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ECE 5616 OE System Design
Robert McLeod 69
The telescopeKeplerian
Shown in the afocal geometry (d=f1+f2). Relaxed eye focuses at ~1m, thus telescope are usually not afocal. Analysis simpler, however.
Afocal: system has no power: ray || to OA
does not intersect OA in image space
f1 f2
M
f
f
M
fh
fh
12
1
1
2
Definition of angular magnification
Via similar triangles
f1 f2
h1 -h’2
1
2
1
2
f
f
h
hM
•Design of ideal imaging systems with geometrical optics–Single and compound lens systems
d
This is both important and fundamental.
h
ECE 5616 OE System Design
Robert McLeod 70
The telescopeGalilean
f1 -f2
h1 h2’
f1 -f2
d
M
f
f
M
fh
fh
12
1
1
2
More compact, upright image. Same afocal
condition: d=f1+f2
•Design of ideal imaging systems with geometrical optics–Single and compound lens systems
Note that formula is identical to Keplerian. This is the advantage
of the sign convention.
1
2
1
2
f
f
h
hM
Really, this is just the Keplerian with the second focal length negative. Lenses are still separated by the sum of the focal lengths, but one is now negative.
ECE 5616 OE System Design
Robert McLeod
Reflective telescopes
71
•Design of ideal imaging systems with geometrical optics–Single and compound lens systems
Gregorian
Cassegrain
Newtonian
Replace first lens with combo of two positive mirrors
Replace first lens with combo of positive & negative mirrors. Shorter throw.
Replace first lens with mirror, use intermediate fold to direct light out of tube. Common hobbyist design, inexpensive.
All replace the first lens of a Keplerian telescope with mirrors.
Schmidt-Cassegrain
Add refractive plate at entrance to correct aberrations, support secondary mirror without struts.
ECE 5616 OE System Design
Robert McLeod
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
= DNP
ECE 5616 OE System Design
Robert McLeod
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
ECE 5616 OE System Design
Robert McLeod
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 eye relief.
Common. Better eye relieve that Huygens.
Achromatic version of Ramsden. Wider field.
ECE 5616 OE System Design
Robert McLeod
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 than orthoscopic.
Most common wide field eye piece.
ECE 5616 OE System Design
Robert McLeod
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
ECE 5616 OE System Design
Robert McLeod 77
Microscope analysisFinite conjugate objective
•Design of ideal imaging systems with geometrical optics–Single and compound lens systems
Focal system. Form image at infinity for
simplicity of analysis.
fobj feyepiece
tube length
Visual magnification of instrument is product of linear magnification of objective and visual magnification of eyepiece:
Standard tube length is 160 mm.
eyepiece
np
obj
tube
eyepiecevobjmicroscopev
f
D
f
l
MMM
Mobj fobj [mm] Typical NA
4 30 0.10
10 16 0.25
20 8 0.40
60 3 0.85
100 1.8 1.3
Note eq.s are approximateltube >> fobj, Dnp >> feyepice
Analysis the same for infinite conjugate objective, but replace objective with two-lens system with magnification Mobj
ECE 5616 OE System Design
Robert McLeod 78
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 image distances, and
achromatic. Design can be simplified by illumination system.
Screen is white, diffuse reflector to
send light into large angle
Mirror flips parity so speaker and viewers
see same image
ECE 5616 OE System Design
Robert McLeod
Camera
79
•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 lens 2: Reflex mirror at 45°3: Focal plane shutter 4: Film or sensor 5: Focusing screen6: Condenser lens 7: Pentaprism8: Eyepiece
Typical camera lens, Nikon AF Micro-Nikkor 105 mm, f/2.8
ECE 5616 OE System Design
Robert McLeod 80
ABCD matrices Matrix formulation of paraxial ray-tracing
•Design of ideal imaging systems with geometrical optics–Paraxial ray-tracing
k
kk
k
kk
k
k
u
y
u
yd
u
yT
10
1
1
1
k
kk
k
k
kk
k
u
y
u
y
u
yR
1
01
Transfer equation
Refraction equation
1
1
1
11111 u
y
u
y
u
yKKK
K
K MRTRTR System matrix
0
0
0
1011
1
1
u
y
u
y
u
y
K
K NTRT Conjugate matrix
1 k
K
y0 0u y11u
-yK+1
1u
1Ku
M
N
Kd
0d
kkkk duyy 1
kkkk yuu
ECE 5616 OE System Design
Robert McLeod 81
Properties of M, N
1 NMTR
1 BCADDC
BAM Determinant = 1
If planes 0 and K+1 are conjugates, final ray height does not depend on initial ray angle:
0120111 uyyK NN
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 uyuK NN
022 N Object at front focal plane
If the system is afocal, the direction of the image-space ray depends 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-space ray 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
ECE 5616 OE System Design
Robert McLeod 82
Use of matrices M, NFind image plane given object
CdDC
CdA
CdDC
CdAdDdBCdA
d
DC
BAd
K
KKK
K
K
1
1
1
1
01
0
)(
10
1
10
1
MTTN
gives the image location 012 NDCd
BAddK
1
1
Conjugate condition
•Design of ideal imaging systems with geometrical optics–Paraxial ray-tracing
1 k
K
y0 0u y11u
-yK+1
1u
1Ku
M
Kd
1d
11
1 11
1
01
ddd
dd
KK
E.g. single lens
ECE 5616 OE System Design
Robert McLeod 83
Form of NAnd EFL, first thick-lens concept
CdAy
yM K
K 11
0
1 N If thenis the magnification
012 N11N
M
122 N Determinant = 1
1Ku00 u
0220211 uyuK NN
1
01
Ku
yF Effective focal length & system power
0
21N
M
M
1
0N
•Design of ideal imaging systems with geometrical optics–Paraxial ray-tracing
tt
tt
tt
t
ttt
0
1
1 11
011 TRTN 0
E.g. single lens