AN INVESTIGATION OF SKYLIGHT POLARIZATION USING A SPECTRO-POLARIMETER. Jonathan Travis Slater. A senior thesis submitted to the faculty of

Transcription

1 AN INVESTIGATION OF SKYLIGHT POLARIZATION USING A SPECTRO-POLARIMETER by Jonathan Travis Slater A senior thesis submitted to the faculty of Brigham Young University - Idaho in partial fulfillment of the requirements for the degree of Bachelor of Science Department of Physics Brigham Young University - Idaho April 2016

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3 Copyright 2016 Jonathan Travis Slater All Rights Reserved

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5 BRIGHAM YOUNG UNIVERSITY - IDAHO DEPARTMENT APPROVAL of a senior thesis submitted by Jonathan Travis Slater This thesis has been reviewed by the research committee, senior thesis coordinator, and department chair and has been found to be satisfactory. Date Dr. Todd Lines, Advisor Date Dr. Richard Hatt, Committee Member Date Dr. Stephen Turcotte, Committee Member Date Dr. Stephen McNeil, Chair

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7 ABSTRACT AN INVESTIGATION OF SKYLIGHT POLARIZATION USING A SPECTRO-POLARIMETER Jonathan Travis Slater Department of Physics Bachelor of Science The Spectro-Polarimeter project sought to measure the skylight polarization across a spectral range by rotating a linear polarizer. The measurements from the Spectro-Polarimeter instrument were used to calculate the corresponding Stokes parameters describing the skylight polarization. However, a number of challenges hindered the successful outcome of the project. Many of these challenges were overcome. The most difficult proved to be an unpredictable instrument response likely caused by a fiber optic cable. As a result, skylight polarization measurements proved less conclusive than anticipated.

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9 ACKNOWLEDGMENTS I would like to thank my research advisor, Dr. Joseph Shaw of the Department of Electrical and Computer Engineering at Montana State University. Dr. Shaw s advice and assistance proved invaluable during the course of the Spectro-Polarimeter research. I am also grateful for the assistance of Paul Nugent and David Riesland at Montana State University s Optical Remote Sensor Laboratory. My research would not have been possible without the funding of the National Science Foundation. I am grateful for the National Science Foundation s sponsorship and support to the Research Experience for Undergraduates program. I would also like to acknowledge the Department of Physics at Montana State University for hosting the Research Experience for Undergraduates program. Thank you to each of the faculty involved in this program. I especially give my thanks to the Department of Physics at Brigham Young University-Idaho. I am grateful for the support and patience of each of my professors; my special thanks to Dr. Todd Lines, Dr. Richard Hatt, Dr. Jon Paul Johnson, and Dr. Stephen Turcotte. Finally, I must express my greatest thanks to my family. I am profoundly grateful for my parents and their unfailing support. Most of all, I am grateful for the love and support of my dear wife, Nicole. You have made all of the difference.

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11 Contents Table of Contents List of Figures xi xiii 1 Introduction Polarization Stokes Parameters and Mueller Matrices Rayleigh and Mie Scattering Maximum Polarization of Skylight Previous Spectro-Polarimeter Research Methods Experimental Apparatus Measurements Principal Plane Calibration Another Randomly Polarized Source Results Initial Data Analysis Measurement Comparison Instrument Response Equatorial Mount Problem Generating Stokes Vectors Conclusion 29 Bibliography 30 A Measurement Direction Code 33 B Data Analysis and Stokes Calculations 39 xi

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13 List of Figures 1.1 Light as an electromagnetic wave Light through a polarizing filter All sky polarization image Spectro-Polarimeter setup Single measurement and data set average Principal plane Integrating sphere calibration Clear day measurement Hazy day measurement Integrating sphere spectral curve Integrating sphere instrument response Equatorial mount problem Normalized Stokes parameters Future polarimeter circuit A.1 Choosing the direction of measurement xiii

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15 Chapter 1 Introduction There are many optical phenomena we can observe in the Earth s atmosphere. Measuring these optical phenomena helps increase our understanding of how the world works. The goal of my project was to study the polarization of skylight using a Spectro-Polarimeter and generate a quantifiable description of the skylight polarization. The Spectro-Polarimeter is an instrument assembled from several commercial components that measures the polarization of skylight within the spectral range of 350 to 2500 nm. A previous project assembled the Spectro-Polarimeter and developed the user interface. My work focused on using skylight polarization measurements to generate Stokes parameters. To introduce the Spectro-Polarimeter project, I will discuss relevant topics such as polarization, the effects of atmospheric scattering on polarization, and quantitative measures of polarization. Furthermore, I will discuss the instrumental setup of the Spectro-Polarimeter, calibration techniques, measurement data, and overall project analysis. 1

16 2 Chapter 1 Introduction 1.1 Polarization Light is an electromagnetic wave. Polarization describes the particular orientation of the electric field of the light. [1] Thus, in addition to irradiance and wavelength, polarization is another measurable characteristic of light. There are several different kinds of polarization; linear, circular, and elliptical are examples of types of polarization. My research focused solely on the linear polarization of skylight. Linear polarization of light is characterized as having the electric field of the propagating electromagnetic wave restricted to a single plane. Figure 1.1 illustrates the electric field of linearly polarized light oscillating in the plane of polarization. Light may also be randomly polarized (often described as unpolarized light). Randomly polarized describes light with an electric field changing randomly in time. The sun outputs light that is randomly polarized. Randomly polarized light can become polarized by scattering, reflection, or transmission through a filter or polarizing medium. [2] When sunlight enters the Earth s atmosphere, randomly polarized light can often become partially polarized as a result of scattering off atmospheric particulates. The chief goal of my research was to measure skylight polarization using a Spectro-Polarimeter. A practical definition of spectropolarimetry is the process of measuring the polarization properties of light, an element, or system over some defined spectral region. [2]

17 1.2 Stokes Parameters and Mueller Matrices 3 Horizontal Polarization y B Plane of polarization E B E v z E B E B x Figure 1.1 Polarization corresponds to the orientation of the electric field ( E). Linearly polarized light has an electric field restricted to the plane of polarization. This figure is adapted from [3]. 1.2 Stokes Parameters and Mueller Matrices A modern quantitative description of polarization uses the Stokes vector containing four quantities called the Stokes parameters. Equation 1.1 shows a frequently used notation for the Stokes vector and Stokes parameters. S = s 0 s 1 s 2 s 3 (1.1) The parameters of the Stokes vector are useful because they are able to describe randomly, totally, or partially polarized light. [1] One method of calculating the Stokes parameters is by passing light through a polarizing filter. [4] For example, light passing through a single linear polarizer with a horizontal transmission axis will become

18 4 Chapter 1 Introduction horizontally polarized. The irradiance of the emerging light in this case is designated as I(0 ). Similarly, light passing through a vertically aligned polarizer becomes vertically polarized and is represented as I(90 ). Figure 1.2 demonstrates how the electric field of incident light becomes horizontally polarized after passing through a polarizing filter. Polarizing Filter Polarizer E E of randomly polarized light oscillates randomly in all directions. Only the component of E perpendicular to the polymer molecules is transmitted. Figure 1.2 Linear polarization caused by a linear polarizer. This figure is adapted from [3]. Each Stokes parameter is defined by a certain combination of polarization states. While there are a number of different methods to calculate the Stokes parameters, I have listed one possible method in Equation 1.2. This method for calculating the Stokes parameters has been adapted from [4].

19 1.2 Stokes Parameters and Mueller Matrices 5 s 0 = I(0 ) + I(90 ) s 1 = I(0 ) I(90 ) s 2 = 2I(45 ) I(0 ) I(90 ) (1.2) s 3 = I(0 ) + I(90 ) 2I cir For the parameters listed in Equation 1.2, the s 3 term describes the degree of circular polarization. Since my research focused solely on linear polarization, I did not use the s 3 parameter in my Stokes vector calculations later on. Instead, I focused on the first three Stokes parameters as these correspond to measures of linear polarization. In order to measure each Stokes parameter, I used a single linear polarizer and rotated the polarizer s transmission axis to the 0 degree, 45 degree, and 90 degree orientations and measured the resulting irradiance. Besides the Stokes vector, quantitative representation of polarization may also involve Mueller matrices. These 4 4 matrices represent the properties of an optical element or system. [2] As light represented by a Stokes vector passes through an optical element or system, the polarization state of the light may be altered. The emerging light has a changed polarization state and is represented by a new Stokes vector. A Mueller matrix is a transformation matrix representing the change the optical element or system causes on the light passing through. [1] One of the potential aspects of the Spectro-Polarimeter project was an option to solve for Mueller matrices associated with the atmospheric conditions causing the polarization state of the measured skylight. Consider Equation 1.3 as an example of a Mueller Matrix applied to a Stokes vector. This setup represents light passing through a linear polarizer. Randomly polarized light (represented by the Stokes vector S) passes through a horizontal linear polarizer (represented by the Mueller matrix M). A new Stokes vector, S, represents

20 6 Chapter 1 Introduction the emerging horizontally polarized light. The total intensity of the emerging light, S, is only half of the intensity of the randomly polarized light, S, because only the horizontal component of the incident light s electric field is transmitted through the polarizer. 1 2 M S S = (1.3) The atmosphere acts similar to a polarizing filter except that the light is not completely polarized. This partially polarized light scattered by the atmosphere may be comprised of multiple polarization states. As a result, Mueller matrices corresponding to the transformation of light as it passes through the atmosphere are more complicated. Nevertheless, one can still solve for these matrices once a Stokes vector is calculated using the data collected from the Spectro-Polarimeter. 1.3 Rayleigh and Mie Scattering Rayleigh and Mie scattering is the process by which sunlight is scattered in the Earth s atmosphere. Molecules that make up air (nitrogen, oxygen, etc.) are constantly vibrating. Photons passing through air interact with air molecules and scatter elastically, causing a change in the direction the photons are traveling. Due to electronic resonances air molecules have at the shorter wavelengths, violet and blue light are scattered more than the longer wavelengths of red, orange, and yellow light. [1] Rayleigh scattering may be considered as a small-size limiting case of Mie scattering. [1] In my research I have defined Mie scattering to be scattering off of any

21 1.4 Maximum Polarization of Skylight 7 particle larger than the wavelength of incident light. Mie scattering is only weakly dependent on the wavelength of light. Consequently, Mie scattering becomes completely independent of wavelength once the size of the scattering particle surpasses the wavelength of the scattered light. [1] One example of Mie scattering is demonstrated by light scattering off of the clouds on an overcast day. The clouds appear white or gray because all of the wavelengths of visible light are equally scattered since the water droplets in clouds are significantly larger than the wavelengths of visible light. 1.4 Maximum Polarization of Skylight There are certain locations in the sky that are more polarized from scattering than others. Rayleigh and Mie scattering play a significant role in differences in the degree of skylight polarization. Rayleigh scattering causes an increase in the degree of polarization of light 90 degrees from the light source. However, Mie scattering will usually decrease the degree of polarization of skylight. The results of my measurements with the Spectro-Polarimeter were directly impacted by both of these types of scattering. Several reasons explain why the polarization at 90 degrees is not 100 percent. These reasons include multiple scattering, molecular anisotropy, ground reflectance, and aerosols. [5] Figure 1.3 is an all-sky image illustrating the degree of linear polarization of skylight. The figure has depicted this band of maximum skylight polarization in orange. At 90 degrees from the sun there is a band of maximum polarization. It is within this band that I made my measurements with the Spectro-Polarimeter.

22 8 Chapter 1 Introduction Figure 1.3 At 90 degrees from the sun there is a band of maximum polarization represented in this figure by the orange band above. Image from [6] and [7]. 1.5 Previous Spectro-Polarimeter Research The Spectro-Polarimeter project is a continuation of previous work at Montana State University s Optical Remote Sensor Laboratory. [8] This prior work focused on the design and assembly of the Spectro-Polarimeter, a user interface to control the Spectro- Polarimeter via a graphical user interface (GUI), and the characterization of the Spectro-Polarimeter instrument. [9] Much of the documentation from the previous researched proved useful in my research.

23 1.5 Previous Spectro-Polarimeter Research 9 The design and assembly of the Spectro-Polarimeter used several commercial products. I will discuss these components in more detail within the Methods chapter. The GUI developed by the previous project was most useful in my measurement process. This interface facilitated control over the Spectro-Polarimeter s equatorial mount, optical rotation stage, and process for recording measurements. I also investigated the instrument characterization during my research. In later sections I will refer to the characterization as the instrument response to polarization states. This particular aspect of the project proved to be the most challenging. I will further explain these challenges in the Results chapter.

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25 Chapter 2 Methods The Spectro-Polarimeter is an assembly of several components of commercial apparatus. For example, the Spectro-Polarimeter uses a commercial spectroradiometer as well as other attachments such as a lens and a linear polarizer. Measuring skylight polarization with the Spectro-Polarimeter required a careful setup and analysis of the data. This chapter will expand on the Spectro-Polarimeter setup, data collection, and calibration techniques. 2.1 Experimental Apparatus The Spectro-Polarimeter instrument is a combination of an Analytical Spectral Devices, Inc. (ASD) FieldSpec Pro Spectroradiometer with an attached optical component containing a linear polarizer, lens, and a rotation stage. In general, the ASD spectroradiometer is designed as a measurement device for relative or absolute light energy. [10] However, in the Spectro-Polarimeter configuration, a rotating polarizer permits the instrument to measure irradiance of light in a particular linear polarization state. 11

26 12 Chapter 2 Methods Figure 2.1 is an image of the Spectro-Polarimeter setup. The optic consisting of a lens and a linear polarizer are attached to a rotation stage. The rotation stage rotates the polarizer to 0, 45, 90, and 135 degree orientations. After passing through the linear polarizer, skylight is transmitted to the spectroradiometer with a fiber optic cable. The fiber optic cable is part of the commercially manufactured ASD spectroradiometer. I secured the fiber optic cable in a coil to the top of the instrument as a preventative measure against the distortion of data that movement of the cable could cause. The spectroradiometer and optic are attached to an Astro-Physics 600E Servo equatorial mount. [11] Both the spectroradiometer and equatorial mount were controlled via laptop computer. The user interface GUI allowed the instrument to be directed toward any part of the sky when the user specifies an elevation and azimuth. The interface also controlled the rotation stage and the spectroradiometer. The Spectro-Polarimeter measures wavelengths ranging from 350 to 2500 nm. This range of wavelengths covers the visible and the short wave infrared (SWIR) spectrums. A single detector is unable to realistically receive data in this entire range of wavelengths. As a result, the spectroradiometer is manufactured with three detectors capable of covering the entire range of 350 to 2500 nm. These detectors group the wavelengths as visible near infrared (VNIR) ranging from 350 to 1050 nm, short wave infrared one (SWIR1) ranging from 900 to 1850 nm, and short wave infrared two (SWIR2) ranging from 1700 to 2500 nm. Each grouping of wavelengths overlaps with each other in order to prevent any loss of data. The VNIR detector uses a 512-channel silicon photodiode array. For both the SWIR1 and SWIR2, the Spectro-Polarimeter uses indium gallium arsenide (InGaAs) detectors.

27 2.1 Experimental Apparatus Figure 2.1 The Spectro-Polarimeter setup on the roof of the Cobleigh Building at Montana State University. The Spectro-Polarimeter uses an equatoral mount, spectroradiometer, and optical configuration with a lens, linear polarizer, and rotation stage. 13

28 14 Chapter 2 Methods 2.2 Measurements I began the process of taking measurements by setting up the Spectro-Polarimeter on the roof of the Cobleigh Building at Montana State University. The Spectro- Polarimeter rests on a standard equatorial mount. Consequently, the mount must be calibrated each time the Spectro-Polarimeter is used. Instructions regarding the equatorial mount calibration are found in [12]. Next, I tested the Spectro-Polarimeter instrument in order to optimize the collection settings. The user interface GUI includes an option to automatically optimize the settings of the Spectro-Polarimeter. The detectors inside the Spectro-Polarimeter perform best when the integration time and gain settings are optimized to maximized readings in the visible and short wave infrared (SWIR) spectrums. Once the Spectro-Polarimeter was ready for measurements, I looked up the current elevation and azimuth of the sun using NOAA s solar calculator website. [13] The coordinates I used on NOAA s Solar Calculator for the Cobleigh Building were N, W. Next, I oriented the Spectro-Polarimeter to a position that was 90 degrees from the sun s current location. As discussed in the introduction, the regions in the sky 90 degrees away from the sun have maximum skylight polarization. Therefore, these are the best regions to direct the Spectro-Polarimeter towards to measure skylight polarization. Once the Spectro-Polarimeter was positioned correctly, I took a series of 20 measurements in a two-minute interval. One of the challenges I noticed early on in the project was that there was very little light measured in the SWIR, particularly the wavelengths above 1700 nm. While it is expected that there is not very much light in these wavelengths, I still hoped to receive some signal in the SWIR. This range of wavelengths also had a great deal of background noise making it very difficult to

29 2.3 Principal Plane 15 distinguish differences between polarization states. My solution to this challenge was to use an average of the 20 measurements in order to cancel out the background noise. Figure 2.2 compares a single measurement (a) with an average of twenty measurements (b). As is evident in the figure, the averaging technique helped reduce the background noise in the SWIR wavelengths. Digital Count/Number /23/ Single Measurement 0 Degrees 45 Degrees 90 Degrees 135 Degrees Digital Count/Number /23/ Data Set Average 0 Degrees 45 Degrees 90 Degrees 135 Degrees Wavelength (nm) Wavelength (nm) (a) Single Measurement (b) Data Set Average Figure 2.2 Averaging a set of measurements taken within a two-minute interval reduced the noise in the SWIR wavelengths. 2.3 Principal Plane During the course of the Spectro-Polarimeter project, I focused on keeping my measurements within the principal plane. The principal plane is the plane containing the sun and the zenith (see Figure 2.3 for a diagram of the principal plane). This simplified the process of locating a position 90 degrees away from the sun. I began by pointing the Spectro-Polarimeter directly at the sun, then moving the instrument 90 degrees across the zenith. Measuring the skylight polarization in the principal plane is a good method to check the reliability of the calculated Stokes parameters. When the instrument is oriented in the principal plane, we expect most of the skylight

30 16 Chapter 2 Methods polarization to be represented by the horizontal polarization (the s 1 parameter). Additionally, we expect the s 2 parameter will not contribute much to the overall skylight polarization and should be close to zero. These expectations follow from princples of Rayleigh scattering. Sun Zenith Direction of observation Principal Plane Figure 2.3 Specto-Polarimeter measurements were primarily made in the principal plane (the plane containing the sun, zenith, and direction towards the region of measurement). Other regions of the sky 90 degrees away from the sun will also have a maximum polarization. I planned to compare Stokes parameters in these regions after my initial measurements and analysis of the Stokes parameters in the principal plane. In preparation for these measurements I wrote a MATLAB code to calculate the corresponding elevation for any specified azimuth within the region 90 degrees away from the sun (see Appendix A).

31 2.4 Calibration Calibration One of the concerns in the analysis of the data involved the response of the instrument to different polarization states. Specifically, the Spectro-Polarimeter is likely to have a variation or instrument response with changes in the polarization state. Since the goal was to measure polarization, this type of variation is less than ideal. I attempted to combat this challenge by testing and calibrating the Spectro-Polarimeter with an integrating sphere. An integrating sphere is an optical device that essentially outputs randomly polarized light. A light source is illuminated into a spherical cavity. This cavity is coated in a white, reflective coating. Since light inside the cavity is consistently scattered off of the cavity walls, the light leaving the integrating sphere does not remain in any particular polarization state. Since the light from the integrating sphere is only emitting randomly polarized light, any orientation of a linear polarizer should give the same result and intensity. In order to test the instrument response of the Spectro-Polarimeter, one simply needs to place the instrument such that it is receiving light directly from the integrating sphere and change the orientation of the polarizer. If there is a variation, then the result can be applied to any data collected in order to get a more accurate picture of the actual polarization state of incident light. Figure 2.4 illustrates the Spectro-Polarimeter setup during the calibration using the integrating sphere. For this calibration process, I used the same methodology as my skylight polarization measurements. I took 20 measurements and averaged each of the polarization states together in order to cancel out any background noise. The results of these measurements indicated that instrument response for the different polarization states was fairly minimal (less than one percent). I will discuss the integrating sphere data in further detail in the Results chapter.

32 18 Chapter 2 Methods There was a key challenge with using the integrating sphere as a calibration source. The integrating sphere in the Optical Remote Sensor Laboratory is only calibrated up to 1100 nm light. Since the Spectro-Polarimeter takes data from 350 to 2500 nm, it is not possible to determine the instrument response using the integrating sphere for wavelengths longer than 1100 nm. Figure 2.4 The setup calibrating the instrument response of the SpectroPolarimeter using an integrating sphere. The integrating sphere is a white spherical cavity that scatters a light source to emit randomly polarized light. 2.5 Another Randomly Polarized Source Another source of randomly polarized light is the sun. The sun emits randomly polarized light in a much larger range of wavelengths than the integrating sphere. Consequently, I attempted to perform the same calibration technique using the sun instead. At the time, it seemed like a fairly simple process. Nevertheless, it was far from simple and proved to be a much less viable solution than the integrating sphere.

33 2.5 Another Randomly Polarized Source 19 I maintained the same calibration method using the sun as the calibration using the integrating sphere. I oriented the Spectro-Polarimeter directly towards the sun and took 20 measurements during the course of two minutes. Since the earth is constantly rotating, the position of the sun constantly changes. Data taken from a fixed position cannot be trusted for more than several minutes. When I examined the averaged sets of measurements taken in the two-minute intervals, each set of data had significant variations in the instrument response. Upon examining single, unaveraged measurements, consecutive measurements taken within seconds of each other also demonstrated significant variation and inconsistency from each other in measuring the instrument response. These variations were more pronounced in the SWIR wavelengths. I was not able to completely surmise the cause of the calibration measurement variations. One possibility is that the fiber optic cable was the cause of this variation. Another possibility is the presence of very thin cirrus clouds or ice crystals could have been changing the polarization state. Neither of these explanations can be completely ruled out as the cause of the variations without further experimentation. Perhaps future research could find some interesting results corresponding to this particular problem. I concluded that the sun was not a feasible solution to check for any instrument response to polarization states. The instrument response to polarization states did not appear to fluctuate as much in the visible spectrum as the SWIR spectrum. With this observation, I decided to continue the next phase of the project and calculate the Stokes parameters. However, I decided to focus solely on the data collected in the visible spectrum since the instrument response in the SWIR spectrum data appeared far more inconsistent. Using only the visible spectrum data meant that I could use the calibration data from the integrating sphere.

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35 Chapter 3 Results The results from the Spectro-Polarimeter research were a step in the right direction. However, it is clear that the instrument itself has certain limitations that cannot yet be overcome with regards to measuring polarization. While some of the results are in line with the expectations of the project, others fall short. I was able to calculate the Stokes parameters corresponding to my skylight polarization measurements. However, the results from which these parameters are derived are not sufficiently conclusive, as will be discussed in this chapter. 3.1 Initial Data Analysis As highlighted in the Methods chapter, I used sets of 20 measurements averaged together as a method of cancelling out background noise from the measurements. I created a MATLAB code (see Appendix B) to read in data stored in comma separated value (CSV) files. The code read in each measurement file and separately averaged the 0 degree, 45 degree, and 90 degree polarization states together. Overall, the averaging did help in reducing the background noise, particularly in the SWIR wavelengths as 21

36 22 Chapter 3 Results was shown in Figure Measurement Comparison As discussed in the introduction, Rayleigh and Mie scattering both have a significant impact on atmospheric polarization. Perfect Rayleigh scattering conditions contribute to a maximum skylight polarization in regions 90 degrees from the sun. However, Mie scattering reduces the overall polarization of skylight. Both of these types of scattering were clearly demonstrated by the Spectro-Polarimeter data by comparing measurements from two different days. Both of these particular days had sunny weather with very few clouds. However, the key difference was in the concentration of aerosols present in the atmosphere. For example, consider Figures 3.1 and 3.2 comparing measurements from two days with different atmospheric conditions. The first day (6/23/15) was very clear with very few aerosols and traits exhibiting mostly Rayleigh scattering. The second day (7/31/15) was very hazy and had a significant amount of aerosols present due to smoke from nearby forest fires. The smoke in the atmosphere tends to cause conditions more closely aligned with that of Mie scattering. As a result, there is an increase in the overall irradiance detected by the Spectro-Polarimeter from the region 90 degrees away from the sun. In particular, the hazy day illustrated by Figure 3.2 shows an increased signal in the SWIR wavelengths. The peaks at approximately 1050, 1240, and 1540 nm are much more pronounced on the hazy day than the clear day.

37 3.2 Measurement Comparison 23 Digital Count/Number /23/ Data Set Average: Clear Day 0 Degrees 45 Degrees 90 Degrees 135 Degrees Wavelength (nm) Figure 3.1 A clear day with few aerosols exhibits more Rayleigh scattering and overall less light from the regions of the sky 90 degrees away from the sun. Digital Count/Number /2/ Data Set Average: Hazy Day 0 Degrees 45 Degrees 90 Degrees 135 Degrees Wavelength (nm) Figure 3.2 A hazy day with a significant amount of aerosols is more characteristic of Mie scattering and results in more scattered light in the regions of the sky 90 degrees away from the sun.

38 24 Chapter 3 Results 3.3 Instrument Response In the Methods chapter I discussed calibration techniques. It was very clear that both methods I attempted to use in order to calibrate the data into meaningful results were inadequate for the full 350 to 2500 nm range. The integrating sphere simply did not provide a sufficient range of wavelength for the calibration and calibration using the sun proved to have too much measurement variation. As a result, I chose to only look at the data from the visible spectrum to calculate the Stokes parameters. Using the calibration data collected by the integrating sphere, I calculated the instrument response to polarization with respect to the 0 degree orientation of the polarizer. This response was divided out of the Spectro-Polarimeter data. I defined the instrument response as the ratio of each polarization state with respect to the 0 degree orientation of the polarizer as shown in Equation 3.1 and used these definitions of instrument response to generate Figure 3.4. R 0 (λ) = I 0 (λ) I 0 (λ) R 45 (λ) = I 45 (λ) I 0 (λ) R 90 (λ) = I 90 (λ) I 0 (λ) (3.1) In addition to the instrument response to polarization states, the Spectro-Polarimeter exhibits an instrument spectral responsivity. This spectral responsivity is characteristic of the silicon detector the Spectro-Polarimeter uses the measure irradiance in the visible spectrum. Figure 3.3 illustrates the spectral curve the Spectro-Polarimeter measures from the integrating sphere.

39 3.3 Instrument Response 25 Digital Count/Number (x 10 4 ) Integrating Sphere Spectral Curve 0 Degrees 45 Degrees 90 Degrees 135 Degrees Wavelength (nm) Figure 3.3 The spectral curve of the integrating sphere as measured by the Specto-Polarimeter. Ratio to 0 degrees Integrating Sphere Instrument Reponse 0 Degrees 45 Degrees 90 Degrees 135 Degrees Wavelength (nm) Figure 3.4 The instrument response obtained from the integrating sphere using the ratios in Equation 3.1 The calibration data in Figure 3.4 suggests that the instrument response to polarization states is fairly minimal. Yet, the significant measurement variation exhibited by a calibration attempt using the sun calls into question the realiabilty of the sky-

40 26 Chapter 3 Results light polarization data. The greatest weakness of the Spectro-Polarimeter is the fiber optic cable attached to the spectroradiometer. When the fiber optic cable is moved, the irradiance as measured by the Spectro-Polarimeter changes. My solution was to fix the fiber optic cable in place. However, this solution did not improve the variability in the data, particularly in methods attempting to use the sun as a calibration source. Another possible cause for this continued variation in instrument response is the change in the temperature of the fiber optic cable as the measurements are taken. When the Spectro-Polarimeter is set up, the instrument remains in direct sunlight during the data collection. It is likely that as the sun heats the fiber optic cable, the index of refraction of the cable changes as well as the response to changes in polarization. In the end, the variability of the instrument response was too great to overcome in order to find sufficiently conclusive results. 3.4 Equatorial Mount Problem The equatorial mount is very useful. With it, a user may enter an elevation and azimuth and the mount will orient the instrument to the corresponding region in the sky. Yet, one of the challenges associated with this feature is that the instrument is tilted from its original orientation. This means the linear polarizer is also tilted from its initial horizontal orientation when measuring the 0 degree polarization state. Moreover, the subsequent measurements of the 45 and 90 orientations of the polarizer are also tilted. However, when the mount moves the Spectro-Polarimeter in order to measure a particular region of the sky, the instrument (and the polarizer) are tilted and are no longer oriented correctly. As a result, the orientations of the polarizer become meaningless. Each time the Spectro-Polarimeter is oriented to a new location in the sky, the tilt changes. Thus, there is no consistent orientation of the linear

41 3.4 Equatorial Mount Problem 27 polarizer and comparisons between separate measurements are no longer meaningful. (a) Spectro-Polarimeter Linear Polarizer (b) Tilted Spectro-Polarimeter Figure 3.5 The linear polarizer (a) has two white lines to show the polarization axis. When the mount tilts the instrument (b), the polarizer is no longer in the horizontal orientation. The solution to this challenge was to apply a rotation matrix to the data such that the data from separate measurements can be compared. The matrix defines θ as the angle at which the mount is tilted. Note the rotation matrix here uses 2θ since this situation deals with intensities rather than amplitudes. More information on this type of rotation matrix is explained in [14] cos(2θ) sin(2θ) sin(2θ) cos(2θ) (3.2)

42 28 Chapter 3 Results 3.5 Generating Stokes Vectors After applying the data set averaging, calibration results, and rotation matrix, I was able to use the Spectro-Polarimeter data to generate a graph representing normalized Stokes vectors in the visible spectrum. I calculated the s 0, s 1, and s 2 parameters using Equation 1.2. Then, I normalized the parameters by letting each parameter be a ratio with respect to the s 0 parameter. Figure 3.6 depicts these normalized Stokes parameters across the visible spectrum. The figure does not quite represent the expected results for measurement of skylight polarization. In particular, the steep rise and fall exhibited in the curves for the s 1 and s 2 parameters suggests that the spectral responsivity of the Spectro-Polarimeter is still present in the data. Unfortunately, I was unable to find a method to remove the spectral responsivity. 1.2 Normalized Stokes Parameters vs Wavelength S 0 1 S 1 S 2 Parameter Ratio to s Wavelength (nm) Figure 3.6 The normalized Stokes parameters as measured on 7/31/15.

43 Chapter 4 Conclusion While not entirely successful, the Spectro-Polarimeter project has been a step in the right direction of skylight polarization measurements. The greatest challenge was the instrument response to polarization states and spectral responsivity of the Spectro- Polarimeter. Had there been a method to fully overcome this challenge, I am confident the results of the Spectro-Polarimeter project would have been more conclusive. In hindsight, one adjustment that might have improved the results would have been to rotate a quarter wave plate and keep the linear polarizer fixed. This setup would permit only one polarization state to enter the instrument at different intensities as the quarter wave plate is rotated. This method would also enable measurement of the s 3 parameter corresponding to circular polarization. However, this setup would still likely have difficulties with inconsistent instrument response. The next developments of this research are underway in the construction of another polarimeter. This new polarimeter will be a much simpler design and will not be able to measure polarization over the entire spectral range. This polarimeter will use a Thorlabs FDS100 photodiode capable of detecting light within wavelengths of 350 to 1100 nm. The photodiode connected to a circuit will output a voltage difference 29

44 30 Chapter 4 Conclusion corresponding to the measured irradiance. A linear polarizer rotated in front of the photodiode will change the voltage output. My goal is to again calculate the Stokes parameters associated with polarization measurements with this polarimeter. Figure 4.1 The suggested circuit for the Thorlabs FDS100 photodiode to be used in a future polarimeter. [15]

45 Bibliography [1] Hecht, E., Optics., 4 ed. Addison-Wesley. [2] Tyo, J. S., Goldstein, D. L., Chenault, D. B., and Shaw, J. A., Review of passive imaging polarimetry for remote sensing applications. Applied Optics, 45(22), Aug, pp [3] Knight, R. D., Physics for Scientists and Engineers with Modern Physics: A Strategic Approach., 3 ed. Pearson Education. [4] Collett, E., Measurement of the four stokes polarization parameters with a single circular polarizer. Optics Communications, 52(2), pp [5] Jackson, J. D., Classical Electrodynamics., 3 ed. Wiley. [6] Shaw, J. A., Pust, N. J., Staal, B., Johnson, J., and Dahlberg, A. R., Continuous outdoor operation of an all-sky polarization imager. [7] Dahlberg, A. R., Pust, N. J., and Shaw, J. A., Effects of surface reflectance on skylight polarization measurements at the mauna loa observatory. Optics Express, 19(17), Aug, pp [8] Shaw, J. A. The optical remote sensor laboratory. 31

46 32 BIBLIOGRAPHY [9] Riesland, D., Burgard, N., and Sharon, Z., Spectro-polarimeter characterization and control. [10] Analytical Spectral Devices, Inc., FieldSpec Pro: User s Guide. [11] Astro-Physics, Inc., Astro-Physics 600E German Equatorial Mount With SMD Servo Motor Drive. [12] Astro-Physics, Inc., Astro-Physics GTO Keypad. [13] Administration, N. O.. A. Noaa solar calculator. [14] Collett, E., Polarized Light: Fundamentals and Applications. Marcel Dekker. [15] Thor Labs, Si Photodiode nm: FDS 100.

47 Appendix A Measurement Direction Code I wrote the following code to assist the user in choosing a direction in which to point the Spectro-Polarimeter for skylight polarization measurements. In order to measure the maximum degree of polarization, the Spectro-Polarimeter should be directed to a region of the sky that is 90 degrees away from the sun. 1 %% Locate Position 90 Degrees From the Sun 2 % Given an azimuth, find the elevation of a point that is 90 degrees 3 % from the current location of the sun. 4 clear; close all; clc; 5 % Jon Slater 6 7 %% User Inputs 8 fprintf('\nenter the following quantities in units of degrees:\n') 9 10 % current azimuth of the sun (use NOAA Solar Calculator) 11 azimuth = input('\nwhat is the azimuth of the sun? '); 12 while azimuth > 360 azimuth < 0 13 fprintf('invalid input for the azimuth.\n') 14 fprintf('choose a value between 0 and 360.\n\n') 15 azimuth = input('what is the azimuth of the sun? '); 16 end % current elevation of the sun (use NOAA Solar Calculator) 19 elevation = input('\nwhat is the elevation of the sun? '); 20 while elevation > 90 elevation < 0 21 fprintf('invalid input for the elevation.\n') 22 fprintf('choose a value between 0 and 90.\n\n') 33

48 34 Chapter A Measurement Direction Code 23 elevation = input('what is the elevation of the sun? '); 24 end % give an azimuth for the direction of observation 27 Az obs = input('\nazimuth in the direction of observation? '); 28 while Az obs > 360 Az obs < 0 29 fprintf('invalid input.\n') 30 fprintf('choose a value between 0 and 360.\n\n') 31 Az obs = input('azimuth in the direction of observation? '); 32 end %% Spherical and Cartesian Coordinate Conversions 35 % converting location of the sun to spherical coordinates 36 phi = azimuth; 37 theta = 90 - elevation; % Spherical to Cartesian coordinates for the sun (North is +x axis) 40 X = sind(theta)*cosd(phi); 41 Y = sind(theta)*sind(phi); 42 Z = cosd(theta); % converting to polar coordinates (2D) 45 polar angle = Az obs; % Cartesian coordinates of the direction of observation (2D) 48 X obs = cosd(polar angle); 49 Y obs = sind(polar angle); %% Normal Vector (ie vector towards the sun) 52 % vector pointing towards the sun 53 normal = [X Y Z]; % equation of the plane given a normal vector 56 a = normal(1); 57 b = normal(2); 58 c = normal(3); 59 Z obs = (- a * X obs - b * Y obs)/c; % find the vector for the direction of observation 62 Observation = [X obs Y obs Z obs]; 63 % normalize the perpendicular vector 64 Observation = Observation./norm(Observation); % Spherical coordinates of location of observation 67 phi obs = atand(y obs/x obs); 68 theta obs = atand(sqrt(x obsˆ2+y obsˆ2)/z obs); % elevation of the point of observation 71 El obs = 90 - theta obs; %% Dot Product Test

49 35 74 % Spherical coordinates 75 test phi = Az obs; 76 test theta = 90 - El obs; 77 % Cartesian coordinates 78 test X = sind(test theta)*cosd(test phi); 79 test Y = sind(test theta)*sind(test phi); 80 test Z = cosd(test theta); 81 % vector in the direction of observation 82 vector = [test X test Y test Z]; 83 test = dot(normal,vector); % if the dot product is not close enough to zero, output an error 86 if abs(test) > 10e-9 87 fprintf('\nerror: Invalid elevation and azimuth values\n\n') 88 return 89 end %% Principal Plane Observation 92 % The best case scernario will be to make observations in the 93 % principal plane if we are using an equatorial mount. A measurement 94 % in the principal plane will give the simplest method of calculating 95 % the Stokes parameters % azimuth for an observation in the principal plane 98 if azimuth < ap = azimuth + 180; 100 else 101 ap = azimuth - 180; 102 end 103 % elevation for an observation in the principal plane 104 ep = 90 - elevation; % converting location to spherical coordinates 107 princ phi = ap; 108 princ theta = 90 - ep; % Spherical to Cartesian coordinates (North is positive x axis) 111 Xp = sind(princ theta)*cosd(princ phi); 112 Yp = sind(princ theta)*sind(princ phi); 113 Zp = cosd(princ theta); % vector pointing towards an observation point in the principal plane 116 principal = [Xp Yp Zp]; %% Outputs 119 % in case the elevation of the point of interest is > 90 degrees 120 if El obs > fprintf('warning: Area of observation is too close to sun!\n\n') 122 flip = El obs - 90; 123 el = 90 - flip; 124 El plot = el;

50 36 Chapter A Measurement Direction Code 125 if Az obs >= az = Az obs - 180; 127 Az plot = az; 128 else 129 az = Az obs + 180; 130 Az plot = az; 131 end 132 fprintf('instead, look at an Azimuth of %3.0f\n',az) 133 fprintf(' and an Elevation of %3.2f \n\n',el) 134 else 135 % output the elevation at which one should look 136 fprintf('\nlook at an elevation of %3.2f degrees\n\n', El obs) 137 El plot = El obs; 138 el = El plot; 139 Az plot = Az obs; 140 end % output notice if sun is too high or observation area too low 143 if elevation > fprintf('the sun is too high for effective measurements.\n') 145 fprintf('consider waiting until the sun is lower.\n\n') 146 elseif (El obs < 10 el < 10) 147 fprintf('observation area is too low for effective measurements') 148 fprintf('\nconsider changing the direction of observation.\n\n') 149 % recommend making the observation in the principal plane 150 fprintf('consider making observations in the principal plane.\n') 151 fprintf('look at an Azimuth of %3.1f\n',ap) 152 fprintf(' and an Elevation of %3.2f \n\n',ep) 153 else 154 % recommend making the observation in the principal plane 155 fprintf('consider making observations in the principal plane.') 156 fprintf('\nlook at an Azimuth of %3.1f\n',ap) 157 fprintf(' and an Elevation of %3.2f \n\n',ep) 158 end %% Visualization Plot 161 quiver3(0, 0, 0, normal(1), normal(2), normal(3),'r') 162 hold on 163 quiver3(0, 0, 0, vector(1), vector(2), vector(3),'b') 164 legend('sun','observation','location','southeast') 165 axis equal 166 xlim([-1,1]) 167 ylim([-1,1]) 168 zlim([0,1]) 169 xlabel('north/south') 170 ylabel('east/west') 171 zlabel('zenith') 172 set(gca,'xticklabel',[],'yticklabel',[],'zticklabel',[]); 173 text1 = text(normal(1),normal(2),normal(3), strcat('az = ',num2str(azimuth),' El = ',num2str(elevation))); 175 text2 = text(vector(1),vector(2),vector(3),...

51 strcat('az = ',num2str(az plot),' El = ',num2str(el plot))); 177 title('locate Position 90 Degrees From The Sun') 178 set(gca,'fontsize',18) 179 set(text1,'fontsize',14) 180 set(text2,'fontsize',14) Locate A Position 90 Degrees From The Sun Az =272 El =62 Zenith Az =92 El =28 sun observation Figure A.1 An example output figure from the program assisting in choosing a direction for measurement. This program permits the user to choose any azimuth and gives a corresponding elevation for a direction 90 degrees away from the sun.

52 38 Chapter A Measurement Direction Code

53 Appendix B Data Analysis and Stokes Calculations I wrote the following code to analyze the data generated by the Spectro-Polarimeter. The program first reads in calibration data from the integrating sphere measurements to calculate the instrument response. Then the program reads in polarization data taken on a particular day and calculates the Stokes parameters. 1 %% Spectro-Polarimeter Visible Light Analysis 2 clear; close all; clc; 3 % Jon Slater 4 5 %% File directory 6 % Set the directory as the folder with the calibration data 7 directory = '/Documents/SpectroPolarimeter/SPIntegratingSphere/6700'; 8 files = dir(fullfile(directory,'*.csv')); 9 L = length(files); % This is to warn the user if there are an incorrect number of files: 12 if mod(l,4) ~= 0 13 for n = 1:4:L 14 fprintf('warning: incorrect number of files\n') 15 end 16 return 17 end 18 39

54 40 Chapter B Data Analysis and Stokes Calculations 19 % divide data into 4 groups with groups: 1:a, a+1:b, b+1:c, c+1:l 20 a = L/4; 21 b = 2*a; 22 c = 3*a; %% Analysis of calibration data at 0 degrees 25 SPdata0 = zeros(2151,a+1); 26 SPdata0(:,1) = 350:2500; 27 i = 2; 28 % readin the data with the polarizer at 0 degrees 29 for j = 1:a 30 filename0 = fullfile(directory,files(j).name); ReadInData = csvread(filename0,1,0); 33 SPdata0(:,i) = ReadInData(:,2); 34 i=i+1; 35 end % finding the average for calibration data w/ polarizer at 0 degrees 38 calib0 = zeros(2151,2); 39 calib0(:,1) = 350:2500; 40 for k = 1:a 41 calib0(:,2) = calib0(:,2) + SPdata0(:,k+1); 42 end 43 calib0(:,2) = calib0(:,2)./a; %% Analysis of polarization data at 45 degrees 46 SPdata45 = zeros(2151,a+1); 47 SPdata45(:,1) = 350:2500; 48 i = 2; 49 % readin the data with the polarizer at 45 degrees 50 for j = a+1:b 51 filename45 = fullfile(directory,files(j).name); ReadInData = csvread(filename45,1,0); 54 SPdata45(:,i) = ReadInData(:,2); 55 i=i+1; 56 end % finding the average for calibration data w/ polarizer at 45 degrees 59 calib45 = zeros(2151,2); 60 calib45(:,1) = 350:2500; 61 for k = 1:a 62 calib45(:,2) = calib45(:,2) + SPdata45(:,k+1); 63 end 64 calib45(:,2) = calib45(:,2)./a; %% Analysis of polarization data at 90 degrees 67 SPdata90 = zeros(2151,a+1); 68 SPdata90(:,1) = 350:2500; 69 i = 2;