Q1' Looking into the Blue Field Entoptoscope with the right eye, a patient sees no luminous darting

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Q1. Looking into the Blue Field Entoptoscope with
the right eye, a patient sees no luminous darting
points in the upper right sector of the
instruments blue background. This signifies

• Occlusion of the right superior- temporal retinal
  vein
• Occlusion of the right inferior-nasal retinal
  vein
• Corneal edema (inferior cornea)
• Macular edema

3
Posterior Vitreous Detachment
Page 2.38
4
Posterior Vitreous Detachment
Vitreous pulls away from the retina at the
posterior pole
5
Q2. A patient who suffered vitreous detachment
two years ago is likely to experience

• Flashes of light and floaters
• Flashes of light
• Vertical lightning streaks and floaters
• Vertical lightning streaks

6
Retinal Detachment
Page 2.39
7
Retinal Tear with Vitreous Detachment
8
Retinal Detachment

• Retinal detachment is a clinical emergency
• Signs (all more likely with a detachment near the
  fovea)
• Photopsia (flashes of light) ? entoptic
• Scotomas (visual field defects)
• Floaters (possibly large) ? entoptic
• Metamorphopsia (distortion of central vision)

9
Retinal Detachment
Metamorphopsia
Appearance to patient with metamorphopsia
Amsler Grid
10
Types of Retinal Detachment

• Rhegmatogeneous Retinal Detachment - due to a
  retinal break (liquefied vitreous enters space
  between RPE and sensory retina ? detachment)
• Tractional Retinal Detachment - due to vitreous
  traction on the underlying retina
• Serous (Exudative) Retinal Detachment - due to
  fluid accumulation beneath the sensory retina
  without a retinal break

11
Types of Retinal Detachment
Tractional
Inner limiting membrane
VITREOUS
Break
RPE
Serous
Rhegmatogeneous
CHOROID
Bruchs Membrane
SCLERA
12
Blue Arcs of the Retina
NO clinical significance
Page 2.39
13
Blue Arcs of the Retina

• Due to secondary electrical activity in the
  retina
• One neuron firing stimulates adjacent neurons all
  the way back along the arcuate nerve fiber bundle
  to the optic disc
• Seen best when fixation target parallel to
  arcuate nerve fiber bundle in stimulated retinal
  region

14
Blue Arcs
Fig 2.24, Page 2.40
15
Blue Arcs
Nasal Field
Temporal Field
N
Disc
16
Blue Spike - Target Horizontal
Fig 2.25, Page 2.40
Fixating nasal edge of horizontal rectangle
(orange)
17
Entoptic Phenomena of Macular Origin
Page 2.41
18
Plane Polarization
19
Plane Polarization Rope Analogy
Zero energy in horizontal plane
20
Plane Polarization Rope Analogy

• Snapping a taut rope vertically at the free end
  causes a vertically oscillating wave to propagate
  horizontally along the length of the rope.
• This is analogous to plane polarized light
• Some crystals (e.g. tourmaline) freely transmit
  light along one crystal axis and totally
  extinguish light along a perpendicular axis ?
  emit plane polarized light from unpolarized
  incident light. Many are also dichroic
  (absorbing some ?s more than others)

21
Vertically Polarized Light

• Vertical plane of vibration (maximum energy)
• Horizontal plane of extinction (zero energy)

zero energy
22
Vertically Polarized Light

• Polarizing sunglasses are plane polarizers with
  vertical transmission axis (cut out horizontally
  polarized light)
• Most reflected glare (e.g. from a lake surface)
  is horizontally polarized

23
Vertically Polarized Light

• Plane polarized light looks no different from
  unpolarized light under normal conditions
• Need an analyzer (second polarizer) to detect
  polarization of incident light
• Crossing two polarizers (one with vertical
  transmission axis second with horizontal
  transmission axis) results in total extinction of
  light

24
Crossed Polarizers
Knowing the transmission axis of one polarizer
(the analyzer) we can rotate the second polarizer
until it is crossed with the analyzer. This
locates the transmission axis of the second
polarizer.
25
Entoptic Phenomena of Macular Origin

• Haidingers Brushes

26
Haidingers Brushes - the Eyes Analyzer

• Human macula contains an analyzer that (under
  specific viewing conditions) can entoptically
  differentiate the transmission and extinction
  axes of plane polarized (P-state) light ?
  transmits differently
• Macular analyzer has polarizing properties and is
  dichroic (selectively absorbing blue light)

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Macular Pigment - Xanthophyll
Macular pigment xanthophyll creates a yellow
filter for light under normal conditions ? blue
cones appear to turn up their sensitivity to
compensate
29
Neuroglial Fibers (Muller Cells)
30
Muller Cell Fibers in Macular Region
Inner retinal layers sloped away from center in
foveal region ? supporting fibers on Muller cells
form a radial pattern
31
Radial Analyzer
Xanthophyll tends to associate with Muller cell
fibers ? yellow radial analyzer
32
Appearance of Haidingers Brushes

• Haidingers brushes appear optimal when viewing a
  rotating plane polarizer through a blue filter

33
Appearance of Haidingers Brushes under optimum
conditions
Fig 2.26, Page 2.41
34
Mechanism of Haidingers Brushes

• Xanthophyll pigment aligned with radial Muller
  fiber arrangement in macular region ? analyzer is
  radial
• Polarized blue light affected differently
  depending on state of polarization
• in transmission axis ? free transmission?
  effectively overcomes yellow filter ? greater
  transmission of blue
• light perpendicular to transmission axis ? fully
  absorbed by xanthophyll pigment ? blue ? blue
  dark (dark)

35
Mechanism of Haidingers Brushes

• Remember under normal conditions, polarized
  light does not look any different from
  unpolarized light
• Need the analyzer to see the state of
  polarization of light

36
Haidingers Brushes Dichroic RA Theory
WHITE LIGHT
BLUE LIGHT
Fig 2.28, Page 2.43
37
Haidingers Brushes Dichroic RA Theory
If we did not have the radial analyzer, what
would we see? Blue light
WHITE LIGHT
BLUE LIGHT
If we did not have the rotating polarizer, what
would we see? Blue light
If we did not have xanthophyll at the macula,
what would we see? Blue light
Fig 2.28, Page 2.43
38
Haidingers Brushes - Clinical Applications

• Diagnosis of macular edema - even small amount of
  macular edema (hard to see with BIO) disrupts
  Muller cell fiber radial analyzer? Haidingers
  brushes not seen
• Detection of eccentric fixation (strabismus
  patient) ? when fixating eccentrically, do not
  see Haidingers Brushes
• Training central fixation seeing Haidingers
  Brushes ? tells patient when they are centrally
  fixating (feedback)

39
Q3. Which entoptic phenomenon could be used to
describe the contour of the retinal nerve fiber
layer?

• Yellow dancing spots
• Blue Arcs of the retina
• Phosphenes
• Moores Lightning Streaks

40
Q4. Which one of the following entoptic phenomena
has no clinical significance?

• Phosphenes
• Corneal halo
• Yellow Dancing Spots
• Haidingers Brushes
• None of the above

41
Recap Key Objectives

• The most clinically important entoptic phenomena
  are phosphenes (possible retinal detachment),
  entoptic haloes (possible corneal edema), and
  macular entoptic phenomena (Haidingers brushes
  macular integrity, central fixation training for
  eccentric fixation)
• Yellow Dancing Spots are clinically significant
  (vascular occlusive disease) but Blue Field
  Entoptoscopes are rarely used in clinical practice

42
Converting Angular to Linear Size
N
a
43
Visual Optics I, 2007-2008

• Chapter 3
• Retinal Image Quality

44
Retinal Image Quality
Page 3.2
Main Goal Define the eyes POINT SPREAD
FUNCTION Translation How does the eyes image of
a point vary with pupil diameter and the nature
of incident light?
Retinal Point Spread Function for 1 7 mm pupil
diameter
45
Page 3.1

• Fovea 5? off-axis
• This gives rise to off-axis aberrations
• Makes role of the pupil (aperture stop) more
  important
• Blurred retinal images centered on pupil rays
  but not on nodal rays

Figure 3.1 Cross-section of the human eye.
Angular separation of optic and visual axes
(typically 5?) makes the eye imperfectly centered
and subject to off-axis aberrations. It also
increases the importance of the pupil in
determining retinal image quality.
46
Retinal Image Quality Topics
Page 3.2

• Interactions between light waves (the basics of
  interference)
• Diffraction at a slit (the basics of diffraction)
• Diffraction at a circular aperture (the pupil)
• Diffraction and resolution of the eye the
  Rayleigh Criterion(diffraction-limited system)
• The net monochromatic wavefront aberration and
  its components
• Dispersion and chromatic aberration
• Scattering of light and intraocular light scatter

47
1. Interference
48
Waves Interfering
Any time two or more waves meet, interference
occurs
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Interactions between Light Waves (the Basics of
Interference)
Common origin of wavelets traversing double slit
assures some degree of coherence
Page 3.3
Figure 3.2 The classical interference set-up
Youngs Double Slit Experiment
51
Constructive Interference
Page 3.4
Component waves in phase
Figure 3.3 - Constructive interference. Waves of
different amplitude are shown (dashed lines).
Because these waves are in phase, crests coincide
and troughs coincide. The resultant amplitude
(solid line) is the sum of the amplitudes of the
two interfering waves.
52
Page 3.4
Partial
180? (?/2) out of phase but different
amplitude 180? out of phase and equal amplitude
Destructive Interference
Total
Figure 3.4 - Destructive interference. (a) Two
waves of different amplitude 180? out of phase.
Resultant amplitude is the difference in absolute
amplitude between the two interfering waves. (b)
If both waves have the same amplitude and are
180? out of phase, total destructive interference
occurs, and the resultant amplitude is zero.
53
Interference
Page 3.5

• Coherence

54
Coherence

• Measure of the ability of two light waves to
  produce interference
• Requires constant phase difference between the
  two interfering waves

55
Coherence

• In Youngs double slit experiment, light from a
  single slit is then divided at the double slit

56
Youngs Double Slit Expt.
Screen
Double Slit
Min
Fig 3.2 Page 3.3
57
Coherence

• In Youngs double slit experiment, light from a
  single slit is then divided at the double slit

• the common origin of waves emitted through the
  double slit makes them coherent - but how
  coherent?
• Coherence is important because higher coherence
  means higher fringe contrast on the screen

58
Coherence

• We can separate coherence properties of real
  sources and slit configurations into two
  categories
• Temporal Coherence
• Spatial Coherence

59
Temporal Coherence
Page 3.5

• The ability of a wave to interfere with another
  (later) portion of itself

60
Temporal Coherence
Screen
Double Slit
Source Slit
Min
Fig 3.2 Page 3.3
61
Temporal Coherence

• The narrower the bandwidth (Dm), the longer it
  takes for the phase of the composite wave to
  change.
• As bandwidth increases (more ?s), the net wave
  shape changes more rapidly through space and
  after a shorter distance we dont even get a
  crest where we expected a crest

Increasing bandwidthdecreases temporalcoherence
Fig 3.5 Page 3.6
62
Temporal Coherence

• The two extreme frequencies (wavelengths) in the
  bandwidth can be used to quantify temporal
  coherence
• When the highest frequency wave has traveled one
  more cycle in space than the lowest (extreme
  frequencies one cycle out of phase), fringe
  contrast decreases to zero (no fringes visible)

Increasing bandwidthdecreases temporalcoherence
Fig 3.5 Page 3.6
63
Temporal Coherence

• Define the time taken for the two extreme
  frequencies (wavelengths) to get one cycle out of
  phase as coherence time

Lab He-Ne laser, Dm 1.3 x 109 Hz? Dt 7.7 x
10-9 seconds
64
Temporal Coherence

• Coherence time yields the more meaningful term,
  coherence length

• The highest quality lasers have coherence
  lengths? 30 km

65
Some Typical Coherence Lengths
A regular incandescent lamp has a similar
bandwidth to daylight (1014 range) and therefore
extremely short coherence length Coherence length
can be improved by adding a narrow bandpass
spectral filter e.g. a red filter may reduce the
bandwidth from several hundred nanometers to less
than fifty
66
Spatial Coherence

• The ability of two separate parts of the same
  wave to produce interference

67
Spatial Coherence
Screen
Interference Pattern
Double Slit
Source Slit
Max
Min
Fig 3.2 Page 3.3
68
Perfect spatial coherence requires

• Interfering waves of equal wavelength and
  amplitude.
• A very small source (ideally a point source) or
  source profile seen by the double slit
• Reason waves are emitted from the source in
  random directions with random phase. For waves
  arriving simultaneously at the double slit, their
  random phases will produce destructive
  interference
• Therefore want as few waves as possible arriving
  simultaneously at the double slit

69
To maximize spatial coherence in Youngs Double
Slit Expt

• Keep the source slit as narrow as possible

• Maintain a large distance between source slit and
  double slit compared to double slit separation

70
Spatial Coherence
Double Slit
Source Slit
71
To maximize spatial coherence in Youngs Double
Slit Expt

• Keep the source slit as narrow as possible
• Maintain a large distance between source slit and
  double slit compared to double slit separation

• Use longer wavelength light (greater separation
  of wavefronts)

72
Examples of Coherence Applications
73
Application Optical Coherence Tomography

• Uses broadband, short coherence length, IR source
• Split light into two paths one enters sample,
  other reflects from reference mirror. Both
  recombine at detector
• Only resolve image when two path-lengths almost
  identical
• Allows precise targeting of tissue locations
• Minimal interference from surrounding tissue

74
OCT Imaging of Fovea
75
High Coherence Applications

• High temporal coherence
• allows DVD lasers to write Gb of information
• allows very high laser output intensity
• has many other laser and fiber optics applications

76
Coherence Summary
77
Coherence whats important?

• Temporal
• coherence length
• distance over which wavelength and phase are
  relatively constant
• maximize coherence length with narrow bandwidth
  light
• narrow bandwidth means light is as close as
  possible to monochromatic

78
Coherence whats important?

• Spatial
• narrow source or source slit
• allows as few waves as possible to be emitted
  toward the double slit
• important because successive waves are incoherent
• relatively long distance between source slit and
  double slit relative to double slit separation
• minimizes potential optical path length
  differences between the two slits of the double
  slit

79
Diffraction at a Slit
80
Huygens Principle
Page 3.7
Slit
Obstacle
All points on a wavefront can be considered as
point sources for the production of secondary
wavelets, and at any later time the new wavefront
position is the envelope (surface of tangency) to
those secondary wavelets
81
Diffraction Through a Slit
Page 3.8
Highest intensity
Figure 3.7 - Plane waves incident at a slit wide
enough to allow several secondary wavelets to
pass through. A diffraction pattern will be seen
on the distant screen.
82
Fraunhofer Diffraction Pattern
Page 3.9
Central max
Figure 3.8 - Diffraction pattern produced on the
distant screen from figure 5. The pattern arises
from superposition of the secondary waves.
Intensity is highest at the central maximum, P0 ,
then drops to zero at the first order minimum.
Intensity then rises and falls less and less at
subsequent maxima and minima.
83
Image for Laser Source
84


85
Slit Geometry and Path Difference to Screen
Page 3.10
Equal distances from AEC to screen
Phase difference along AEC ? phase difference at
screen
Figure 3.9 - Construction for finding the path
difference between the waves traveling from the
top (A), center (D) and bottom (B) of the slit to
the same point, P, on the distant screen. Points
along the line AC are all equidistant from P.
86
Screen Angle for Total Destructive Interference
Page 3.11
?
?
Phase difference between top and bottom of slit
BC
Figure 3.10 - When , destructive
interference results on the screen. Each wave
traveling through the upper part of the slit
cancels a corresponding wave (matching line
pattern in figure) traveling through the lower
part of the slit.
87
Page 3.12
All possible phases traveling through AEC ? all
possible phases arriving at point P on screen
Another point in time same effect
Figure 3.11 - Phase distribution along AC (Figure
8) for (a) and (d) first order minimum (different
phases at A)
88
Screen Angle for Total Destructive Interference
Page 3.11
E
All possible phases traveling through AEC ? all
possible phases arriving at point P on screen
Figure 3.10 - When , destructive
interference results on the screen. Each wave
traveling through the upper part of the slit
cancels a corresponding wave (matching line
pattern in figure) traveling through the lower
part of the slit.
89
Screen Angle for Total Destructive Interference
Page 3.11
E
A
Figure 3.10 - When , destructive
interference results on the screen. Each wave
traveling through the upper part of the slit
cancels a corresponding wave (matching line
pattern in figure) traveling through the lower
part of the slit.
90
Angle of First Order Diffraction Minimum
Page 3.12
From Figure 3.9
91
Higher Order Minima (m order)
Page 3.12
92
Fraunhofer Diffraction Pattern
Page 3.9
Central max
How does width of the central max vary with slit
width? Central max bounded on either side by
first order minimum
Figure 3.8 - Diffraction pattern produced on the
distant screen from figure 5. The pattern arises
from superposition of the secondary waves.
Intensity is highest at the central maximum, P0 ,
then drops to zero at the first order minimum.
Intensity then rises and falls less and less at
subsequent maxima and minima.
93
Angle of First Order Minimum Effect of Slit
Width
For ? 587.6 nm, and slit widths (d) of 20?,
10?, 5?, and ? find the width of the central
maximum. The central maximum extends to the first
order minimum, an angle ? either side of the
center of the central maximum
2? 5.74?

• d 20? 11.75 ?m
• d 10? 5.88 ?m
• d 5? 2.94 ?m
• d ? 0.59 ?m

2? 11.4?
2? 23.0?
2? 180? ?
?d ? ?? ? widen central max.
OBJ
94
d 10? 5.88 ?m
d 20? 11.75 ?m
Page 3.14
Diffraction Pattern vs. Slit Width
d ? 0.59 ?m
d 5? 2.94 ?m
Figure 3.12 - Central maximum of diffraction
pattern for d (a) 20?, (b) 10?, (c) 5? and (d)
?. Intensity distribution is approximate. Width
of zero order maximum increases as slit width
narrows. At the same time, maximum intensity
decreases. Overall width of central maximum
corresponds to 2?.
95
Key Point Diffraction at a Slit

• Width of the central maximum varies inversely
  with slit width. Therefore
• a wider slit produces a narrower central maximum
• a narrower slit produces a broader central
  maximum

OBJ
96
Page 3.15
Figure 3.13 - Screen image seen through a narrow
slit according to (a) geometrical optics note
the sharp image border, (b) physical optics,
producing a diffraction pattern. The intensity
distribution within the diffraction pattern gives
a hazy appearance to the edge of the image. The
diffracted image (b) is wider than the
theoretical geometrical image.
97
Diffraction at a Circular Aperture
Page 3.15
98
Diffraction at a Circular Aperture
Page 3.15
This intensity profile is what the eye sees for
every object point (assuming the eye is
diffraction-limited)
Airy Disc
OBJ
Figure 3.14 - Intensity distribution in the Airy
Disc pattern (central maximum bordered by first
order minimum). Higher order maxima are much
lower in intensity.
99
Features of the Circular Aperture Diffraction
Pattern
The Airy Disc is bordered by the first order
minimum (angle ? from center)
Radius of the Airy Disc corresponds to angle ?.
diameter to 2?
Beyond the Airy disc is a series of annular
higher order maxima and minima
100
Equation for First Order Minimum
Page 3.16
Airy Disc
OBJ
Figure 3.14 - Intensity distribution in the Airy
Disc pattern (central maximum bordered by first
order minimum). Higher order maxima are much
lower in intensity.
101
Airy Discs and Retinal Image Quality
Page 3.16
As the pupil constricts (d decreases), the Airy
Disc for each object point broadens. Small pupil
diameter would therefore make the task of
resolving two closely adjacent point sources much
more difficult
102
Diffraction and Resolution the Rayleigh Criterion
Two closely adjacent point sources will just be
resolved if they are separated by a distance
equal to the radius of an Airy Disc (for
identical point sources, the Airy Discs will be
identical)
OBJ
103
Converting Angular to Linear Size
N
x
? 6 meters
104
Rayleigh Criterion
Page 3.17
Figure 3.14 - Separation of Airy discs for two
closely adjacent point sources for (a) small
pupil images not resolved, (b) larger pupil
images just resolved (Rayleigh criterion),
(c) pupil larger again images easily resolved.
105
Page 3.18
Airy discs separated by the radius of one Airy
disc ? just enough drop in intensity between
peaks to see images as separate
Figure 3.15 - Relationship between separation of
Airy discs and radius of one Airy disc for the
Rayleigh Criterion.
106
Diffraction and Resolution of the Eye
Page 3.18
107
Large Pupil Small Airy Discs
ADD
h?
108
Small Pupil Large Airy Discs
ADD
h?
109
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110
Diffraction and Resolution of the Eye
Page 3.18

• If diffraction were the only image-degrading
  effect on retinal image quality, resolution would
  continue to increase with pupil diameter.
• Aberrations limit the improvement, because they
  increasingly degrade images through larger pupils
• Optimal pupil diameter (highest retinal image
  quality) strikes a balance between diffraction
  and aberrations

OBJ
111
Diffraction AberrationsWhat happens to the
Rayleigh Criterion?

• How well does the Rayleigh criterion hold up when
  we re-introduce aberrations to our ideal
  diffraction-limited system?

• To address this question, Rabbetts (1989) studied
  patients ability to resolve square-wave gratings
  (similar to measuring visual acuity) with various
  pupil diameters

112
Square wave Gratings
Low spatial frequency
Medium spatial frequency
High spatial frequency
113
VA Chart equivalence of square wave gratings
114
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115
Page 3.19
Roughly equivalent toVA chart performance
Figure 3.17 - Resolution of a square-wave grating
as a function of pupil diameter (for constant
retinal illumination). --------- Rayleigh
criterion (resolution for diffraction-limited
system) _________ experimentally determined
resolution.
116
Diffraction-Limited System
Rayleigh Criterion
Fig 3.17 Page 3.19
117
Experimental Grating Resolution
Rayleigh Criterion
Fig 3.17 Page 3.19
118
Experimental Grating Resolution
Rayleigh Criterion
Fig 3.17 Page 3.19
119
Experimental Grating Resolution
Rayleigh Criterion
Fig 3.17 Page 3.19
120
Experimental Grating Resolution
OBJ
Rayleigh Criterion
Fig 3.17 Page 3.19
121
Point Spread Function vs. Pupil Size

• Another way to view the interaction between
  diffraction and aberrations is to look at the
  retinal point spread function for various pupil
  diameters
• The point spread function shows the net effect of
  all image-degrading influences (diffraction,
  aberrations, defocus, and others) on an object
  point

122
Diffraction-Limited Eye
Notice that the best image (least spread) occurs
with the largest pupil
A . Roorda, University of Houston
123
Aberrations increasingly degrade the image for
larger pupils
A . Roorda, University of Houston
124
Resolution Limit of the Eye Anatomy vs. Optics
Page 3.20
This is the optical limit for resolution
according to the Rayleigh Criterion
125
Page 3.20
Foveal Cone Mosaic
Figure 3.18 Upper foveal cone mosaic, showing
the region of highest density (smallest cones) in
the foveola (slightly below center). Note that
the pattern is not entirely regular (number of
neighbors per cone). An occasional rod can be
seen toward the edges. Lower the pattern in the
central foveolar region (lower) shows a regular
hexagonal (six-neighbor) cone matrix.
126
Anatomical Optimization of the Fovea
Page 3.21
Foveolar hexagonal cone matrix

• Avascular
• Maximum cone density
• 11 projection cone ? ganglion cell
• Outer retinal layers displaced away from fovea
• Macular xanthophyll pigment absorbs blue light
  (reduces scatter and chromatic aberration)

127
Anatomical (Receptor) Limit of Resolution
Page 3.21
Foveolar hexagonal cone matrix
To resolve two images as separate, there must be
at least one unstimulated receptor in between the
stimulated receptors
128
Anatomical (Receptor) Limit of Resolution
Page 3.21
One unstimulated receptor in between two
stimulated receptors
Angular separation for receptor limit
Figure 3.19 Two closely adjacent sources
subtending angle ? at the nodal point of the
(simplified schematic) eye and stimulating two
receptors separated by one unstimulated receptor.
Based on a cone separation of 2 ?m, angle ?
corresponds to a distance of 4 ?m on the fovea?
This is the receptor limit for resolution.
129
Anatomical (Receptor) Limit of Resolution
Page 3.21
Rayleigh Criterion
130
Anatomical (Receptor) Limit of Resolution
Page 3.21
OBJ
Rayleigh criterion closely matches receptor limit
? foveal cones match the optics of a
diffraction-limited system
131
Combining Interference Diffraction
Page 3.24
132
Construction for First Order Interference Maximum
Page 3.24
Figure 3.20 - Double slit interference with a
distant screen. Construction for finding the
path difference between waves traveling from the
two slits to point Q on a distant screen (making
an angle ? with the axis). Since the
construction is identical geometrically to that
shown in Figure 8 for diffraction, points along
the line AC are all equidistant from Q.
133
Construction for First Order Interference Maximum
Page 3.26
Figure 3.21 - Double slit interference with a
distant screen. When BC ?, waves from each
slit are in phase at A and C (equidistant from
point Q on the screen). The result is
constructive interference at the screen.
134
Construction for First Order Interference Maximum
Page 3.25
135
Interference versus Diffraction same Geometry
Page S8
Figure S5 Same constructions for (a)
interference maxima and (b) diffraction minima
136
Interference versus Diffraction
Diffraction at each slit? for BC ? (min 1)
must be much ______ ?
greater
137
Interference/Diffraction versus Slit Width
Page S9
Narrow slits
Wider slits
Figure S6 - (a) Double slit interference pattern
for narrow slits. Diffraction has little effect
due to the large angle of diffraction, so the
screen pattern is due to interference alone. (b)
Same slit separation, but wider slits. Solid line
shows net effect at screen. Approaching the first
diffraction minimum, diffraction effects (dashed
line) progressively reduce the intensity of
interference maxima (fourth interference maximum
canceled in this case).
138
Single vs Double Slit
139
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140
Interference/Diffraction versus Slit Width
Page S10
Figure S7 upper
141
Screen Intensity Profile
Slit Width ? e.g. 5 ? 10?4 mm Slit Separation
20 ? 10?2 mm
142
Interference/Diffraction versus Slit Width
Page 3.29
Figure 3.24 lower
143
Screen Intensity Profile
Slit Width 2? 10?3 mm Slit Separation 20
? 10?2 mm
144
Page 3.30
Figure 3.25upper
Slit Width 5? 2.5 ? 10?3 mm Slit Separation 20
? 10?2 mm
145
Interference/Diffraction versus Slit Width
Page 3.30
Figure 3.25 lower
146
Screen Intensity Profile
Slit Width 10? 5 ? 10?3 mm Slit Separation 20
? 10?2 mm
147
Slit Width ? e.g. 5 ? 10?4 mm Slit Separation
20 ? 10?2 mm
Slit Width 2? 10?3 mm Slit Separation 20
? 10?2 mm
Slit Width 5? 2.5 ? 10?3 mm Slit Separation 20
? 10?2 mm
Slit Width 10? 5 ? 10?3 mm Slit Separation 20
? 10?2 mm
148
Multi-slit Interference/Diffraction
Page 3.32
Figure 3.26 - Interference patterns for same slit
spacing for (a) two slits, (b) three slits, (c)
four slits, (d) many slits (diffraction grating).
149
Diffraction Grating
Page 3.33
Figure 3.27 - Pattern obtained from white light
with a diffraction grating. The central maximum
is white, higher order maxima are wavelength
dependent. Red (longer wavelength) diffracts
through a larger angle than blue (shorter
wavelength)
150
Many Slits Diffraction Grating
I
q
Fig 3.26 Page 3.32
151
Many Slits Diffraction Grating
Showing all wavelengths
I
Green
Yellow
Blue
Orange
Violet
Red
m 1
m 2
m 0
q
Fig 3.27 Page 3.33
152
Practice Problem 3
The two figures below show screen intensity
profiles for a double slit. Slit separation is
the same in both cases, but slit width differs.
In which figure are the slits wider?
1st order Diffraction minimum
Interference maxima
153
Practice Problem 3
The two figures below show screen intensity
profiles for a double slit. Slit separation is
the same in both cases, but slit width differs.
In which figure are the slits wider?
1st order Diffraction minimum
A
B
154
Practice Problem 3
The two figures below show screen intensity
profiles for a double slit. Slit separation is
the same in both cases, but slit width differs.
In which figure are the slits wider?
A
?
B
155
Practice Problem 4
All four figures show screen intensity profiles
for a double slit. In which figure is the slit
separation greatest?
156
Practice Problem 4
Greatest slit separation?
Interference
Greatest separation ? smallest angle (maxima
closest together)
157
Practice Problem 4
Greatest slit separation?
Interference
Greatest separation ? smallest angle (maxima
closest together)
158
Practice Problem 5
159
Practice Problem 6
All four figures show screen intensity profiles
for a double slit.
In which figure is the slit width greatest?
160
Practice Problem 6
Greatest slit width?
Diffraction
Greatest width ? smallest angle of diffraction
(1st order minimum)
161
Practice Problem 6
Greatest slit width?
Diffraction
?
162
Greatest slit separation
Smallest slit separation
Greatest slit separation
Widest slit?
Widest slit
163
Slit Width 0.5 ?m Slit Sepn 10 ?m
Slit Width 0.25 ?m Slit Sepn 2.5 ?m
Slit Width 2.5 ?m Slit Sepn 10 ?m
Slit Width 2.5 ?m Slit Sepn 5 ?m