Polarization Sensitive Imaging

Inhaltsverzeichnis (Table of Contents)

• Chapter 1. Introduction ..................................................................................................... 1-38
  • 1.1 Background ............................................................................................................... 1
  • 1.2 Origin and purpose of the thesis ............................................................................... 3
  • 1.3 Formulism for completely polarized light ................................................................ 5
    • 1.3.1 The polarization ellipse...................................................................................... 5
    • 1.3.2 Jones matrix formulism ..................................................................................... 8
  • 1.4 Formulism for partially polarized light .................................................................. 13
    • 1.4.1 Stokes polarimetry ........................................................................................... 13
    • 1.4.2 The Poincare sphere method ............................................................................ 16
  • 1.5 Generalized formulism for polarization: coherency matrix .................................... 17
  • 1.6 Mueller matrix formulism ...................................................................................... 19
    • 1.6.1 Mueller matrix decomposition ......................................................................... 21
  • 1.7 Basic interferometric techniques for polarization imaging .................................... 24
    • 1.7.1 Michelson interferometer ................................................................................. 24
    • 1.7.2 Sagnac interferometer ...................................................................................... 25
    • 1.7.3 Mach-Zehnder interferometer .......................................................................... 25
    • 1.7.4 Digital holographic interferometry .................................................................. 26
    • 1.7.5 Off-axis holography ......................................................................................... 27
    • 1.7.6 Digital hologram processing ............................................................................ 28
  • 1.8 Optical anisotropy ................................................................................................... 32
    • 1.8.1 Dichroism ......................................................................................................... 33
    • 1.8.2 Birefringence .................................................................................................... 34
    • 1.8.3 Polarizance ....................................................................................................... 35
    • 1.8.4 Depolarization .................................................................................................. 35
  • 1.9 Liquid crystals and associated optical anisotropy ................................................... 35
    • 1.9.1 Classification of Liquid crystal alignments ...................................................... 36
    • 1.9.2 Spatial light modulator ..................................................................................... 37
  • 1.10 Structure of the thesis: an overview ...................................................................... 38
• Chapter 2. Polarization sensitive digital holography for polarimetric analysis of spatial light modulator…………………………………………………………………………...43-60
  • 2.1 Introduction ............................................................................................................. 43
  • 2.2 Double shot Jones matrix imaging of reflective LC-SLM ...................................... 46
    • 2.2.1 Polarization sensitive digital holography ......................................................... 46
    • 2.2.2 Complex field modulation of LC-SLM ............................................................ 49
    • 2.2.3 Reference calibration of LC-SLM display ....................................................... 50
    • 2.2.4 Jones matrix elements of LC-SLM .................................................................. 55
  • 2.3 Anisotropic properties of LC-SLM ......................................................................... 56
    • 2.3.1 Jones matrix polar decomposition .................................................................... 58
    • 2.3.2 Algebraic method of Jones matrix decomposition ........................................... 60
  • 2.4 Polarization modulation of LC-SLM ...................................................................... 63
  • 2.5 Conclusion ............................................................................................................... 65
• Chapter 3. Mueller-Stokes polarimetry and associated statistical modalities……….68-76
  • 3.1 Introduction ............................................................................................................ 68
  • 3.2 Mueller matrix imaging of reflective sample (LC-SLM) ....................................... 69
    • 3.2.1 Spatial anomalies in spatial light modulator .................................................... 73
    • 3.2.2 Spatially addressable polarization properties of LC-SLM .............................. 73
    • 3.2.3 Statistical interpretation of Mueller matrix images of LC-SLM ..................... 78
  • 3.3 Conclusion .............................................................................................................. 83
• Chapter 4. Polarization driven lateral shearing digital holography………………...86-100
  • 4.1 Introduction ............................................................................................................ 86
  • 4.2 Theoretical background .......................................................................................... 89
    • 4.2.1 Cyclic lateral shearing interferometry (CLSI) ................................................. 89
    • 4.2.2 Polarization sensitive cyclic lateral shearing interferometry (PCLSI) ............ 90
  • 4.3 Experimental demonstration of PCLSI ................................................................... 91
    • 4.3.1 Complex field modulation of LC-SLM ........................................................... 91
    • 4.3.2 Simultaneous Jones-Mueller matrix measurement of transmissive anisotropic objects ................................................................................................................................ 100
  • 4.4 Conclusion ............................................................................................................ 111
• Chapter 5. Spatial light modulator based intensity compensated polarization coded aperture………………………………………………………………………………..113-110
  • 5.1 Introduction .......................................................................................................... 113
  • 5.2 Polarization coded apertures ................................................................................. 115
    • 5.2.1 Polarization coded annular aperture .............................................................. 115
    • 5.2.2 Polarization coded binary Fresnel zone plate ................................................ 117
  • 5.3 Imaging characteristics of PCA enabled diffraction limited imaging system ...... 118
    • 5.3.1 Extended depth of field of diffraction limited lens ........................................ 118
    • 5.3.2 Intensity point spread function of PCA enabled imaging system .................. 120
    • 5.3.3 Axial intensity of PCA enabled BFZP ........................................................... 122
  • 5.4 Conclusion ............................................................................................................. 123

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

This thesis focuses on developing novel polarization-sensitive imaging techniques and their applications in the polarimetric characterization of anisotropic materials, primarily liquid crystals (LCs) and spatial light modulators (SLMs). The main objectives are to explore Jones matrix imaging (JMI) and Mueller matrix imaging (MMI) techniques and investigate their capabilities for anisotropic measurements. The thesis aims to address limitations in existing techniques, such as stability and efficiency, by developing a compact and stable experimental framework for simultaneous Jones-Mueller matrix measurements. The key themes explored in the thesis include:

• Advanced polarization-sensitive imaging techniques
• Polarimetric characterization of anisotropic materials
• Development of intensity-compensated polarization coded apertures (PCAs)
• Enhancement of imaging characteristics of diffraction-limited systems
• Statistical analysis of Mueller matrix images

Zusammenfassung der Kapitel (Chapter Summaries)

• Chapter 1 provides the fundamental theoretical concepts of polarization optics, including Stokes polarimetry, Jones matrix calculus, and Mueller matrix calculus. It also introduces the basics of digital holography and interferometry, crucial for the experimental work presented in subsequent chapters. The chapter concludes with a detailed description of liquid crystals and their optical anisotropy, followed by a brief overview of spatial light modulators (SLMs) and their working principles.
• Chapter 2 introduces a polarization-sensitive digital holographic technique for determining the Jones matrix of an anisotropic object in reflection mode. The technique is experimentally demonstrated for the polarimetric calibration of a reflective LC-SLM. The chapter analyzes the polarimetric features of the LC-SLM with respect to its gray scales and investigates its anisotropic properties using Jones matrix decomposition methods.
• Chapter 3 focuses on the spatially addressable polarimetric characterization of an LC-SLM using Mueller-Stokes polarimetry. The chapter examines the spatial anomalies in the SLM display and calibrates them by determining the Mueller matrices at different gray scales. The chapter further analyzes the Mueller matrix images statistically, using probability density functions and central moment parameters, to understand the polarization characteristics of the SLM.
• Chapter 4 presents a novel polarization-assisted lateral shearing interferometric technique for simultaneously determining the Jones and Mueller matrices of anisotropic objects. The technique is experimentally validated for measuring the Jones-Mueller matrices of two homogeneous phase retarders and a homogeneously aligned LC sample. The chapter demonstrates the compactness and stability of the technique in the presence of external vibrations.
• Chapter 5 explores the potential of polarization coded apertures (PCAs) for enhancing the imaging characteristics of a diffraction-limited imaging system. Two types of PCAs, namely, polarization coded annular apertures and polarization coded binary Fresnel zone plates, are experimentally demonstrated using an LC-SLM. The chapter analyzes the improved depth of field (DOF) and axial intensity of the PCA-enabled imaging system.

Schlüsselwörter (Keywords)

This thesis investigates polarization-sensitive imaging techniques, specifically Jones matrix imaging (JMI) and Mueller matrix imaging (MMI), for the polarimetric characterization of anisotropic materials. It focuses on the application of these techniques to liquid crystals (LCs) and spatial light modulators (SLMs), particularly examining their spatial non-uniformities and modulation characteristics. The study also introduces and experimentally demonstrates intensity-compensated polarization coded apertures (PCAs) as a method for enhancing the imaging characteristics of a diffraction-limited system. Additionally, the thesis explores the statistical analysis of Mueller matrix images using probability density functions and central moment parameters. The primary keywords encompass: polarization-sensitive imaging, Jones matrix, Mueller matrix, anisotropic materials, liquid crystals, spatial light modulators, polarization coded apertures, depth of field, axial intensity, statistical analysis.