Upload File

oxford physics: second year, optics - university of oxford diffraction pattern formed in the image...

  • Home
  • Documents
  • Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,
78

Upload: truongkhanh

Post on 10-Mar-2018

222 views

Category:

Documents


5 download

Report

TRANSCRIPT

Page 1: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,
Page 2: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

P. Ewart

The science of light

Page 3: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

• Lecture notes: On web site

NB outline notes!

• Textbooks:

Hecht, Optics

Lipson, Lipson and Lipson, Optical Physics

Further reading:

Brooker, Modern Classical Optics

• Problems: Material for four tutorials

plus past Finals papers A2

• Practical Course: Manuscripts and Experience

Oxford Physics: Second Year, Optics

Page 4: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Structure of the Course

1. Physical Optics (Interference) Diffraction Theory (Scalar)

Fourier Theory

2. Analysis of light (Interferometers)

Diffraction Gratings

Michelson (Fourier Transform)

Fabry-Perot

3. Polarization of light (Vector)

Oxford Physics: Second Year, Optics

Page 5: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Astronomical observatory, Hawaii, 4200m above sea level.

Page 6: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Multi-segment

Objective mirror,

Keck Obsevatory

Page 7: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Hubble Space Telescope, HST,

In orbit

Page 8: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

HST Deep Field

Oldest objects

in the Universe:

13 billion years

Page 9: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

HST Image: Gravitational lensing

Page 10: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

SEM Image:

Insect head

Page 11: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Coherent Light:

Laser physics:

Holography,

Telecommunications

Quantum optics

Quantum computing

Ultra-cold atoms

Laser nuclear ignition

Medical applications

Engineering

Chemistry

Environmental sensing

Metrology ……etc.!

Page 12: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

CD/DVD Player: optical tracking assembly

Page 13: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

• Astronomy and Cosmology

• Microscopy

• Spectroscopy and Atomic Theory

• Quantum Theory

• Relativity Theory

• Lasers

Oxford Physics: Second Year, Optics

Optics in Physics

Page 14: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Lecture 1: Waves and Diffraction

• Interference

• Analytical method

• Phasor method

Page 15: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

u

t, x

T

Time

or distance

axis

t,z

u

Phase change of 2p

Page 16: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

dsin

d

r1

r2

P

D

Page 17: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Real

Imag

inar

y

u

Phasor diagram

Page 18: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

u /roup

u /ro

Phasor diagram for 2-slit interference

uo r

uo r

Page 19: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Lecture 2: Diffraction theory

• Diffraction at a finite slit - Analytical method

- Phasor method

• 2-D diffraction at apertures

• Fraunhofer diffraction

Page 20: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

ysin

+a/2

-a/2

r

r y+ sin

P

D

y dy

Diffraction from a single slit

Page 21: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

-10 -5 0 5 10

0.0

0.2

0.4

0.6

0.8

1.0

pp p ppp

sinc2()

Intensity pattern from

diffraction at single slit

Page 22: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

asin

+a/2

-a/2

r

P

D

Page 23: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

/

RO

R

R =

P

P

Phasors and resultant

at different angles

Page 24: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

R RP

R sin /2

R

Page 25: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Phasor arc tofirst minimum

Phasor arc tosecond minimum

Page 26: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

y

x

z

Page 27: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Diffraction from a rectangular aperture

Page 28: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Intensity

y

x

Diffraction pattern from circular aperture

Point Spread Function

Page 29: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Diffraction from a circular aperture

Page 30: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Diffraction from circular apertures

Page 31: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Dust

pattern

Diffraction

pattern

Basis of particle sizing instruments

Page 32: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Lecture 3: Diffraction theory

and wave propagation

• Fraunhofer diffraction

• Fresnel’s theory of wave propagation

• Fresnel-Kirchoff diffraction integral

Page 33: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Fraunhofer Diffraction

How linear is linear?

A diffraction pattern for which the

phase of the light at the

observation point is a

linear function of the position

for all points in the diffracting

aperture is Fraunhofer diffraction

Page 34: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

R

R R

R

a a

diffracting aperture

source observingpoint

<

Page 35: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Fraunhofer Diffraction

A diffraction pattern formed in the image

plane of an optical system is

Fraunhofer diffraction

Page 36: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

O

P

A

BC

f

Page 37: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

u v

Equivalent lenssystem

Fraunhofer diffraction: in image plane of system

Diffracted

waves

imaged

Page 38: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

(a)

(b)

O

O

P

P

Equivalent lens system:

Fraunhofer diffraction is independent of aperture position

Page 39: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Fresnel’s Theory of wave propagation

Page 40: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

dS

n

r

Pz-z 0

Plane wave surface

Huygens secondary sources on wavefront at -z

radiate to point P on new wavefront at z = 0

unobstructed

Page 41: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

rn

q

n

P

Construction of elements of equal area on wavefront

rn

q

n

Page 42: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

(q+ /2)

q

p

Rp

First Half Period Zone

(q+/2)

q

p

Rp

Resultant, Rp, represents amplitude from 1st HPZ

Page 43: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

p

/2

q

q

PO

Phase difference of /2

at edge of 1st HPZ

Page 44: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

As n a infinity resultant a ½ diameter of 1st HPZ

Rp

Page 45: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Fresnel-Kirchoff diffraction integral

ikrop e

r

Suiu )rn,(

d

Fresnel-Kirchoff diffraction integral

Page 46: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Babinet’s Principle

Page 47: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Lectures 1 - 3: The story so far

• Scalar diffraction theory:

Analytical methods

Phasor methods

• Fresnel-Kirchoff diffraction integral:

propagation of plane waves

Page 48: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Gustav Robert Kirchhoff

(1824 –1887)

Joseph Fraunhofer

(1787 - 1826)

Augustin Fresnel

(1788 - 1827)

Fresnel-Kirchoff Diffraction Integral

ikrop e

r

Suiu )rn,(

d

Phase at observation is

linear function of position

in aperture:

= k sin y

Page 49: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Lecture 4: Fourier methods

• Fraunhofer diffraction as a

Fourier transform

• Convolution theorem – solving difficult diffraction problems

• Useful Fourier transforms and convolutions

Page 50: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

ikrop ern

r

uiu ).(

dS

xexuAu xi

p d)()(

Fresnel-Kirchoff diffraction integral:

Simplifies to:

where = ksin

Note: A() is the Fourier transform of u(x)

The Fraunhofer diffraction pattern is proportional to the Fourier transform of the transmission function (amplitude function) of the diffracting aperture

Page 51: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

'd).'().'()()()( xxxgxfxgxfxh

The Convolution function:

The Convolution Theorem:

The Fourier transform, F.T., of f(x) is F()

F.T., of g(x) is G()

F.T., of h(x) is H()

H() = F().G()

The Fourier transform of a convolution of f and g

is the product of the Fourier transforms of f and g

Page 52: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Monochromatic

Wave

Fourier

Transform

T

.o p/T

Page 53: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

xo x

V(x)

V( )

-function

Fourier transform

Power spectrum

V()V()* = V2

= constant

V

Page 54: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

xS x

V(x)

V( )

Comb of -functions

Fourier transform

Page 55: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

g(x-x’ ) f(x’ )

h(x)

Constructing a double slit function by convolution

Oxford Physics: Second Year, Optics

Page 56: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

g(x-x’ ) f(x’ )

h(x)

Triangle as a convolution of two “top-hat” functions

This is a self-convolution or Autocorrelation function

Oxford Physics: Second Year, Optics

Page 57: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Lecture 5: Theory of imaging

• Fourier methods in optics

• Abbé theory of imaging

• Resolution of microscopes

• Optical image processing

• Diffraction limited imaging

Page 58: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Joseph Fourier (1768 –1830)

Oxford Physics: Second Year, Optics

• Heat transfer theory:

- greenhouse effect

• Fourier series

• Fourier synthesis and analysis

• Fourier transform as analysis

Page 59: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Ernst Abbé (1840 -1905)

Page 60: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

a

dd’

f Du v

u(x) v(x)

Fourier plane

Abbé theory of imaging (coherent light)

Fourier plane

Page 61: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

The compound microscope

Objective magnification = v/u Eyepiece magnifies real image of object

Page 62: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Diffracted orders from high spatial frequencies miss the objective lens

So high spatial frequencies are missing from the image.

max defines the numerical aperture… and resolution

Page 63: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Fourier

plane

Image

plane

Image processing

Page 64: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Optical simulation of

“X-Ray diffraction”

a b

a’ b’

(a) and (b) show objects:

double helix

at different angle of view

Diffraction patterns of

(a) and (b) observed in

Fourier plane

Computer performs Inverse Fourier transform To find object “shape”

Page 65: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

a

dd’

f Du v

u(x) v(x)

Fourier plane

amplitude or phase object

Page 66: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics Schlieren photography

Source

CollimatingLens

ImagingLens

KnifeEdge

ImagePlane

Refractiveindex variation

Fourier

Plane

Page 67: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Schlieren photography of combustion

Schlieren film of ignition

Courtesy of Prof C R Stone

Eng. Science, Oxford University

Page 68: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Intensity

y

x

Diffraction pattern from circular aperture

Point Spread Function, PSF

Page 69: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Lecture 6: Optical instruments and

Fringe localisation

• Interference fringes

• What types of fringe?

• Where are fringes located?

• Interferometers

Page 70: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

• Interference by:

• Division of wavefront - Young’s slits: 2 beams

- N-slit grating: multiple beams

• Division of amplitude - Michelson: 2 beams

- Fabry-Perot: multiple beams

What kind of interference fringes and where are they?

Page 71: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

What kind of interference fringes and where are they?

Depends on: Type of light source – Point source - Extended source Division of wavefront – Point sources Division of amplitude by – Reflection from: Wedged surfaces Parallel surfaces

Page 72: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

non-localised fringes

Plane

waves

Division of wavefront Young’s slits

Usually observed under Fraunhofer conditions – large distance from slits

Non-localized fringes

Page 73: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Z

Oxford Physics: Second Year, Optics

to 8

f

Plane

waves

Fraunhofer condition

Division of wavefront Diffraction grating

Fringes localized at infinity

Page 74: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

P’

P

O

Wedged reflecting surfaces Point source

Division of Amplitude

Fringes of Equal thickness

Non-localized

Page 75: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

OPP’

’

Parallel reflecting surfaces Point source

Division of Amplitude

Fringes of Equal inclination

Non-localized

Page 76: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

P’

P

R

OS

R’

Wedged Reflecting surfaces

Extended source

Division of Amplitude

Localized in plane of wedge, near apex

Equal thickness

Page 77: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

t

2t=x

sourceimages

2t=x

path difference cos x

circular fringe

constant

Parallel reflecting surfaces Extended source

Division of Amplitude

Localized at infinity

Fringes of equal inclination

Page 78: Oxford Physics: Second Year, Optics - University of Oxford diffraction pattern formed in the image plane of an optical system is Fraunhofer diffraction Oxford Physics: Second Year,

Oxford Physics: Second Year, Optics

Wedged Parallel

Point

Source

Non-localised

Equal thickness

Non-localised

Equal inclination

Extended

Source

Localised in plane

of Wedge

Equal thickness

Localised at infinity

Equal inclination

Summary: fringe type and localisation


Diffraction, Numerical Integration - School of Physics · Web viewDiffraction, Numerical Integration Subject Matlab, Computational Physics Keywords annular apertures, diffraction

Single crystal X-ray diffraction and SAXS · Rigaku Oxford Diffraction X-RAY SOURCES Rigaku Oxford Diffraction offers several sources to fi t the needs of your experimental samples

Neutron diffraction of crystalline materials...Oxford Neutron School – Diffraction - 2013 Scope of the lecture Diffraction techniques (X-ray, neutron) are used to study thin films

Chapter 15S Fresnel diffraction - Binghamton Universitybingweb.binghamton.edu/~suzuki/Math-Physics/LN-15S_Fresnel_diffraction.pdfChapter 15S Fresnel-Kirchhoff diffraction Masatsugu

Diffraction Of Light In Physics

Physics 213 General Physics Lecture 19. 1 Last Meeting: Diffraction Today: Optical Instruments

1 DIFFRACTION and Forward Physics – 2 DIFFRACTION and Forward Physics – 2 M. Arneodo, M.Diehl, V.A.Khoze, P.Newman & with a bit of personal flavour Plan

OXFORD UNIVERSITY - Physics & Maths Tutorpmt.physicsandmathstutor.com/download/Physics/PAT/Papers/PAT 20… · OXFORD UNIVERSITY PHYSICS APTITUDE TEST Wednesday 5 November 2014 Question

DOING PHYSICS WITH MATLAB DIFFRACTION … Physics with Matlab Quantum Mechanics Waves and Particles 1 DOING PHYSICS WITH MATLAB DIFFRACTION PHYSICS WAVE ... Simulation of the interference

Diffraction Physics

Teaching Physics at Oxford

Department of Physics Physics 128 X-RAY DIFFRACTION CRYSTALLOGRAPHYweb.physics.ucsb.edu/~phys128/experiments/xray/xray.pdf · Department of Physics Physics 128 X-RAY DIFFRACTION CRYSTALLOGRAPHY

1. Basic crystallography 2. Basic diffraction physics 3 ... · X-ray analysis 1. Basic crystallography 2. Basic diffraction physics 3. Experimental methods ... Basic diffraction physics

Oxford IB Physics - Weebly

Introduction of diffraction theory in solid state physics

Physics at Oxford - University of Oxford · undergraduate degree courses at the university of oxford for entry in 2018 physics at oxford

DIFFRACTION and Forward Physics – 2

Lecture 29 Physics 2102 Jonathan Dowling Ch. 36: Diffraction

The physics of diffraction

Lattices and Symmetry Scattering and Diffraction (Physics)csrri.iit.edu/~howard/ACASchool/lectures07/Kaduk...1 Lattices and Symmetry Scattering and Diffraction (Physics) James A. Kaduk

DIFFRACTION: Journal for Physics Education and Applied Physics

2. THE PHYSICS OF DIFFRACTION GRATINGS

X-RAY DIFFRACTION in POWDERS - Rutgers Physics & Astronomy

OXFORD MASTER SERIES IN PHYSICS

upgrade your physics - Department of Physics - University of Oxford

Diffraction Physics 202 Professor Lee Carkner Lecture 26

The Physics of Diffraction Gratings

Diffraction II Physics 2415 Lecture 38 Michael Fowler, UVa

SOLID STATE PHYSICSucapahh/teaching/3C25/Lecture05s.pdf · SOLID STATE PHYSICS Lecture 5 A.H. Harker Physics and Astronomy UCL. Structure & Diffraction Crystal Diffraction (continued)

Core Physics – Energy L/O :- To understand diffraction Diffraction Exam Date -

Feynman physics lectures v1 ch30 1962 02-23 diffraction

Oxford Physics Newsletter

Physics, Oxford

AP Physics B - Diffraction

X-Ray Diffraction and Characterization of Crystalline …X-Ray Diffraction and Characterization of Crystalline Materials K. Prathap Associate Professor in Physics, Department of Physics,