DOCSLIB.ORG

Conical Diffraction: Complexifying Hamilton's Diabolical Legacy Mike

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Conical Diffraction: Complexifying Hamilton's Diabolical Legacy Mike Conical Diffraction: Complexifying Hamilton’s Diabolical Legacy Mike R. Jeffrey A thesis submitted to the University of Bristol in accordance with the requirements of the degree of Ph.D. in the Faculty of Science H. H. Wills Physics Laboratory September 2007 word count 32,795 Abstract The propagation of light along singular directions in anisotropic media teems with rich asymptotic phenomena that are poorly understood. We study the refraction and diffraction of light beams through crystals exhibiting biaxial birefringence, optical activity, and dichroism. The optical properties and length of the crystal are related to the beam’s width, wavenumber, and alignment, by just three parameters defined by the effect of the crystal on a paraxial plane wave. Singular axes are crystal directions in which the refractive indices are degenerate. In transparent biaxial crystals they are a pair of optic axes corresponding to conical intersections of the propagating wave surface. This gives rise to the well understood phenomenon of conical diffraction. Our interest here is in dichroic and optically active crystals. Dichroism splits each optic axis into pairs or rings of singular axes, branch points of the complex wave surface. Optical activity destroys the optic axis degeneracy but creates a ring of wave surface inflection points. We study the unknown effect of these degeneracy structures on the diffracted light field, predicting striking focusing and interference phenomena. Focusing is understood by the coalescence of real geometric rays, while geometric interference is included by endowing rays with phase to constitute complex rays. Optical activity creates a rotationally symmetric cusped caustic surface threaded by an axial focal line, which should be easy to observe experimentally. Dichroism washes out focusing effects and the field is dominated by exponential gradients crossing anti-Stokes surfaces. A duality is predicted between dichroism and beam alignment for gaussian beams: both are described by a single parameter controlling transition between conical and double refraction. For transparent crystals we predict simple optical angular momentum effects accompanied by a torque on the crystal. We also report new observations with a biaxial crystal that test the established theory of conical diffraction. For Fiona. Acknowledgments A debt of gratitude to my supervisor, Michael Berry, for presenting me with such a wonderfully old problem, the opportunity to delve into dusty volumes penned by the giants of 19th century physics, conjure phenomena with echoes through two centuries of researches on light, and dabble in the mathematical heart of physics old and new. My perspective on physics owes so much to the insightful teaching of John Hannay and Michael Berry, and I thank them for a glimpse of that curious geometric world with which physics is rendered comprehensible. For their guidance, encouragement, and nudging in new directions, I am thankful to: John Hannay, John Nye, John Alcock, Jonathan Robbins, and Jon Keating. In my work I have occasionally relied on the help of people not called Jo(h)n, among them: Matthias Schmidt, who I thank for his daring and patience in confronting a century old german tome; James Lunney and Masud Mansuripur who I thank for their collaborative contribution; Miss Turner and Mr Everitt (and his pet brick), who helped mould a young enquiring mind; and Mark Dennis, whose advice was invaluable in the transition of this unlearned undergrad into a naive but infinitesimally more learned postgrad. I would like to thank Michael and his family for their hospitality throughout my PhD research. Also, even the solitary musings of a theorist turn stale without the distractions of one’s fellow theory group inmates (listed in order of decoherence on an average Friday): Tony, Cath, Bramms, Luis, another John, Morgan, Nadav, Gary, Andy 2. Thanks also × to Steve for helping me master La τ ek$%. { } My dearest thanks to those who have made it easy for me to indulge, and even en- couraged me to continue, in endless distractions mathematical and physical, above all: my wife and her family, Fluffy, and the distinguished UH alumni. We are all students, but some of us will never learn. Authors Declaration I declare that the work in this thesis was carried out in accordance with the regulations of the University of Bristol. The work is original except where indicated by special reference in the text, and no part of the thesis has been submitted for any other academic award. Any views expressed in the thesis are those of the author. SIGNED DATE “They, that will, may suppose it an aggregate of various peripatetic qualities. Others may suppose it multitudes of unimaginable small and swift corpuscles .. springing from shining bodies at great distances one after another; but yet without any sensible interval of time, and continually urged forward .. But they, that not like this, may suppose light any other corporeal emanation, or any impulse or motion of any other medium, or aethereal spirit diffused through the main body of aether, or what else they can imagine proper for this purpose .. To avoid dispute, and make this hypothesis general, let every man here take his fancy; only whatever light be, I suppose it consists of rays differing from one another in contingent circumstances, as bigness, form or vigour.” Isaac Newton on the nature of light, Royal Society, 1675 (Whittaker 1951) This thesis includes the following content published by the author: Chapter 4.1 Berry M V, & Jeffrey M R, (2007) Progress in Optics in press Hamilton’s diabolical point at the heart of crystal optics Chapter 4.2 Berry M V, & Jeffrey M R, (2006) J.Opt.A 8 363-372 Chiral conical diffraction Chapters 3 and 4.2 Jeffrey M R, (2006) Photon06 online conference proceedings http://photon06.org/Diffractive%20optics%20Thurs%2014.15.pdf Conical diffraction in optically active crystals Chapter 4.3 Berry M V, & Jeffrey M R, (2006) J.Opt.A 8 1043-1051 Conical diffraction complexified: dichroism and the transition to double refraction Chapter 4.4 Jeffrey M R, (2007) J.Opt.A 9 634-641 The spun cusp complexified: complex ray focusing in chiral conical diffraction Chapter 4.5 Berry M V, Jeffrey M R & Mansuripur M J, (2005) J.Opt.A 7 685-690 Angular momentum in conical diffraction Chapter 4.6 Berry M V, Jeffrey M R & Lunney J G, (2006) Proc.R.Soc.A 462 1629-1642 Conical diffraction: observations and theory Contents 1 Introduction 1 1.1 HistoricalContext ............................... 4 1.2 HistoryofthePhenomenon . 7 2 Paraxial Optics and Asymptotics 17 2.1 OpticsofAnisotropicCrystals. ..... 18 2.2 Principles of Paraxial Light Propagation . ........ 23 2.3 Hamiltonian Formulation . 26 2.4 Complex Ray Directions: So Where Should We Point The Beam?...... 32 2.5 Eigenwave Representation . 35 2.6 Asymptotics of the Geometrical Optics Limit . ....... 37 2.7 ...andHamilton’sPrinciple. 41 2.8 InsidetheCrystal................................ 44 3 The Wave Surfaces 47 3.1 Fresnel’s Wave Surface and Hamilton’s Cones . ....... 48 3.2 TheParaxialPhaseSurfaces. 54 4 The Phenomena of “So-Called” Conical Diffraction 59 4.1 BiaxialCrystals................................. 61 4.1.1 So-called conical refraction . 64 4.1.2 Diffractionintherings. 66 4.1.3 Uniformisation and rings in the focal image plane . ....... 71 4.1.4 Thebrightaxialspike . .. .. .. .. .. .. .. .. 74 4.2 Biaxial Crystals with Optical Activity . ....... 77 4.2.1 The “trumpet horn” caustic of chiral conical refraction........ 80 xv xvi CONTENTS 4.2.2 Voigt’s “Trompeten Trichters”: rays inside the chiral crystal . 81 4.2.3 Diffraction and the caustic horn . 84 4.2.4 Uniformisation over the caustic . 86 4.2.5 TheStokesset .............................. 88 4.2.6 Thespuncuspandaxialspot . 90 4.2.7 Fringesnearthefocalplane . 94 4.3 DichroicBiaxialCrystals. 97 4.3.1 Conical refraction complexified . 99 4.3.2 Complex geometric interference . 101 4.3.3 Gaussian beams and the transition to double refraction .......104 4.3.4 Anoteoncirculardichroism . 111 4.3.5 Imaginary conical refraction . 112 4.4 Dichroic Biaxial Crystals with Optical Activity . ..........114 4.4.1 Chiral conical refraction complexified . 116 4.4.2 Thecomplexwhisker. .118 4.4.3 Diffraction ................................120 4.4.4 Thecomplexifiedspuncusp . .122 4.5 Angular Momentum in Conical Diffraction . 124 4.5.1 Paraxial optical angular momentum . 124 4.5.2 Nonchiral .................................125 4.5.3 Chiralitydominated . .126 4.5.4 Strongly biaxial or chiral crystals . 127 4.5.5 Torqueonthecrystal . .. .. .. .. .. .. .. .127 4.6 Observations of Biaxial Conical Diffraction . ........129 5 Concluding Remarks 137 A Solutions to the chiral quartic 145 B Spherical conical refraction 147 C Glossary of key symbols 151 Bibliography 153 List of Figures 1.1 Lloyd’s discovery of conical refraction . ........ 8 1.2 Conical diffraction of a pencil of rays . ...... 9 1.3 Theconicalrefractionlunes . 10 1.4 Photographs of chiral conical diffraction . ........ 11 1.5 Thediabolicalpoint .............................. 13 2.1 Fresnel’s wave surface and rotated coordinates . ......... 22 2.2 The parameters of paraxial conical refraction . ......... 26 2.3 ThePoincar´eSphere .............................. 31 2.4 Real and complex rays in stationary phase analysis . ......... 43 3.1 Theopticaxes .................................. 49 3.2 Duality of the wave and ray surfaces . 52 3.3 Geometry of internal and external conical refraction . ........... 53 3.4 Theparaxialwavesurfaces . 57 4.1 Evolution of the conical diffraction rings . ........ 62 4.2 Simulation of the conical diffraction ring evolution . ........... 63 4.3 The rays of internal conical refraction . ....... 65 4.4 The rays of external conical refraction . ....... 65 4.5 Asymptoticsofthesecondaryrings . ..... 69 4.6 The regimes of conical diffraction . ..... 70 4.7 Ringsinthefocalimageplane. 73 4.8 Aperture-induced oscillations in the focal plane . ........... 74 4.9 Intensityoftheaxialspike. 75 4.10 Intensity sections of the bright caustic horn . .......... 78 xvii xviii LIST OF FIGURES 4.11 The rings of chiral conical diffraction . ........ 79 4.12 Rays of chiral conical refraction . ....... 81 4.13 Ray intensity through the crystal .
Load more

Recommended publications
  • Huygen's Explanation of Double Refraction
    06/08/2018 Before this lecture there were two lectures: 1. Introduction about this course. 2. Qualitative description about the various polarizations. Retarders • In retarders, one polarization gets ‘retarded’, or delayed, with respect to the other one. There is a final phase difference between the 2 components of the polarization. Therefore, the polarization is changed. • Most retarders are based on birefringent materials (quartz, mica, polymers) that have different indices of refraction depending on the polarization of the incoming light. 3 Phase shift of half wavelength Quarter Wave plate Circular polarization (IV) 7 How to generate Polarized Light? 1.Dichroic materials 2.Polarizer 3.Birefringent materials 4.Reflection 5.Scattering Wire grid polarizer Polaroid How to generate Polarized Light? 1.Dichroic materials 2.Polarizer 3.Birefringent materials 4.Reflection 5.Scattering Birefringence How to generate Polarized Light? 1.Dichroic materials 2.Polarizer 3.Birefringent materials 4.Reflection 5.Scattering Polarized Reflecting Light • When an unpolarized light wave reflects off a non-metallic surface, it can be completely polarized, partially polarized or unpolarized depending on the angle of incidence. A completely polarized wave occurs for an angle called Brewster’s angle (named after Sir David Brewster) Snell's law Incident Reflected ray ray p n 90o 1 n2 r n1sin P = n2sin r n1sin P = n2sin r = n2sin (90-P) = n2cos P tan P = n2/n1 P = Brewster’s angel Reflection • When an unpolarized wave reflects off a nonmetallic surface, the reflected wave is partially plane polarized parallel to the surface. The amount of polarization depends upon the angle (more later). The reflected ray contains more vibrations parallel to the reflecting surface while the transmitted beam contains more vibrations at right angles to these.
    [Show full text]
  • How to Generate Polarized Light?
    Before this lecture there were two lectures: 1. Qualitative description of polarization and generation of various polarized light. 2. Quantitative derivation and explaining the observations. 08/08/2017 How to generate Polarized Light? 1.Dichroic materials 2.Polarizer 3.Birefringent materials 4.Reflection 5.Scattering Wire grid polarizer Birefringence Polarized Reflecting Light • When an unpolarized light wave reflects off a non-metallic surface, it can be completely polarized, partially polarized or unpolarized depending on the angle of incidence. A completely polarized wave occurs for an angle called Brewster’s angle (named after Sir David Brewster) Snell's law Incident Reflected ray ray p n 90o 1 n2 r n1sin P = n2sin r n1sin P = n2sin r = n2sin (90-P) = n2cos P tan P = n2/n1 P = Brewster’s angel Reflection • When an unpolarized wave reflects off a nonmetallic surface, the reflected wave is partially plane polarized parallel to the surface. The amount of polarization depends upon the angle (more later). The reflected ray contains more vibrations parallel to the reflecting surface while the transmitted beam contains more vibrations at right angles to these. Applications • Knowing that reflected light or glare from surfaces is at least partially plane polarized, one can use Polaroid sunglasses. The polarization axes of the lenses are vertical as the glare usually comes from reflection off horizontal surfaces. Polarized Lens on a Camera Reduce Reflections Polarization by Scattering • When a light wave passes through a gas, it will be absorbed and then re-radiated in a variety of directions. This process is called scattering. y Gas molecule z O Unpolarized x sunlight Light scattered at right angles is plane-polarized Polarization by Scatterings Retarders • In retarders, one polarization gets ‘retarded’, or delayed, with respect to the other one.
    [Show full text]
  • Polarisation
    Polarisation In plane polarised light, the plane containing the direction of POLARISATION vibration and propagation of light is called plane of vibration. Polarisation Plane which is perpendicular to the plane of vibration is called plane of polarisation. The phenomenon due to which vibrations of light waves are restricted in a particular plane is called polarisation. In an ordinary beam of light from a source, the vibrations occur normal to the direction of propagation in all possible planes. Such beam of light called unpolarised light. If by some methods (reflection, refraction or scattering) a beam of light is produced in which vibrations are confined to only one plane, then it is called as plane polarised light. Hence, polarisation is the phenomenon of producing plane polarised light from unpolarised light. In above diagram plane ABCD represents the plane of vibration and EFGH represents the plane of polarisation. There are three type of polarized light 1) Plane Polarized Light 2) Circularly Polarized Light 3) Elliptically Polarized Light Page 1 of 12 Prof. A. P. Manage DMSM’s Bhaurao Kakatkar College, Belgaum Polarisation Huygen’s theory of double refraction According to Huygen’s theory, a point in a doubly refracting or birefringent crystal produces 2 types of wavefronts. The wavefront corresponding to the O-ray is spherical wavefront. The ordinary wave travels with same velocity in all directions and so the corresponding wavefront is spherical. The wavefront corresponding to the E-ray is ellipsoidal wavefront. Extraordinary waves have different velocities in Polarised light can be produced by either reflection, different directions, so the corresponding wavefront is elliptical.
    [Show full text]
  • Experiment 5 Polarization and Modulation of Light
    Experiment 5 Polarization and Modulation of Light 1. Objective Understanding the definition of polarized and un-polarized light. Understanding polarizer and analyzer definition, Maluse’s law. Retarding plates definition and application 2. Theory Polarized light: A propagating light (Electromagnetic wave; EM) has its electric and magnetic fields. These fields are perpendicular to one another as well as to the propagation direction. Polarization of an EM wave (light) describes the behavior of the electric field vector of the light as it propagates through a medium. If light wave has E-field oscillating in random directions (but perpendicular to the propagation direction) is called unpolarized. If the direction of E-field oscillation is well defined, it is called polarized (Figure 1). Figure 1. If the E-field oscillates at all time within a well-defined line, it said that EM is linearly polarized. In a linearly polarized light, the E-field vibrations and propagating direction (z axis here) defines a plane of vibrations shown in figure 2.a. The E-field oscillations in the plane of polarization can be represented by the superposition of two fields Ex and Ey with the right magnitude and phase (Figure 2.b, figure 2.c) E (z,t) E cos(t kz) x xo Ey (z,t) Eyo cos(t kz) Where Ø is the phase difference between Ex and Ey , which defines the delay between Ex and Ey . y Plane of polarization E ^ x y Ey ^x ^ xEx Ex y^E E y z E (a) (b) (c) Figure(a) A 2.linearly a) Electric polarized field in awave linearly has polarized its electric wave field oscillates oscillations along a line defined perpendicular along a to line propagation direction.
    [Show full text]
  • ∑ ∑ Discrete Modeling of Homometric and Isovector Divisions
    Crystallography Reports, Vol. 48, No. 2, 2003, pp. 167–170. Translated from Kristallografiya, Vol. 48, No. 2, 2003, pp. 199–202. Original Russian Text Copyright © 2003 by V. Rau, T. Rau. THEORY OF CRYSTAL STRUCTURES Discrete Modeling of Homometric and Isovector Divisions V. G. Rau and T. F. Rau Vladimir State Pedagogical University, Vladimir, Russia e-mail: [email protected] Received April 24, 2001 Abstract—As a further development of the method of discrete modeling of packings, the uniqueness of the division of the packing spaces into homometric (isovector) polyominoes is studied on the basis of the relation between the basic and vector systems of points. The particular criterion of the packing-space division based on the concept of the isovector nature of polyominoes with different numbers of points is formulated. © 2003 MAIK “Nauka/Interperiodica”. Earlier, we suggested a criterion of division of a (periodic basic system). In comparison with the nonpe- two-dimensional space into arbitrarily shaped polyomi- riodic basic system, the periodic basic system has some noes within the framework of the method of discrete additional interpoint distances associated with the modeling of molecules–polyominoes in the periodic translation vectors. The complete set of the interpoint space of a crystal lattice [1]. The criterion based on the distances rij = rj Ð ri = rk transforms the vector system concept of a packing multispace (PMS) of the Nth order of points in both nonperiodic and periodic basic sys- represented as a superposition of the sublattices with tems constructed on the lattice with the same basis vec- the sublattice index N is formulated as follows.
    [Show full text]
  • Technical Journal
    VOLUME XXII JULY, 1943 NUMBER 2 P- 2 S / V 3 THE BELL SYSTEM TECHNICAL JOURNAL DEVOTED TO THE SCIENTIFIC AND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION A Mineral Survey for Piezo-Electric Materials —W. L. Bond 145 The Fundamental Equations of Electron Motion (Dynam­ ics of High Speed Particles) . L. A. MacColl 153 Quartz Crystal Applications W. P. Mason 178 Methods for Specifying Quartz Crystal Orientation and Their Determination by Optical Means . W. L. Bond 224 A Note on the Transmission Line Equation in Terms of Im p ed a n ce...........................................................J. R. Pierce 263 Abstracts of Technical Articles by Bell System Authors . 266 Contributors to this I s s u e ..........................................................268 AMERICAN TELEPHONE AND TELEGRAPH COMPANY NEW YORK 50c per copy $1.50 per Year THE BELL SYSTEM TECHNIC AL J OURNAL Published quarterly by the ?OI/ American Telephone and Telegraph Company 195 Broadway, New York, N. Y. EDITORS R. W. King J. O. Perrine EDITORIAL BOARD F. B. Jewett W. H. Harrison O. B. Blackwell O. E. Buckley A. B. Clark H. S. Osborne S. Bracken M. J. Kelly F. A. Cowan SUBSCRIPTIONS Subscriptions are accepted at Si.50 per year. Single copies are 50 cents each. The foreign postage is 35 cents per year or 9 cents per copy. Copyright, 1943 American Telephone and Telegraph Company P R IN T E D IN U . S A. Bell System Technical Journal, July, 1943 For the purposes of record and assistance to librarians, and for the information of subscribers, it is to be noted that there was no April 1943 issue of the Bell System Technical Journal.
    [Show full text]
  • Stokes Parameters in the Unfolding of an Optical Vortex Through a Birefringent Crystal
    Stokes parameters in the unfolding of an optical vortex through a birefringent crystal Florian Flossmann, Ulrich T. Schwarz and Max Maier Naturwissenschaftliche Fakultat¨ II-Physik, Universitat¨ Regensburg, Universitatsstraße¨ 31, D-93053 Regensburg, Germany [email protected] Mark R. Dennis School of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, UK [email protected] Abstract: Following our earlier work (F. Flossmann et al., Phys. Rev. Lett. 95 253901 (2005)), we describe the fine polarization structure of a beam containing optical vortices propagating through a birefringent crystal, both experimentally and theoretically. We emphasize here the zero surfaces of the Stokes parameters in three-dimensional space, two transverse dimensions and the third corresponding to optical path length in the crystal. We find that the complicated network of polarization singularities reported earlier – lines of circular polarization (C lines) and surfaces of linear polarization (L surfaces) – can be understood naturally in terms of the zeros of the Stokes parameters. © 2006 Optical Society of America OCIS codes: (260.1440) Birefringence; (260.2110) Electromagnetic Theory; (260.5430) Po- larization; (999.9999) Singular Optics References and links 1. J. F. Nye, Natural focusing and fine structure of light: caustics and wave dislocations, IoP Publishing, 1999. 2. M. S. Soskin and M. Vasnetsov, “Singular optics,” Prog. Opt. 42 219–276 (2001). 3. J.F. Nye, “Lines of circular polarization in electromagnetic wave fields,” Proc. R. Soc. Lond. A 389 279–290 (1983). 4. M.R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213 201–221 (2002). 5. M.V.
    [Show full text]
  • Determination of Degree of Anisotropy of Ktp Crystal Using Reflectance Anisotropy Spectroscopy Technique
    DETERMINATION OF DEGREE OF ANISOTROPY OF KTP CRYSTAL USING REFLECTANCE ANISOTROPY SPECTROSCOPY TECHNIQUE By Fekadu Gashaw A THESIS PRESENTED TO THE SCHOOL OF GRADUATE STUDIES ADDIS ABABA UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in PHYSICS ADDIS ABABA, ETHIOPIA JUNE 2006 A DDIS ABABA UNIVERSITY DEAPRMENT OF PHYSICS The undersigned hereby certify that they have read and recommend to the Faculty of Science for acceptance a senior project entitled “Determination of Degree of Anisotropy of KTP crystal using Reflectance Anisotropy Spectroscopy Technique ” by Fekadu Gashaw Master of Science. Dated: June 2006 Supervisor: Dr. Araya Asfaw Readers: Dr. Dereje Ayalew Dr. Mebratu G/mariam ii ADDIS ABABA UNIVERSITY Date: June 2006 Author: Fekadu Gashaw Title: Determination of Degree of Anisotropy of KTP crystal using Reflectance Anisotropy Spectroscopy Technique Department: Deaprment of Physics Degree: M.Sc. Convocation: July Year: 2006 Permission is herewith granted to Addis Ababa University to circulate and to have copied for non-commercial purposes, at its discretion, the above title upon the request of individuals or institutions. Signature of Author iii This Work is Dedicated to My parents and Feru iv Table of Contents Table of Contents v List of Tables vii List of Figures viii Acknowledgements x Abstract xi 1 LIGHT AND MATTER 5 1.1 Maxwell’s Equation . 5 1.2 Propagation of Light through Medium . 7 1.2.1 Electromagnetic wave in Isotropic Dielectric Material . 7 1.2.2 Light in Anisotropic Dielectric (crystal) Medium . 12 1.3 Reflection and Refraction of light at plane boundary . 19 1.4 Amplitudes of Reflected and Refracted waves .
    [Show full text]
  • Development, Principles, and Applications of Automated Ice Fabric Analyzers
    MICROSCOPY RESEARCH AND TECHNIQUE 62:2–18 (2003) Development, Principles, and Applications of Automated Ice Fabric Analyzers 1 1 2 3 L.A. WILEN, * C.L. DIPRINZIO, R.B. ALLEY, AND N. AZUMA 1Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701 2EMS Environment Institute and Department of Geosciences, The Pennsylvania State University, University Park, Pennsylvania 16802 3Nagaoka University of Technology, Nagaoka, Niigata 940-2137, Japan KEY WORDS ice fabric; ice texture; c-axes; nearest-neighbor correlation; polygonization; Schmidt plot; Rigsby stage; fabric analysis ABSTRACT We review the recent development of automated techniques to determine the fabric and texture of polycrystalline ice. The motivation for the study of ice fabric is first outlined. After a brief introduction to the relevant optical concepts, the classic manual technique for fabric measurement is described, along with early attempts at partial automation. Then, the general principles behind fully automated techniques are discussed. We describe in some detail the simi- larities and differences of the three modern instruments recently developed for ice fabric studies. Next, we discuss briefly X-ray, radar, and acoustic techniques for ice fabric characterization. We also discuss the principles behind automated optical techniques to measure fabric in quartz rock samples. Finally, examples of new applications that have been facilitated by the development of the ice fabric instruments are presented. Microsc. Res. Tech. 62:2–18, 2003. © 2003 Wiley-Liss, Inc. INTRODUCTION TO ICE FABRIC Shoji and Higashi, 1978). As ice flows, the crystal tex- AND TEXTURE ture and fabric evolve in a way that depends on the The fabric of ice refers to the distribution of crystal deformation rate and symmetry as well as temperature axes of an assemblage of ice crystals.
    [Show full text]