Transcript 10 - Northeastern University

ECE-1466
Modern Optics
Course Notes
Part 2
Prof. Charles A. DiMarzio
Northeastern University
Spring 2002
March 02002
Chuck DiMarzio, Northeastern University
10100-2-1
Lens Equation as Mapping
f = 10 cm.
50
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30
20
s', Image Dist., cm.
• 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
40
10
0
-10
-20
-30
-40
-50
-60
-40
L4’
Chuck DiMarzio, Northeastern University
-20
0
20
s, Object Dist., cm.
L1 L2 L3
40
60
L4
10100-2-2
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’)
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B
Chuck DiMarzio, Northeastern University
H
V V’
H’
B’
10100-2-3
An Example; 10X Objective
F
F’
F’
F
A’
A
• s= 16 mm
• s’=160 mm (A common standard)
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Chuck DiMarzio, Northeastern University
10100-2-4
The Simple Magnifier
F
A’
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A
F’
Chuck DiMarzio, Northeastern University
10100-2-5
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 D=10 mm
• f# 1 Means f=10 mm
• Maximum Mm=25
For the Interested Student: What if s>f ?
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Chuck DiMarzio, Northeastern University
10100-2-6
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
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Ending with a word about
ray tracing and optical
design.
Chuck DiMarzio, Northeastern University
10100-2-7
Microscope
F’
F
F’
F
A’
A
• Two-Step Magnification
– Objective Makes a Real Image
– Eyepiece Used as a Simple Magnifier
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Chuck DiMarzio, Northeastern University
10100-2-8
Microscope Objective
F
F’
F’
F
A’
A
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Chuck DiMarzio, Northeastern University
10100-2-9
Microscope Eyepiece
F
F’
A2
A
A2’
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F’
F
Chuck DiMarzio, Northeastern University
10100-2-10
Microscope Effective Lens
H
H’
192 mm
Barrel Length = 160 mm
FA
f2=16mm
f1=16mm
D
19.2 mm
Effective Lens:
f = -1.6 mm
H’
H
A
F’
D’
19.2 mm
F’
F
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Chuck DiMarzio, Northeastern University
10100-2-11
Microscope Effective Lens
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Chuck DiMarzio, Northeastern University
10100-2-12
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
March 02002
Ending with a word about
ray tracing and optical
design.
Chuck DiMarzio, Northeastern University
10100-2-13
Stops, Pupils, and Windows (1)
• Intuitive Description
– Pupil Limits Amount of Light Collected
– Window Limits What Can Be Seen
Window
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Chuck DiMarzio, Northeastern University
Pupil
10100-2-14
Stops, Pupils and Windows (2)
Images in
Object Space
Entrance Pupil
Limits Cone of
Rays from Object
Entrance Window
Limits Cone of
Rays From Entrance
Pupil
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Physical
Components
Aperture Stop
Limits Cone of
Rays from Object
which Can Pass
Through the System
Field Stop
Limits Locations of
Points in Object
which Can Pass
Through System
Chuck DiMarzio, Northeastern University
Images in
Image Space
Exit Pupil Limits
Cone of Rays from
Image
Exit Window Limits
Cone of Rays From
Exit Pupil
10100-2-15
Finding the Entrance Pupil
• Find all apertures in
object space
L4’ is L4 seen through L1-L3
L1 L2 L3 L4
• Entrance Pupil
Subtends Smallest
Angle from Object
L3’ L4’
L1 L2’
L3’ is L3 seen through L1-L2
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Chuck DiMarzio, Northeastern University
10100-2-16
Finding the Entrance Window
• Entrance Window
Subtends Smallest
Angle from Entrance
Pupil
L3’ L4’
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L1 L2’
• 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
Chuck DiMarzio, Northeastern University
10100-2-17
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 it’s a rifle scope)
2) The Pupil begins to act like a window
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Chuck DiMarzio, Northeastern University
10100-2-18
Microscope Field Stop
F
F’
Entrance
Window
Field Stop
= Exit Window
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Chuck DiMarzio, Northeastern University
10100-2-19
f-Number & Numerical Aperture
Numerical Aperture
f-Number
f
q
A
F’ A’
F
D is Lens Diameter
5
f#, f-number
4
3
2
1
0
0
0.2
0.4
0.6
NA, Numerical Aperture
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0.8
1
Chuck DiMarzio, Northeastern University
10100-2-20
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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Chuck DiMarzio, Northeastern University
10100-2-21
Field of View
Film=
Exit
Window
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Chuck DiMarzio, Northeastern University
10100-2-22
Chief Ray
Aperture
Stop
Exit
Pupil
Field
Stop
• Chief Ray passes through the center of every pupil
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Chuck DiMarzio, Northeastern University
10100-2-23
Hints on Designing A Scanner
• Place the mirrors at pupils
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Chuck DiMarzio, Northeastern University
Put Mirrors Here
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Aberrations
• Failure of Paraxial Optics Assumptions
– Ray Optics Based On sin(q)=tan(q)=q
– Spherical Waves f=f0+2px2/rl
• Next Level of Complexity
– Ray Approach: sin(q)=q+q3/3!
– Wave Approach: f=f0+2px2/rl+cr4+...
• A Further Level of Complexity
– Ray Tracing
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Chuck DiMarzio, Northeastern University
10100-2-25
Examples of Aberrations (1)
1
Paraxial Imaging
0.5
0
-0.5
-1
-10
m4061_3
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-5
0
5
10
Chuck DiMarzio, Northeastern University
R = 2,
n=1.00, n’=1.50
s=10, s’=10
In this example for a
ray having height h
at the surface,
s’(h)<s’(0).
10100-2-26
Example of Aberrations (2)
0.2
D z(h=1.0)
Longitudinal
Aberration = D z
D z(h=0.6)
0.15
0.1
0.05
Transverse
Aberration =D x
0
-0.05
Where Exactly is
the image?
-0.1
-0.15
2D x(h=1.0)
m4061_3
-0.2
8.5
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9
9.5
10
10.5
Chuck DiMarzio, Northeastern University
What is its
diameter?
10100-2-27
Spherical Aberrations
Beam
Size, m
-2
5
q, Shape Factor
q
R2 + R1
R2  R1
s=1m, s’=4cm
10
n=1.5
0
-5
-1
10
s ' s
p
s '+ s
-0.5
0
p, Position Factor
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n=2.4
n=4
0.5
10
10
-3
n=2.4
-4
-5
1 -6
10
-5
n=1.5
n=4
DL at 10 mm
DL at 1.06 mm
500 nm
Chuck DiMarzio, Northeastern University
0
5
q, Shape Factor
10100-2-28
Ray Tracing Fundamentals
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Chuck DiMarzio, Northeastern University
10100-2-29
Ray Tracing (1)
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Chuck DiMarzio, Northeastern University
10100-2-30
Ray Tracing (2)
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Chuck DiMarzio, Northeastern University
10100-2-31
If One Element Doesn’t Work...
“Let George Do It”
Add Another Lens
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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Aspherics
Chuck DiMarzio, Northeastern University
10100-2-32
Summary of Concepts So Far
•
•
•
•
Paraxial Optics with Thin Lenses
Thick Lenses (Principal Planes)
Apertures: Pupils and Windows
Aberration Correction
– Analytical
– Ray Tracing
• What’s Missing? Wave Optics
March 02002
Chuck DiMarzio, Northeastern University
10100-2-33