ParaxialRayTracingAndSimpleInstruments.pdf
Transcript of ParaxialRayTracingAndSimpleInstruments.pdf
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The telescopeKeplerian
Shown in the afocal geometry (d=f 1+f 2). Relaxed eye focuses at~1m, thus telescope are usually not afocal. Analysis simpler,however.
Afocal : system has no
power: ray || to OAdoes not intersect OA
in image space
f 1 f 2
f
f
M
f h
f h
1
2
1
1
2
Definition of angular magnification
Via similar triangles
f 1 f 2
h1 -h’2
1
2
1
2
f
f
h
h M
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
d
This is both important and fundamental.
h
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The telescopeGalilean
f 1 -f 2
h1 h2’
f 1 -f 2
d
f
f
M
f h
f h
1
2
1
1
2
More compact, upright
image. Same afocalcondition: d=f 1+f 2
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
Note that formula isidentical to Keplerian.This is the advantage
of the sign convention.
1
2
1
2
f
f
h
h M
Really, this is just the Keplerian with the second focal lengthnegative. Lenses are still separated by the sum of the focal lengths, but one is now negative.
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Reflective telescopes
71
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
Gregorian
Cassegrain
Newtonian
Replace first lens withcombo of two positivemirrors
Replace first lens withcombo of positive &negative mirrors.Shorter throw.
Replace first lens withmirror, useintermediate fold todirect light out oftube. Common
hobbyist design,inexpensive.
All replace the first lens of a Keplerian telescope with mirrors.
Schmidt-Cassegrain
Add refractive plate atentrance to correctaberrations, supportsecondary mirrorwithout struts.
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The compound microscope
72
1. “Compound” = two cascaded single-lens imaging systems.• Objective produces magnified real “intermediate” image• Eyepiece produces magnified virtual image
2. Two types of objectives• Older “finite conjugate”, z´ = 160 mm “tube length”• Modern “infinite conjugate” objective + ~160 mm “tube lens”
http://www.microscopyu.com/articles/optics/components.html
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
Finite conjugate
Infinite conjugate
= D NP
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Anatomy of a modern
microscope
73
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
http://www.microscopyu.com/articles/optics/components.html
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Eye pieces (1/2)Used in microscopes and telescopes
74
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
Huygens
Ramsden
Kellner
Flat toward eye,cheap but bad eyerelief.
Common. Better eye
relieve that Huygens.
Achromatic version
of Ramsden. Widerfield.
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Eye pieces (2/2)Used in microscopes and telescopes
75
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
Orthoscopic
Plossl
Erfle
Better image quality,±20° field.
Better image quality
over large field.Distortion worse thanorthoscopic.
Most common wide
field eye piece.
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Microscope conjugate
planes and illumination
76http://microscopy.berkeley.edu/courses/tlm/cmpd/cmpd.html
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
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Microscope analysisFinite conjugate objective
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
Focal system. Formimage at infinity for
simplicity of analysis.
f obj f eyepiece
tube length
Visual magnification of instrument is product of linearmagnification of objective and visual magnification of eyepiece:
Standard tube length is 160 mm.
eyepiece
np
obj
tube
eyepiecevobjmicroscopev
f
D
f l
M M M
Mobj f obj [mm] Typical NA
4 30 0.10
10 16 0.25
20 8 0.4060 3 0.85
100 1.8 1.3
Note eq.s are approximate
ltube >> f obj, Dnp >> f eyepice
Analysis the same for infinite conjugate objective, but replaceobjective with two-lens system with magnification Mobj
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Overhead projector
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
Illumination systemgives uniform, directed,white illumination
Condenser lens
Fresnel lens
Platen
Projection lens must be flat field, work
over a range of imagedistances, andachromatic. Designcan be simplified byillumination system.
Screen is white,
diffuse reflector tosend light into large
angle
Mirror flips parity sospeaker and viewers
see same image
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Camera
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•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
35mm Camera• Single lens reflex• Wide range of lenses
available cheaply• 46.5mm from mount to
film plane• Image size:24 mm×36 mm.
http://en.wikipedia.org/wiki/Single-lens_reflex_camera
Optical layout1: Front-mount lens2: Reflex mirror at 45°3: Focal plane shutter4: Film or sensor5: Focusing screen6: Condenser lens7: Pentaprism8: Eyepiece
Typicalcameralens, NikonAF Micro- Nikkor 105mm, f/2.8
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ABCD matricesMatrix formulation of paraxial ray-tracing
•Design of ideal imaging systems with geometrical optics
–Paraxial ray-tracing
k
k
k
k
k k
k
k
u
y
u
yd
u
yT
10
1
1
1
k
k
k
k
k
k k
k
u
y
u
y
u
yR
1
01
Transfer equation
Refraction equation
1
1
1
1
1111 u
y
u
y
u
y
K K K K
K M R T R T R System
matrix
0
0
0
1
011
1
1
u
y
u
y
u
y
K
K N T R T Conjugate
matrix
1 k
K y0 0
u y11u
-yK+1
1u
1K u
M
N
K d
0d
k k k k d u y y 1
k k k k yuu
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Properties of M, N
1 N M T R
1 BC AD DC
B AM Determinant = 1
If planes 0 and K+1 are conjugates, final ray height does notdepend on initial ray angle:
0120111 u y yK N N
012 N Conjugate condition
If plane 0 is the object space focal plane, the slope at the exit plane depends only on the object height:
0220211 u yuK N N
022 N Object at front focal plane
If the system is afocal, the direction of the image-space raydepends only on the direction of the object-space ray:
021 N Afocal condition
Write out the matrix equation for N:
If plane K+1 is the image space focal plane, the image-spaceray height depends only on the entrance angle:
011 N Image at rear focal plane
•Design of ideal imaging systems with geometrical optics
–Paraxial ray-tracing
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Use of matrices M, N Find image plane given object
C d DC
C d A
C d DC
C d Ad Dd BC d A
d
DC
B Ad
K
K K K
K
K
1
1
1
1
01
0
)(10
1
10
1
MT T N
gives the image location012 N DC d
B Ad d K
1
1
Conjugate condition
•Design of ideal imaging systems with geometrical optics
–Paraxial ray-tracing
1 k
K
y00u y
1
1u-y
K+1
1u
1K u
M
K d
1d
11
1 11
1
01
d d d
d d
K
K
E.g. single lens
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Form of N And EFL, first thick-lens concept
C d A y
y M K
K 110
1N If then
is the magnification012 N
11N
M 122 N Determinant = 1
1K u00 u
0220211 u yuK N N
1
01
K u
yF Effective focal length & system power
0
21N
M
M
1
0N
•Design of ideal imaging systems with geometrical optics
–Paraxial ray-tracing
t t
t t
t t
t
t t t
0
1
1 11011 T R T N 0
E.g. single lens