Download The telescope

•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
ECE 5616 OE System Design
The telescope
Keplerian
Shown in the afocal geometry (d=f1+f2). Relaxed eye focuses at
~1m, thus telescope are usually not afocal. Analysis simpler,
however.
d
f1
f2
Afocal: system has no
power: ray || to OA
does not intersect OA
h1
-h’2
in image space
M
h2
f
 2
h1
f1
f1
f2


h
M 



1
Robert McLeod
Definition of angular magnification
h
h
f2
f1
M
f1

f2
Via similar triangles
This is both important and fundamental.
69
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
ECE 5616 OE System Design
The telescope
Galilean
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.
f1
h1
-f2
h2’
h2
f2
M

h1
f1
f1
-f2


M 
d


h
f1


h
f2
  f1 
1
Robert McLeod
More compact, upright
image. Same afocal
condition: d=f1+f2
f2
Note that formula is
identical to Keplerian.
This is the advantage
of the sign convention.
M
70
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
ECE 5616 OE System Design
Reflective telescopes
All replace the first lens of a Keplerian telescope with mirrors.
Newtonian
Replace first lens with
mirror, use
intermediate fold to
direct light out of
tube. Common
hobbyist design,
inexpensive.
Replace first lens with
combo of two positive
mirrors
Gregorian
Replace first lens with
combo of positive &
negative mirrors.
Shorter throw.
Cassegrain
Schmidt-Cassegrain
Robert McLeod
Add refractive plate at
entrance to correct
aberrations, support
secondary mirror
without struts.
71
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
ECE 5616 OE System Design
The compound microscope
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”
Finite conjugate
= DNP
Infinite conjugate
Robert McLeod
http://www.microscopyu.com/articles/optics/components.html
72
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
ECE 5616 OE System Design
Anatomy of a modern
microscope
Robert McLeod
http://www.microscopyu.com/articles/optics/components.html
73
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
ECE 5616 OE System Design
Eye pieces (1/2)
Used in microscopes and telescopes
Flat toward eye,
cheap but bad eye
relief.
Huygens
Common. Better eye
relieve that Huygens.
Ramsden
Achromatic version
of Ramsden. Wider
field.
Kellner
Robert McLeod
74
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
ECE 5616 OE System Design
Eye pieces (2/2)
Used in microscopes and telescopes
Better image quality,
±20° field.
Orthoscopic
Better image quality
over large field.
Distortion worse than
orthoscopic.
Plossl
Most common wide
field eye piece.
Erfle
Robert McLeod
75
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
ECE 5616 OE System Design
Microscope conjugate
planes and illumination
Robert McLeod
http://microscopy.berkeley.edu/courses/tlm/cmpd/cmpd.html
76
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
ECE 5616 OE System Design
Microscope analysis
Finite conjugate objective
fobj
feyepiece
Focal system. Form
image at infinity for
simplicity of analysis.
tube length
Standard tube length is 160 mm.
Visual magnification of instrument is product of linear
magnification of objective and visual magnification of eyepiece:
M v  microscope  M obj M v eyepiece
 ltube
 
 f
 obj
Note eq.s are approximate
 ltube >> fobj, Dnp >> feyepice

 Dnp

 f

 eyepiece 
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
Analysis the same for infinite conjugate objective, but replace
objective with two-lens system with magnification Mobj
Robert McLeod
77
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
ECE 5616 OE System Design
Overhead projector
Mirror flips parity so
speaker and viewers
see same image
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
Platen
Fresnel lens
Illumination system
gives uniform, directed,
white illumination
Condenser lens
Robert McLeod
78
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
ECE 5616 OE System Design
Camera
35mm Camera
• Single lens reflex
• Wide range of lenses
available cheaply
• 46.5mm from mount to
film plane
• Image size:
24 mm×36 mm.
Typical
camera
lens, Nikon
AF MicroNikkor 105
mm, f/2.8
Optical layout
1: Front-mount lens
2: Reflex mirror at 45°
3: Focal plane shutter
4: Film or sensor
5: Focusing screen
6: Condenser lens
7: Pentaprism
8: Eyepiece
Robert McLeod
http://en.wikipedia.org/wiki/Single-lens_reflex_camera
79
•Design of ideal imaging systems with geometrical optics
–Paraxial ray-tracing
ECE 5616 OE System Design
ABCD matrices
Matrix formulation of paraxial ray-tracing
 yk   1
u     
 k  k
0  yk 
 yk 
 Rk  



1 u k 
uk 
 y k 1  1 d k   yk 
 yk 
u   0 1  u    Tk u  
 k 
 k 1  
 k
yk 1  yk  u k d k
y0
k
u1
 u1
u0 y1
u k  u k  y k k
Transfer equation
M
1
Refraction equation
K
d K
-yK+1
d0
u K 1
N
 y1 
 y1 
 yK 
u    R K TK 1R K 1  T1R1 u   M u 
 1
 1
 K
 y1 
 y0 
 y K 1 
u   T1R1T0 u    N u  
 K 1 
 0
 0
Robert McLeod
System
matrix
Conjugate
matrix
80
•Design of ideal imaging systems with geometrical optics
–Paraxial ray-tracing
ECE 5616 OE System Design
Properties of M, N
A B
M 
 AD  BC  1
C D
Determinant = 1
R  T  M  N 1
Write out the matrix equation for N:
y K 1  N11 y0  N12u0
u K 1  N 21 y0  N 22 u0
If planes 0 and K+1 are conjugates, final ray height does not
depend on initial ray angle:
N12  0
Conjugate condition
If plane 0 is the object space focal plane, the slope at the exit
plane depends only on the object height:
N 22  0
Object at front focal plane
If plane K+1 is the image space focal plane, the image-space
ray height depends only on the entrance angle:
N11  0
Image at rear focal plane
If the system is afocal, the direction of the image-space ray
depends only on the direction of the object-space ray:
N 21  0
Robert McLeod
Afocal condition
81
•Design of ideal imaging systems with geometrical optics
–Paraxial ray-tracing
ECE 5616 OE System Design
Use of matrices M, N
Find image plane given object
M
1
y0
k
u1
 u1
u0 y1
K
d K
-yK+1
 d1
u K 1
N  TK 1MT0
1 d K   A B  1  d1 

 C D  0 1 
0
1




 A  d K C B  d K D  d1 ( A  d K C ) 



C
D
d
C
1


0 
 A  d K C
Conjugate condition


D  d1C 
 C
d K  
d1 A  B
d1C  D
N12  0 gives the image location
E.g. single lens
d K  
Robert McLeod
d11  0
1
1

 
d1     1
d K d1
82
•Design of ideal imaging systems with geometrical optics
–Paraxial ray-tracing
ECE 5616 OE System Design
Form of N
And EFL, first thick-lens concept
M 
y K 1
 N11  A  d K C
y0
1
N 22 
M
F
y0
1

  u K 1
If N12  0 then
N11 is the magnification
Determinant = 1
Effective focal length & system power
u0  0
u K 1
0
u K 1  N 21 y0  N 22 u0
N 21  
0 
M
N



1
M


Robert McLeod
E.g. single lens
N  T1R1T0
0
1   t  t t  t1  1t   


1  t
 

 tt 0 

t 



t

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