Measurements of skylight polarization: a case study in urban region with high-loading aerosol Lianghai Wu,* Jun Gao, Zhiguo Fan, and Jun Zhang Hefei University of Technology, BOX 98, Anhui Province, 230009 China *Corresponding author: [email protected] Received 9 September 2014; revised 27 November 2014; accepted 27 November 2014; posted 20 January 2015 (Doc. ID 222648); published 30 January 2015

We investigate skylight polarization patterns in an urban region using our developed full-Stokes imaging polarimeter. A detailed description of our imaging polarimeter and its calibration are given, then, we measure skylight polarization patterns at wavelength λ
488 nm and at solar elevation between −05°100 and 35°420 in the city of Hefei, China. We show that in an urban region with high-loading aerosols: (1) the measured degree of linear polarization reaches the maximum near sunset, and large areas of unpolarized sky exist in the forward sunlight direction close to the Sun; (2) the position of neural points shifts from the local meridian plane and, if compared with a clear sky, alters the symmetrical characteristics of celestial polarization pattern; and (3) the observed circular polarization component is negligible. © 2015 Optical Society of America OCIS codes: (290.5855) Scattering, polarization; (290.1090) Aerosol and cloud effects; (010.1310) Atmospheric scattering; (120.5410) Polarimetry. http://dx.doi.org/10.1364/AO.54.00B256

1. Introduction

Skylight polarization patterns, including degree and angle of polarization, have been the subject of numerous theoretical and experimental investigations in recent decades. The pattern of the polarization angle is relatively stable under various sky conditions [1–3]; thus many animals, such as ants [4], amphibians [5], birds [6], and bees [7], can make use of these rich sources as an important clue for orientation, however, the pattern of the degree of polarization is sensitive to variations of atmosphere components; hence, it can provide additional information for atmosphere investigation, such as cirrus observation [2] and aerosol retrieval [8]. Sun position and atmosphere are two key elements accounting for variations of skylight polarization. Many research efforts have been made for different sky conditions, such as clear [4,9], cloudy [2,10], overcast [11], foggy [3], twilight [8,12], moonlit [13], and

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even during solar eclipse [14]. Skylight is polarized mainly due to scattering by atmosphere particles (e.g., air molecules, aerosols, water droplets, etc.) [15,16]. Therefore, under certain solar positions, the skylight polarization patterns mainly depend on atmosphere components. In recent years, various man-made aerosols have been released into the atmosphere following rapid economic growth in developing countries such as China. These man-made aerosols affect the air quality and cause many indirect problems, such as deteriorating visibility, human health risk, and flooding [17,18]. The increasing aerosol loading also brings many unexpected influences on skylight polarization patterns, especially aerosols become dominant, because their optical properties are complex and distinctive from air molecules. As a consequence, we consider the skylight polarization patterns in an urban region with aerosols for the following reasons: • The aerosol pollution in urban regions of China is unique when compared with many other places. In many cities of China, seasonal or monthly mean

mass concentration of aerosols is around 100 μg∕m3 while for European cities this value is 5 μg∕m3, even for polluted U.S. urban regions, like the city of Los Angeles, this value is only 20 μg∕m3 [17]. Due to massive automobile, industrial and dust emissions, even in the clear sky of summer, aerosols’ mass concentration has a mean value 400 μg∕m3 and can be up to 600 μg∕m3 in Hefei[19]. This makes the diagnosis of aerosol impact on skylight polarization distribution relatively easy. • We are also interested in circular polarization that might exist under the high-loading aerosol atmosphere. Some vector radiative transfer models have simulated required conditions for the existence of circularly polarized light in the atmosphere [20– 22]. Simulation results show that a nonzero circular polarization component exists even under small atmosphere optical depth [20,22]. Slonaker and Liou [21] pointed out that nonzero circular polarization exists under required conditions including multiple-scattering and short wavelength observations (i.e., less than 0.5 μm). Our goal is to measure and compare the sky polarization patterns of aerosol-loading and clear skies. In the paper, we investigate prerequisites for the observation of skylight polarization including circularly polarized light, such as wavelength, weather condition, and the ideal observation direction in the sky. We then build an imaging polarimeter and calibrate its Mueller matrix. The imaging polarimeter used here is designed following the optical design of the RADS-II CCD camera system [23] and the LCVRbased Stokes polarimeters [24]. We use a rotating quarter-wave retarder to achieve time-sequential polarization images at fixed wavelength. In the experiments, we measure linearly and circularly polarized light features of clear sky with aerosols at different solar elevations near sunset. For comparison, a pair of results under an almost aerosol-free atmosphere are also included. We compare the measured results between a high-loading aerosol sky and an aerosol-free one, and discuss potential influences introduced by a high-loading aerosol sky on polarization-sensitive animals. 2. Materials and Methods

In this section, we investigate the required environmental conditions for the occurrence of nonzero circular polarization in the atmosphere and identify essential prerequisites for the observation. After that, we build a time-sequential stokes polarimeter with the spectral band concluded from the theoretical studies. Finally, the related system calibration and error estimation are made. A.

Wavelength Band Selected

Spectral considerations are among the first issues to be addressed when pursuing a particular application of imaging polarimeters. Since linearly polarized skylight is abundant in the visible spectral bands, we need to identify an ideal wavelength for the

observation of circularly polarized light for aerosol loading atmosphere. The transformation procedure of polarization states in the single and multiple scattering events is diagnosed here. The polarization status of light is typically described with the Stokes vector [25], S
IQUV
I 0  I 90 ; I 0 − I 90 ; I 45 − I 135 ; I R − I L . I 0 , I 90 , I 45 , and I 135 correspond to light intensity after propagating through an ideal linear polarizer at directions of 0°, 90°, 45°, and 135°. Similarly, I R and I L correspond to right and left circular polarizers, respectively. With different combinations of Stokes components, polarization states vary from partial elliptic polarization to linear polarization I > 0; Q; U ≠ 0; V
0 or circular polarization I > 0; V ≠ 0. The light coming directly from the Sun is unpolarized. Skylight is polarized due to the scattering of atmosphere particles like air molecules (Rayleigh scattering) or aerosols, and ice crystal or cirrus (Mie scattering). In general, scattering phase matrix P determines the transformation process of polarization status [22], 2

P11 6 P21 P
6 4 P31 P41

P12 P22 P32 P42

P13 P23 P33 P43

3 P14 P24 7 7: P34 5 P44

(1)

If scatters have a symmetry plane and random spatial distribution, the matrix P can be simplified to eight elements. And for spherical scatters described by Rayleigh or Mie theory, the matrix further simplifies to have four independent elements [22]. In a single scattering event, Rayleigh and Mie scattering can hardly produce any circular polarization. The magnitude of the V component is the product of unpolarized solar incident light I 0 ; 0; 0; 0 and phase matrix P. Only irregular particles without any symmetry planes could produce circular polarization in a single scattering. Circular polarization component generated from this is really rare because the contributions by random distributed irregular particles to total circular polarization mostly cancel each other. Circular polarization in the sky is mainly induced by the multiple scattering of atmosphere particles. In multiscattering events, unpolarized incident light I 0 ; 0; 0; 0 leads to nonzero V component after two times of scatterings [21], V
I 0 p12 P34 sin 2π − i2  cos 2i1 − cos 2π − i2  sin 2i1 ; (2) where p12 and P34 refer to phase matrix elements in the first and second scattering events, respectively. i1 and i2 refer to the angles between the scattering plane and the local meridian planes containing the incident and scattered vectors in the first and second scattering events. From Eq. (2), we can see that the V component is proportional to the product of p12 P34. With the Rayleigh and Mie scattering theory together, briefly, 1 February 2015 / Vol. 54, No. 4 / APPLIED OPTICS

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(2) the observation wavelength band is smaller than the radius of the dominant Mie scattering particles. Suggested by Dong et al.’s work [27], the size of aerosol particles in the Hefei area follow the log-normal distribution with mode radius rmod
0.710 μm and distribution width σ
0.847. Slonaker et al. [21] suggested that nonzero circular polarization required short wavelength observation (i.e., less than 0.5 μm). Apart from this, to compute the Stokes vector of interested scenes, sufficient light is needed for the camera imaging while small light intensity would introduce great errors to the measurement. The spectral irradiance of the Sun attenuated exponentially with decreasing of the wavelength when λ ≤ 0.5 μm. Thus, the chosen wavelength is around the peak of spectral distribution of solar radiation and there will be still sufficient light for camera imaging while all the other spectral lights have been filtered away.

the generation of the V component works as follows: parts of unpolarized incident solar light are transformed into linear polarization through Rayleigh scattering, which is the primary event under clear skies, and then the second Mie scattering event transforms linearly polarized light into circularly polarized light. It should be noted that in the first scattering event, although the phase matrix P of Mie particle also contains nonzero p12 , its contribution to the total can be ignored when compared with those from the large amount of the air molecules, especially under clear skies where Rayleigh scattering dominates. And the P34 of Rayleigh scattering’s phase matrix is zero; so, only via Mie scattering could most of the circularly polarized light be produced in the second scattering event from linearly polarized light. Since theV component is related with P34 , to identify optimal conditions for the formation and observation of circular polarization, we evaluate the variation of P34 with respect to scattering angles at different wavelengths and sizes. In urban environments, where the majority of anthropogenic aerosols occur, the most likely aerosol types are water-soluble, water-insoluble, and soot [26]. Figure 1 shows values of P34 in terms of scattering angle at wavelengths 0.35, 0.55, and 0.75 μm for different size aerosols with refractive index m
1.416  0.0021i. We can see here the nonzero P34 mainly exist in the scattering of particles with larger radius r relative to light wavelength λ, and mostly prefer at scattering angle θ < π∕2, namely forward direction. P34 values vibrate severely between negative and positive signs within a small scattering angle. As for particles with radius r < λ, the magnitude of P34 decreases dramatically close to zero and almost can be ignored, such as r
0.02 μm at λ
0.35 μm, or r
0.45 μm at λ
0.55 μm and λ
0.75 μm. We would like to stress that this is a rough analysis. For a more reliable diagnosis, one may refer to some radiative transfer models [20]. We set our observation wavelength to λ
488 nm based on the following considerations. From the simulation in Fig. 1, we can see that the following prerequisites need to be met before the observation of circular polarization: (1) both Rayleigh and Mie scattering events occur in the atmosphere, and 1

0.6

The design of the instrument focuses on two aspects: (1) possess the ability of measuring both linear and circular polarization, and (2) have a full-sky field of view. We built our system based on the work of Pust and Shaw [24]. Figure 2 illustrates the optical layout of our system, containing a Sigma 8 mm fish-eye lens, two 120 mm doublelet lenses, a dichroic filter, a quarter-wave retarder, a linear polarizer, a 60 mm microlens, and a Nikon D800 camera. Those cells are chosen to be compatible with the working wavelength λ
488 nm. We use one rotating quarterwave retarder and position the spectral filter before the retarder. Scene images are captured with the Nikon D800, which is self-contained and has 14-bit intensity information. The tested field of view of the system is nearly up to 178°, which facilitates the observation of the celestial polarization patterns. The use of the Nikon camera frees the system from the reliance of external electrical power and supporting equipment like a computer during measurements. With its 14-bit data, the quantization error of measured intensity is up to 0.01 while the measured intensity is usually greater than 20, so the polarization errors due to quantization could be eliminated. The 35 mm sensor

1

0.02 0.15 0.45 2.15

0.8

B. System Design and Principles of Measurements

1

0.02 0.15 0.45 2.15

0.8 0.6

0.6

0.4

0.4

0.2

0.2

0.2

P34 0

P34 0

P34 0

-0.2

-0.2

-0.2

-0.4

-0.4

-0.4

-0.6

-0.6

-0.6

-0.8

-0.8

-0.8

-1

-1

0

20

40

60

80

100

120

140

160

180

0.02 0.15 0.45 2.15

0.8

0.4

0

20

40

60

80

100

120

140

160

180

-1

0

20

40

60

80

100

Scattering Angle

Scattering Angle

Scattering Angle

λ=0.35um

λ=0.55um

λ=0.75um

120

140

160

180

Fig. 1. P34 distribution of representative urban aerosol model (referenced from OPAC [26]) at wavelength λ
0.35 μm, 0.55 μm, and 0.75 μm under four radius scales, 0.02 μm, 0.15 μm, 0.45 μm, 2.15 μm. B258

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3 Laser Line Filter 5 Linear Polarizer

1 Fisheye Lens

2 Doublelet

4 Quarter-wave Retarder

7 CMOS Sensor

6 Macro lens

(a) Optical layout of the system

(b) Real system image Fig. 2. Optical layout and actual picture of our imaging polarimeter.

provides high-quality images with resolutions up to 7360 × 4912 and offers great convenience in choosing the imaging lens. Moreover, the camera’s light sensitivity ISO ranges from 100 to 6400, which is particularly useful for the experiments conducted under weak light conditions like twilight sky. In the sky, the most general type of polarization is partial polarization and its Stokes vector can be decomposed into a polarized and an unpolarized component. Thus, for the most general situations, we p have I ≥ Q2  U 2  V 2 . Generally, not the Stokes vector itself but its derived parameters are used to describe the polarization characters of the sense like the angle of polarization, which is defined as tan 2χ
U∕Q, and degree of polarization p 2 2 2 P
Q  U  V ∕I. If V component is ignored, P becomes the degree of linear polarization  p Pl
Q2  U 2 ∕I. Similarly, the degree of circular polarization is defined as Pc
V∕I:

(3)

For the imaging polarimeter, Stokes vector transformation through an optical system can be represented as a linear process with 4 × 4 system Mueller matrix Msys . The system Mueller matrix describes the relationship between Stokes vector S of input light and output light as Sout
Msys · Sin :

(4)

By rotating the quarter-wave retarder, the system’s Mueller matrix associated with the beam path from the microlens to the camera in configuration j is Msys θj 
Mm · Mp · Rθj  · Mr · R−θj  · Md · Mf ; (5) where Mm , Mp , Mr , Md , and Mf are the Mueller matrix of the microlens, polarizer, retarder, doublelet lens, and fish-eye lens, respectively. Rθj  is the rotation matrix for the retarder at angle θ with respect to the fast axis,

2

1 60 Rθj 
6 40 0

0 cos2θj  sin2θj  0

0 − sin2θj  cos2θj  0

3 0 07 7: 05 1

(6)

The intensity I out (the first term of Stokes vector Sout ) is the camera-recorded intensity of light rays that passes through the system and can be expressed as a product of the input Stokes Sin
I in ; Qin ; U in ; V in  and the first row of the system Mueller matrix Mj 0; ∶
M j;00 ; M j;01 ; M j;02 ; M j;03 , I jout
M j;00 I in  M j;01 Qin  M j;02 U in  M j;03 V in : (7) To solve Eq. (7), the Mj 0; ∶ has to be known. For the device shown in Fig. 2, the Mueller matrix is determined mainly by the linear polarizer and quarterwave retarder. Ideally, the Mueller matrix for the retarder with fast axis at angle 0° is 2

1 60 Mr 0
6 40 0

0 0 1 0 0 0 0 −1

3 0 07 7: 15 0

(8)

And for a linear polarizer with transmission axis oriented at angle 0°, 2

1 16 1 LP0
6 240 0

1 1 0 0

0 0 0 0

3 0 07 7: 05 0

(9)

If we treat other optical components as ideal elements without depolarization effect in Eq. (5), we can compute Mj 0; ∶ at each rotational angle. Under this assumption, we can construct a coefficient matrix A containing nMj 0; ∶ with recorded intensity at each configuration. We get the relation between incoming Stokes vector and recorded intensity, I
A · Sin ; 1 February 2015 / Vol. 54, No. 4 / APPLIED OPTICS

(10) B259

T where I
I 1out ; …; I N out  and

2

M 1;00 6 .. A
4 .

M 1;01 .. .

M 1;02 .. .

M N;00

M N;01

M N;02

3 M 1;03 .. 7: . 5 M N;03

error matrix of Eq. (13). In the method, the augmented matrix  Q Ic  can be rewritten as 2P (11)

When the rank of coefficient matrix A is 4, the Eq. (10) can be solved by Sin
AT A−1 AT I:

(12)

Obviously, matrix A is essential for the calculation of Stokes vector Sin. To build matrix A, we need to identify at least four system Mueller matrix Msys with linearly independent first row at different configurations. Ideally, it is easy to construct such a matrix A if other optical elements are ideal. However, due to the uncertainty of optical devices, the imaging polarimeter needs to be calibrated before measurements. This issue is addressed in the next section. C.

Q

Q · Mj 0; ∶
Ic ;

(13)

where Ic is the recorded intensity of corresponding input Stokes vector. Due to the pseudorandom noise that can appear in matrix Q and Ic in polarization measurement, we apply the total least square method [28] to find the optimized vector Mj 0; ∶, which minimizes the B260

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UIc 4

Q

0

Ic

VQIc VIc Ic

⊤

: (14)

P Here U, , V are the singular value decomposition of matrix  Q Ic . After the decomposition, the Mueller matrix vector Mj 0; ∶ is given by Mj 0; ∶
−VQIc V−1 Ic Ic :

(15)

We calibrate 12 system configurations with the retarder rotating from 0° to 165° in steps of 15°. Then we compute pairwise linear correlation between each of the calibrated vectors and sort out a linearly independent subset from them. The final calibrated matrix A is comprised of Mj 0; ∶ at direction 0°, 30°, 45°, and 120°:

System Mueller Matrix Calibration

In the calibration, we focus on removing Mueller matrix bias induced by depolarization effects of optical components in the matrix A. The calibration system consists of a polarization state generator (including a polarizer, a quarter-wave retarder, a dichroic filter, and a laser source at λ
488 nm), a PAX polarimeter (wavelength range 400–700 nm, Thorlabs), and a optical power meter (resolution 100 pW). We refer to the fixed linear polarizer’s zero orientation x and its normal orientation y as the reference coordinate (the light propagation direction is x × y). We start from generating a group of normalized Stokes vectors. With the help of a PAX polarimeter, the 12 generated polarization states are adjusted to be spanned evenly over the whole Poincare sphere with equal intensity. We try to maximize the irrelevance of input light’s polarization states, which helps to reduce the calibration error. Then, the system calibration is performed as follows: (1) rotate the retarder to N different directions with respect to the system reference coordinate; (2) at each configuration, record the intensity of the different polarization states after they propagate through the system; and (3) solve the calibration equation to get coefficient matrix A. Mathematically, four polarization states are sufficient to find Mueller parameters at each configuration. To improve the calibration accuracy, we use 12 polarization states arranged in matrix Q in which each row is one Stokes vector. Then we have

Ic 
 U Q

3 0  P 5 VQQ VI c Q

2

0.5000 6 0.5000 6 A
6 6 0.5000 4 0.5000 0.5000

0.0675 0.5034 0.0060 0.4899 0.0521

−0.0235 −0.0789 0.1518 −0.1115 0.2637

3 −0.3622 −0.1076 7 7 0.3377 7 7: (16) 0.1172 5 −0.3347

In the calibration, we provide an additional parameter at direction 165°, which can help to improve the measuring accuracy. D.

Full-Sky Polarization Imaging

Some preparations need to be made before experiments. The whole system is fixed on a tripod to avoid mechanical vibration. The front fish-eye lens is positioned horizontally with its center aligned to the zenith of sky to ensure the acquired images are zenithcentered. All automatic functions in the digital camera (e.g., smoothing, noise reduction, and contrast enhancement) are switched off. The focus, time of exposure, and light sensitivity ISO are all needed to be modified manually along with environmental changes, so that all images at a certain time are acquired with the same settings. In the experiments, digital images are taken at five different directions of the quarter-wave retarder as selected before. Preprocessing: An image mask is used to sort the efficient imaging areas which contains the sensor area with 3.2 megapixels. The images are stored in NEF format retaining 14-bit data (a raw, unprocessed data file of the Nikon camera). Before computation, we decode those images into 16-bit TIFF output format using the open-source program Dcraw http://www.cybercom.net/~dcoffin/dcraw/. This procedure transforms only the unique Nikon raw format to a more commonly used TIFF format to facilitate data processing, and retains the data accuracy consistent with the previous NEF format. The projection of imaging pixels of the system onto the

actual solar elevation is θs
0.5πr∕R, where r is the distance in pixels between a certain position and the image center (corresponding to the zenith sky), and R indicates the radius of the imaging area in pixels. The projection relationship here is uncalibrated since the deviation would not change the distribution of sky polarization patterns and value tendency. Stokes vector computation: According to Eq. (12), the degree of linear polarization Pl , degree of circular polarization Pc , and angle of polarization χ (referenced to the plane defined by the system optical axis and zero direction of the linear polarizer) are all derived from the Stokes vector S. Error elimination: Errors could be introduced into the computation of polarization parameters through the following ways, and should, therefore, be eliminated or minimized. • Inhomogeneous sunlight irradiation. Occurs if the images of the sky are taken under different illuminations. This may happen when the Sun is blocked by moving clouds and emerging again in a single measurement duration. This error could be eliminated if checked carefully. • Target motion artefact. Originates from the moving of the target, scene (e.g., moving clouds, trees, water waves, and the Sun), or the polarimeter itself in a single measurement duration. This is an inherent problem for rotating polarimeters. This type of error can be reduced by minimizing the measurement duration and fixing the polarimeter properly. Here we mainly focus on the measuring of clear and aerosol-loaded skies where the polarization characters nearly remain consistent in a single experiment. • Inaccurate alignment of the retarder. The rotation of the optical axis of λ∕4 retarder has an inaccuracy of 0.5°. We try to eliminate this error through careful labeling of the desired graduation before the experiment. • Under-exposition noise. The errors of Stokes computation increase rapidly with the decrease of light intensity I, because the value of sensor noise becomes comparable with the signal. This is a significant error for experiments during the twilight period. To reduce this error, we try to enhance measured intensity in two ways: (1) increasing the explosion time, and (2) setting a higher ISO value. However, the increase of explosion time may induce the error of target motion artefacts mentioned above, and a high ISO value may induce thermal noise of the sensor. This is always a trade-off between the explosion time and ISO value. We try to find a balance by increasing explosion time up to 2 s and the ISO to 1600. In our experience, this can meet the measuring requirements of most periods of twilight sky with acceptable errors. 3. Results

Figure 3 describes the patterns of degree of linear polarization Pl and angle of polarization χ of the aerosol-loaded sky measured from evening sunset

to the twilight period at local time 18:04, 18:33, 18:53, and 19:25, respectively. Those results were collected on 08 July 2013 in Hefei, China. The sunset occurred at 19:23. We measured the polarization patterns of the entire celestial hemisphere at the top of Yi-fu Science and Education Building (latitude 31°840 N, longitude 117°29″ E). On that day, the sky was clear with urban aerosols and the local air quality index (AQI) was around 120, which means for particles less than 2.5 μm mass concentration is around 75 μg∕m3 or 150 μg∕m3 for size less than 10.0 μm. The local AQI data was acquired from http://aqicn .org/. We took images from 18:04 to 20:05 with 10 min interval and ignored the cases without significant variations between or after those presented times. For comparison, as shown in Fig. 4, we also investigated skylight polarization patterns of clear sky on 13 July 2013 at the same location. Before the experiment was performed, the city had a heavy rain shower that lasted almost the whole night and brought away a large proportion of suspended aerosols in the air. The local AQI was around 30, which indicates a particle mass concentration around 20 μg∕m3 . And the measurements were taken in the coming morning at solar elevation αs
22°570 and 35°420 . We can see in the figure that the patterns of linear polarization (the map of Pl and χ) distributed regularly along the solar and antisolar meridians with maximum Pl
0.57 and 0.46. Two neutral points, Babinet and Arago, are located along the meridians. The unpolarized sky areas at the forward direction are restricted within a small viewing angle near the Sun. The observed linear polarization patterns under high-loading aerosol atmosphere have the following features while some of them are shared with clear sky: • PL of skylight increased with increasing angular distance from the Sun and reached its maximum at 90° from the Sun. Note that due to forward scattering of aerosols, patches of sky at 18:04 and 18:23 near the Sun are totally unpolarized. Neutral points (i.e., the Babinet point located near the Sun and the Arago point at the opposite antisolar area) are almost unpolarized (PL
0) and located away from the solar and antisolar meridians. • χ between −π∕4 and π∕4 is dominant throughout the whole sky, while χ in the ranges of −π∕2; −π∕4 and π∕4; π∕2 only exists between the neutral points and the local horizons. The neutral points are positioned at intersections of different ranges of angle of polarization. • If compared with clear sky, the PL and χ under high-loading aerosol do not symmetrically distribute along the solar and antisolar meridians. The axis of symmetry shifts a few degrees from the local meridian. For example, at 18:53 the local meridian does not cross two neutral points and a certain angular difference exists. 1 February 2015 / Vol. 54, No. 4 / APPLIED OPTICS

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Angle of Polarization

Degree of Linear Polarization Pl

Skylight Intensity I 18:04

= 14 03'

s

= 107 57 '

s

18:33

= 08 20'

s

= 111 20'

s

18:53 s s

= 04 26' = 113 51' Loc

ian

ian

erid

erid

al M

al M

Loc

19:25 s s

= 01 50' = 120 28'

Degree of Linear Polarization 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Angle of Polarization -1.5

-1

-0.5

0.5

0

1.5

1

Degree of Circular Polarization -1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Fig. 3. Skylight polarization patterns of the sky with intense aerosol loading during the sunset. The data were acquired on 08 July 2013 in Hefei, China (local time is Universal Time+08h). The left most column of images are skylight intensity, I, acquired when the quarter-wave retarder’s fast axis was oriented at 0° direction. Each image is labeled with the local time at which it was taken as well as the solar elevation αs and solar azimuth ϕs . The second column on the left displays the full-sky patterns of degree of linear polarization, Pl . The third column on the left indicates the angle of polarization, χ with unit rad. The maps of Pl and χ are visualized, respectively, in false color with colormaps displayed at the bottom. The angle ΔΘ defines the angular difference between the local meridian plane and the real symmetry axis, the line crossing neutral points and the local zenith.

For circular polarization components, we can see from Table 1, the measured degree of circular polarization along the local median is comparable with system error. Table 2 gives the maximum values of skylight polarization degree along the local meridian at different times throughout the experiment. The maximum value is determined by n clustered points under the same range, n > 15. The value here is not the lower and upper error, but the bin edge of the value. As can B262

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be seen, with the decrease of the Sun elevation, the linear degree of polarization Pl increases from 0.36 to 0.61 at the sunset. 4. Discussion A. Altered Asymmetry of the Skylight Polarization

Since the polarized light is abundant in natural environments, many animals take advantage of skylight information for navigation or orientation [29]. Due to

Angle of Polarization

Degree of Linear Polarization

Skylight Intensity I

Pl

07:35 22 57 '

s

102 17 '

s

08:14 s 35 42 ' 95 19 '

s

Degree of Linear Polarization 0

0.1

0.2

0.3

0.4

0.5

0.6

0.8

0.7

0.9

1

Angle of Polarization -1.5

-1

-0.5

0.5

0

1.5

1

Degree of Circular Polarization -1

-0.8 -0.6 -0.4 -0.2

0

0.2

0.6

0.4

0.8

1

Fig. 4. Similar to Fig. 3, but for the results of linear polarization patterns of clear sky on 13 July 2013.

Table 1.

Value of Circular Polarization Components along Local Median for Clear and High-Loading Aerosol Sky

−75°

−60°

−35°

−15°

0°

15°

35°

60°

75°

−0.007 −0.004

−0.006 −0.005

−0.005 −0.006

0.002 0.002

0.003 −0.003

0.003 −0.002

−0.008 −0.006

−0.005 0.007

−0.006 0.003

Viewing angle from zenith Clear sky (07:35) High-loading aerosol (18:53)

Table 2.

Local time

Value of Skylight Polarization Degree from 18:04 to 19:43 on 08 July 2013

18:04

18:14

18:22

18:33

18:43

Pl αs

0.36  0.01 14°030

0.45  0.03 15°130

0.50  0.05 13°430

0.49  0.03 08°200

0.53  0.03 09°530

Local time Pl αs

18:53 0.56  0.05 04°260

19:03 0.49  0.03 06°300

19:16 0.63  0.05 04°150

19:25 0.61  0.01 −01°500

19:43 — −05°100

the complex changes of skylight polarization during the day, twilight skylight polarization is regarded as the most important clue for those animals, because at sunrise and sunset the skylight polarization patterns are relatively simple. This could be the only time during which many animals with poorly developed polarization sense would be able to use to their advantage. This phenomenon has been found in many different animals, such as bees, ants and even birds, during their foraging and migrating [30]. Navigation during twilight is based on knowledge of the solar-antisolar or meridians coinciding with

the mirror symmetry axis of the polarization pattern. However, as shown in Fig. 3, under the heavy-loading aerosol atmosphere, the neutral points are off the local meridian plane and an angular difference around 13.5 deg exists in the symmetry axis of skylight polarization patterns and the solar-antisolar line. Thus, polarization-sensitive animals inevitably disorient themselves when they use this altered skylight polarization pattern as they did for navigation and it may cause severe tragedies. Similar examples of animal disorientation elicited by anomalous sky polarization have been reported in total solar eclipse 1 February 2015 / Vol. 54, No. 4 / APPLIED OPTICS

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periods and smoky skies during forest fires [30]. Here, we reported a new case. With the increase of anthropogenic aerosol emission, those animals could suffer serious consequences and an uncertain future. B.

Circular Polarization

For high solar elevations, the skylight intensity consists mostly of light generated from the first scattering. At sunset, the linear polarization reaches its maximum at the zenith area (same as p12 ). If the second scattering affected those linear polarization components, circular polarization components could be generated in the forward direction (same as P34 ). Since the measurements along the local median contain a relatively large range of scattering angles, they are suitable for observing the existence of circularly polarized light. In Table 1, the circular polarization components are almost negligible for both cases. This is consistent with many previous observations and simulations. However, this may also indicate that the amount of circularly polarized light is beyond the capability of our system. C.

Uncertainty in the Measurement

Although we have calibrated the front optical path as a unit, the relationship between the fish-eye lens’ off-axis angle and Mueller matrix elements may still be an uncertainty. Apart from the potential error sources listed at the end of Subsection 2.D, the fish-eye lens also could alter the Stokes parameters of the incident light. Within the calibration results of the reduced Mueller matrix of the sigma 8 mm fisheye lens (like [31] and [32], which mainly focus on the measuring of linear polarization), the m12 and m13 of the lens’ Mueller matrix were almost equal to zero, which means the polarization states were unchanged after passing through the fish-eye lens. In fact, most optics lenses have little depolarization effect [24]. In the system built in [24], the calibration results indicated that only slight changes in the lens’ matrix with respect to unity had been found. And the fish-eye lens was close to an identity matrix at the center, but slightly worse at high incidence angles. 5. Conclusions

In this paper we discussed building an imaging polarimeter that also has the potential to measure circular polarization. The calibration was also introduced. From the comparison between measurements of clear sky and high-loading aerosol atmosphere, we can derive the following conclusions: • In the high-loading aerosol atmosphere, skylight polarization patterns do not distribute symmetrically along the local meridian plane any more. There is a certain angular difference between the real symmetry axis and local meridian. • We show that the observed circular polarization component is negligible under both clear and highloading aerosol skies. B264

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