Application of Polarimetry to Surveillance and Underwater Imaging

Abstract

This dissertation discusses two major topics: The separation of images with polarimetric imaging and the total internal reflection under water. It is organized as follows. Chapter 1 is the introduction and it talks about the basics of polarization optics. It starts with the Maxwell’s equations to derive the wave equation of plane electromagnetic waves, and then talks about the Jones vectors and Jones matrices, which describe the polarization properties of monochromatic waves and of optical components that are illuminated by the waves. The Fresnel reflection is then discussed using the Jones calculus. After that, the discussion is extended to polychromatic light, where the Stokes vectors and Mueller matrices are used instead. The Mueller matrices for Fresnel reflection is given at last. In chapter 2 and chapter 3, image separation with unpolarized objects and polarized objects are studied. The Mueller matrix equations for scenes with various reflectors are derived, and the algorithms that solve the corresponding scalar equations for separated images are developed. In the algorithms, the correlation between images is evaluated by a metric function – edge overlap – that is developed specifically for this image separation application. A variety of test scenes and separation results are shown to demonstrate the advantages and disadvantages of the proposed separation method. In addition, a limit of this method imposed by the signal-to-noise ratio of the captured images is estimated. At the end, the extension of the proposed method to scenes with multiple reflectors are discussed. Chapter 4 serves are the introduction to the second topic. It goes over the situations in Nature that total internal reflection could happen, and briefly studies the related polarization effects. Chapter 5 and chapter 6 then focus on the total internal reflection at the water-air interface. In chapter 5, the conversion from linearly polarized light to circularly/elliptically polarized light in total internal reflection is studied, and a maximum conversion efficiency is calculated. A maximum degree-of-circular-polarization circle is predicted in the captured reflected image, and the relation between the degree-of-circular-polarization of the reflected light and the surface properties of the captured objects in the image are found to resemble the Umov effect. Meanwhile, chapter 6 calculates the same conversion efficiency across a water bubble and computes various “average” conversion efficiencies. Finally, chapter 7 summarizes the above studies. The study of image separation has found applications in surveillance while the study of total internal reflection is currently mainly of academic interests. However, the additional information in the polarization properties of light has not been fully appreciated and made use of in most optical systems. We hope that the studies in this dissertation could shine a light on the future applications of polarization optics.