july 2003 chuck dimarzio, northeastern university 10351-4-1 eceg105 & eceu646 optics for...
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![Page 1: July 2003 Chuck DiMarzio, Northeastern University 10351-4-1 ECEG105 & ECEU646 Optics for Engineers Course Notes Part 4: Apertures, Aberrations Prof. Charles](https://reader035.vdocuments.mx/reader035/viewer/2022070415/5697c0291a28abf838cd7925/html5/thumbnails/1.jpg)
July 2003 Chuck DiMarzio, Northeastern University 10351-4-1
ECEG105 & ECEU646 Optics for Engineers
Course NotesPart 4: Apertures, Aberrations
Prof. Charles A. DiMarzio
Northeastern University
Fall 2003
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-2
Advanced Geometric Optics
• Introduction• Stops, Pupils, and
Windows• f-Number• Examples
– Magnifier
– Microscope
• Aberrations
• Design Process– From Concept through
Ray Tracing
– Finalizing the Design
– Fabrication and Alignment
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-3
Some Assumptions We Made
• All lenses are infinite in diameter– Every ray from every part of the object reaches
the image
• Angles are Small:– sin()=tan()=– cos()=1
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-4
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,z) – to object space (x’,y’,z’)
s, s’ are z coordinates
H H’V V’BB’
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-5
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
-60 -40 -20 0 20 40 60-50
-40
-30
-20
-10
0
10
20
30
40
50
s, Object Dist., cm.
s',
Imag
e D
ist.
, cm
.
f = 10 cm.
L1 L2 L3 L4L4’
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-6
Stops, Pupils, and Windows (1)
• Intuitive Description– Pupil Limits Amount of Light Collected
– Window Limits What Can Be Seen
PupilWindow
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-7
Stops, Pupils and Windows (2)
Aperture StopLimits Cone of Rays from Object which Can Pass Through the System
Field StopLimits Locations of Points in Object which Can Pass Through System
Physical Components
Images in Object Space
Entrance Pupil Limits Cone of Rays from Object
Entrance Window Limits Cone of Rays From Entrance Pupil
Images in Image Space
Exit Pupil Limits Cone of Rays from Image
Exit Window Limits Cone of Rays From Exit Pupil
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-8
Finding the Entrance Pupil
• Find all apertures in object space
L1 L2 L3 L4
L4’ is L4 seen through L1-L3
L3’ is L3 seen through L1-L2
• Entrance Pupil Subtends Smallest Angle from Object
L1 L2’L4’L3’
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-9
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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July 2003 Chuck DiMarzio, Northeastern University 10351-4-10
Field of View
Film=ExitWindow
f=28 mm
f=55 mm
f=200 mm
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-11
Example: The Telescope
ApertureStop
FieldStop
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-12
The Telescope in Object SpacePrimary
Secondary
Secondary’
EntrancePupilEntrance
Window
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-13
The Telescope in Image SpacePrimary
Secondary
Primary’’
ExitPupil
ExitWindow
Stopped 26 Sep 03
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-14
Chief Ray
ApertureStop
FieldStop
ExitPupil
• Chief Ray passes through the center of every pupil
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-15
Hints on Designing A Scanner• Place the mirrors at pupils
Put Mirrors Here
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-16
f-Number & Numerical Aperture
F’
FA
A’
f
D is Lens Diameter
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
NA, Numerical Aperture
f#, f
-num
ber
f-Number Numerical Aperture
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-17
Importance of Aperture
• ``Fast’’ System– Low f-number, High NA (NA1, f# 1)– Good Light Collection (can use short exposure)– Small Diffraction Limit (/D)– Propensity for Aberrations (sin
• Corrections may require multiple elements
– Big Diameter • Big Thickness Weight, Cost• Tight Tolerance over Large Area
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-18
The Simple Magnifier
FF’AA’
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-19
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# Means f=10 mm
• Maximum Mm=25
For the Interested Student: What if s>f ?
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-20
Microscope
• Two-Step Magnification– Objective Makes a Real Image
– Eyepiece Used as a Simple Magnifier
F’F
A’A
F’F
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-21
Microscope Objective
F’F
A’A
F’F
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-22
Microscope Eyepiece
F’F
A2A
F’F
A2’
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-23
Microscope Effective Lens
A
D’D
F F’
H H’
A
F
H
F’
H’
192 mm
19.2 mm 19.2 mm
f1=16mmf2=16mm
Barrel Length = 160 mm
Effective Lens:f = -1.6 mm
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-24
Microscope Aperture Stop
F’F
ApertureStop=EntrancePupil
ExitPupil
Put the Entrance Pupil of your eyeat the Exit Pupil of the System, Not at the Eyepiece, because1) It tickles (and more if it’s a rifle scope)2) The Pupil begins to act like a window
Image
Analysis in Image Space
Stopped here 30 Sep 03
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-25
Microscope Field Stop
F’F
Field Stop= Exit Window
EntranceWindow
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-26
Microscope Effective Lens
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-27
Aberrations
• Failure of Paraxial Optics Assumptions– Ray Optics Based On sin()=tan()=– Spherical Waves =0+2x2/
• Next Level of Complexity– Ray Approach: sin()=– Wave Approach: =0+2x2/c
• A Further Level of Complexity– Ray Tracing
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-28
Examples of Aberrations (1)
-10 -5 0 5 10-1
-0.5
0
0.5
1
R = 2,n=1.00, n’=1.50s=10, s’=10
Paraxial Imaging
In this example for a ray having height h at the surface, s’(h)<s’(0).
m4061_3
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-29
8.5 9 9.5 10 10.5-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Example of Aberrations (2)
m4061_3
z(h=0.6)
z(h=1.0)LongitudinalAberration = z
Transverse Aberration = x
x(h=1.0)
Where Exactly is the image?
What is its diameter?
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-30
Spherical Aberration Thin Lens in Air
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-31
Transverse Spherical Aberration
sxh
s(0)
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-32
Evaluating Transverse SA
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-33
Coddington Shape Factors
q=0-1 +1
p=0-1 +1
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-34
Numerical Examples
-5 0 510
-6
10-5
10-4
10-3
10-2
Beam Size, m
q, Shape Factor
s=1m, s’=4cm
DL at 10 m
n=2.4 n=1.5
n=4
DL at 1.06 m 500 nm
1-1 -0.5 0 0.5
-5
0
5
p, Position Factor
q, S
hap
e F
acto
r
n=4
n=2.4
n=1.5
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-35
Phase Description of Aberrations
EntrancePupil Exit
Pupil
Object
Imagez
yv
• Mapping from object space to image space• Phase changes introduced in pupil plane
– Different in different parts of plane
– Can change mapping or blur images
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-36
Coordinates for Phase Analysis
2a a
0<<1
z
yv
v
u
y
xh
phase
v
Solid Line is phase of a spherical wave toward the image point.Dotted line is actual phase.Our goal is to find(,h).
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-37
Aberration Terms
Odd Terms involve tilt,not considered here.
cos
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-38
Second Order
Image Position Terms:
The spherical wave is approximated by a second-order phase term, so this error is simply a change in focal length.
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-39
Fourth Order (1)
Spherical Aberration Astigmatism and Field Curvature
S SagittalPlane
TangentialPlane T
Sample Images
At T
At S
2 is focus: depends on h2 and h2cos
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-40
Fourth Order (2)
Object
BarrelDistortion
PincushionDistortion
y
x
Coma
u
v
2cos is Tilt: Dependson h3
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-41
Example: Mirrors
r1
r2
By Fermat’s Principle,r1+r2 = constant
Result is an Ellipse with these foci.One focus at infinity requires a parabolaFoci co-located requires a sphere.
z
v
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-42
Mirrors for Focussing
-0.1 -0.08 -0.06 -0.04 -0.02 0-0.1
-0.05
0
0.05
0.1
EllipseParabola
Sphere
s=30 cm,s’=6cm
Note:These Mirrors have a very large NA to illustrate the errors. In most mirrors, the errors could not be seen on this scale.
v, cm.
z, cm.
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-43
Numerical Example
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-44
Optical Design Process
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-45
Ray Tracing Fundamentals
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-46
Ray Tracing (1)
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-47
Ray Tracing (2)
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-48
If One Element Doesn’t Work...
Add Another Lens “Let George Do It”
AsphericsDifferent Index?Smaller angles withhigher index. Thus germanium is better than ZnSe in IR. Not much hope in the visible.
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July 2003 Chuck DiMarzio, Northeastern University 10351-4-49
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