CHEM-E5225 :Electron Microscopy Imaging I

Size: px
Start display at page:

Download "CHEM-E5225 :Electron Microscopy Imaging I"

Transcription

1 CHEM-E5225 :Electron Microscopy Imaging I Yanling Ge

2 Outline Amplitude Contrast Phase Contrast Images Thickness and Bending Effects

3 Amplitude Contrast Amplitude phase TEM STEM Incoherent elastic -> Mass-thickness contrast Coherent elastic -> Diffraction contrast

4 What is contrast? - Difference in intensity For eyes > 5-10%, 16 gray level

5 Amplitude Contrast BF and DF Images BF and DF interpretable amplitude contrast Objective Aperture: minimize lens aberrations, enhance diffraction contrast. Usage of it depends on what features of specimen cause scattering. For soft materials to form image without aperture will enhance mass-thickness contrast by losing diffraction contrast! First, view DP!

6 Mechanism of mass-thickness contrast Thicker or higher-z areas of the specimen will scatter more electrons off axis than thinner. Mass-thickness contrast arises from incoherent elastic (Rutherford scatter). The cross section for elastic scattering is a function of Z. Thickness increase, more elastic scattering because the mean free path remains fixed.

7 Mass-Thickness Contrast scattering (Rutherford scattering) of electrons, which is strong function of atomic number Z (hence the mass or the density r) and the thickness, t, of he specimen.) At low angles (< 5 ): mass-thickness contrast dominates but it also competes with Bragg-diffraction contrast; At high angles (>5 ): where Bragg scattering is usually negligible, the low-intensity scattered beams depends on atomic number (Z) only, - so called Z-contrast. Mass-thickness contrast is the critical contrast mechanism for biological materials. And it is usually taken without objective aperture to minimize diffraction contrast.

8 Mass-Thickness contrast TEM images (A) TEM BF image of latex particles on a carbon support film showing thickness contrast only. (B) Latex particles on a carbon film shadowed to reveal the shape of the particles through the addition of selective mass contrast (the edge of the shadow) to the image. (C) Reverse print of (B) exhibits a 3D appearance. TEM variables: objective aperture size and the kv Be careful when interpreting 2D images of 3D specimens.

9 Mass-Thickness Contrast STEM image In a STEM you have more flexibility than in a TEM because by varying L, you change the collection angle of your detector and create, in effect, a variable objective aperture. In summary, there are occasions when you might want to use STEM massthickness contrast images: The specimen is so thick that chromatic aberration limits the TEM resolution. The specimen is beam-sensitive. The specimen has inherently low contrast in TEM and you can t digitize your TEM image or negative. Your specimen is ideally suited for HRTEM by Z-contrast imaging. TEM BF STEM BF Image processed TEM BF

10 Mass-Thickness Contrast Specimens Showing Mass-Thickness Contrast Carbon Replica Thickness contrast Shadowed effect Thickness + Mass contrast Extraction replica Mass + Thickness contrast

11 Mass-Thickness Contrast Quantitative Mass-Thickness Contrast The probability that an electron scattered through greater than a given angle b. Higher-Z specimens scatter more, especially in higher β. Lowering E 0 increase scattering. Thicker specimen scattering more. Variable for control mass-thickness contrast: Z, t, β, E 0.

12 Z-Contrast high-resolution (atomic), mass-thickness, imaging technique Z-Contrast images are also termed as HAADF images. Bragg effects are avoided if the HAADF detector only gathers electrons scattered through an angle of > 50 mrad (~3 ). Imaging away from strong two-beam conditions and closer to zone-axis orientations is wise. The image resolution is determined by the probe size. STEM ADF detector collecting low angle elastically scattered electrons of single heavy atoms on low-z substrate. Inelastic scattering is removed by EELS, but diffraction contrast is preserved in the low angle EELS single.

13 TEM Diffraction Contrast - Coherent elastic scattering Good strong diffraction contrast in both BF and DF images need to be in two-beam condition, in which only one diffracted beam is strong. The direct beam is the other strong spot in the pattern. For crystalline bulk specimen, to study defects, BF and CDF must be done in two-beam condition, which is a time consuming and patient work! Two-beam condition: good contrast, simple interpretation. Deviation parameter: s must small and positive for best contrast from defects (The excess hkl Kikuchi line, just outside the hkl spot). Two-beam CDF, tilt weak h-k-l to center. Related DP to image, showing g vector in image.

14 Two-Beam Condition - CDF BF WBDF CDF

15 Tilt sample and beam guide by Kikuchi line

16 The incident beam must be coherent, i.e., the convergence angle must be very small. The specimen must be tilted to a tow-beam condition. Only the direct beam or the one strong diffracted beam must be collected by the objective aperture. In order to have same condition in STEM as in TEM: a T = a S β T = β S STEM Diffraction Contrast Or according principle of reciprocity: a S = β T a T = β S STEM images are rarely used to show diffraction-contrast images of crystal defects. This is solely the domain of TEM.

17 BF STEM BF STEM βs smaller BF TEM

18 Phase-Contrast Images

19 Introduction Phase contrast arise due to the difference in the phase of electron waves scattered through a thin specimen. A phase-contrast image requires the selection of more than one beam. In general, the more beams collected, the higher the resolution of the image. Phase-contrast is very sensitive to many factors: the appearance of the image varies with small changes in the thickness, orientation, or scattering factor of the specimen, and variations in the focus or astigmatism of the objective lens.

20 The Origin of Lattice Fringes Two beam condition, interference of direction beam and diffracted beam. The intensity of phase contrast is a sinusoidal oscillation normal to g, with a periodicity that depends on s and t. This simple analysis shows that the location of a fringe does not necessarily correspond to the location of a lattice plane.

21 Some Practical Aspects of Lattice Fringes s = 0, hkl // optic axis s 0; hkl edge on If s 0 If s is not zero, then the fringes will shift by an amount which depends on both the magnitude of s and the value of t, but the periodicity will not change noticeably. The fringe periodicity is the same as the spacing of the planes which give rise to g. This result holds wherever s = 0 no matter how 0 and g are located relative to the optic axis, even if the diffraction planes are not parallel to the optic axis. We expect this s dependence to affect the image when the foil bends slightly, as is often the case for thin specimens. We also expect to see thickness variations in many-beam images, since s may be non-zero for all of the beams; s may also vary from beam to beam.

22 The image real structure! In general, this array of spots bears no direct relationship to the position of atoms in the crystal. Fringes are not direct images of the structure, but just give you information on lattice spacing and orientation. There is cases that these images can only be interpreted using extensive computer simulation.

23 Moiré Patterns General Moiré Fringes Translational Moiré Fringes Rotational Moiré Fringes

24 Experimental Observations of Moiré Fringes Translational Moiré Patterns We know that the top of an inclined island is not in contact with the substrate yet it shows fringes; so this reminds us that moiré fringes do not tell us about the interface structure! Rotational Moiré Patterns

25 Dislocations and Moiré Fringes

26 Fresnel Contrast magnetic domain wall In any situation where the inner potential changes abruptly, we can produce Fresnel fringes if we image that region out of focus. Magnetic-Domain Walls

27 Fresnel Contrast from Voids or Gas Bubbles By orienting the region of interest so that s = 0; the cavity then reduces the thickness of material locally. By using Fresnel contrast Caution: Small particles can give similar contrast to small voids, the Fresnel contrast can easily be misinterpreted as a core-shell structure! In the Fresnel technique, the image shows contrast whenever the objective lens is not focused on the bottom surface of the specimen. A dark fringe at under focus and a bright fringe at over focus.

28 Fresnel Contrast from Lattice Defects When you use the Fresnel-fringe technique to study grain boundaries or analyze intergranular films, you must orient the boundary in the edge-on position so that you can probe the potential at the boundary. Using the Fresnel-fringe technique to image end-on low angle grain boundaries assume there is a change in the mean inner potential at the core of the dislocation.

29 Thickness and Bending Effects

30 Thickness and Bending effects - Diffraction contrast All TEM specimens are thin but their thickness invariably changes. Because the specimens are so thin they also bend elastically, i.e., the lattice planes physically rotate. The planes also bend when lattice defects are introduced.

31 The Origin of Thickness Fringes and Bend Contours two beam condition s eff effective excitation error x g extinction distance The diffracted intensity is periodic in the two independent quantities, t and s eff. If we imaging the situation where t remains constant but s (and hence s eff ) varies locally, then we produce bend contours. Similarly, if s remains constant while t varies, then thickness fringes will result.

32 Thickness Fringes Intensity of both the 0 and g beams oscillate as t varies. Furthermore, these oscillations are complementary for the DF and BF images. As a rule of thumb, when other diffracted beams are present the effective extinction distance is reduced. At greater thicknesses, absorption occurs and the contrast is reduced.

33 Thickness Fringes and DP A general rule in TEM is that, whenever we see a periodicity in real space (i.e., in the image), there must be a corresponding array of spots in reciprocal space; the converse is also true.

34 Bend Contours (Annoying Artifact, Useful Tool, Invaluable Insight)

35 ZAPs and Real-Space Crystallography Although the ZAP is distorted, the symmetry of the zone axis is clear and such patterns have been used as a tool for real-space crystallographic analysis. Each contour is uniquely related to a particular set of diffraction panes, so the ZAP does not automatically introduce the twofold rotation axis that we are used to in SAD patterns. Also in this case, a small g in the DP gives a small spacing in the image, contrary to the usual inverse relationship between image and DP.

36 Summary: We can define a parameter x g which is usually about 10 x g and is really a fudge factor which modifies the Howie-Whelan equations to fit the experimental observations. The different Bloch waves are scattered differently. If they don t contribute to the image, we say that they were absorbed. We thus have anomalous absorption which quite normal! Usable thicknesses are limited to about 5x g, but you can optimize this if you channel the less-absorbed Bloch wave. Absorption Effects

37 homework Question based home work: T23.2; T23.11; T23.16

diffraction patterns obtained with convergent electron beams yield more information than patterns obtained with parallel electron beams:

diffraction 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 information

TEM Imaging and Dynamical Scattering

TEM Imaging and Dynamical Scattering 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

More information

homework Question: T P417, and select 2 other questions from the rest questions of chapter 22 and 24.

homework 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 information

I sinc seff. sinc. 14. Kinematical Diffraction. Two-beam intensity Remember the effective excitation error for beam g?

I 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 information

Scattering/Wave Terminology A few terms show up throughout the discussion of electron microscopy:

Scattering/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 information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY 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 information

Transmission Electron Microscopy 2. Scattering and Diffraction

Transmission 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 information

Chapter 4 Imaging Lecture 18

Chapter 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 information

Crystal Quality Analysis Group

Crystal 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 information

3. Image formation, Fourier analysis and CTF theory. Paula da Fonseca

3. 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 information

Diffraction. Single-slit diffraction. Diffraction by a circular aperture. Chapter 38. In the forward direction, the intensity is maximal.

Diffraction. 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 information

Dynamical Theory of X-Ray Diffraction

Dynamical 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 information

Simulation 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. 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 information

specular diffuse reflection.

specular 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 information

Chapter 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 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 information

Cover Page. The handle holds various files of this Leiden University dissertation

Cover Page. The handle   holds various files of this Leiden University dissertation Cover Page The handle http://hdl.handle.net/1887/48877 holds various files of this Leiden University dissertation Author: Li, Y. Title: A new method to reconstruct the structure from crystal images Issue

More information

Chapter 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 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 information

v4.3 Author of this manual: A. J. D Alfonso, B. D. Forbes, L. J. Allen

v4.3 Author of this manual: A. J. D Alfonso, B. D. Forbes, L. J. Allen µstem v4.3 A transmission electron microscopy simulation suite, in particular for scanning transmission electron microscopy. Author of this manual: A. J. D Alfonso, B. D. Forbes, L. J. Allen Adrian D Alfonso,

More information

Chapter 2: Wave Optics

Chapter 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 information

DETERMINATION OF THE ORIENTATION OF AN EPITAXIAL THIN FILM BY A NEW COMPUTER PROGRAM CrystalGuide

DETERMINATION 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 information

Final Exam. Today s Review of Optics Polarization Reflection and transmission Linear and circular polarization Stokes parameters/jones calculus

Final 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 information

Simple, complete, and novel quantitative model of holography for students of science and science education

Simple, complete, and novel quantitative model of holography for students of science and science education Journal of Physics: Conference Series Simple, complete, and novel quantitative model of holography for students of science and science education To cite this article: Dale W Olson 2013 J. Phys.: Conf.

More information

Diffraction and Interference of Plane Light Waves

Diffraction 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 information

Conceptual Physics 11 th Edition

Conceptual Physics 11 th Edition Conceptual Physics 11 th Edition Chapter 28: REFLECTION & REFRACTION This lecture will help you understand: Reflection Principle of Least Time Law of Reflection Refraction Cause of Refraction Dispersion

More information

(Refer Slide Time: 00:10)

(Refer Slide Time: 00:10) Fundamentals of optical and scanning electron microscopy Dr. S. Sankaran Department of Metallurgical and Materials Engineering Indian Institute of Technology, Madras Module 02 Unit-4 Phase contrast, Polarized

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION doi:10.1038/nature12009 Supplementary Figure 1. Experimental tilt series of 104 projections with a tilt range of ±72.6 and equal slope increments, acquired from a Pt nanoparticle using HAADF- STEM (energy:

More information

Waves & Oscillations

Waves & 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 information

Chapter 24. Wave Optics

Chapter 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 information

OPSE FINAL EXAM Fall CLOSED BOOK. Two pages (front/back of both pages) of equations are allowed.

OPSE FINAL EXAM Fall CLOSED BOOK. Two pages (front/back of both pages) of equations are allowed. CLOSED BOOK. Two pages (front/back of both pages) of equations are allowed. YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT. ALL NUMERICAL ANSERS MUST HAVE UNITS INDICATED.

More information

Figure 1: Derivation of Bragg s Law

Figure 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 information

ANOMALOUS SCATTERING FROM SINGLE CRYSTAL SUBSTRATE

ANOMALOUS 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 information

Announcement. Fraunhofer Diffraction. Physics Waves & Oscillations 4/17/2016. Spring 2016 Semester Matthew Jones

Announcement. 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 information

An Intuitive Explanation of Fourier Theory

An Intuitive Explanation of Fourier Theory An Intuitive Explanation of Fourier Theory Steven Lehar slehar@cns.bu.edu Fourier theory is pretty complicated mathematically. But there are some beautifully simple holistic concepts behind Fourier theory

More information

Chapter 24. Wave Optics

Chapter 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 information

High spatial resolution measurement of volume holographic gratings

High 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 information

Waves & Oscillations

Waves & 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 information

Single-particle electron microscopy (cryo-electron microscopy) CS/CME/BioE/Biophys/BMI 279 Nov. 16 and 28, 2017 Ron Dror

Single-particle electron microscopy (cryo-electron microscopy) CS/CME/BioE/Biophys/BMI 279 Nov. 16 and 28, 2017 Ron Dror Single-particle electron microscopy (cryo-electron microscopy) CS/CME/BioE/Biophys/BMI 279 Nov. 16 and 28, 2017 Ron Dror 1 Last month s Nobel Prize in Chemistry Awarded to Jacques Dubochet, Joachim Frank

More information

L 32 Light and Optics [3]

L 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 information

Electromagnetic waves

Electromagnetic waves Electromagnetic waves Now we re back to thinking of light as specifically being an electromagnetic wave u u u oscillating electric and magnetic fields perpendicular to each other propagating through space

More information

Wave Phenomena Physics 15c. Lecture 19 Diffraction

Wave 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 information

Lecture 4. Physics 1502: Lecture 35 Today s Agenda. Homework 09: Wednesday December 9

Lecture 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 information

Diffraction I - Geometry. Chapter 3

Diffraction 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 information

Cryo-electron microscopy Cryo-EM. Garry Taylor

Cryo-electron microscopy Cryo-EM. Garry Taylor Cryo-electron microscopy Cryo-EM Garry Taylor www.st-andrews.ac.uk/~glt2/bl3301 Electron has a wavelength de Broglie relationship: m v = h / λ or λ = h / mv Accelerate e - in a field of potential V, it

More information

INTERFERENCE. where, m = 0, 1, 2,... (1.2) otherwise, if it is half integral multiple of wavelength, the interference would be destructive.

INTERFERENCE. where, m = 0, 1, 2,... (1.2) otherwise, if it is half integral multiple of wavelength, the interference would be destructive. 1.1 INTERFERENCE When two (or more than two) waves of the same frequency travel almost in the same direction and have a phase difference that remains constant with time, the resultant intensity of light

More information

X-ray Powder Diffraction

X-ray Powder Diffraction X-ray Powder Diffraction Chemistry 754 Solid State Chemistry Lecture #8 April 15, 2004 Single Crystal Diffraction Diffracted Beam Incident Beam Powder Diffraction Diffracted Beam Incident Beam In powder

More information

Physics 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 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 information

Ray Optics I. Last time, finished EM theory Looked at complex boundary problems TIR: Snell s law complex Metal mirrors: index complex

Ray 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 information

Waves & Oscillations

Waves & 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 information

Basic optics. Geometrical optics and images Interference Diffraction Diffraction integral. we use simple models that say a lot! more rigorous approach

Basic optics. Geometrical optics and images Interference Diffraction Diffraction integral. we use simple models that say a lot! more rigorous approach Basic optics Geometrical optics and images Interference Diffraction Diffraction integral we use simple models that say a lot! more rigorous approach Basic optics Geometrical optics and images Interference

More information

E x Direction of Propagation. y B y

E x Direction of Propagation. y B y x E x Direction of Propagation k z z y B y An electromagnetic wave is a travelling wave which has time varying electric and magnetic fields which are perpendicular to each other and the direction of propagation,

More information

Chapter 35 &36 Physical Optics

Chapter 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 information

12/7/2012. Biomolecular structure. Diffraction, X-ray crystallography, light- and electron microscopy. CD spectroscopy, mass spectrometry

12/7/2012. Biomolecular structure. Diffraction, X-ray crystallography, light- and electron microscopy. CD spectroscopy, mass spectrometry phase difference at a given distance constructive/destructive interference Biomolecular structure. Diffraction, X-ray crystallography, light- and electron microscopy. CD spectroscopy, mass spectrometry

More information

3 Interactions of Light Waves

3 Interactions of Light Waves CHAPTER 22 3 Interactions of Light Waves SECTION The Nature of Light BEFORE YOU READ After you read this section, you should be able to answer these questions: How does reflection affect the way we see

More information

PHY 222 Lab 11 Interference and Diffraction Patterns Investigating interference and diffraction of light waves

PHY 222 Lab 11 Interference and Diffraction Patterns Investigating interference and diffraction of light waves PHY 222 Lab 11 Interference and Diffraction Patterns Investigating interference and diffraction of light waves Print Your Name Print Your Partners' Names Instructions April 17, 2015 Before lab, read the

More information

Simple Spatial Domain Filtering

Simple Spatial Domain Filtering Simple Spatial Domain Filtering Binary Filters Non-phase-preserving Fourier transform planes Simple phase-step filters (for phase-contrast imaging) Amplitude inverse filters, related to apodization Contrast

More information

Contrast Optimization A new way to optimize performance Kenneth Moore, Technical Fellow

Contrast Optimization A new way to optimize performance Kenneth Moore, Technical Fellow Contrast Optimization A new way to optimize performance Kenneth Moore, Technical Fellow What is Contrast Optimization? Contrast Optimization (CO) is a new technique for improving performance of imaging

More information

Chapter 38. Diffraction Patterns and Polarization

Chapter 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 information

UNIT VI OPTICS ALL THE POSSIBLE FORMULAE

UNIT 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 information

Instruction Sheet Martin Henschke, Fresnel mirror art. no.:

Instruction Sheet Martin Henschke, Fresnel mirror art. no.: Physics Educational Tools Dr. Martin Henschke Gerätebau Dieselstr. 8, 50374 Erftstadt, Germany www.henschke-geraetebau.de/english/ Instruction Sheet Martin Henschke, 2006-05-16 Fresnel mirror art. no.:

More information

CHAPTER 26 INTERFERENCE AND DIFFRACTION

CHAPTER 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 information

Ray Optics. Lecture 23. Chapter 23. Physics II. Course website:

Ray 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 information

f. (5.3.1) So, the higher frequency means the lower wavelength. Visible part of light spectrum covers the range of wavelengths from

f. (5.3.1) So, the higher frequency means the lower wavelength. Visible part of light spectrum covers the range of wavelengths from Lecture 5-3 Interference and Diffraction of EM Waves During our previous lectures we have been talking about electromagnetic (EM) waves. As we know, harmonic waves of any type represent periodic process

More information

Fresnel's biprism and mirrors

Fresnel'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 information

Interference of Light

Interference of Light Interference of Light Review: Principle of Superposition When two or more waves interact they interfere. Wave interference is governed by the principle of superposition. The superposition principle says

More information

PHYSICS. Chapter 33 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT

PHYSICS. 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 information

Diffraction. Introduction: Diffraction is bending of waves around an obstacle (barrier) or spreading of waves passing through a narrow slit.

Diffraction. Introduction: Diffraction is bending of waves around an obstacle (barrier) or spreading of waves passing through a narrow slit. Introduction: Diffraction is bending of waves around an obstacle (barrier) or spreading of waves passing through a narrow slit. Diffraction amount depends on λ/a proportion If a >> λ diffraction is negligible

More information

v5.1 Authors of this manual (in alphabetical order): L. J. Allen, H. G. Brown, A. J. D Alfonso, S.D. Findlay, B. D. Forbes March 21, 2018

v5.1 Authors of this manual (in alphabetical order): L. J. Allen, H. G. Brown, A. J. D Alfonso, S.D. Findlay, B. D. Forbes March 21, 2018 µstem v5.1 A transmission electron microscopy simulation suite, in particular for scanning transmission electron microscopy. Authors of this manual (in alphabetical order): L. J. Allen, H. G. Brown, A.

More information

Waves & Oscillations

Waves & Oscillations Physics 42200 Waves & Oscillations Lecture 41 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 information

V3.0 STEM. for xhrem (WinHREM /MacHREM ) Scanning Transmission Electron Microscope Image Simulation Program. User's Guide

V3.0 STEM. for xhrem (WinHREM /MacHREM ) Scanning Transmission Electron Microscope Image Simulation Program. User's Guide V3.0 STEM for xhrem (WinHREM /MacHREM ) Scanning Transmission Electron Microscope Image Simulation Program User's Guide Scanning Transmission Electron Microscope Image Simulation Program User's Guide Contents

More information

Chapter 36. Diffraction. Copyright 2014 John Wiley & Sons, Inc. All rights reserved.

Chapter 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 information

Chapter 36. Diffraction. Dr. Armen Kocharian

Chapter 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 information

OPTI-521 Graduate Report 2 Matthew Risi Tutorial: Introduction to imaging, and estimate of image quality degradation from optical surfaces

OPTI-521 Graduate Report 2 Matthew Risi Tutorial: Introduction to imaging, and estimate of image quality degradation from optical surfaces OPTI-521 Graduate Report 2 Matthew Risi Tutorial: Introduction to imaging, and estimate of image quality degradation from optical surfaces Abstract The purpose of this tutorial is to introduce the concept

More information

(Refer Slide Time: 00:11)

(Refer Slide Time: 00:11) Fundamentals of optical and scanning electron microscopy Dr S Sankaran Department of Metallurgical and Materials Engineering Indian Institute of Technology, Madras Module 01 Unit-1 Fundamentals of optics

More information

Michelson Interferometer

Michelson 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 information

College Physics B - PHY2054C

College 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 information

X-ray Crystallography

X-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 information

Experiment 5: Polarization and Interference

Experiment 5: Polarization and Interference Experiment 5: Polarization and Interference Nate Saffold nas2173@columbia.edu Office Hour: Mondays, 5:30PM-6:30PM @ Pupin 1216 INTRO TO EXPERIMENTAL PHYS-LAB 1493/1494/2699 Introduction Outline: Review

More information

To see how a sharp edge or an aperture affect light. To analyze single-slit diffraction and calculate the intensity of the light

To see how a sharp edge or an aperture affect light. To analyze single-slit diffraction and calculate the intensity of the light Diffraction Goals for lecture To see how a sharp edge or an aperture affect light To analyze single-slit diffraction and calculate the intensity of the light To investigate the effect on light of many

More information

Chapter 25. Wave Optics

Chapter 25. Wave Optics Chapter 25 Wave Optics Interference Light waves interfere with each other much like mechanical waves do All interference associated with light waves arises when the electromagnetic fields that constitute

More information

Physical or wave optics

Physical or wave optics Physical or wave optics In the last chapter, we have been studying geometric optics u light moves in straight lines u can summarize everything by indicating direction of light using a ray u light behaves

More information

The sources must be coherent. This means they emit waves with a constant phase with respect to each other.

The sources must be coherent. This means they emit waves with a constant phase with respect to each other. CH. 24 Wave Optics The sources must be coherent. This means they emit waves with a constant phase with respect to each other. The waves need to have identical wavelengths. Can t be coherent without this.

More information

1 Laboratory #4: Division-of-Wavefront Interference

1 Laboratory #4: Division-of-Wavefront Interference 1051-455-0073, Physical Optics 1 Laboratory #4: Division-of-Wavefront Interference 1.1 Theory Recent labs on optical imaging systems have used the concept of light as a ray in goemetrical optics to model

More information

Lenses lens equation (for a thin lens) = (η η ) f r 1 r 2

Lenses 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 information

Lecture PowerPoints. Chapter 24 Physics: Principles with Applications, 7 th edition Giancoli

Lecture 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 information

d has a relationship with ψ

d has a relationship with ψ Principle of X-Ray Stress Analysis Metallic materials consist of innumerable crystal grains. Each grain usually faces in a random direction. When stress is applied on such materials, the interatomic distance

More information

Diffraction and Interference of Plane Light Waves

Diffraction 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 information

Conceptual Physics Fundamentals

Conceptual 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 information

Chapter 15. Light Waves

Chapter 15. Light Waves Chapter 15 Light Waves Chapter 15 is finished, but is not in camera-ready format. All diagrams are missing, but here are some excerpts from the text with omissions indicated by... After 15.1, read 15.2

More information

EM Waves Practice Problems

EM Waves Practice Problems PSI AP Physics 2 Name 1. Sir Isaac Newton was one of the first physicists to study light. What properties of light did he explain by using the particle model? 2. Who was the first person who was credited

More information

Today s Outline - April 17, C. Segre (IIT) PHYS Spring 2018 April 17, / 22

Today 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 information

ACCURATE TEXTURE MEASUREMENTS ON THIN FILMS USING A POWDER X-RAY DIFFRACTOMETER

ACCURATE 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 information

The diffraction pattern from a hexagonally-shaped hole. Note the six-fold symmetry of the pattern. Observation of such complex patterns can reveal

The diffraction pattern from a hexagonally-shaped hole. Note the six-fold symmetry of the pattern. Observation of such complex patterns can reveal The diffraction pattern from a hexagonally-shaped hole. Note the six-fold symmetry of the pattern. Observation of such complex patterns can reveal the underlying symmetry structure of the object that diffracts

More information

Experimental Competition. Sample Solution

Experimental Competition. Sample Solution The 37th International Physics Olympiad Singapore Experimental Competition Wednesday, 1 July, 006 Sample Solution a. A sketch of the experimental setup Part 1 Receiver Rotating table Goniometer Fixed arm

More information

Physical Optics. You can observe a lot just by watching. Yogi Berra ( )

Physical 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 information

Coherent Gradient Sensing Microscopy: Microinterferometric Technique. for Quantitative Cell Detection

Coherent Gradient Sensing Microscopy: Microinterferometric Technique. for Quantitative Cell Detection Coherent Gradient Sensing Microscopy: Microinterferometric Technique for Quantitative Cell Detection Proceedings of the SEM Annual Conference June 7-10, 010 Indianapolis, Indiana USA 010 Society for Experimental

More information

INTERFERENCE. (i) When the film is quite thin as compared to the wavelength of light,

INTERFERENCE. (i) When the film is quite thin as compared to the wavelength of light, (a) Reflected System: For the thin film in air the ray BG suffers reflection at air medium (rare to denser) boundary, it undergoes a phase change of π and a path change of λ/2, while the ray DF does not,

More information

Lecture 21. Physics 1202: Lecture 22 Today s Agenda

Lecture 21. Physics 1202: Lecture 22 Today s Agenda Physics 1202: Lecture 22 Today s Agenda Announcements: Team problems today Team 16: Navia Hall, Laura Irwin, Eric Kaufman Team 18: Charles Crilly Jr, Kyle Eline, Alexandra Vail Team 19: Erica Allen, Shana

More information

Wave Optics. Physics 2B. If two waves exist at the same point in space at the same time, they will interfere with each other.

Wave Optics. Physics 2B. If two waves exist at the same point in space at the same time, they will interfere with each other. Physics 2B Wave Optics Interference If two waves exist at the same point in space at the same time, they will interfere with each other. Interference Superposition Principle for Waves The Principle of

More information

Diffraction and Interference Lab 7 PRECAUTION

Diffraction and Interference Lab 7 PRECAUTION HB 11-14-07 Diffraction and Interference Lab 7 1 Diffraction and Interference Lab 7 Equipment laser, eye goggles, optical bench, slide holder, slide with 4 single slits, slide with 4 double slits, 11X14

More information

Physics 123 Optics Review

Physics 123 Optics Review Physics 123 Optics Review I. Definitions & Facts concave converging convex diverging real image virtual image real object virtual object upright inverted dispersion nearsighted, farsighted near point,

More information