TEM Imaging and Dynamical Scattering
|
|
- Janice Campbell
- 6 years ago
- Views:
Transcription
1 TEM Imaging and Dynamical Scattering Duncan Alexander EPFL-CIME 1 Aspects of TEM imaging Objective lens focus Objective lens astigmatism Image delocalization Dynamical scattering 2-beam theory Thickness fringes Bend contours Double diffraction Contents 2
2 Objective lens focus A full ray diagram schematic of the objective lens will go from object plane to image plane and shows both focusing of the objective lens and diffraction pattern formation in the back focal plane see first TEM lectures and exercises today The image plane of the objective lens forms the object plane for the next lens in the series (i.e. the first intermediate lens); this is defined as the image plane. That is, the two lenses are coupled. At correct focus a point object is focused to a point in this image plane If we decrease objective lens strength the rays come to a point below this plane; this is called under focus. At the image plane there is an out of focus image which is then projected onto our detector This under focus image is basically equivalent to having correct objective focus but moving the sample down Figure from Williams & Carter Transmission Electron Microscopy 3 Objective lens focus Very important: when the sample is in focus there is minimum contrast (see phase contrast lectures) Quiz 1: which of these images is in focus? Image 3 is in focus: no Fresnel fringe at edge of hole, no specular ( speckled ) contrast in the carbon film, therefore it has little contrast 4
3 Objective lens astigmatism When image is astigmatic different axes in the image plane have different focal points. This can be seen as different Fresnel fringes for different image directions Here seen for different objective foci 5 Which of these images of GaN nano-wires was taken with an objective aperture? 1 2 6
4 Image delocalization TEM image with no objective aperture. Image formed from direct beam and diffracted beams. Dark-field images from diffracted beams delocalize from bright-field image of direct beam. Gives shadow images that move with objective focus (draw ray diagrams for out of focus image). 7 Image delocalization Image of same nanowires but with objective aperture to make bright-field image. No diffracted beams => no shadow images. This is how you should take your TEM data! 8
5 Diffraction contrast on/off zone axis In bright-field imaging, zone axis condition => more scattering to diffracted beams Therefore intensity in direct beam goes down and bright-field image has strong contrast Example: GaN nanowire CBED SADP BF Off zone axis CBED SADP BF On zone axis 9 Dynamical scattering 10
6 TEM diffraction recap Reciprocal lattice + relrods => multi-beam scattering Excitation error s =>! deviation from Bragg condition hkl 0 11 Dynamical scattering " X-ray scattering is primarily kinematical: because interaction of X-ray with matter is weak, an X-ray is typically scattered at most one time SADP of Si on [1 1 0] zone axis " In contrast because of the coulomb interaction electrons have a strong interaction with matter " As a result they are often scattered many times on their path through a sample: dynamical scattering " Scattering and intensities in different diffracted beams are therefore not independent of each other, making them hard (impossible) to interpret 12
7 2-beam dynamical scattering " Consider Bragg condition combined with high probability of scattering 13 2-beam dynamical scattering " Consider Bragg condition combined with high probability of scattering!b 000 ghkl 14
8 2-beam dynamical scattering " Consider Bragg condition combined with high probability of scattering!b 000 ghkl 15 2-beam dynamical scattering " Consider Bragg condition combined with high probability of scattering!b 000 ghkl 16
9 2-beam dynamical scattering " Consider Bragg condition combined with high probability of scattering!b 000 ghkl 17 2-beam dynamical scattering " Consider Bragg condition combined with high probability of scattering!b 000 ghkl 18
10 2-beam dynamical scattering " Consider Bragg condition combined with high probability of scattering!b 000 ghkl 19 2-beam: Ig as function of excitation error s " For sample thickness t, excitation error s, from Howie-Whelan equations or Bloch wave theory the following can be derived: Intensity in the diffracted beam: Intensity in the direct beam: Extinction distance: 20
11 2-beam dynamical scattering " Plot Ig vs s for different t " Model using: #g= 100 nm #'('%)*'"# #'('+)*'"# $ % $ % envelope!"!"# $% &!"!"# $% & " As thickness t increases intensity curve modulates more quickly in s 21 2-beam dynamical scattering " Plot Ig vs s for different t " Model using: #g= 100 nm #'('%)*'"# #'('++*'"# $ % $ %!"!"# $% &!"!"# $% & " Only have maximum in Ig at s = 0 for: (integer n) 22
12 2-beam dynamical scattering " Plot Ig vs s for different t " Model using: #g= 100 nm #'('%)*'"# #'('+**'"# $ % $ %!"!"# $% &!"!"# $% & " When: (integer n) then: Ig = 0 at s = 0 23 Thickness fringes " For s = 0: " Ig and I0 modulate in t, and are in anti-phase with each other: " When thickness t = n#g (integer n) intensity in diffracted beam Ig = 0.! This is why #g is called the extinction distance 24
13 2-beam imaging of thickness fringes " Use cleaved wedge sample of Si to study thickness fringes " 90 wedge of Si of increasing thickness imaged in projection " Excite 2-beam Bragg condition (s = 0) and take bright-field and dark-field images " See bright and dark fringes from g and 000 reflections in anti-phase Bright field Dark field 25 2-beam imaging of thickness fringes " Extract normalised intensity vs thickness profiles from images " Compare to dynamical scattering simulation Simple model (no absorption): $ * $! 26
14 2-beam imaging of thickness fringes " Extract normalised intensity vs thickness profiles from images " Compare to dynamical scattering simulation: model with absorption works very well! Model with absorption: $ * $! 27 Thickness fringes as function of s " As excitation error s increased, fringes modulate faster in t " Demonstrate with g(3g) weak beam imaging condition with very large s " s ~0.1 nm 1 therefore dominates over #g term in: Dark field s = 0 Dark field s ~0.1 nm 1 28
15 Thickness fringes in nanocrystal Even without choosing specific diffraction conditions, crystalline objects of varying thickness often show thickness fringes, depending on their diffraction condition Such fringes are regularly seen in bright-field images of strongly diffracting nanocrystals, such as this BaTiO3 powder: 29 Bend contours Thinned foils of crystalline samples are very often bent, e.g. from internal stress relief as the material is made thinner As the crystal bends, the local diffraction condition changes. For instance an (hkl) plane in the 2-beam condition will only be at s = 0 at the locations where the plane is at the exact Bragg condition relative to the incident e beam This leads to changes in contrast known as bend contours Bend contours: bright field Bend contours: dark field 30
16 Bend contour formation " Parallel incident e beam illuminating deformed sample " Orientation of crystal plane with respect to incident beam depends on location 31 Bend contour formation (dark-field) " Parallel incident e beam illuminating deformed sample " Orientation of crystal plane with respect to incident beam depends on location Deformed Ni 3 (Al,Ti) superalloy θ! 32
17 Bend contour formation (dark-field) " Parallel incident e beam illuminating deformed sample " Orientation of crystal plane with respect to incident beam depends on location " Bending of lattice equivalent to rocking Ewald sphere through the relrod!! DF image samples Ig vs s Deformed Ni 3 (Al,Ti) superalloy k D k I g 0 33 Bend contour formation (bright-field) " At first approximation see dark lines in bright-field image wherever a lattice plane comes into the exact Bragg condition! parallel pair of dark lines for each plane " Exact intensity profiles more complicated because of full dynamical scattering nature (e.g. modelled using Bloch wave theory) Bright-field image 34
18 Bend contour formation (bright-field) " At first approximation see dark lines in bright-field image wherever a lattice plane comes into the exact Bragg condition! parallel pair of dark lines for each plane " Exact intensity profiles more complicated because of full dynamical scattering nature (e.g. modelled using Bloch wave theory) Bright-field image θ! θ! 35 Bend contour formation (zone axis) " At low index ( important ) zone axis pairs of dark lines for each diffracting plane converge together " On zone axis exact intensity patterns more complex from full dynamical scattering " Can use this to help find zone axis in your sample! Deformed crystal on zone axis SADP from zone axis centre 36
19 Bend contours: consequence for imaging " For precise diffraction contrast (e.g. dark-field) imaging of crystal phases or strong beam imaging of defects, need very flat region of interest " If sample is distorted, condition only holds along bend contour and images are poor Dark-field images of $ -Ni3(Al,Ti) phase: Flat region of interest Bent region of interest 37 Dynamical scattering: double diffraction " Double diffraction is a type of dynamical scattering where the re-diffraction of one beam to another beam produces diffraction spots which are kinematically forbidden " Common example: silicon diffraction pattern on [1 1 0] zone axis: Kinematical simulation % % $"$"$ %!"!"# % $"$"$!"!"#!"!"! %% $"$"$ Experimental SADP % $"$"$ 38
20 Dynamical scattering: double diffraction " Double diffraction is dynamical scattering where the re-diffraction of one beam to another beam produces extra diffraction spots which are kinematically forbidden " Common example: silicon diffraction pattern on [1 1 0] zone axis: Kinematical simulation Experimental SADP % % % $"$"$ $"$"$!"!"# % % % $"$"$!"!"! % $"$"$ 0 0 2!"!"# " Example double diffraction event: 39 Ewald sphere/reciprocal lattice representation " Diffracted beam wave vector kd acts as direct beam for new scattering event " Centre additional reciprocal lattice, Ewald sphere at end of kd " Convolution of reciprocal lattice with itself 40
21 Ewald sphere/reciprocal lattice representation " Diffracted beam wave vector kd acts as direct beam for new scattering event " Centre additional reciprocal lattice, Ewald sphere at end of kd " Convolution of reciprocal lattice with itself 41 Ewald sphere/reciprocal lattice representation " Diffracted beam wave vector kd acts as direct beam for new scattering event " Centre additional reciprocal lattice, Ewald sphere at end of kd " Convolution of reciprocal lattice with itself 42
22 Ewald sphere/reciprocal lattice representation " Diffracted beam wave vector kd acts as direct beam for new scattering event " Centre additional reciprocal lattice, Ewald sphere at end of kd " Convolution of reciprocal lattice with itself 43 Double diffraction by second lattice " Re-diffraction by another crystal lattice can also occur if e -beam propagates through two different superposed lattices " Leads to formation of characteristic satellite spots Example: NiO reflections re-diffracted by Ni during in-situ NiO reduction Epitaxial relationship between the two FCC structures (NiO: a = 0.42 nm Ni: a = 0.37 nm) Images by Quentin Jeangros, EPFL/CSEM 44
23 Summary on imaging and dynamical effects Good TEM imaging requires correct use of objective defocus and astigmatism Imaging crystalline objects will often be subject to delocalisation (ghost images) use bright-field imaging with an objective aperture to cut these out! As the beam propagates across at TEM sample, we typically have dynamical scattering: multiple elastic scattering Intensities in different diffraction spots are then interdependent and therefore hard to interpret Dynamical scattering also leads to effects of thickness fringes, bend contours and double diffraction in your TEM data 45
CHEM-E5225 :Electron Microscopy Imaging I
CHEM-E5225 :Electron Microscopy Imaging I 2018.11 Yanling Ge Outline Amplitude Contrast Phase Contrast Images Thickness and Bending Effects Amplitude Contrast Amplitude phase TEM STEM Incoherent elastic
More informationdiffraction patterns obtained with convergent electron beams yield more information than patterns obtained with parallel electron beams:
CBED-Patterns Principle of CBED diffraction patterns obtained with convergent electron beams yield more information than patterns obtained with parallel electron beams: specimen thickness more precise
More informationI sinc seff. sinc. 14. Kinematical Diffraction. Two-beam intensity Remember the effective excitation error for beam g?
1 14. Kinematical Diffraction Two-beam intensity Remember the effective excitation error for beam g? seff s 1 The general two-beam result for g was: sin seff T ist g Ti e seff Next we find the intensity
More informationCrystal Quality Analysis Group
Crystal Quality Analysis Group Contents Contents 1. Overview...1 2. Measurement principles...3 2.1 Considerations related to orientation and diffraction conditions... 3 2.2 Rocking curve measurement...
More informationDynamical Theory of X-Ray Diffraction
Dynamical Theory of X-Ray Diffraction ANDRE AUTHIER Universite P. et M. Curie, Paris OXFORD UNIVERSITY PRESS Contents I Background and basic results 1 1 Historical developments 3 1.1 Prologue 3 1.2 The
More informationspecular diffuse reflection.
Lesson 8 Light and Optics The Nature of Light Properties of Light: Reflection Refraction Interference Diffraction Polarization Dispersion and Prisms Total Internal Reflection Huygens s Principle The Nature
More informationFigure 1: Derivation of Bragg s Law
What is Bragg s Law and why is it Important? Bragg s law refers to a simple equation derived by English physicists Sir W. H. Bragg and his son Sir W. L. Bragg in 1913. This equation explains why the faces
More informationDiffraction I - Geometry. Chapter 3
Diffraction I - Geometry Chapter 3 Outline ❽ Diffraction basics ❽ Braggs law ❽ Laue equations ❽ Reciprocal space and diffraction ❽ Units for x-ray wavelengths ❽ Diffraction methods Laue photographs Rotation
More informationDETERMINATION OF THE ORIENTATION OF AN EPITAXIAL THIN FILM BY A NEW COMPUTER PROGRAM CrystalGuide
The Rigaku Journal Vol. 16/ number 1/ 1999 Technical Note DETERMINATION OF THE ORIENTATION OF AN EPITAXIAL THIN FILM BY A NEW COMPUTER PROGRAM CrystalGuide R. YOKOYAMA AND J. HARADA X-Ray Research Laboratory,
More informationTransmission Electron Microscopy 2. Scattering and Diffraction
Transmission Electron Microscopy 2. Scattering and Diffraction EMA 6518 Spring 2007 01/07 Outline Why are we interested in electron scattering? Terminology of scattering The characteristics of electron
More informationChapter 38. Diffraction Patterns and Polarization
Chapter 38 Diffraction Patterns and Polarization Diffraction Light of wavelength comparable to or larger than the width of a slit spreads out in all forward directions upon passing through the slit This
More informationChapter 36. Diffraction. Dr. Armen Kocharian
Chapter 36 Diffraction Dr. Armen Kocharian Diffraction Light of wavelength comparable to or larger than the width of a slit spreads out in all forward directions upon passing through the slit This phenomena
More informationPhysics I : Oscillations and Waves Prof. S Bharadwaj Department of Physics & Meteorology Indian Institute of Technology, Kharagpur
Physics I : Oscillations and Waves Prof. S Bharadwaj Department of Physics & Meteorology Indian Institute of Technology, Kharagpur Lecture - 20 Diffraction - I We have been discussing interference, the
More informationhomework Question: T P417, and select 2 other questions from the rest questions of chapter 22 and 24.
homework Question: T 24.13 P417, and select 2 other questions from the rest questions of chapter 22 and 24. 22 Amplitude Contrast CHAPTER PREVIEW We ve already mentioned in Chapters 2 4 that TEM image
More informationToday s Outline - April 17, C. Segre (IIT) PHYS Spring 2018 April 17, / 22
Today s Outline - April 17, 2018 C. Segre (IIT) PHYS 570 - Spring 2018 April 17, 2018 1 / 22 Today s Outline - April 17, 2018 Diffraction enhanced imaging C. Segre (IIT) PHYS 570 - Spring 2018 April 17,
More informationChapter 2: Wave Optics
Chapter : Wave Optics P-1. We can write a plane wave with the z axis taken in the direction of the wave vector k as u(,) r t Acos tkzarg( A) As c /, T 1/ and k / we can rewrite the plane wave as t z u(,)
More information3. Image formation, Fourier analysis and CTF theory. Paula da Fonseca
3. Image formation, Fourier analysis and CTF theory Paula da Fonseca EM course 2017 - Agenda - Overview of: Introduction to Fourier analysis o o o o Sine waves Fourier transform (simple examples of 1D
More informationRay Optics I. Last time, finished EM theory Looked at complex boundary problems TIR: Snell s law complex Metal mirrors: index complex
Phys 531 Lecture 8 20 September 2005 Ray Optics I Last time, finished EM theory Looked at complex boundary problems TIR: Snell s law complex Metal mirrors: index complex Today shift gears, start applying
More informationDiffraction. Single-slit diffraction. Diffraction by a circular aperture. Chapter 38. In the forward direction, the intensity is maximal.
Diffraction Chapter 38 Huygens construction may be used to find the wave observed on the downstream side of an aperture of any shape. Diffraction The interference pattern encodes the shape as a Fourier
More informationDiffraction and Interference of Plane Light Waves
1 Diffraction and Interference of Plane Light Waves Introduction In this experiment you will become familiar with diffraction patterns created when a beam of light scatters from objects placed in its path.
More informationLecture 4. Physics 1502: Lecture 35 Today s Agenda. Homework 09: Wednesday December 9
Physics 1502: Lecture 35 Today s Agenda Announcements: Midterm 2: graded soon» solutions Homework 09: Wednesday December 9 Optics Diffraction» Introduction to diffraction» Diffraction from narrow slits»
More informationChapter 36. Diffraction. Copyright 2014 John Wiley & Sons, Inc. All rights reserved.
Chapter 36 Diffraction Copyright 36-1 Single-Slit Diffraction Learning Objectives 36.01 Describe the diffraction of light waves by a narrow opening and an edge, and also describe the resulting interference
More informationACCURATE TEXTURE MEASUREMENTS ON THIN FILMS USING A POWDER X-RAY DIFFRACTOMETER
ACCURATE TEXTURE MEASUREMENTS ON THIN FILMS USING A POWDER X-RAY DIFFRACTOMETER MARK D. VAUDIN NIST, Gaithersburg, MD, USA. Abstract A fast and accurate method that uses a conventional powder x-ray diffractometer
More informationChapter 35 &36 Physical Optics
Chapter 35 &36 Physical Optics Physical Optics Phase Difference & Coherence Thin Film Interference 2-Slit Interference Single Slit Interference Diffraction Patterns Diffraction Grating Diffraction & Resolution
More informationChapter 8: Physical Optics
Chapter 8: Physical Optics Whether light is a particle or a wave had puzzled physicists for centuries. In this chapter, we only analyze light as a wave using basic optical concepts such as interference
More informationRay Optics. Lecture 23. Chapter 23. Physics II. Course website:
Lecture 23 Chapter 23 Physics II Ray Optics Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Let s finish talking about a diffraction grating Diffraction Grating Let s improve (more
More informationFinal Exam. Today s Review of Optics Polarization Reflection and transmission Linear and circular polarization Stokes parameters/jones calculus
Physics 42200 Waves & Oscillations Lecture 40 Review Spring 206 Semester Matthew Jones Final Exam Date:Tuesday, May 3 th Time:7:00 to 9:00 pm Room: Phys 2 You can bring one double-sided pages of notes/formulas.
More informationANOMALOUS SCATTERING FROM SINGLE CRYSTAL SUBSTRATE
177 ANOMALOUS SCATTERING FROM SINGLE CRYSTAL SUBSTRATE L. K. Bekessy, N. A. Raftery, and S. Russell Faculty of Science, Queensland University of Technology, GPO Box 2434, Brisbane, Queensland, Australia
More informationWaves & Oscillations
Physics 42200 Waves & Oscillations Lecture 40 Review Spring 2016 Semester Matthew Jones Final Exam Date:Tuesday, May 3 th Time:7:00 to 9:00 pm Room: Phys 112 You can bring one double-sided pages of notes/formulas.
More informationAnnouncement. Fraunhofer Diffraction. Physics Waves & Oscillations 4/17/2016. Spring 2016 Semester Matthew Jones
Physics 42200 Waves & Oscillations Lecture 39 Fresnel Diffraction Spring 2016 Semester Matthew Jones Announcement Final Exam Tuesday, May 3 rd 7:00 9:00 pm Room PHYS 112 You can bring one sheet of notes,
More informationChapter 24. Wave Optics
Chapter 24 Wave Optics Diffraction Huygen s principle requires that the waves spread out after they pass through slits This spreading out of light from its initial line of travel is called diffraction
More informationChapter 24. Wave Optics. Wave Optics. The wave nature of light is needed to explain various phenomena
Chapter 24 Wave Optics Wave Optics The wave nature of light is needed to explain various phenomena Interference Diffraction Polarization The particle nature of light was the basis for ray (geometric) optics
More informationWaves & Oscillations
Physics 42200 Waves & Oscillations Lecture 39 Fresnel Diffraction Spring 2016 Semester Matthew Jones Announcement Final Exam Tuesday, May 3 rd 7:00 9:00 pm Room PHYS 112 You can bring one sheet of notes,
More informationHigh spatial resolution measurement of volume holographic gratings
High spatial resolution measurement of volume holographic gratings Gregory J. Steckman, Frank Havermeyer Ondax, Inc., 8 E. Duarte Rd., Monrovia, CA, USA 9116 ABSTRACT The conventional approach for measuring
More informationWaves & Oscillations
Physics 42200 Waves & Oscillations Lecture 41 Review Spring 2013 Semester Matthew Jones Final Exam Date:Tuesday, April 30 th Time:1:00 to 3:00 pm Room: Phys 112 You can bring two double-sided pages of
More informationWave Phenomena Physics 15c. Lecture 19 Diffraction
Wave Phenomena Physics 15c Lecture 19 Diffraction What We Did Last Time Studied interference > waves overlap Amplitudes add up Intensity = (amplitude) does not add up Thin-film interference Reflectivity
More informationLecture 16 Diffraction Ch. 36
Lecture 16 Diffraction Ch. 36 Topics Newtons Rings Diffraction and the wave theory Single slit diffraction Intensity of single slit diffraction Double slit diffraction Diffraction grating Dispersion and
More informationScattering/Wave Terminology A few terms show up throughout the discussion of electron microscopy:
1. Scattering and Diffraction Scattering/Wave Terology A few terms show up throughout the discussion of electron microscopy: First, what do we mean by the terms elastic and inelastic? These are both related
More informationChapter 24. Wave Optics. Wave Optics. The wave nature of light is needed to explain various phenomena
Chapter 24 Wave Optics Wave Optics The wave nature of light is needed to explain various phenomena Interference Diffraction Polarization The particle nature of light was the basis for ray (geometric) optics
More informationLight diffraction from colloidal crystals with low dielectric constant modulation: Simulations using single-scattering theory
PHYSICAL REVIEW B 77, 23544 28 Light diffraction from colloidal crystals with low dielectric constant modulation: Simulations using single-scattering theory Alexander Tikhonov, Rob D. Coalson, and Sanford
More informationAP Physics Problems -- Waves and Light
AP Physics Problems -- Waves and Light 1. 1975-4 (Physical Optics) a. Light of a single wavelength is incident on a single slit of width w. (w is a few wavelengths.) Sketch a graph of the intensity as
More informationIntermediate Physics PHYS102
Intermediate Physics PHYS102 Dr Richard H. Cyburt Assistant Professor of Physics My office: 402c in the Science Building My phone: (304) 384-6006 My email: rcyburt@concord.edu My webpage: www.concord.edu/rcyburt
More information1. Polarization effects in optical spectra of photonic crystals
Speech for JASS 05. April 2005. Samusev A. 1. Polarization effects in optical spectra of photonic crystals Good afternoon. I would like to introduce myself. My name is Anton Samusev. I m a student of Saint
More informationFresnel's biprism and mirrors
Fresnel's biprism and mirrors 1 Table of Contents Section Page Back ground... 3 Basic Experiments Experiment 1: Fresnel's mirrors... 4 Experiment 2: Fresnel's biprism... 7 2 Back ground Interference of
More informationL 32 Light and Optics [3]
L 32 Light and Optics [3] Measurements of the speed of light The bending of light refraction Total internal reflection Dispersion Dispersion Rainbows Atmospheric scattering Blue sky red sunsets Light and
More informationPhysics 214 Midterm Fall 2003 Form A
1. A ray of light is incident at the center of the flat circular surface of a hemispherical glass object as shown in the figure. The refracted ray A. emerges from the glass bent at an angle θ 2 with respect
More informationPY212 Lecture 25. Prof. Tulika Bose 12/3/09. Interference and Diffraction. Fun Link: Diffraction with Ace Ventura
PY212 Lecture 25 Interference and Diffraction Prof. Tulika Bose 12/3/09 Fun Link: Diffraction with Ace Ventura Summary from last time The wave theory of light is strengthened by the interference and diffraction
More informationX-ray Diffraction from Materials
X-ray Diffraction from Materials 2008 Spring Semester Lecturer; Yang Mo Koo Monday and Wednesday 14:45~16:00 8. Experimental X-ray Diffraction Procedures 8.1 Diffraction Experiments using Films 8.1.1 Laue
More informationPhysical Optics. You can observe a lot just by watching. Yogi Berra ( )
Physical Optics You can observe a lot just by watching. Yogi Berra (1925-2015) OBJECTIVES To observe some interference and diffraction phenomena with visible light. THEORY In a previous experiment you
More informationDIFFRACTION 4.1 DIFFRACTION Difference between Interference and Diffraction Classification Of Diffraction Phenomena
4.1 DIFFRACTION Suppose a light wave incident on a slit AB of sufficient width b, as shown in Figure 1. According to concept of rectilinear propagation of light the region A B on the screen should be uniformly
More informationLIGHT. Speed of light Law of Reflection Refraction Snell s Law Mirrors Lenses
LIGHT Speed of light Law of Reflection Refraction Snell s Law Mirrors Lenses Light = Electromagnetic Wave Requires No Medium to Travel Oscillating Electric and Magnetic Field Travel at the speed of light
More informationSUPPLEMENTARY INFORMATION
SUPPLEMENTARY INFORMATION doi:10.1038/nature10934 Supplementary Methods Mathematical implementation of the EST method. The EST method begins with padding each projection with zeros (that is, embedding
More informationLab 12 - Interference-Diffraction of Light Waves
Lab 12 - Interference-Diffraction of Light Waves Equipment and Safety: No special safety equipment is required for this lab. Do not look directly into the laser. Do not point the laser at other people.
More informationMirror Example Consider a concave mirror radius -10 cm then = = Now consider a 1 cm candle s = 15 cm from the vertex Where is the image.
Mirror Example Consider a concave mirror radius -10 cm then r 10 f = = = 5 cm 2 2 Now consider a 1 cm candle s = 15 cm from the vertex Where is the image 1 s 2 1 = = r s 1 1 2 + = = s s r 1 1 = 0.13333
More informationChapter 24 - The Wave Nature of Light
Chapter 24 - The Wave Nature of Light Summary Four Consequences of the Wave nature of Light: Diffraction Dispersion Interference Polarization Huygens principle: every point on a wavefront is a source of
More informationChapter 36 Diffraction
Chapter 36 Diffraction In Chapter 35, we saw how light beams passing through different slits can interfere with each other and how a beam after passing through a single slit flares diffracts in Young's
More informationRay Optics. Lecture 23. Chapter 34. Physics II. Course website:
Lecture 23 Chapter 34 Physics II Ray Optics Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Today we are going to discuss: Chapter 34: Section 34.1-3 Ray Optics Ray Optics Wave
More informationConceptual Physics Fundamentals
Conceptual Physics Fundamentals Chapter 14: PROPERTIES OF LIGHT This lecture will help you understand: Reflection Refraction Dispersion Total Internal Reflection Lenses Polarization Properties of Light
More informationPHYS:1200 LECTURE 32 LIGHT AND OPTICS (4)
1 PHYS:1200 LECTURE 32 LIGHT AND OPTICS (4) The first three lectures in this unit dealt with what is for called geometric optics. Geometric optics, treats light as a collection of rays that travel in straight
More informationGRAZING-INCIDENCE X-RAY DIFFRACTOMETER FOR DETERMINING IN-PLANE STRUCTURE OF THIN FILMS. Kazuhiko Omote and Jimpei Harada
Copyright(c)JCPDS-International Centre for Diffraction Data 2000,Advances in X-ray Analysis,Vol.43 192 GRAZING-INCIDENCE X-RAY DIFFRACTOMETER FOR DETERMINING IN-PLANE STRUCTURE OF THIN FILMS Kazuhiko Omote
More informationMDHS Science Department SPH 4U - Student Goal Tracking Sheet
Name: Unit name: Wave Nature of light Goals for this unit: MDHS Science Department SPH 4U - Student Goal Tracking Sheet 1) I can explain wave behaviour and apply the properties to the Wave Theory of Light.
More information25 The vibration spiral
25 The vibration spiral Contents 25.1 The vibration spiral 25.1.1 Zone Plates............................... 10 25.1.2 Circular obstacle and Poisson spot.................. 13 Keywords: Fresnel Diffraction,
More informationPhysics 1C, Summer 2011 (Session 1) Practice Midterm 2 (50+4 points) Solutions
Physics 1C, Summer 2011 (Session 1) Practice Midterm 2 (50+4 points) s Problem 1 (5x2 = 10 points) Label the following statements as True or False, with a one- or two-sentence explanation for why you chose
More informationX-ray Crystallography
X-ray Crystallography Rhodes, Chapters 2, 5 Chapters 3 and 4 include some general considerations MacPherson (on reserve in library), Chapters 1, 3, and 4 What does anything look like? We see objects by
More informationCoherent Diffraction Imaging with Nano- and Microbeams
Diffraction Imaging with Nano- and Microbeams Why does lensless need? Mark A Pfeifer Cornell High Energy Synchrotron Source Cornell University Ithaca, NY 14850 map322@cornell.edu XLD 2011 June 28, 2011
More informationRay Optics. Physics 11. Sources of Light Rays: Self-Luminous Objects. The Ray Model of Light
Physics 11 Ray Optics Ray Model of Light Reflection Plane Mirrors Spherical Mirrors Ray Tracing Images from a Concave Mirror Images from a Convex Mirror Slide 18-3 The Ray Model of Light Sources of Light
More informationPH 222-3A Fall Diffraction Lectures Chapter 36 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition)
PH 222-3A Fall 2012 Diffraction Lectures 28-29 Chapter 36 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) 1 Chapter 36 Diffraction In Chapter 35, we saw how light beams passing through
More informationMirror Example Consider a concave mirror radius r = -10 cm then. Now consider a 1 cm candle s = 15 cm from the vertex Where is the image.
Mirror Example Consider a concave mirror radius r = -0 cm then r 0 f 5 cm 2 2 Now consider a cm candle s = 5 cm from the vertex Where is the image s 2 r s 2 s s r 0.3333 5 5 f s' 0.333 M ' s 7.5 Magnification
More informationWAVELENGTH MANAGEMENT
BEAM DIAGNOS TICS SPECIAL PRODUCTS OEM DETECTORS THZ DETECTORS PHOTO DETECTORS HIGH POWER SOLUTIONS POWER DETECTORS ENERGY DETECTORS MONITORS Camera Accessories WAVELENGTH MANAGEMENT UV CONVERTERS UV Converters
More informationChapter 12 Notes: Optics
Chapter 12 Notes: Optics How can the paths traveled by light rays be rearranged in order to form images? In this chapter we will consider just one form of electromagnetic wave: visible light. We will be
More informationPHYSICS. Chapter 33 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 33 Lecture RANDALL D. KNIGHT Chapter 33 Wave Optics IN THIS CHAPTER, you will learn about and apply the wave model of light. Slide
More informationOPTICS MIRRORS AND LENSES
Downloaded from OPTICS MIRRORS AND LENSES 1. An object AB is kept in front of a concave mirror as shown in the figure. (i)complete the ray diagram showing the image formation of the object. (ii) How will
More informationMirrors. N.G. Schultheiss translated and adapted by K. Schadenberg
Mirrors N.G. Schultheiss translated and adapted by K. Schadenberg 1 Introduction This module Mirrors summarizes and extents your basic knowledge about mirrors. After this module you can proceed with the
More informationChapter 24. Wave Optics
Chapter 24 Wave Optics Wave Optics The wave nature of light is needed to explain various phenomena Interference Diffraction Polarization The particle nature of light was the basis for ray (geometric) optics
More informationX-Ray Diffraction Analysis of III-V Superlattices: Characterization, Simulation and Fitting
X-Ray Diffraction Analysis of III-V Superlattices: Characterization, Simulation and Fitting Enlong Liu Xiangyu Wu Abstract Three samples of III-V semiconductor superlattice (SL) are investigated by X-ray
More informationChapter 4 Imaging Lecture 18
Chapter 4 Imain Lecture 18 d (110) Class Announcement Term Project presentation: startin at :03 PM, Monday, Nov. 17, 08 in CHE 10 Presentation time: 10 min./person Submission: submit a PDF file of your
More informationLecture Outline Chapter 26. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.
Lecture Outline Chapter 26 Physics, 4 th Edition James S. Walker Chapter 26 Geometrical Optics Units of Chapter 26 The Reflection of Light Forming Images with a Plane Mirror Spherical Mirrors Ray Tracing
More informationModule 18: Diffraction-I Lecture 18: Diffraction-I
Module 18: iffraction-i Lecture 18: iffraction-i Our discussion of interference in the previous chapter considered the superposition of two waves. The discussion can be generalized to a situation where
More informationUNIT VI OPTICS ALL THE POSSIBLE FORMULAE
58 UNIT VI OPTICS ALL THE POSSIBLE FORMULAE Relation between focal length and radius of curvature of a mirror/lens, f = R/2 Mirror formula: Magnification produced by a mirror: m = - = - Snell s law: 1
More informationCollege Physics B - PHY2054C
Young College - PHY2054C Wave Optics: 10/29/2014 My Office Hours: Tuesday 10:00 AM - Noon 206 Keen Building Outline Young 1 2 3 Young 4 5 Assume a thin soap film rests on a flat glass surface. Young Young
More informationSimulation and Analysis of Kikuchi Patterns Including Double Diffraction Effect. (SAKI3d) User s manual. X.Z. LI, Ph. D.
Simulation and Analysis of Kikuchi Patterns Including Double Diffraction Effect (SAKI3d) User s manual X.Z. LI, Ph. D (May 6, 2018) Copyright 2011-2018 LANDYNE All Right Reserved 1 Contents 1. Introduction...3
More informationHow to achieve this goal? (1) Cameras
How to achieve this goal? (1) Cameras History, progression and comparisons of different Cameras and optics. Geometry, Linear Algebra Images Image from Chris Jaynes, U. Kentucky Discrete vs. Continuous
More informationLecture PowerPoints. Chapter 24 Physics: Principles with Applications, 7 th edition Giancoli
Lecture PowerPoints Chapter 24 Physics: Principles with Applications, 7 th edition Giancoli This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching
More informationTowards 0.1 mm spatial resolution
Submitted for publication in ICNS Proceedings Towards 0.1 mm spatial resolution A. D. Stoica and X. L. Wang Spallation Neutron Source 701 Scarboro Road Oak Ridge National Laboratory Oak Ridge, TN 37831,
More informationCondenser Optics for Dark Field X-Ray Microscopy
Condenser Optics for Dark Field X-Ray Microscopy S. J. Pfauntsch, A. G. Michette, C. J. Buckley Centre for X-Ray Science, Department of Physics, King s College London, Strand, London WC2R 2LS, UK Abstract.
More informationTutorial Solutions. 10 Holographic Applications Holographic Zone-Plate
10 Holographic Applications 10.1 Holographic Zone-Plate Tutorial Solutions Show that if the intensity pattern for on on-axis holographic lens is recorded in lithographic film, then a one-plate results.
More informationLenses lens equation (for a thin lens) = (η η ) f r 1 r 2
Lenses lens equation (for a thin lens) 1 1 1 ---- = (η η ) ------ - ------ f r 1 r 2 Where object o f = focal length η = refractive index of lens material η = refractive index of adjacent material r 1
More informationMichelson Interferometer
Michelson Interferometer The Michelson interferometer uses the interference of two reflected waves The third, beamsplitting, mirror is partially reflecting ( half silvered, except it s a thin Aluminum
More informationFormulas of possible interest
Name: PHYS 3410/6750: Modern Optics Final Exam Thursday 15 December 2011 Prof. Bolton No books, calculators, notes, etc. Formulas of possible interest I = ɛ 0 c E 2 T = 1 2 ɛ 0cE 2 0 E γ = hν γ n = c/v
More informationAP* Optics Free Response Questions
AP* Optics Free Response Questions 1978 Q5 MIRRORS An object 6 centimeters high is placed 30 centimeters from a concave mirror of focal length 10 centimeters as shown above. (a) On the diagram above, locate
More informationIntroduction to Computer Vision. Introduction CMPSCI 591A/691A CMPSCI 570/670. Image Formation
Introduction CMPSCI 591A/691A CMPSCI 570/670 Image Formation Lecture Outline Light and Optics Pinhole camera model Perspective projection Thin lens model Fundamental equation Distortion: spherical & chromatic
More informationDiffraction and Interference of Plane Light Waves
PHY 92 Diffraction and Interference of Plane Light Waves Diffraction and Interference of Plane Light Waves Introduction In this experiment you will become familiar with diffraction patterns created when
More informationSupplementary Figure 1 Optimum transmissive mask design for shaping an incident light to a desired
Supplementary Figure 1 Optimum transmissive mask design for shaping an incident light to a desired tangential form. (a) The light from the sources and scatterers in the half space (1) passes through the
More informationCHAPTER 26 INTERFERENCE AND DIFFRACTION
CHAPTER 26 INTERFERENCE AND DIFFRACTION INTERFERENCE CONSTRUCTIVE DESTRUCTIVE YOUNG S EXPERIMENT THIN FILMS NEWTON S RINGS DIFFRACTION SINGLE SLIT MULTIPLE SLITS RESOLVING POWER 1 IN PHASE 180 0 OUT OF
More informationChapter 82 Example and Supplementary Problems
Chapter 82 Example and Supplementary Problems Nature of Polarized Light: 1) A partially polarized beam is composed of 2.5W/m 2 of polarized and 4.0W/m 2 of unpolarized light. Determine the degree of polarization
More informationWave Optics. April 11, 2014 Chapter 34 1
Wave Optics April 11, 2014 Chapter 34 1 Announcements! Exam tomorrow! We/Thu: Relativity! Last week: Review of entire course, no exam! Final exam Wednesday, April 30, 8-10 PM Location: WH B115 (Wells Hall)
More informationPHYSICS. Chapter 34 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 34 Lecture RANDALL D. KNIGHT Chapter 34 Ray Optics IN THIS CHAPTER, you will learn about and apply the ray model of light Slide 34-2
More informationCh. 26: Geometrical Optics
Sec. 6-1: The Reflection of Light Wave Fronts and Rays Ch. 6: Geometrical Optics Wave front: a surface on which E is a maximum. Figure 5-3: Plane Wave *For this wave, the wave fronts are a series of planes.
More informationTextbook Reference: Physics (Wilson, Buffa, Lou): Chapter 24
AP Physics-B Physical Optics Introduction: We have seen that the reflection and refraction of light can be understood in terms of both rays and wave fronts of light. Light rays are quite compatible with
More informationDiffraction Diffraction occurs when light waves pass through an aperture Huygen's Principal: each point on wavefront acts as source of another wave
Diffraction Diffraction occurs when light waves pass through an aperture Huygen's Principal: each point on wavefront acts as source of another wave If light coming from infinity point source at infinity
More information