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Interference and Diffraction
Introduction to Physical Optics
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
What is Light?
• To understand
physical optics, let’s
review how we think
about and measure
light, which is part of
electromagnetic
radiation.
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Electromagnetic Radiation
10-15 m
10-6 m
10-2 m
103 m
• EM radiation is made up of an electric field and a
magnetic field.
• Particle-wave duality of EM radiation.
– Light as a particle
– Light as a wave (physical optics)
• Includes x-rays as well as light, IR (heat) and radio
waves.
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Optics
• Optics contains two areas of study:
– Geometrical Optics
– Physical Optics
• Recall: Geometrical optics, or ray optics, is
the study of light that travels as a “ray,” in
straight lines.
– Light rays passing through lenses and
bouncing off mirrors
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
What is Physical Optics?
• Physical optics, or wave optics, is the
study of how light interacts with objects
similar in size to its wavelength.
– Light energy travels as a wave (not a ray).
– Wave optics concerns the characteristics of
light such as wavelength, intensity, phase,
and orientation.
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Wavelength

 Wavelength is the distance between two
identical points on a wave. (, lambda)
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Frequency
time
unit of time
 Frequency is the number of cycles per unit of
time. (, nu)
 It is inversely proportional to the wavelength.
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Wavelength and
Frequency Relation
 = v/
 Wavelength is proportional to the velocity, v.
 Wavelength is inversely proportional to the frequency.
 eg. AM radio wave has a long wavelength (~200 m), therefore it has
a low frequency (~KHz range).
 In the case of EM radiation in a vacuum, the equation becomes
 = c/
Where c is the speed of light (3 x 108m/s)
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Photons
 Photons are little “packets” of energy.
 Each photon’s energy is proportional to its
frequency.
 A photon’s energy is represented by “h”
E = h
Energy = (Planck’s constant) x (frequency of photon)
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Light Wave
• Transverse Wave
– Travels perpendicular to
change of amplitude.
E
B
Direction of Travel
– The case of light:
• Light waves are called electromagnetic waves because they
contain two types of energy that change amplitudes.
• Both electrical and magnetic energy vary perpendicular to each
other.
• Light is a transverse wave because the direction of travel is
perpendicular to the amplitude change of BOTH electrical and
magnetic fields.
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Light Intensity
• Intensity of a monochromatic light relates
to the brightness of that light.
– The intensity of an electromagnetic wave is
proportional to the amplitude squared.
Higher Intensity
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Lower Intensity
Chester F. Carlson Center for Imaging Science
Wave Phase
• Phase:
– The phase of light refers to the timing and position
of two or more waves.
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Chester F. Carlson Center for Imaging Science
Waves ‘In Phase’
• In Phase:
– Two waves that are “in
phase” move together with
the same motions.
• They are at the same cyclic
position at the same time.
– Example
• The turn signal on the car in front of you blinks at the same
time as your signal.
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Waves ‘Out of Phase’
• Out of Phase:
– Two waves that are “out of
phase” do NOT move together
with the same motions.
• At the same time they are at
different cyclic positions.
– Example
• The turn signal inside your car alternates with the
signal of the car in front of you.
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Interference
• Two waves of the same type and
frequency can interfere when they meet at
the same place.
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Interference
• Superposition occurs when waves combine
to form a new wave.
– Constructive Interference
• Waves in phase always superpose to add amplitudes.
=
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Interference
• Superposition occurs when waves combine
to form a new wave.
– Destructive Interference
• Waves out of phase superpose to subtract amplitudes.
=
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Interference
• Coherent waves are continuously in phase
with each other.
– Example:
Laser Light
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Chester F. Carlson Center for Imaging Science
Interference
• The phases of incoherent waves vary
randomly.
– Example:
Light bulb
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Chester F. Carlson Center for Imaging Science
Interference
• To observe interference:
• Use light that that has the same frequency, and is
coherent; e.g. LASER light.
• Split a light beam into two paths.
– amplitude splitting
• Allow the two beams to meet (recombine) at the
same location on a viewing screen or detector.
Beam-splitter
Laser
Mirror
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Mirror
Viewing Screen
Chester F. Carlson Center for Imaging Science
Interference
• To observe interference:
• When the two beams recombine at the viewing
plane they produce interference patterns of dark
and bright fringes because the distances traveled
by the beams determine their phases relative to
each other.
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Thin Films
• Thin films, such as gasoline,
oil, or soap bubbles, also
cause interference by
amplitude splitting.
s1
s2
– One light source (sun), is used
to create two virtual light
sources, splitting the amplitude
of the original.
• The first source is the reflection
off the first surface of the film.
• The second source is the
reflection off the second surface
of the film.
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Thin Films
• Thickness
– The distance between the two surfaces is half the
distance between the virtual sources -- this path
difference determines the wavelength(s) of the
reflected light.
• Oil or gasoline on wet pavement is seen as different colors as
the thickness of the film changes.
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Interference
• Fringes
– When two or more beams of coherent light
interfere, patterns appear in the form of
fringes (dark and bright bands of light).
Constructive
interference:
waves from two
slits combine in
phase
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Interference
• Fringes
– The bright spots are caused by constructive
interference, and the dark spots by
destructive interference
Destructive
interference:
waves from two
slits combine
out of phase
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Diffraction
• Diffraction will cause interference fringes
to form when a single beam interacts with
an object nearly the same size as the
wavelength of the light.
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Chester F. Carlson Center for Imaging Science
Diffraction
• A circular hole or just a tiny circular
shaped particle could create the diffraction
pattern below:
– Alternating fringes of concentric circular rings
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Chester F. Carlson Center for Imaging Science
Diffraction
• Many tiny dust particles can decrease the
resolving power of a lens by overlapping
many diffraction patterns.
• Loss of resolving power = difficult to distinguish
fine details
Resolving Power:
High
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Low
Chester F. Carlson Center for Imaging Science
Diffraction Gratings
• What is a diffraction grating?
– A transmission grating is an opaque plate that
has numerous equally spaced parallel slits
that serve to break up light into its
component wavelengths.
– A reflection grating is to similarly space
numerous reflective surfaces.
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Diffraction Gratings
• The slits cause light to diffract
– Shorter wavelengths (e.g. blue) interfere
constructively at a smaller angle than longer
wavelengths
– As a result, a grating spreads incident white
light out into a spectrum of colors.
Grating
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Interference Applications
• Diffraction Gratings
– Iridescent colors: When the diffracted color
changes with the angle an object is looked at.
• Many birds, insects, and fish have iridescent
colorings via diffraction (feathers make excellent
gratings!).
Imaging Science Fundamentals
Chester F. Carlson Center for Imaging Science
Summary
• Physical optics is the
study of light
traveling as a wave.
• Coherent light of the
same frequency can
interfere both
constructively and
destructively,
sometimes forming
fringe patterns.
Imaging Science Fundamentals
• Diffraction of light due
to tiny objects causes
diffraction patterns to
form.
• Diffraction gratings
are used to diffract
light into its
component
wavelengths.
Chester F. Carlson Center for Imaging Science