The present book is an extended version of my doctoral work on polarization optics and digital holography, which depicts the preliminary concepts of polarization optics and deals with their some novel applications in digital holography and computational imaging.
First, it's about basic concepts and development of polarization-sensitive imaging techniques, advancing the existing polarization-sensitive interferometry and digital holographic (DH) techniques. Secondly, the techniques have been applied for the polarimetric characterization of anisotropic samples. In particular, aforesaid polarimetric investigations are mainly focused on the LC cells and SLMs. Further, some crucial issues in computational imaging, for instance, limited depth of field (DOF), and axial intensity of diffraction-limited imaging systems under low light throughput have been examined thoroughly. Attempts have been put forward to address the imaging artifacts using the concept of polarization coded apertures (PCAs), which are experimentally demonstrated using the polarization modulation characteristics of LC-SLM.
The goal of this book is to disseminate its contribution to wider researcher fraternity. It is expected that this book will serve as a preliminary guide for undergraduate and postgraduate students, research scholars who are interested to pursue their research in polarization optics and holography domain.
Table of Contents
Chapter 1. Introduction
1.1 Background
1.2 Origin and purpose of the thesis
1.3 Formulism for completely polarized light
1.3.1 The polarization ellipse
1.3.2 Jones matrix formulism
1.4 Formulism for partially polarized light
1.4.1 Stokes polarimetry
1.4.2 The Poincare sphere method
1.5 Generalized formulism for polarization: coherency matrix
1.6 Mueller matrix formulism
1.6.1 Mueller matrix decomposition
1.7 Basic interferometric techniques for polarization imaging
1.7.1 Michelson interferometer
1.7.2 Sagnac interferometer
1.7.3 Mach-Zehnder interferometer
1.7.4 Digital holographic interferometry
1.7.5 Off-axis holography
1.7.6 Digital hologram processing
1.8 Optical anisotropy
1.8.1 Dichroism
1.8.2 Birefringence
1.8.3 Polarizance
1.8.4 Depolarization
1.9 Liquid crystals and associated optical anisotropy
1.9.1 Classification of Liquid crystal alignments
1.9.2 Spatial light modulator
1.10 Structure of the thesis: an overview
Chapter 2. Polarization sensitive digital holography for polarimetric analysis of spatial light modulator
2.1 Introduction
2.2 Double shot Jones matrix imaging of reflective LC-SLM
2.2.1 Polarization sensitive digital holography
2.2.2 Complex field modulation of LC-SLM
2.2.3 Reference calibration of LC-SLM display
2.2.4 Jones matrix elements of LC-SLM
2.3 Anisotropic properties of LC-SLM
2.3.1 Jones matrix polar decomposition
2.3.2 Algebraic method of Jones matrix decomposition
2.4 Polarization modulation of LC-SLM
2.5 Conclusion
Chapter 3. Mueller-Stokes polarimetry and associated statistical modalities
3.1 Introduction
3.2 Mueller matrix imaging of reflective sample (LC-SLM)
3.2.1 Spatial anomalies in spatial light modulator
3.2.2 Spatially addressable polarization properties of LC-SLM
3.2.3 Statistical interpretation of Mueller matrix images of LC-SLM
3.3 Conclusion
Chapter 4. Polarization driven lateral shearing digital holography
4.1 Introduction
4.2 Theoretical background
4.2.1 Cyclic lateral shearing interferometry (CLSI)
4.2.2 Polarization sensitive cyclic lateral shearing interferometry (PCLSI)
4.3 Experimental demonstration of PCLSI
4.3.1 Complex field modulation of LC-SLM
4.3.2 Simultaneous Jones-Mueller matrix measurement of transmissive anisotropic objects
4.4 Conclusion
Chapter 5. Spatial light modulator based intensity compensated polarization coded aperture
5.1 Introduction
5.2 Polarization coded apertures
5.2.1 Polarization coded annular aperture
5.2.2 Polarization coded binary Fresnel zone plate
5.3 Imaging characteristics of PCA enabled diffraction limited imaging system
5.3.1 Extended depth of field of diffraction limited lens
5.3.2 Intensity point spread function of PCA enabled imaging system
5.3.3 Axial intensity of PCA enabled BFZP
5.4 Conclusion
Research Objectives and Themes
This thesis aims to advance polarization-sensitive imaging techniques and apply them to the polarimetric characterization of anisotropic materials, particularly liquid crystal spatial light modulators (LC-SLMs). It explores novel methods to overcome challenges in computational imaging, such as limited depth of field and spatial anomalies, while simultaneously retrieving accurate phase and polarization information of anisotropic samples using integrated Jones-Mueller matrix measurement frameworks.
- Polarization-sensitive digital holography for analyzing LC-SLM components.
- Mueller-Stokes polarimetry and statistical analysis of anisotropic samples.
- Polarization-driven lateral shearing interferometry for simultaneous Jones-Mueller matrix extraction.
- Development of intensity-compensated polarization coded apertures (PCAs) to enhance depth of field and imaging resolution.
- Calibration of optical anisotropy and modulation characteristics in liquid crystal devices.
Auszug aus dem Buch
1.2 Origin and purpose of the thesis
Polarization is an inherent characteristic of electromagnetic wave, circumventing the various aspects of the electric field oscillations of light. It was first observed by Erasmus Bartholin [5] during his experiment on calcite crystal in the form of double refraction followed by Christian Huygens [6], Thomas Young [7], Louis Malus [8], David Brewster [9], extensively. In general, the polarization characteristics of a medium can be studied in terms of change in polarization state during transmission or reflection of light from it. These polarization characteristics of a medium can be interpreted using various techniques, viz., Jones matrix calculus [10–14], Stokes calculus [15,16], Poincare sphere [17], and Mueller matrix calculus [16,18], etc.
The first mathematical formulation for defining the polarization state of an optical beam was given by George Gabriel Stokes in terms of four measurable quantities by measuring the intensity of light, known as Stokes polarization parameters (SPPs) [15]. The Stokes vector consists of a set of four quantities that are measured in terms of intensity and describe the polarization of light. The Poincare sphere, conceived by Henri Poincare is a geometrical technique for the study of polarization state [17]. In 1943, another technique was proposed for the study of the interaction of polarized light with an anisotropic medium, which can change its state of polarization, known as Mueller matrix calculus [18]. In Mueller matrix calculus, the optical device is described in terms of a matrix of order 4x4, which are basically the intensity measurements of light.
Summary of Chapters
Chapter 1. Introduction: This chapter provides the fundamental concepts of polarization optics, including Stokes, Jones, and Mueller matrix formalisms, and introduces interferometric and digital holographic techniques.
Chapter 2. Polarization sensitive digital holography for polarimetric analysis of spatial light modulator: The chapter focuses on using digital holography to extract the Jones matrix and polarimetric features of LC-SLMs, demonstrating the technique through reflective calibration.
Chapter 3. Mueller-Stokes polarimetry and associated statistical modalities: This chapter explores the spatial assessment of LC-SLM modulation through Mueller matrix imaging and introduces statistical methods to interpret its anisotropic response.
Chapter 4. Polarization driven lateral shearing digital holography: A new interferometric approach is proposed here for the simultaneous measurement of Jones-Mueller matrices, allowing for robust, compact characterization of anisotropic samples.
Chapter 5. Spatial light modulator based intensity compensated polarization coded aperture: The final chapter demonstrates the use of polarization-coded apertures (PCAs) to improve diffraction-limited imaging systems, specifically extending the depth of field and enhancing axial intensity.
Key Keywords
Polarimetry, Digital Holography, Mueller Matrix, Jones Matrix, Anisotropy, Liquid Crystals, Spatial Light Modulator, SLM, Polarization Coded Apertures, Depth of Field, Interferometry, Stokes Parameters, Phase Modulation, Optical Diagnostic Technique, Computational Imaging
Frequently Asked Questions
What is the primary motivation for this research?
The thesis aims to solve current limitations in polarization-sensitive imaging and optical characterization by developing compact, stable experimental frameworks capable of simultaneously measuring both Jones and Mueller matrices, thereby providing a more complete description of anisotropic materials like liquid crystals.
What are the main research areas covered?
The work covers polarization optics, digital holography, computational imaging techniques, the statistical interpretation of optical properties, and the implementation of polarization-coded apertures for wavefront shaping.
What is the central research question?
The thesis addresses how to advance polarization-sensitive imaging and characterization techniques to resolve imaging artifacts—such as limited depth of field and spatial non-uniformities—in anisotropic materials using compact experimental designs.
Which scientific methods are utilized?
The research utilizes Jones matrix calculus, Mueller-Stokes polarimetry, digital holographic interferometry, and a novel polarization-driven lateral shearing interferometric technique to perform precise polarimetric measurements.
What is the focus of the main body of the work?
The main body details the experimental development and validation of digital holographic and lateral shearing techniques for characterizing the modulation properties of LC-SLMs and determining the anisotropic characteristics of various samples.
How can this work be described by keywords?
The work is defined by terms such as polarimetry, digital holography, Mueller/Jones matrices, anisotropy, liquid crystal spatial light modulators, and polarization coded apertures.
How does the proposed polarization-driven lateral shearing interferometry perform?
This technique provides a compact and stable setup that does not require additional reference arms, allowing for the simultaneous determination of Jones and Mueller matrices for transmissive anisotropic objects, even in the presence of vibrations.
What unique contributions does this thesis make regarding SLM characterization?
It provides a comprehensive, spatially resolved study of LC-SLMs, identifying spatial anomalies that were previously ignored, and offers direct methods to calibrate these effects using statistical interpretations like the Probability Density Function (PDF) and Central Moment Parameters (CMPs).
- Arbeit zitieren
- Vipin Tiwari (Autor:in), 2023, Polarization Sensitive Imaging, München, GRIN Verlag, https://www.grin.com/document/1401529
