ECE-1466 Modern Optics Course Notes Part 2

1
ECE-1466Modern OpticsCourse NotesPart 2

• Prof. Charles A. DiMarzio
• Northeastern University
• Spring 2002

2
Lens Equation as Mapping

• The mapping can be applied to all ranges of z.
  (not just on the appropriate side of the lens)
• We can consider the whole system or any part.
• The object can be another lens

L1
L2
L3
L4
L4
3
What We Have Developed

• Description of an Optical System in terms of
  Principal Planes, Focal Length, and Indices of
  Refraction
• These equations describe a mapping
• from image space (x,y,s)
• to object space (x,y,s)

4
An Example 10X Objective
F
F
F
F
A
A

• s 16 mm
• s160 mm (A common standard)

5
The Simple Magnifier
F
F
A
A
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The Simple Magnifier (2)

• Image Size on Retina Determined by x/s
• No Reason to go beyond s 250 mm
• Magnification Defined as
• No Reason to go beyond D10 mm
• f ?1 Means f10 mm
• Maximum Mm25

For the Interested Student What if sgtf ?
7
Where Are We Going?

• Geometric Optics
• Reflection
• Refraction
• The Thin Lens
• Multiple Surfaces
• (From Matrix Optics)
• Principal Planes
• Effective Thin Lens
• Stops
• Field
• Aperture
• Aberrations

Ending with a word about ray tracing and optical
design.
8
Microscope
F
F
F
F
A
A

• Two-Step Magnification
• Objective Makes a Real Image
• Eyepiece Used as a Simple Magnifier

9
Microscope Objective
F
F
F
F
A
A
10
Microscope Eyepiece
F
F
F
F
A2
A
A2
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Microscope Effective Lens
H
H
192 mm
Barrel Length 160 mm
A
f216mm
F
F
f116mm
Effective Lens f -1.6 mm
D
D
19.2 mm
19.2 mm
H
H
A
F
F
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Microscope Effective Lens
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Where Are We Going?

• Geometric Optics
• Reflection
• Refraction
• The Thin Lens
• Multiple Surfaces
• (From Matrix Optics)
• Principal Planes
• Effective Thin Lens
• Stops
• Field
• Aperture
• Aberrations

Ending with a word about ray tracing and optical
design.
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Stops, Pupils, and Windows (1)

• Intuitive Description
• Pupil Limits Amount of Light Collected
• Window Limits What Can Be Seen

Window
Pupil
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Stops, Pupils and Windows (2)
Physical Components
Images in Object Space
Images in Image Space
Aperture Stop Limits Cone of Rays from Object
which Can Pass Through the System
Entrance Pupil Limits Cone of Rays from Object
Exit Pupil Limits Cone of Rays from Image
Field Stop Limits Locations of Points in Object
which Can Pass Through System
Entrance Window Limits Cone of Rays From Entrance
Pupil
Exit Window Limits Cone of Rays From Exit Pupil
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Finding the Entrance Pupil

• Find all apertures in object space

• Entrance Pupil Subtends Smallest Angle from Object

L4 is L4 seen through L1-L3
L1
L2
L3
L4
L1
L2
L4
L3
L3 is L3 seen through L1-L2
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Finding the Entrance Window

• Entrance Window Subtends Smallest Angle from
  Entrance Pupil

• Aperture Stop is the physical object conjugate to
  the entrance pupil
• Field Stop is the physical object conjugate to
  the entrance window
• All other apertures are irrelevant

L1
L2
L4
L3
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Microscope Aperture Stop
Analysis in Image Space
F
F
Exit Pupil
Image
Aperture Stop Entrance Pupil
Put the Entrance Pupil of your eye at the Exit
Pupil of the System, Not at the Eyepiece,
because 1) It tickles (and more if its a rifle
scope) 2) The Pupil begins to act like a window
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Microscope Field Stop
F
F
Entrance Window
Field Stop Exit Window
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f-Number Numerical Aperture
Numerical Aperture
f-Number
f
q
F
A
A
F
D is Lens Diameter
5
4
3
f, f-number
2
1
0
0
0.2
0.4
0.6
0.8
1
NA, Numerical Aperture
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Importance of Aperture

• Fast System
• Low f-number, High NA (NA?1, f ?1)
• Good Light Collection (can use short exposure)
• Small Diffraction Limit (l/D)
• Propensity for Aberrations (sin q ? q)
• Corrections may require multiple elements
• Big Diameter ?
• Big Thickness ? Weight, Cost
• Tight Tolerance over Large Area

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Field of View
Film Exit Window
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Chief Ray
Aperture Stop
Exit Pupil
Field Stop

• Chief Ray passes through the center of every pupil

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Hints on Designing A Scanner

• Place the mirrors at pupils

Put Mirrors Here
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Aberrations

• Failure of Paraxial Optics Assumptions
• Ray Optics Based On sin(q)tan(q)q
• Spherical Waves ff02px2/rl
• Next Level of Complexity
• Ray Approach sin(q)qq3/3!
• Wave Approach ff02px2/rlcr4...
• A Further Level of Complexity
• Ray Tracing

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Examples of Aberrations (1)
Paraxial Imaging
1
0.5
R 2, n1.00, n1.50 s10, s10
0
In this example for a ray having height h at the
surface, s(h)lts(0).
-0.5
m4061_3
-1
-10
-5
0
5
10
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Example of Aberrations (2)
0.2
D z(h1.0)
Longitudinal Aberration D z Transverse
Aberration D x
D z(h0.6)
0.15
0.1
0.05
0
-0.05
Where Exactly is the image? What is its diameter?
-0.1
-0.15
2D x(h1.0)
m4061_3
-0.2
8.5
9
9.5
10
10.5
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Spherical Aberrations
Beam Size, m
-2
10
5
s1m, s4cm
-3
10
n2.4
n1.5
n1.5
-4
n4
10
0
q, Shape Factor
DL at 10 mm
n2.4
-5
10
DL at 1.06 mm
n4
500 nm
1
-6
10
-5
-1
-0.5
0
0.5
-5
0
5
p, Position Factor
q, Shape Factor
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Ray Tracing Fundamentals
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Ray Tracing (1)
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Ray Tracing (2)
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If One Element Doesnt Work...
Let George Do It
Add Another Lens
Aspherics
Different Index? Smaller angles with higher
index. Thus germanium is better than ZnSe in IR.
Not much hope in the visible.
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Summary of Concepts So Far

• Paraxial Optics with Thin Lenses
• Thick Lenses (Principal Planes)
• Apertures Pupils and Windows
• Aberration Correction
• Analytical
• Ray Tracing
• Whats Missing? Wave Optics