Laser Speckle and Applications in Optics

Size: px
Start display at page:

Download "Laser Speckle and Applications in Optics"

Transcription

1 Laser Speckle and Applications in Optics M. FRANCON Optics Laboratory Faculty of Sciences University of Paris Paris, France Translated by HENRI H. ARSENAULT Department of Physics Laval University Quebec, Canada ACADEMIC PRESS New York San Francisco London 1979 A Subsidiary of Harcourt Brace Jovanovich, Publishers

2 Contents Preface Chapter I Speckle in the Image of an Object Illuminated with Laser Light 1.1 Image of a Point Source. Fourier Transforms The Image of a Point Source in the Presence of a Slight Defect of Focus The Images of Two Monochromatic Point Sources The Images of a Large Number of Point Sources Distributed at Random The Spectrum of a Large Number of Coherent Point Sources The Spectrum of a Large Number of Coherent Point Sources Forming Identical Groups Having the Same Orientation and Distributed at Random Speckle in the Image of an Object Illuminated with a Laser Changing the Structure of a Speckle by Displacing the Plane of Focus The Speckle Patterns Produced in the Image of a Diffuse Object under a Change of Wavelength White-Light Speckle 19

3 VI Chapter II Contents Speckle Produced at a Finite Distance by a Diffusing Object Illuminated by a Laser 2.1 Fresnel and Fraunhofer Diffraction in Three Dimensions Speckle Produced at a Finite Distance by a Diffuse Object Speckle Produced by a Laterally Displaced Diffusing Object Speckle Produced by a Diffuse Object When the Orientation of the Incident Light Beam Is Changed Speckle Produced by a Diffuse Object under an Axial Translation of the Plane of Observation or of the Object Speckle Produced by a Diffuse Object under a Change of Wavelength Speckle Produced by a Diffuse Object When the Wavelength and the Position of the Plane of Observation Are Changed Speckle Produced by a Diffuse Object Itself Illuminated with Another Speckle Pattern 33 Chapter III Interference with Scattered Light 3.1 Historical Background Principles of Interference with Scattered Light Interference with Two Identical Diffusers The Burch Interferometer Interference Patterns Obtained from Two Laterally Shifted Diffusers Interference Patterns Obtained from Two Different Axially Shifted Diffusers 47 Chapter IV Interference Patterns Produced by Photographic Superposition of Laterally Shifted Speckle Patterns 4.1 Amplitude Transmitted by a Photographic Plate after Development The Fundamental Experiment of Burch and Tokarski The Superposition of a Series of Successive Exposures on the Same Holographic Plate Simultaneous Recordings with Birefringent Plates Recording with a Continuous Displacement of the Photographic Plate Recordings Obtained When the Orientation of the Incident Beam Is Changed Recordings Made with Polarized Light Recordings Obtained When the Orientation of the Diffuse Object Is Changed Recordings Made with More Than One Wavelength 62

4 Contents Vit Chapter V Interference Patterns Produced by Photographic Superposition of Axially Shifted Speckle Patterns 5.1 Circular Interference Fringes Produced by Two Successive Recordings on the Same Photographic Plate A Change of Wavelength between the Two Exposures A Change of Wavelength and a Displacement of the Photographic Plate between Exposures Circular Interference Fringes Produced by Two Successive Recordings on the Same Photographic Plate of the Image of a Diffuse Object Circular Interference Fringes Obtained with a Single Exposure by Means of an Amplitude Diffuser Circular Interference Fringes Obtained with More Than One Exposure When the Photographic Plate Is Axially Translated between Each Exposure Hyperbolic or Elliptical Fringes 72 Chapter VI Optical Processing of Images Modulated by Speckle 6.1 Introduction The Principle of a Technique to Extract the Difference between Two Images The Light Distribution in the Image Plane Improving the Profile of the Fringes and the Quality of the Images Image Coding and Decoding Image Multiplexing by Superposition of Laterally Shifted Speckle Patterns Image Multiplexing with Oriented Speckle Patterns 85 Chapter VII The Study of Displacements and Deformations of Diffuse Objects by Means of Speckle Photography 7.1 The Study of Lateral Displacements of a Diffuse Object When the Displacement Is Greater Than the Diameter of a Speckle Grain The Study of Lateral Displacements of a Diffuse Object When the Displacement Is Smaller Than the Diameter of a Speckle Grain The Study of Lateral Displacements of a Diffuse Object Illuminated with Two Beams When the Displacement Is Smaller Than the Diameter of a Speckle Grain The Study of the Lateral Displacement of a Diffuse Object with a Diffuse Reference Surface 95

5 Vlll Contents 7.5 The Study of the Axial Displacement of a Diffuse Object with a Diffuse Reference Surface The Speckle Observed in the Focal Plane of Lens О The Use of an Auxiliary Speckle Pattern to Illuminate a Diffuse Surface The Study of the Rotation of a Diffuse Surface The Study of the Vibrations of a Diffuse Object The Study of the Variations of the Slopes of a Diffuse Object 106 Chapter VIII Speckle in Astronomy 8.1 The Image of a Star at the Focus of a Telescope in the Presence of Atmospheric Turbulence The Study of Double Stars at the Focus of a Telescope in the Presence of Atmospheric Turbulence The Measurement of the Apparent Diameters of Stars by A. Labeyrie's Methods The Measurement of the Apparent Diameters of Stars with Multiple Telescopes 118 Chapter IX The Study of Surface Roughness 9.1 Surface Deviations The Use of Speckle to Study Surface Roughness Surface Roughness Measurement by the Correlation of Two Speckle Patterns Obtained by Changing the Incidence of a Laser Beam The Real-Time Measurement of Surface Roughness by the Amplitude Correlation of Two Speckle Patterns Corresponding to Two Orientations of the Laser Beam Surface Roughness Measurement by the Correlation of Two Speckle Patterns Obtained with Two Wavelengths Surface Roughness Measurements with a Source Having a Wide Bandwidth Surface Roughness Measurements with Partially Coherent Light 129 Chapter X Various Applications of Speckle 10.1 Differential Interferometry of Transparent Objects by Double-Exposure Speckle Photography The Use of Two Wavelengths to Study the Shape of Diffuse Objects The Use of Speckle to Determine the Transfer Function of an Optical System The Study of the Aberrations of an Optical System by Speckle Photography 137

6 Contents ix 10.5 The Focusing of a Lens by Means of Speckle Laser Speckle for Determining the Ametropia of the Eye The Use of the Double Exposure of a Random Distribution of Intensity to Measure Atmospheric Turbulence The Measurement of Motion Trajectories by Speckle Photography The Determination of the Velocities of Different Parts of a Diffuse Object by Speckle Photography An Example of Industrial Application of Speckle Interferometry 146 References 149 Index 159

PRINCIPLES OF PHYSICAL OPTICS

PRINCIPLES OF PHYSICAL OPTICS PRINCIPLES OF PHYSICAL OPTICS C. A. Bennett University of North Carolina At Asheville WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION CONTENTS Preface 1 The Physics of Waves 1 1.1 Introduction

More information

PHY410 Optics Exam #3

PHY410 Optics Exam #3 PHY410 Optics Exam #3 NAME: 1 2 Multiple Choice Section - 5 pts each 1. A continuous He-Ne laser beam (632.8 nm) is chopped, using a spinning aperture, into 500 nanosecond pulses. Compute the resultant

More information

Contents Preface iii 1 Origins and Manifestations of Speckle 2 Random Phasor Sums 3 First-Order Statistical Properties

Contents Preface iii 1 Origins and Manifestations of Speckle 2 Random Phasor Sums 3 First-Order Statistical Properties Contents Preface iii 1 Origins and Manifestations of Speckle 1 1.1 General Background............................. 1 1.2 Intuitive Explanation of the Cause of Speckle................ 2 1.3 Some Mathematical

More information

Speckle phenomenon and its potential for metrology

Speckle phenomenon and its potential for metrology Joint International Physics Summer School Optics (Olomouc, August 28 September 01, 2017) Speckle phenomenon and its potential for metrology Pavel Horváth* & Petr Šmíd** *Palacký University, Faculty of

More information

Astronomical Optics. Second Edition DANIEL J. SCHROEDER ACADEMIC PRESS

Astronomical Optics. Second Edition DANIEL J. SCHROEDER ACADEMIC PRESS Astronomical Optics Second Edition DANIEL J. SCHROEDER Professor of Physics and Astronomy, Emeritus Department of Physics and Astronomy Beloit College, Beloit, Wisconsin ACADEMIC PRESS A Harcourt Science

More information

Optics.

Optics. Optics www.optics.rochester.edu/classes/opt100/opt100page.html Course outline Light is a Ray (Geometrical Optics) 1. Nature of light 2. Production and measurement of light 3. Geometrical optics 4. Matrix

More information

DRONACHARYA COLLEGE OF ENEGINEERING DEPARTMENT OF APPLIED SCEINCE AND HUMANITIES SHORT ANSWER QUESTIONS: Unit-I. Chapter I: Interference

DRONACHARYA COLLEGE OF ENEGINEERING DEPARTMENT OF APPLIED SCEINCE AND HUMANITIES SHORT ANSWER QUESTIONS: Unit-I. Chapter I: Interference DRONACHARYA COLLEGE OF ENEGINEERING DEPARTMENT OF APPLIED SCEINCE AND HUMANITIES SUBJECT: PHYSICS-I CODE: PHY-101-F SHORT ANSWER QUESTIONS: Unit-I Chapter I: Interference 1. State the condition for sustained

More information

Michelson Interferometer

Michelson Interferometer Michelson Interferometer Objective Determination of the wave length of the light of the helium-neon laser by means of Michelson interferometer subsectionprinciple and Task Light is made to produce interference

More information

DIFFRACTION PHYSICS THIRD REVISED EDITION JOHN M. COWLEY. Regents' Professor enzeritus Arizona State University

DIFFRACTION PHYSICS THIRD REVISED EDITION JOHN M. COWLEY. Regents' Professor enzeritus Arizona State University DIFFRACTION PHYSICS THIRD REVISED EDITION JOHN M. COWLEY Regents' Professor enzeritus Arizona State University 1995 ELSEVIER Amsterdam Lausanne New York Oxford Shannon Tokyo CONTENTS Preface to the first

More information

Optical Shop Testing. Second Edition. Edited by DANIEL MALACARA. John Wiley & Sons, Inc. A Wiley-Interscience Publication

Optical Shop Testing. Second Edition. Edited by DANIEL MALACARA. John Wiley & Sons, Inc. A Wiley-Interscience Publication Optical Shop Testing Second Edition Edited by DANIEL MALACARA A Wiley-Interscience Publication John Wiley & Sons, Inc. New York I Chichester I Brisbane I Toronto I Singapore Contents Preface to the Second

More information

Optics Optical Testing and Testing Instrumentation Lab

Optics Optical Testing and Testing Instrumentation Lab Optics 513 - Optical Testing and Testing Instrumentation Lab Lab #6 - Interference Microscopes The purpose of this lab is to observe the samples provided using two different interference microscopes --

More information

n The visual examination of the image of a point source is one of the most basic and important tests that can be performed.

n The visual examination of the image of a point source is one of the most basic and important tests that can be performed. 8.2.11 Star Test n The visual examination of the image of a point source is one of the most basic and important tests that can be performed. Interpretation of the image is to a large degree a matter of

More information

Metrology and Sensing

Metrology and Sensing Metrology and Sensing Lecture 5: Interferometry I 08--6 Herbert Gross Winter term 08 www.iap.uni-jena.de Schedule Optical Metrology and Sensing 08 No Date Subject Detailed Content 6.0. Introduction Introduction,

More information

Light as Wave Motion p. 1 Huygens' Ideas p. 2 Newton's Ideas p. 8 Complex Numbers p. 10 Simple Harmonic Motion p. 11 Polarized Waves in a Stretched

Light as Wave Motion p. 1 Huygens' Ideas p. 2 Newton's Ideas p. 8 Complex Numbers p. 10 Simple Harmonic Motion p. 11 Polarized Waves in a Stretched Introduction p. xvii Light as Wave Motion p. 1 Huygens' Ideas p. 2 Newton's Ideas p. 8 Complex Numbers p. 10 Simple Harmonic Motion p. 11 Polarized Waves in a Stretched String p. 16 Velocities of Mechanical

More information

Metrology and Sensing

Metrology and Sensing Metrology and Sensing Lecture 5: Interferometry I 06--09 Herbert Gross Winter term 06 www.iap.uni-jena.de Preliminary Schedule No Date Subject Detailed Content 8.0. Introduction Introduction, optical measurements,

More information

Modeling of the fringe shift in multiple beam interference for glass fibers

Modeling of the fringe shift in multiple beam interference for glass fibers PRAMANA c Indian Academy of Sciences Vol. 70, No. 4 journal of April 2008 physics pp. 643 648 Modeling of the fringe shift in multiple beam interference for glass fibers A M HAMED 1 Physics Department,

More information

Today. MIT 2.71/2.710 Optics 11/10/04 wk10-b-1

Today. MIT 2.71/2.710 Optics 11/10/04 wk10-b-1 Today Review of spatial filtering with coherent illumination Derivation of the lens law using wave optics Point-spread function of a system with incoherent illumination The Modulation Transfer Function

More information

Physics of Light and Optics

Physics of Light and Optics Physics of Light and Optics Justin Peatross and Harold Stokes Brigham Young University Department of Physics and Astronomy All Publication Rights Reserved (2001) Revised April 2002 This project is supported

More information

International Journal of Scientific & Engineering Research, Volume 4, Issue 7, July ISSN

International Journal of Scientific & Engineering Research, Volume 4, Issue 7, July ISSN International Journal of Scientific & Engineering Research, Volume 4, Issue 7, July-2013 96 Performance and Evaluation of Interferometric based Wavefront Sensors M.Mohamed Ismail1, M.Mohamed Sathik2 Research

More information

Metrology and Sensing

Metrology and Sensing Metrology and Sensing Lecture 5: Interferometry I 017-11-16 Herbert Gross Winter term 017 www.iap.uni-jena.de Preliminary Schedule No Date Subject Detailed Content 1 19.10. Introduction Introduction, optical

More information

Chapter 16 Holography

Chapter 16 Holography Chapter 16 Holography Virtually all recording devices for light respond to light intensity. Problem: How to record, and then later reconstruct both the amplitude and phase of an optical wave. [This question

More information

Nature of Light Part 2

Nature of Light Part 2 Nature of Light Part 2 Fresnel Coefficients From Helmholts equation see imaging conditions for Single lens 4F system Diffraction ranges Rayleigh Range Diffraction limited resolution Interference Newton

More information

SPECKLE INTERFEROMETRY AS A TOOL FOR FINE MEASUREMENTS

SPECKLE INTERFEROMETRY AS A TOOL FOR FINE MEASUREMENTS SPECKLE INTERFEROMETRY AS A TOOL FOR FINE MEASUREMENTS By Amany Khalil Ibrahim Helwan University B.Sc. Physics & Computer Science, Faculty of Science, Helwan University (1999) SUBMITTED IN PARTIAL FULFILLMENT

More information

Lecture 9: Introduction to Diffraction of Light

Lecture 9: Introduction to Diffraction of Light Lecture 9: Introduction to Diffraction of Light Lecture aims to explain: 1. Diffraction of waves in everyday life and applications 2. Interference of two one dimensional electromagnetic waves 3. Typical

More information

Principles of Electron Optics

Principles of Electron Optics Principles of Electron Optics Volume 2 Applied Geometrical Optics by P. W. HAWKES CNRS Laboratory of Electron Optics, Toulouse, France and E. KASPER Institut für Angewandte Physik Universität Tübingen,

More information

Interference, Diffraction and Fourier Theory. ATI 2014 Lecture 02! Keller and Kenworthy

Interference, Diffraction and Fourier Theory. ATI 2014 Lecture 02! Keller and Kenworthy Interference, Diffraction and Fourier Theory ATI 2014 Lecture 02! Keller and Kenworthy The three major branches of optics Geometrical Optics Light travels as straight rays Physical Optics Light can be

More information

Name : Roll No. :.... Invigilator s Signature :.. CS/B.Tech (NEW)/SEM-2/PH-201/2013 2013 PHYSICS - I Time Allotted : 3 Hours Full Marks : 70 The figures in the margin indicate full marks. Candidates are

More information

Optical Sciences Center, Rm 704 University of Arizona Tucson, AZ Office Hours: Call for appointment or see after class

Optical Sciences Center, Rm 704 University of Arizona Tucson, AZ Office Hours: Call for appointment or see after class Term: Spring 2000 Course #: OPTI 505 Course Title: Diffraction and Interferometry Instructor: James C. Wyant Optical Sciences Center, Rm 704 University of Arizona Tucson, AZ 85721 Phone: 520-621-2448 E-Mail:

More information

Phys102 Lecture Diffraction of Light

Phys102 Lecture Diffraction of Light Phys102 Lecture 31-33 Diffraction of Light Key Points Diffraction by a Single Slit Diffraction in the Double-Slit Experiment Limits of Resolution Diffraction Grating and Spectroscopy Polarization References

More information

PLOTTING ORBITS OF BINARY STARS FROM THE INTERFEROMETRIC DATA

PLOTTING ORBITS OF BINARY STARS FROM THE INTERFEROMETRIC DATA PLOTTING ORBITS OF BINARY STARS FROM THE INTERFEROMETRIC DATA by Driss Takir University of North Dakota Visiting Research Intern at the Indian Institute of Astrophysics A Report Submitted to the Indian

More information

High-Resolution. Transmission. Electron Microscopy

High-Resolution. Transmission. Electron Microscopy Part 4 High-Resolution Transmission Electron Microscopy 186 Significance high-resolution transmission electron microscopy (HRTEM): resolve object details smaller than 1nm (10 9 m) image the interior of

More information

Lecture 11: Introduction to diffraction of light

Lecture 11: Introduction to diffraction of light Lecture 11: Introduction to diffraction of light Diffraction of waves in everyday life and applications Diffraction in everyday life Diffraction in applications Spectroscopy: physics, chemistry, medicine,

More information

Electronic Imaging in Astronomy

Electronic Imaging in Astronomy Ian S, McLean Electronic Imaging in Astronomy Detectors and Instrumentation (Second Edition) j""v Published f udiisnea in association with witn fyj Springer Praxis PubUshing Publisl PR Chichester, UK Contents

More information

Optics, Optoelectronics and Photonics

Optics, Optoelectronics and Photonics Optics, Optoelectronics and Photonics Engineering Principles and Applications Alan Billings Emeritus Professor, University of Western Australia New York London Toronto Sydney Tokyo Singapore v Contents

More information

Metrology and Sensing

Metrology and Sensing Metrology and Sensing Lecture 5: Interferometry I 07--6 Herbert Gross Winter term 07 www.iap.uni-jena.de Preliminary Schedule No Date Subject Detailed Content 9.0. Introduction Introduction, optical measurements,

More information

Topic 4 &11 Review Waves & Oscillations

Topic 4 &11 Review Waves & Oscillations Name: Date: Topic 4 &11 Review Waves & Oscillations 1. A source produces water waves of frequency 10 Hz. The graph shows the variation with horizontal position of the vertical displacement of the surface

More information

PMARIZED LI6HT FUNDAMENTALS AND APPLICATIONS EBWABD COLLETT. Measurement Concepts, Inc. Colts Neck, New Jersey

PMARIZED LI6HT FUNDAMENTALS AND APPLICATIONS EBWABD COLLETT. Measurement Concepts, Inc. Colts Neck, New Jersey PMARIZED LI6HT FUNDAMENTALS AND APPLICATIONS EBWABD COLLETT Measurement Concepts, Inc. Colts Neck, New Jersey Marcel Dekker, Inc. New York Basel Hong Kong About the Series Preface A Historical Note iii

More information

Coherence and width of spectral lines with Michelson interferometer

Coherence and width of spectral lines with Michelson interferometer Coherence and width of spectral lines TEP Principle Fraunhofer and Fresnel diffraction, interference, spatial and time coherence, coherence conditions, coherence length for non punctual light sources,

More information

Phys 531 Lecture 27 6 December 2005

Phys 531 Lecture 27 6 December 2005 Phys 531 Lecture 27 6 December 2005 Final Review Last time: introduction to quantum field theory Like QM, but field is quantum variable rather than x, p for particle Understand photons, noise, weird quantum

More information

Waves Part III Electromagnetic waves

Waves Part III Electromagnetic waves Waves Part III Electromagnetic waves Electromagnetic (light) waves Transverse waves Transport energy (and momentum) Can travel through vacuum (!) and certain solids, liquids and gases Do not transport

More information

Chapter 5. Diffraction Part 2

Chapter 5. Diffraction Part 2 EE 430.43.00 06. nd Semester Chapter 5. Diffraction Part 06. 0. 0. Changhee Lee School of Electrical and Computer Engineering Seoul National niv. chlee7@snu.ac.kr /7 Changhee Lee, SN, Korea 5.5 Fresnel

More information

Efficient sorting of orbital angular momentum states of light

Efficient sorting of orbital angular momentum states of light CHAPTER 6 Efficient sorting of orbital angular momentum states of light We present a method to efficiently sort orbital angular momentum (OAM) states of light using two static optical elements. The optical

More information

Wavefront Sensing using Polarization Shearing Interferometer. A report on the work done for my Ph.D. J.P.Lancelot

Wavefront Sensing using Polarization Shearing Interferometer. A report on the work done for my Ph.D. J.P.Lancelot Wavefront Sensing using Polarization Shearing Interferometer A report on the work done for my Ph.D J.P.Lancelot CONTENTS 1. Introduction 2. Imaging Through Atmospheric turbulence 2.1 The statistics of

More information

Exam 3--PHYS 202--S10

Exam 3--PHYS 202--S10 ame: Exam 3--PHYS 202--S0 Multiple Choice Identify the choice that best completes the statement or answers the question A person uses a convex lens that has a focal length of 25 cm to inspect a gem The

More information

UNIT-5 EM WAVES UNIT-6 RAY OPTICS

UNIT-5 EM WAVES UNIT-6 RAY OPTICS UNIT-5 EM WAVES 2 Marks Question 1. To which regions of electromagnetic spectrum do the following wavelengths belong: (a) 250 nm (b) 1500 nm 2. State any one property which is common to all electromagnetic

More information

Physical Optics. Lecture 7: Coherence Herbert Gross.

Physical Optics. Lecture 7: Coherence Herbert Gross. Physical Optics Lecture 7: Coherence 07-05-7 Herbert Gross www.iap.uni-jena.de Physical Optics: Content No Date Subject Ref Detailed Content 05.04. Wave optics G Complex fields, wave equation, k-vectors,

More information

Transmission Electron Microscopy

Transmission Electron Microscopy L. Reimer H. Kohl Transmission Electron Microscopy Physics of Image Formation Fifth Edition el Springer Contents 1 Introduction... 1 1.1 Transmission Electron Microscopy... 1 1.1.1 Conventional Transmission

More information

Techniques for direct imaging of exoplanets

Techniques for direct imaging of exoplanets Techniques for direct imaging of exoplanets Aglaé Kellerer Institute for Astronomy, Hawaii 1. Where lies the challenge? 2. Contrasts required for ground observations? 3. Push the contrast limit Recycle!

More information

3.4 Elliptical Parameters of the Polarization Ellipse References

3.4 Elliptical Parameters of the Polarization Ellipse References Contents Preface to the Second Edition Preface to the First Edition A Historical Note Edward Collett iii v xiii PART 1: THE CLASSICAL OPTICAL FIELD Chapter 1 Chapter 2 Chapter 3 Chapter 4 Introduction

More information

Fourier Optics - Exam #1 Review

Fourier Optics - Exam #1 Review Fourier Optics - Exam #1 Review Ch. 2 2-D Linear Systems A. Fourier Transforms, theorems. - handout --> your note sheet B. Linear Systems C. Applications of above - sampled data and the DFT (supplement

More information

Optics. n n. sin c. sin

Optics. n n. sin c. sin Optics Geometrical optics (model) Light-ray: extremely thin parallel light beam Using this model, the explanation of several optical phenomena can be given as the solution of simple geometric problems.

More information

Polarized Light. Second Edition, Revised and Expanded. Dennis Goldstein Air Force Research Laboratory Eglin Air Force Base, Florida, U.S.A.

Polarized Light. Second Edition, Revised and Expanded. Dennis Goldstein Air Force Research Laboratory Eglin Air Force Base, Florida, U.S.A. Polarized Light Second Edition, Revised and Expanded Dennis Goldstein Air Force Research Laboratory Eglin Air Force Base, Florida, U.S.A. ш DEK KER MARCEL DEKKER, INC. NEW YORK BASEL Contents Preface to

More information

High-Resolution Imagers

High-Resolution Imagers 40 Telescopes and Imagers High-Resolution Imagers High-resolution imagers look at very small fields of view with diffraction-limited angular resolution. As the field is small, intrinsic aberrations are

More information

B.Tech. First Semester Examination Physics-1 (PHY-101F)

B.Tech. First Semester Examination Physics-1 (PHY-101F) B.Tech. First Semester Examination Physics-1 (PHY-101F) Note : Attempt FIVE questions in all taking least two questions from each Part. All questions carry equal marks Part-A Q. 1. (a) What are Newton's

More information

OPTICS. Learning by Computing, with Examples Using Mathcad, Matlab, Mathematica, and Maple. K.D. Möller. Second Edition. With 308 Illustrations

OPTICS. Learning by Computing, with Examples Using Mathcad, Matlab, Mathematica, and Maple. K.D. Möller. Second Edition. With 308 Illustrations Optics OPTICS Learning by Computing, with Examples Using Mathcad, Matlab, Mathematica, and Maple Second Edition K.D. Möller With 308 Illustrations Includes CD-ROM With Mathcad Matlab Mathematica 123 K.D.

More information

Optical Systems Program of Studies Version 1.0 April 2012

Optical Systems Program of Studies Version 1.0 April 2012 Optical Systems Program of Studies Version 1.0 April 2012 Standard1 Essential Understand Optical experimental methodology, data analysis, interpretation, and presentation strategies Essential Understandings:

More information

1. Consider the biconvex thick lens shown in the figure below, made from transparent material with index n and thickness L.

1. Consider the biconvex thick lens shown in the figure below, made from transparent material with index n and thickness L. Optical Science and Engineering 2013 Advanced Optics Exam Answer all questions. Begin each question on a new blank page. Put your banner ID at the top of each page. Please staple all pages for each individual

More information

Comparative Measurement in Speckle Interferometry using Fourier Transform

Comparative Measurement in Speckle Interferometry using Fourier Transform Egypt. J. Solids, Vol. (30), No. (2), (2007) 253 Comparative Measurement in Speckle Interferometry using Fourier Transform Nasser A. Moustafa Physics Department, Faculty of Science, Helwan University,

More information

The science of light. P. Ewart

The science of light. P. Ewart The science of light P. Ewart Oxford Physics: Second Year, Optics Parallel reflecting surfaces t images source Extended source path difference xcos 2t=x Fringes localized at infinity Circular fringe constant

More information

SOFT X-RAYS AND EXTREME ULTRAVIOLET RADIATION

SOFT X-RAYS AND EXTREME ULTRAVIOLET RADIATION SOFT X-RAYS AND EXTREME ULTRAVIOLET RADIATION Principles and Applications DAVID ATTWOOD UNIVERSITY OF CALIFORNIA, BERKELEY AND LAWRENCE BERKELEY NATIONAL LABORATORY CAMBRIDGE UNIVERSITY PRESS Contents

More information

Density Field Measurement by Digital Laser Speckle Photography

Density Field Measurement by Digital Laser Speckle Photography Density Field Measurement by Digital Laser Speckle Photography by M. Kawahashi and H. Hirahara Saitama University Department of Mechanical Engineering Shimo-Okubo 255, Urawa, Saitama, 338-8570, Japan ABSTRACT

More information

PS210 - Optical Techniques. Section VI

PS210 - Optical Techniques. Section VI PS210 - Optical Techniques Section VI Section I Light as Waves, Rays and Photons Section II Geometrical Optics & Optical Instrumentation Section III Periodic and Non-Periodic (Aperiodic) Waves Section

More information

PHYSICS PAPER 1 (THEORY)

PHYSICS PAPER 1 (THEORY) PHYSICS PAPER 1 (THEORY) (Three hours) (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.) ---------------------------------------------------------------------------------------------------------------------

More information

Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : , 1 O P T I C S 1. Define resolving power of a telescope & microscope and give the expression for its resolving power. 2. Explain briefly the formation of mirage in deserts. 3. The radii of curvature of

More information

Michelson Interferometer. crucial role in Einstein s development of the Special Theory of Relativity.

Michelson Interferometer. crucial role in Einstein s development of the Special Theory of Relativity. Michelson Interferometer The interferometer Michelson experiment Interferometer of Michelson and Morley played 0 a crucial role in Einstein s development of the Special Theory of Relativity. Michelson

More information

Chapter 7. Interference of Light

Chapter 7. Interference of Light Chapter 7. Interference of Light Last Lecture Superposition of waves Laser This Lecture Two-Beam Interference Young s Double Slit Experiment Virtual Sources Newton s Rings Film Thickness Measurement by

More information

2.71. Final examination. 3 hours (9am 12 noon) Total pages: 7 (seven) PLEASE DO NOT TURN OVER UNTIL EXAM STARTS PLEASE RETURN THIS BOOKLET

2.71. Final examination. 3 hours (9am 12 noon) Total pages: 7 (seven) PLEASE DO NOT TURN OVER UNTIL EXAM STARTS PLEASE RETURN THIS BOOKLET 2.71 Final examination 3 hours (9am 12 noon) Total pages: 7 (seven) PLEASE DO NOT TURN OVER UNTIL EXAM STARTS Name: PLEASE RETURN THIS BOOKLET WITH YOUR SOLUTION SHEET(S) MASSACHUSETTS INSTITUTE OF TECHNOLOGY

More information

Spatial phase-shifting moiré tomography

Spatial phase-shifting moiré tomography Spatial phase-shifting moiré tomography Song Yang,, Zhao Zhimin, Chen YunYun, He Anzhi College of Natural Science Nanking University of Aeronautics & Astronautics, Nanking, 006 P. R. China Department of

More information

Chapter 6 SCALAR DIFFRACTION THEORY

Chapter 6 SCALAR DIFFRACTION THEORY Chapter 6 SCALAR DIFFRACTION THEORY [Reading assignment: Hect 0..4-0..6,0..8,.3.3] Scalar Electromagnetic theory: monochromatic wave P : position t : time : optical frequency u(p, t) represents the E or

More information

ABSTRACT 1. INTRODUCTION

ABSTRACT 1. INTRODUCTION Laser Speckle Suppression by the Phase Modulation of Input Beam in a Multimode Fiber Cong Yang* 1,2,3, Jian Han 1,2, Yuanjie Wu 1,2,3, Huiqi Ye 1,2, Dong Xiao 1,2 1.National Astronomical Observatories

More information

Principles of Electron Optics

Principles of Electron Optics Principles of Electron Optics Volume 1 Basic Geometrical Optics by P. W. HAWKES CNRS Laboratory of Electron Optics, Toulouse, France and E. KASPER Institut für Angewandte Physik Universität Tübingen, Federal

More information

OPSE FINAL EXAM Fall 2015 YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT.

OPSE FINAL EXAM Fall 2015 YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT. CLOSED BOOK. Equation Sheet is provided. YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT. ALL NUMERICAL ANSERS MUST HAVE UNITS INDICATED. (Except dimensionless units like

More information

Experiment O-2. The Michelson Interferometer

Experiment O-2. The Michelson Interferometer Experiment O-2 The Michelson Interferometer The Michelson interferometer is one of the best known and historically important interferometers. It is a very accurate length-measuring device and has been

More information

THE OBSERVATION AND ANALYSIS OF STELLAR PHOTOSPHERES

THE OBSERVATION AND ANALYSIS OF STELLAR PHOTOSPHERES THE OBSERVATION AND ANALYSIS OF STELLAR PHOTOSPHERES DAVID F. GRAY University of Western Ontario, London, Ontario, Canada CAMBRIDGE UNIVERSITY PRESS Contents Preface to the first edition Preface to the

More information

Photoelasticity of Glass

Photoelasticity of Glass H. Aben, C. GuiUemet Photoelasticity of Glass With 218 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest Contents Preface v Part One The Basics of Photoelasticity

More information

PHYSICS PAPER 1 (THEORY)

PHYSICS PAPER 1 (THEORY) PHYSICS PAPER 1 (THEORY) (Three hours) (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.) ---------------------------------------------------------------------------------------------------------------------

More information

PHYSICS 370 OPTICS. Instructor: Dr. Fred Otto Phone:

PHYSICS 370 OPTICS. Instructor: Dr. Fred Otto Phone: PHYSICS 370 OPTICS Instructor: Dr. Fred Otto Phone: 457-5854 Office: Pasteur 144 E-mail: fotto@winona.edu Text: F.L. Pedrotti, L.S. Pedrotti, and L.M. Pedrotti, Introduction to Optics, 3 rd Ed., 2000,

More information

JRE Group of Institutions ASSIGNMENT # 1 Special Theory of Relativity

JRE Group of Institutions ASSIGNMENT # 1 Special Theory of Relativity ASSIGNMENT # 1 Special Theory of Relativity 1. What was the objective of conducting the Michelson-Morley experiment? Describe the experiment. How is the negative result of the experiment interpreted? 2.

More information

Crash Course on Optics I & II. COST Action IC1101 OPTICWISE 4 th Training School

Crash Course on Optics I & II. COST Action IC1101 OPTICWISE 4 th Training School Crash Course on Optics I & II COST Action IC1101 OPTICWISE 4 th Training School Introductory Concepts Fermat s principle Snell s law Total internal refraction Dispersion Aberrations Interference and Diffraction

More information

Introduction to Interferometer and Coronagraph Imaging

Introduction to Interferometer and Coronagraph Imaging Introduction to Interferometer and Coronagraph Imaging Wesley A. Traub NASA Jet Propulsion Laboratory and Harvard-Smithsonian Center for Astrophysics Michelson Summer School on Astrometry Caltech, Pasadena

More information

Part 1 - Basic Interferometers for Optical Testing

Part 1 - Basic Interferometers for Optical Testing Part 1 - Basic Interferometers for Optical Testing Two Beam Interference Fizeau and Twyman-Green interferometers Basic techniques for testing flat and spherical surfaces Mach-Zehnder Zehnder,, Scatterplate

More information

Michelson Interferometry and Measurement of the Sodium Doublet Splitting

Michelson Interferometry and Measurement of the Sodium Doublet Splitting Michelson Interferometry and Measurement of the Sodium Doublet Splitting PHYS 3330: Experiments in Optics Department of Physics and Astronomy, University of Georgia, Athens, Georgia 30602 (Dated: Revised

More information

Week 7: Interference

Week 7: Interference Week 7: Interference Superposition: Till now we have mostly discusssed single waves. While discussing group velocity we did talk briefly about superposing more than one wave. We will now focus on superposition

More information

FIRST YEAR PHYSICS. Unit 4: Light II

FIRST YEAR PHYSICS. Unit 4: Light II FIRST YEAR PHYSICS Unit 4: Light II Contents PHASORS...3 RESOLUTION OF OPTICAL INSTRUMENTS...5 Rayleigh s criterion... 7 MORE ON DIFFRACTION...11 Multiple slits:... 11 Diffraction gratings... 14 X-RAY

More information

Lecture 19 Optical MEMS (1)

Lecture 19 Optical MEMS (1) EEL6935 Advanced MEMS (Spring 5) Instructor: Dr. Huikai Xie Lecture 19 Optical MEMS (1) Agenda: Optics Review EEL6935 Advanced MEMS 5 H. Xie 3/8/5 1 Optics Review Nature of Light Reflection and Refraction

More information

Chapter 10. Interference of Light

Chapter 10. Interference of Light Chapter 10. Interference of Light Last Lecture Wave equations Maxwell equations and EM waves Superposition of waves This Lecture Two-Beam Interference Young s Double Slit Experiment Virtual Sources Newton

More information

Brewster Angle and Total Internal Reflection

Brewster Angle and Total Internal Reflection Lecture 4: Polarization Outline 1 Polarized Light in the Universe 2 Brewster Angle and Total Internal Reflection 3 Descriptions of Polarized Light 4 Polarizers 5 Retarders Christoph U. Keller, Utrecht

More information

Wave Motion and Electromagnetic Radiation. Introduction Jan. 18, Jie Zhang

Wave Motion and Electromagnetic Radiation. Introduction Jan. 18, Jie Zhang Wave Motion and Electromagnetic Radiation Introduction Jan. 18, 2010 Jie Zhang PHYS 306 Spring, 2010 Introduction This class is about the physics of LIGHT. Textbook: Optics by Ghatak (2010) Content What

More information

Lecture 9: Speckle Interferometry. Full-Aperture Interferometry. Labeyrie Technique. Knox-Thompson Technique. Bispectrum Technique

Lecture 9: Speckle Interferometry. Full-Aperture Interferometry. Labeyrie Technique. Knox-Thompson Technique. Bispectrum Technique Lecture 9: Speckle Interferometry Outline 1 Full-Aperture Interferometry 2 Labeyrie Technique 3 Knox-Thompson Technique 4 Bispectrum Technique 5 Differential Speckle Imaging 6 Phase-Diverse Speckle Imaging

More information

The science of light. P. Ewart

The science of light. P. Ewart The science of light P. Ewart Lecture notes: On web site NB outline notes! Textbooks: Hecht, Optics Lipson, Lipson and Lipson, Optical Physics Further reading: Brooker, Modern Classical Optics Problems:

More information

Alternative speckle photography techniques for plastic deformation investigation

Alternative speckle photography techniques for plastic deformation investigation Alternative speckle photography techniques for plastic deformation investigation L.B. Zuev, V.V. Gorbatenko and K.V. Pavlichev Institute of Strength Physics and Materials Science, SB RAS /4, Academichesky

More information

Laser Optics-II. ME 677: Laser Material Processing Instructor: Ramesh Singh 1

Laser Optics-II. ME 677: Laser Material Processing Instructor: Ramesh Singh 1 Laser Optics-II 1 Outline Absorption Modes Irradiance Reflectivity/Absorption Absorption coefficient will vary with the same effects as the reflectivity For opaque materials: reflectivity = 1 - absorptivity

More information

Page 2. Q1.Electrons and protons in two beams are travelling at the same speed. The beams are diffracted by objects of the same size.

Page 2. Q1.Electrons and protons in two beams are travelling at the same speed. The beams are diffracted by objects of the same size. Q1.Electrons and protons in two beams are travelling at the same speed. The beams are diffracted by objects of the same size. Which correctly compares the de Broglie wavelength λ e of the electrons with

More information

For more sample papers visit :

For more sample papers visit : PHYSICS (THEORY) (Three hours) For more sample papers visit : www.4ono.com Answer all questions in Part I and six questions from Part II, choosing two questions from each of the Sections A, B and C. All

More information

A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth.

A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth. Waves_P2 [152 marks] A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth. The beam is incident normally on a double slit. The distance between the slits

More information

iprom Optical Interferometry Prof. Dr. -Ing. Rainer Tutsch Institut für Produktionsmesstechnik IPROM Technische Universität Braunschweig

iprom Optical Interferometry Prof. Dr. -Ing. Rainer Tutsch Institut für Produktionsmesstechnik IPROM Technische Universität Braunschweig Optical Interferometry Prof. Dr. -Ing. Rainer Tutsch Institut für Produktionsmesstechnik IPROM Technische Universität Braunschweig Frontiers of Metrology April 1, 01 I P NSTITUT FÜR RODUKTIONSMESSTECHNIK

More information

P5 Revision Questions

P5 Revision Questions P5 Revision Questions Part 2 Question 1 How can microwaves be used to communicate? Answer 1 Sent from transmitter, received and amplified by satellite in space, re-transmitted back to earth and picked

More information

Measurments with Michelson interferometers

Measurments with Michelson interferometers Please do not remove this manual from from the lab. It is available at www.cm.ph.bham.ac.uk/y2lab Optics Measurments with Michelson interferometers Objectives In this experiment you will: Understand the

More information

COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, August 23, 2004, 12:14 PM)

COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, August 23, 2004, 12:14 PM) COMPUTER GENERATED HOLOGRAMS Optical Sciences 67 W.J. Dallas (Monday, August 3, 4, 1:14 PM) PART IV: CHAPTER FOUR OPTICAL TESTING Part IV: Chapter Four Page 1 of 1 Introduction In optical testing an element

More information

Concave mirrors. Which of the following ray tracings is correct? A: only 1 B: only 2 C: only 3 D: all E: 2& 3

Concave mirrors. Which of the following ray tracings is correct? A: only 1 B: only 2 C: only 3 D: all E: 2& 3 Concave mirrors Which of the following ray tracings is correct? A: only 1 B: only 2 C: only 3 D: all E: 2& 3 1 2 3 c F Point C: geometrical center of the mirror, F: focal point 2 Concave mirrors Which

More information