer measurements,” Remote Sens. Environ. 101, 519–533 (2006).
[Crossref]

2005 (1)

M. Herman, J. L. Deuzé, A. Marchand, B. Roger, and P. Lallart, “Aerosol remote sensing from POLDER/ADEOS over the ocean: improved retrieval using a nonspherical particle model,” J. Geophys. Res. 110, D10S02 (2005).
[Crossref]

2004 (1)

2002 (1)

J. A. Shaw, “Infrared polarization in the natural earth environment,” Proc. SPIE 4819, 129–138 (2002).
[Crossref]

2001 (1)

2000 (2)

F. J. Iannarilli, J. A. Shaw, S. H. Jones, and H. E. Scott, “Snapshot LWIR hyperspectral polarimetric imager for ocean surface sensing,” Proc. SPIE 4133, 270–283 (2000).
[Crossref]

O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements,” J. Geophys. Res. 105, 20673–20696 (2000).
[Crossref]

1999 (3)

J. A. Shaw, “Degree of linear polarization in spectral radiances from water-viewing infrared radiometers,” Appl. Opt. 38, 3157–3165 (1999).
[Crossref]

I. Aben, F. Helderman, D. M. Stam, and P. Stammes, “Spectral fine structure in the polarisation of skylight,” Geophys. Res. Lett. 26, 591–594 (1999).
[Crossref]

D. M. Stam, J. F. De Haan, and J. W. Hovenier, “Degree of linear polarization of light emerging from the cloudless atmosphere in the oxygen A band,” J. Geophys. Res. 104, 16843–16858 (1999).
[Crossref]

1998 (1)

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[Crossref]

1997 (1)

D. Lambrinos, M. Maris, H. Kobayashi, T. Labhart, R. Pfeifer, and R. Wehner, “An autonomous agent navigating with a polarized light compass,” Adapt. Behav. 6, 131–161 (1997).
[Crossref]

1984 (1)

D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32, 785–790 (1984).
[Crossref]

1964 (1)

A. Ångström, “The parameters of atmospheric turbidity,” Tellus 16, 64–75 (1964).

1899 (1)

L. Rayleigh, “On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue sky,” Philos. Mag. 47(287), 375–384 (1899).
[Crossref]

1871 (1)

J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41(271), 107–120 (1871).
[Crossref]

Aben, I.

I. Aben, F. Helderman, D. M. Stam, and P. Stammes, “Spectral fine structure in the polarisation of skylight,” Geophys. Res. Lett. 26, 591–594 (1999).
[Crossref]

Acharya, P. K.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Godlen, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, “MODTRAN5: 2006 update,” Proc. SPIE 6233, 508–515 (2006).
[Crossref]

Adler-Godlen, S. M.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Godlen, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, “MODTRAN5: 2006 update,” Proc. SPIE 6233, 508–515 (2006).
[Crossref]

Anderson, G. P.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Godlen, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, “MODTRAN5: 2006 update,” Proc. SPIE 6233, 508–515 (2006).
[Crossref]

Ångström, A.

A. Ångström, “The parameters of atmospheric turbidity,” Tellus 16, 64–75 (1964).

Ariste, A. L.

D. M. Harrington, J. R. Kuhn, and A. L. Ariste, “Daytime sky polarization calibration limitations,” Proc. SPIE 9912, 99126S (2016).
[Crossref]

Aycock, T.

T. Aycock, A. Lompado, T. Wolz, and D. Chenault, “Passive optical sensing of atmospheric polarization for GPS denied operations,” Proc. SPIE 9838, 98380Y (2016).
[Crossref]

Bagnulo, S.

M. F. Sterzik, S. Bagnulo, and E. Palle, “Biosignatures as revealed by spectropolarimetry of Earthshine,” Nature 483, 64–66 (2012).
[Crossref]

Banner, M. L.

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19, 055503 (2008).
[Crossref]

Bates, D. R.

D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32, 785–790 (1984).
[Crossref]

Berk, A.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Godlen, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, “MODTRAN5: 2006 update,” Proc. SPIE 6233, 508–515 (2006).
[Crossref]

Bernier, A.

D. A. Lavigne, M. Breton, G. Fournier, J. M. Charette, V. Rivet, and A. Bernier, “Target discrimination of man-made objects using passive polarimetric signatures acquired in the visible and infrared spectral bands,” Proc. SPIE 8160, 816007 (2011).
[Crossref]

Bernstein, L. S.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Godlen, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, “MODTRAN5: 2006 update,” Proc. SPIE 6233, 508–515 (2006).
[Crossref]

Bhandari, P.

Bigué, L.

Blumer, R. V.

M. A. Miller, R. V. Blumer, and J. D. Howe, “Active and passive SWIR imaging polarimetry,” Proc. SPIE 4481, 87–99 (2011).
[Crossref]

Blumthaler, M.

A. Kreuter, C. Emde, and M. Blumthaler, “Measuring the influence of aerosols and albedo on sky polarization,” Atmos. Res. 98, 363–367 (2010).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Borel, C. C.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Godlen, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, “MODTRAN5: 2006 update,” Proc. SPIE 6233, 508–515 (2006).
[Crossref]

Bosche, E.

Breton, M.

D. A. Lavigne, M. Breton, G. Fournier, J. M. Charette, V. Rivet, and A. Bernier, “Target discrimination of man-made objects using passive polarimetric signatures acquired in the visible and infrared spectral bands,” Proc. SPIE 8160, 816007 (2011).
[Crossref]

Buis, J. P.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[Crossref]

Cairns, B.

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. I. Mischenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206 (2009).
[Crossref]

D. J. Diner, A. Davis, B. Hancock, G. Gutt, R. A. Chipman, and B. Cairns, “Dual-photoelastic-modulator-based polarimetric imaging concept for aerosol remote sensing,” Appl. Opt. 46, 8428–8445 (2007).
[Crossref]

Chami, M.

M. Chami, “Importance of the polarization in the retrieval of oceanic constituents from the remote sensing reflectance,” J. Geophys. Res. 112, C05026 (2007).
[Crossref]

Charette, J. M.

D. A. Lavigne, M. Breton, G. Fournier, J. M. Charette, V. Rivet, and A. Bernier, “Target discrimination of man-made objects using passive polarimetric signatures acquired in the visible and infrared spectral bands,” Proc. SPIE 8160, 816007 (2011).
[Crossref]

Chen, Y.

B. Stark, M. McGee, and Y. Chen, “Short wave infrared (SWIR) imaging systems using small Unmanned Aerial Systems (sUAS),” in International Conference on Unmanned Aircraft Systems (ICUAS) (2015), pp. 495–501.

Chenault, D.

T. Aycock, A. Lompado, T. Wolz, and D. Chenault, “Passive optical sensing of atmospheric polarization for GPS denied operations,” Proc. SPIE 9838, 98380Y (2016).
[Crossref]

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, and H. Schultz, “Wave slope measurement using imaging polarimetry,” Proc. SPIE 7317, 73170B (2009).
[Crossref]

Chenault, D. B.

Chetwynd, J. H.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Godlen, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, “MODTRAN5: 2006 update,” Proc. SPIE 6233, 508–515 (2006).
[Crossref]

Chipman, R. A.

Chowdhary, J.

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. I. Mischenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206 (2009).
[Crossref]

Chu, J.

J. Chu, K. Zhao, Q. Zhang, and T. Wang, “Construction and performance test of a novel polarization sensor for navigation,” Sens. Actuators A 148, 75–82 (2008).
[Crossref]

Cooley, T. W.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Godlen, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, “MODTRAN5: 2006 update,” Proc. SPIE 6233, 508–515 (2006).
[Crossref]

Corrada-Emmanuel, A.

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19, 055503 (2008).
[Crossref]

Coulson, K. L.

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak, 1988).

Dahl, L. M.

L. M. Dahl, M. J. Tauc, and J. A. Shaw, “Cloud thermodynamic phase detection using an all-sky imaging polarimeter,” Proc. SPIE 10407, 104070O (2017).
[Crossref]

L. M. Dahl and J. A. Shaw, “Visible-to-SWIR wavelength variation of skylight polarization,” Proc. SPIE 9613, 96130P (2015).
[Crossref]

Dahlberg, A.

Davis, A.

de Boer, J.

G. van Harten, J. de Boer, J. H. H. Rietjens, F. Snik, A. Di Noia, O. P. Hasekamp, J. Vonk, H. Volten, J. M. Smit, J. S. Henzing, and C. U. Keller, “Atmospheric aerosol characterization with a ground-based SPEX spectropolarimetric instrument,” Atmos. Meas. Tech. 7, 4341–4351 (2014).
[Crossref]

De Haan, J. F.

D. M. Stam, J. F. De Haan, and J. W. Hovenier, “Degree of linear polarization of light emerging from the cloudless atmosphere in the oxygen A band,” J. Geophys. Res. 104, 16843–16858 (1999).
[Crossref]

Deuzé, J.

Z. Li, P. Goloub, C. Devaux, X. Gu, J. Deuzé, Y. Qiao, and F. Zhao, “Retrieval of aerosol optical and physical properties from ground-based spectral, multi-angular, and polarized sun-photometer measurements,” Remote Sens. Environ. 101, 519–533 (2006).
[Crossref]

Deuzé, J. L.

J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007).
[Crossref]

M. Herman, J. L. Deuzé, A. Marchand, B. Roger, and P. Lallart, “Aerosol remote sensing from POLDER/ADEOS over the ocean: improved retrieval using a nonspherical particle model,” J. Geophys. Res. 110, D10S02 (2005).
[Crossref]

Devaux, C.

Z. Li, P. Goloub, C. Devaux, X. Gu, J. Deuzé, Y. Qiao, and F. Zhao, “Retrieval of aerosol optical and physical properties from ground-based spectral, multi-angular, and polarized sun-photometer measurements,” Remote Sens. Environ. 101, 519–533 (2006).
[Crossref]

DeVlaminck, V.

Di Noia, A.

G. van Harten, J. de Boer, J. H. H. Rietjens, F. Snik, A. Di Noia, O. P. Hasekamp, J. Vonk, H. Volten, J. M. Smit, J. S. Henzing, and C. U. Keller, “Atmospheric aerosol characterization with a ground-based SPEX spectropolarimetric instrument,” Atmos. Meas. Tech. 7, 4341–4351 (2014).
[Crossref]

Diah, S. Z. M.

S. B. Karman, S. Z. M. Diah, and I. C. Gebeshuber, “Bio-inspired polarized skylight-based navigation sensor: a review,” Sensors 12, 14232–14261 (2012).
[Crossref]

Diner, D. J.

Driggers, R. G.

R. G. Driggers, V. Hodgkin, and R. Vollmerhausen, “What good is SWIR? Passive day comparison of VIS, NIR, and SWIR,” Proc. SPIE 8706, 87060L (2013).
[Crossref]

Dubovik, O.

O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements,” J. Geophys. Res. 105, 20673–20696 (2000).
[Crossref]

Dugan, J. P.

B. A. Hooper, B. Van Pelt, J. Z. Williams, J. P. Dugan, M. Yi, C. C. Piotrowski, and C. Miskey, “Airborne spectral polarimeter for ocean wave research,” J. Atmos. Ocean. Technol. 32, 805–815 (2015).
[Crossref]

Dunagan, S.

K. Knobelspiesse, B. van Diedenhoven, A. Marshak, S. Dunagan, B. Holben, and I. Slutsker, “Cloud thermodynamic phase detection with polarimetrically sensitive passive sky radiometers,” Atmos. Meas. Tech. 8, 1537–1554 (2015).
[Crossref]

Eck, T. F.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[Crossref]

Emde, C.

A. Kreuter, C. Emde, and M. Blumthaler, “Measuring the influence of aerosols and albedo on sky polarization,” Atmos. Res. 98, 363–367 (2010).
[Crossref]

Engheta, N.

S. Lin, K. M. Yemelyanov, E. N. Pugh, and N. Engheta, “Polarization enhanced visual surveillance techniques,” in IEEE International Conference on Networking, Sensing and Control (2004), Vol. 1, pp. 216–221.

Fenn, R. W.

E. P. Shettle and R. W. Fenn, “Models for the aerosols for the lower atmosphere and the effects of humidity variations on their optical properties,” (1979).

Fischer, J.

Fournier, G.

D. A. Lavigne, M. Breton, G. Fournier, J. M. Charette, V. Rivet, and A. Bernier, “Target discrimination of man-made objects using passive polarimetric signatures acquired in the visible and infrared spectral bands,” Proc. SPIE 8160, 816007 (2011).
[Crossref]

Fox, M.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Godlen, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, “MODTRAN5: 2006 update,” Proc. SPIE 6233, 508–515 (2006).
[Crossref]

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B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[Crossref]

Shaw, J. A.

L. M. Dahl, M. J. Tauc, and J. A. Shaw, “Cloud thermodynamic phase detection using an all-sky imaging polarimeter,” Proc. SPIE 10407, 104070O (2017).
[Crossref]

L. M. Dahl and J. A. Shaw, “Visible-to-SWIR wavelength variation of skylight polarization,” Proc. SPIE 9613, 96130P (2015).
[Crossref]

N. J. Pust and J. A. Shaw, “Wavelength dependence of the degree of polarization in cloud-free skies: simulations of real environments,” Opt. Express 20, 15559–15568 (2012).
[Crossref]

A. Dahlberg, N. J. Pust, and J. A. Shaw, “Effects of surface reflectance on skylight polarization measurements at the Mauna Loa Observatory,” Opt. Express 19, 16008–16021 (2011).
[Crossref]

N. J. Pust, A. Dahlberg, M. Thomas, and J. A. Shaw, “Comparison of full-sky polarization and radiance observations to radiative transfer simulations which employ AERONET products,” Opt. Express 19, 18602–18613 (2011).
[Crossref]

N. J. Pust and J. A. Shaw, “Digital all-sky polarization imaging of partly cloudy skies,” Appl. Opt. 47, H190–H198 (2008).
[Crossref]

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
[Crossref]

N. J. Pust and J. A. Shaw, “Dual-field imaging polarimeter using liquid crystal variable retarders,” Appl. Opt. 45, 5470–5478 (2006).
[Crossref]

J. A. Shaw, “Infrared polarization in the natural earth environment,” Proc. SPIE 4819, 129–138 (2002).
[Crossref]

J. A. Shaw, “Polarimetric measurements of long-wave infrared spectral radiance from water,” Appl. Opt. 40, 5985–5990 (2001).
[Crossref]

F. J. Iannarilli, J. A. Shaw, S. H. Jones, and H. E. Scott, “Snapshot LWIR hyperspectral polarimetric imager for ocean surface sensing,” Proc. SPIE 4133, 270–283 (2000).
[Crossref]

J. A. Shaw, “Degree of linear polarization in spectral radiances from water-viewing infrared radiometers,” Appl. Opt. 38, 3157–3165 (1999).
[Crossref]

Shettle, E. P.

A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Godlen, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, “MODTRAN5: 2006 update,” Proc. SPIE 6233, 508–515 (2006).
[Crossref]

E. P. Shettle and R. W. Fenn, “Models for the aerosols for the lower atmosphere and the effects of humidity variations on their optical properties,” (1979).

Slutsker, I.

K. Knobelspiesse, B. van Diedenhoven, A. Marshak, S. Dunagan, B. Holben, and I. Slutsker, “Cloud thermodynamic phase detection with polarimetrically sensitive passive sky radiometers,” Atmos. Meas. Tech. 8, 1537–1554 (2015).
[Crossref]

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[Crossref]

Smirnov, A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[Crossref]

Smit, J. M.

G. van Harten, J. de Boer, J. H. H. Rietjens, F. Snik, A. Di Noia, O. P. Hasekamp, J. Vonk, H. Volten, J. M. Smit, J. S. Henzing, and C. U. Keller, “Atmospheric aerosol characterization with a ground-based SPEX spectropolarimetric instrument,” Atmos. Meas. Tech. 7, 4341–4351 (2014).
[Crossref]

Snik, F.

G. van Harten, J. de Boer, J. H. H. Rietjens, F. Snik, A. Di Noia, O. P. Hasekamp, J. Vonk, H. Volten, J. M. Smit, J. S. Henzing, and C. U. Keller, “Atmospheric aerosol characterization with a ground-based SPEX spectropolarimetric instrument,” Atmos. Meas. Tech. 7, 4341–4351 (2014).
[Crossref]

C. U. Keller, H. M. Schmid, L. B. Venema, H. Hanenburg, R. Jager, M. Kasper, P. Martinez, F. Rigal, M. Rodenhuis, R. Roelfsema, F. Snik, C. Verninaud, and N. Yaitskova, “EPOL: the exoplanet polarimeter for EPICS at the E-ELT,” in Ground-based and Airborne Instrumentation for Astronomy III (SPIE, 2010), Vol. 7735, paper 77356G.

Souaidia, N.

Stam, D. M.

D. M. Stam, “Spectropolarimetric signatures of Earth-like extrasolar planets,” Astron. Astrophys. 482, 989–1007 (2008).
[Crossref]

I. Aben, F. Helderman, D. M. Stam, and P. Stammes, “Spectral fine structure in the polarisation of skylight,” Geophys. Res. Lett. 26, 591–594 (1999).
[Crossref]

D. M. Stam, J. F. De Haan, and J. W. Hovenier, “Degree of linear polarization of light emerging from the cloudless atmosphere in the oxygen A band,” J. Geophys. Res. 104, 16843–16858 (1999).
[Crossref]

Stammes, P.

E. Bosche, P. Stammes, T. Ruhtz, R. Preusker, and J. Fischer, “Effect of aerosol microphysical properties on polarization of skylight: sensitivity study and measurements,” Appl. Opt. 45, 8790–8805 (2006).
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I. Aben, F. Helderman, D. M. Stam, and P. Stammes, “Spectral fine structure in the polarisation of skylight,” Geophys. Res. Lett. 26, 591–594 (1999).
[Crossref]

Stark, B.

B. Stark, M. McGee, and Y. Chen, “Short wave infrared (SWIR) imaging systems using small Unmanned Aerial Systems (sUAS),” in International Conference on Unmanned Aircraft Systems (ICUAS) (2015), pp. 495–501.

Sterzik, M. F.

M. F. Sterzik, S. Bagnulo, and E. Palle, “Biosignatures as revealed by spectropolarimetry of Earthshine,” Nature 483, 64–66 (2012).
[Crossref]

Strutt, J. W.

J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41(271), 107–120 (1871).
[Crossref]

Takakura, Y.

Tanré, D.

J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007).
[Crossref]

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[Crossref]

Tauc, M. J.

L. M. Dahl, M. J. Tauc, and J. A. Shaw, “Cloud thermodynamic phase detection using an all-sky imaging polarimeter,” Proc. SPIE 10407, 104070O (2017).
[Crossref]

Terrier, P.

Thomas, M.

Travis, L. D.

F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. I. Mischenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206 (2009).
[Crossref]

Tyo, J. S.

van Diedenhoven, B.

K. Knobelspiesse, B. van Diedenhoven, A. Marshak, S. Dunagan, B. Holben, and I. Slutsker, “Cloud thermodynamic phase detection with polarimetrically sensitive passive sky radiometers,” Atmos. Meas. Tech. 8, 1537–1554 (2015).
[Crossref]

van Harten, G.

G. van Harten, J. de Boer, J. H. H. Rietjens, F. Snik, A. Di Noia, O. P. Hasekamp, J. Vonk, H. Volten, J. M. Smit, J. S. Henzing, and C. U. Keller, “Atmospheric aerosol characterization with a ground-based SPEX spectropolarimetric instrument,” Atmos. Meas. Tech. 7, 4341–4351 (2014).
[Crossref]

Van Pelt, B.

B. A. Hooper, B. Van Pelt, J. Z. Williams, J. P. Dugan, M. Yi, C. C. Piotrowski, and C. Miskey, “Airborne spectral polarimeter for ocean wave research,” J. Atmos. Ocean. Technol. 32, 805–815 (2015).
[Crossref]

Venema, L. B.

C. U. Keller, H. M. Schmid, L. B. Venema, H. Hanenburg, R. Jager, M. Kasper, P. Martinez, F. Rigal, M. Rodenhuis, R. Roelfsema, F. Snik, C. Verninaud, and N. Yaitskova, “EPOL: the exoplanet polarimeter for EPICS at the E-ELT,” in Ground-based and Airborne Instrumentation for Astronomy III (SPIE, 2010), Vol. 7735, paper 77356G.

Vermote, E.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[Crossref]

Verninaud, C.

C. U. Keller, H. M. Schmid, L. B. Venema, H. Hanenburg, R. Jager, M. Kasper, P. Martinez, F. Rigal, M. Rodenhuis, R. Roelfsema, F. Snik, C. Verninaud, and N. Yaitskova, “EPOL: the exoplanet polarimeter for EPICS at the E-ELT,” in Ground-based and Airborne Instrumentation for Astronomy III (SPIE, 2010), Vol. 7735, paper 77356G.

Vollmerhausen, R.

R. G. Driggers, V. Hodgkin, and R. Vollmerhausen, “What good is SWIR? Passive day comparison of VIS, NIR, and SWIR,” Proc. SPIE 8706, 87060L (2013).
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Volten, H.

G. van Harten, J. de Boer, J. H. H. Rietjens, F. Snik, A. Di Noia, O. P. Hasekamp, J. Vonk, H. Volten, J. M. Smit, J. S. Henzing, and C. U. Keller, “Atmospheric aerosol characterization with a ground-based SPEX spectropolarimetric instrument,” Atmos. Meas. Tech. 7, 4341–4351 (2014).
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Vonk, J.

G. van Harten, J. de Boer, J. H. H. Rietjens, F. Snik, A. Di Noia, O. P. Hasekamp, J. Vonk, H. Volten, J. M. Smit, J. S. Henzing, and C. U. Keller, “Atmospheric aerosol characterization with a ground-based SPEX spectropolarimetric instrument,” Atmos. Meas. Tech. 7, 4341–4351 (2014).
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Wang, T.

J. Chu, K. Zhao, Q. Zhang, and T. Wang, “Construction and performance test of a novel polarization sensor for navigation,” Sens. Actuators A 148, 75–82 (2008).
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F. Waquet, B. Cairns, K. Knobelspiesse, J. Chowdhary, L. D. Travis, B. Schmid, and M. I. Mischenko, “Polarimetric remote sensing of aerosols over land,” J. Geophys. Res. 114, D01206 (2009).
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Wehner, R.

D. Lambrinos, M. Maris, H. Kobayashi, T. Labhart, R. Pfeifer, and R. Wehner, “An autonomous agent navigating with a polarized light compass,” Adapt. Behav. 6, 131–161 (1997).
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Williams, J. Z.

B. A. Hooper, B. Van Pelt, J. Z. Williams, J. P. Dugan, M. Yi, C. C. Piotrowski, and C. Miskey, “Airborne spectral polarimeter for ocean wave research,” J. Atmos. Ocean. Technol. 32, 805–815 (2015).
[Crossref]

Wolff, L. B.

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19, 055503 (2008).
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Wolz, T.

T. Aycock, A. Lompado, T. Wolz, and D. Chenault, “Passive optical sensing of atmospheric polarization for GPS denied operations,” Proc. SPIE 9838, 98380Y (2016).
[Crossref]

Yaitskova, N.

C. U. Keller, H. M. Schmid, L. B. Venema, H. Hanenburg, R. Jager, M. Kasper, P. Martinez, F. Rigal, M. Rodenhuis, R. Roelfsema, F. Snik, C. Verninaud, and N. Yaitskova, “EPOL: the exoplanet polarimeter for EPICS at the E-ELT,” in Ground-based and Airborne Instrumentation for Astronomy III (SPIE, 2010), Vol. 7735, paper 77356G.

Yalcin, J.

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19, 055503 (2008).
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S. Lin, K. M. Yemelyanov, E. N. Pugh, and N. Engheta, “Polarization enhanced visual surveillance techniques,” in IEEE International Conference on Networking, Sensing and Control (2004), Vol. 1, pp. 216–221.

Yi, M.

B. A. Hooper, B. Van Pelt, J. Z. Williams, J. P. Dugan, M. Yi, C. C. Piotrowski, and C. Miskey, “Airborne spectral polarimeter for ocean wave research,” J. Atmos. Ocean. Technol. 32, 805–815 (2015).
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Zappa, C. J.

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19, 055503 (2008).
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Zhang, Q.

J. Chu, K. Zhao, Q. Zhang, and T. Wang, “Construction and performance test of a novel polarization sensor for navigation,” Sens. Actuators A 148, 75–82 (2008).
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Z. Li, P. Goloub, C. Devaux, X. Gu, J. Deuzé, Y. Qiao, and F. Zhao, “Retrieval of aerosol optical and physical properties from ground-based spectral, multi-angular, and polarized sun-photometer measurements,” Remote Sens. Environ. 101, 519–533 (2006).
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Zhao, K.

J. Chu, K. Zhao, Q. Zhang, and T. Wang, “Construction and performance test of a novel polarization sensor for navigation,” Sens. Actuators A 148, 75–82 (2008).
[Crossref]

Adapt. Behav. (1)

D. Lambrinos, M. Maris, H. Kobayashi, T. Labhart, R. Pfeifer, and R. Wehner, “An autonomous agent navigating with a polarized light compass,” Adapt. Behav. 6, 131–161 (1997).
[Crossref]

Appl. Opt. (8)

Astron. Astrophys. (1)

D. M. Stam, “Spectropolarimetric signatures of Earth-like extrasolar planets,” Astron. Astrophys. 482, 989–1007 (2008).
[Crossref]

Atmos. Meas. Tech. (2)

G. van Harten, J. de Boer, J. H. H. Rietjens, F. Snik, A. Di Noia, O. P. Hasekamp, J. Vonk, H. Volten, J. M. Smit, J. S. Henzing, and C. U. Keller, “Atmospheric aerosol characterization with a ground-based SPEX spectropolarimetric instrument,” Atmos. Meas. Tech. 7, 4341–4351 (2014).
[Crossref]

K. Knobelspiesse, B. van Diedenhoven, A. Marshak, S. Dunagan, B. Holben, and I. Slutsker, “Cloud thermodynamic phase detection with polarimetrically sensitive passive sky radiometers,” Atmos. Meas. Tech. 8, 1537–1554 (2015).
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J. Atmos. Ocean. Technol. (1)

B. A. Hooper, B. Van Pelt, J. Z. Williams, J. P. Dugan, M. Yi, C. C. Piotrowski, and C. Miskey, “Airborne spectral polarimeter for ocean wave research,” J. Atmos. Ocean. Technol. 32, 805–815 (2015).
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D. M. Stam, J. F. De Haan, and J. W. Hovenier, “Degree of linear polarization of light emerging from the cloudless atmosphere in the oxygen A band,” J. Geophys. Res. 104, 16843–16858 (1999).
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J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007).
[Crossref]

Meas. Sci. Technol. (1)

C. J. Zappa, M. L. Banner, H. Schultz, A. Corrada-Emmanuel, L. B. Wolff, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19, 055503 (2008).
[Crossref]

Nature (1)

M. F. Sterzik, S. Bagnulo, and E. Palle, “Biosignatures as revealed by spectropolarimetry of Earthshine,” Nature 483, 64–66 (2012).
[Crossref]

Opt. Express (5)

Philos. Mag. (2)

J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41(271), 107–120 (1871).
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L. Rayleigh, “On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue sky,” Philos. Mag. 47(287), 375–384 (1899).
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Proc. SPIE (12)

D. M. Harrington, J. R. Kuhn, and A. L. Ariste, “Daytime sky polarization calibration limitations,” Proc. SPIE 9912, 99126S (2016).
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A. Berk, G. P. Anderson, P. K. Acharya, L. S. Bernstein, L. Muratov, J. Lee, M. Fox, S. M. Adler-Godlen, J. H. Chetwynd, M. L. Hoke, R. B. Lockwood, J. A. Gardner, T. W. Cooley, C. C. Borel, P. E. Lewis, and E. P. Shettle, “MODTRAN5: 2006 update,” Proc. SPIE 6233, 508–515 (2006).
[Crossref]

J. A. Shaw, “Infrared polarization in the natural earth environment,” Proc. SPIE 4819, 129–138 (2002).
[Crossref]

L. M. Dahl and J. A. Shaw, “Visible-to-SWIR wavelength variation of skylight polarization,” Proc. SPIE 9613, 96130P (2015).
[Crossref]

D. A. Lavigne, M. Breton, G. Fournier, J. M. Charette, V. Rivet, and A. Bernier, “Target discrimination of man-made objects using passive polarimetric signatures acquired in the visible and infrared spectral bands,” Proc. SPIE 8160, 816007 (2011).
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M. A. Miller, R. V. Blumer, and J. D. Howe, “Active and passive SWIR imaging polarimetry,” Proc. SPIE 4481, 87–99 (2011).
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R. G. Driggers, V. Hodgkin, and R. Vollmerhausen, “What good is SWIR? Passive day comparison of VIS, NIR, and SWIR,” Proc. SPIE 8706, 87060L (2013).
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M. P. Hansen and D. S. Malchow, “Overview of SWIR detectors, cameras, and applications,” Proc. SPIE 6939, 69390I (2008).
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T. Aycock, A. Lompado, T. Wolz, and D. Chenault, “Passive optical sensing of atmospheric polarization for GPS denied operations,” Proc. SPIE 9838, 98380Y (2016).
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J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, and H. Schultz, “Wave slope measurement using imaging polarimetry,” Proc. SPIE 7317, 73170B (2009).
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L. M. Dahl, M. J. Tauc, and J. A. Shaw, “Cloud thermodynamic phase detection using an all-sky imaging polarimeter,” Proc. SPIE 10407, 104070O (2017).
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F. J. Iannarilli, J. A. Shaw, S. H. Jones, and H. E. Scott, “Snapshot LWIR hyperspectral polarimetric imager for ocean surface sensing,” Proc. SPIE 4133, 270–283 (2000).
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Z. Li, P. Goloub, C. Devaux, X. Gu, J. Deuzé, Y. Qiao, and F. Zhao, “Retrieval of aerosol optical and physical properties from ground-based spectral, multi-angular, and polarized sun-photometer measurements,” Remote Sens. Environ. 101, 519–533 (2006).
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B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[Crossref]

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J. Chu, K. Zhao, Q. Zhang, and T. Wang, “Construction and performance test of a novel polarization sensor for navigation,” Sens. Actuators A 148, 75–82 (2008).
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S. B. Karman, S. Z. M. Diah, and I. C. Gebeshuber, “Bio-inspired polarized skylight-based navigation sensor: a review,” Sensors 12, 14232–14261 (2012).
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S. Lin, K. M. Yemelyanov, E. N. Pugh, and N. Engheta, “Polarization enhanced visual surveillance techniques,” in IEEE International Conference on Networking, Sensing and Control (2004), Vol. 1, pp. 216–221.

C. U. Keller, H. M. Schmid, L. B. Venema, H. Hanenburg, R. Jager, M. Kasper, P. Martinez, F. Rigal, M. Rodenhuis, R. Roelfsema, F. Snik, C. Verninaud, and N. Yaitskova, “EPOL: the exoplanet polarimeter for EPICS at the E-ELT,” in Ground-based and Airborne Instrumentation for Astronomy III (SPIE, 2010), Vol. 7735, paper 77356G.

B. Stark, M. McGee, and Y. Chen, “Short wave infrared (SWIR) imaging systems using small Unmanned Aerial Systems (sUAS),” in International Conference on Unmanned Aircraft Systems (ICUAS) (2015), pp. 495–501.

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Figures (27)

Fig. 1.
Fig. 1. Photographs from 20 October 2014 and 10 August 2014, showing conditions similar to the “clean” (top) and “smoky” (bottom) aerosol cases, respectively. For the modeled smoky case on 3 August 2014, there would have been significantly more haze, as the aerosol content was higher (500 nm AOD of 1.03, compared with 0.3 on 10 August).
Fig. 2.
Fig. 2. Outline of the radiative transfer model used to determine the DoLP for skylight viewed from the ground. The input parameters included AERONET aerosol parameters, MODTRAN transmission spectra, and measured surface reflectance spectra.
Fig. 3.
Fig. 3. MODTRAN simulated transmission spectrum for a zenith path through the 1976 U. S. Standard Atmosphere with no aerosols or clouds on 18 August 2014.
Fig. 4.
Fig. 4. MODTRAN simulation of molecular absorption bands for an atmosphere containing no aerosols or clouds.
Fig. 5.
Fig. 5. Interpolated and extrapolated AERONET Rayleigh optical depths and aerosol optical depths for a clean atmosphere on 19 October 2014, a moderately hazy atmosphere on 18 August 2014, and a smoky atmosphere on 3 August 2014.
Fig. 6.
Fig. 6. Interpolated AERONET complex indices of refraction for a clean atmosphere on 19 October 2014, a moderately hazy atmosphere on 18 August 2014, and a smoky atmosphere on 3 August 2014.
Fig. 7.
Fig. 7. AERONET-retrieved aerosol volume size distributions ( dV ( r ) / d ln ( r ) [ μm 3 / μm 2 ]) for a clean atmosphere on 19 October 2014, a moderately hazy atmosphere on 18 August 2014, and a smoky atmosphere on 3 August 2014.
Fig. 8.
Fig. 8. Maximum skylight DoLP modeled using full measured aerosol parameters with green grass surface reflectance.
Fig. 9.
Fig. 9. Maximum skylight DoLP modeled for the three test days using full measured aerosol parameters and zero surface reflectance.
Fig. 10.
Fig. 10. Maximum skylight DoLP modeled with five different spectrally constant surface reflectance values and measured aerosol parameters from 18 August 2014. Skylight polarization over the entire VIS–SWIR spectrum has a similar spectral shape for the different surface reflectance values.
Fig. 11.
Fig. 11. Green grass and sand surface reflectance measurements with their corresponding modeled maximum skylight DoLP. For green vegetation, the absorption bands of chlorophyll are responsible for low reflectance values in the VIS spectrum, leading to a higher polarization.
Fig. 12.
Fig. 12. Modeled maximum skylight degree of linear polarization for a Rayleigh scattering environment with the aerosol optical depth spectrally fixed to 10 6 (essentially zero) and with zero surface reflectance. With no aerosols, maximum skylight polarization in the SWIR reached an upper limit of 95%.
Fig. 13.
Fig. 13. Modeled maximum skylight DoLP for three different values of spectrally fixed aerosol optical depth ( τ aer ) with zero surface reflectance and AERONET data products (Rayleigh optical depth, aerosol volume size distribution, and aerosol index of refraction) from 18 August 2014. In the SWIR, with the aerosol optical depth greater than the Rayleigh optical depth, the skylight polarization decreased with wavelength.
Fig. 14.
Fig. 14. Modeled maximum skylight DoLP for a constant aerosol optical depth ( τ aer = 0.001 ) greater than the SWIR Rayleigh optical depth, paired with different AERONET-retrieved aerosol volume size distributions from three varying environments: a clean atmosphere on 19 October 2014, a moderately hazy atmosphere on 18 August 2014, and a smoke-filled atmosphere on 3 August 2014.
Fig. 15.
Fig. 15. Maximum skylight DoLP modeled using AERONET-retrieved aerosol optical depths and index of refraction with zero surface reflectance for different volume size distributions.
Fig. 16.
Fig. 16. Spectral scattering cross section and the phase matrix P 12 element from each day.
Fig. 17.
Fig. 17. Maximum skylight DoLP modeled with the aerosol optical depth and volume size distribution from 18 August 2014 paired with the different AERONET-retrieved refractive indices for the three test days.
Fig. 18.
Fig. 18. SWIR rotating-polarizer imaging polarimeter.
Fig. 19.
Fig. 19. Interpolated and extrapolated AERONET aerosol optical depths for a clean atmosphere on 28 April 2015 and a smoky atmosphere on 20 August 2015.
Fig. 20.
Fig. 20. AERONET-retrieved aerosol volume size distributions ( dV ( r ) / d ln ( r ) [ μm 3 / μm 2 ]) for a clean atmosphere on 28 April 2015 and a smoky atmosphere on 20 August 2015.
Fig. 21.
Fig. 21. Interpolated AERONET complex indices of refraction for a clean atmosphere on 28 April 2015 and a smoky atmosphere on 20 August 2015.
Fig. 22.
Fig. 22. Measured green grass spectra and MODIS-retrieved surface reflectance in the 1.628–1.652 μm band and spatially averaged over a circle of 50 km radius centered on our observation site.
Fig. 23.
Fig. 23. Reference image of our measurement on 28 April 2015. The solar azimuth and elevation angles were 114° and 41°, respectively.
Fig. 24.
Fig. 24. SOS modeled maximum skylight polarization across the 1.5–1.8 μm validation band for a clean sky on 28 April 2015 and a sky containing thick wildfire smoke on 20 August 2015.
Fig. 25.
Fig. 25. (Top) Measured DoLP on 28 April 2015. Skylight polarization was measured to decrease top-down from 13% to 8%. (Bottom) Fisheye modeled maximum DoLP dependence averaged over 1.5–1.8 μm. The red arrow indicates the polarimeter pointing direction, where the modeled maximum polarization was 8%.
Fig. 26.
Fig. 26. Reference image of our measurement on 20 August 2015. The solar azimuth and elevation angles were 193° and 56°, respectively.
Fig. 27.
Fig. 27. (Top) Measured DoLP on 20 August 2015. Skylight DoLP was measured to decrease top-down from 45% to 36%. (Bottom) Simulated all-sky fisheye DoLP image averaged over 1.5–1.8 μm. Across the band of maximum polarization, the modeled DoLP ranged from 45% to 54%, with a band-average value of 48%. The red arrow indicates the portion of sky the polarimeter was viewing, in which the modeled polarization was 46%–44%.

Equations (4)

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DoLP = S 1 2 + S 2 2 S 0 ,
T = e ( τ aer + τ ray + τ mol ) ,
α = ln ( τ 1 τ 2 ) ln ( λ 1 λ 2 ) ,
τ λ = τ 0 ( λ λ 0 ) α .

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