ECE 5616 OE System Design
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
Keplerian
Shown in the afocal geometry (d=f
1
+f
2
). Relaxed eye focuses at
~1m, thus telescope are usually not afocal. Analysis simpler, however.
d f
1 f
2 Afocal : system has no power: ray || to OA h
1
-h’
2 does not intersect OA in image space
M
 h
2
 h
1
  f
2 f
1 f
1 f
2
  h
M




Definition of angular magnification
  h f
2 h f
1
 1
M
  f
1 f
2
Via similar triangles
This is both important and fundamental.
Robert McLeod 69

ECE 5616 OE System Design
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems h
1
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.
f
1
-f
2 h
2
’
More compact, upright image. Same afocal condition: d=f
1
+f
2
M
 h
2
 h
1
  f
2 f
1 f
1
-f
2
 d
M




 h f
2 h 
 f
1

 
 1
M f
1 f
2
Robert McLeod

Note that formula is identical to Keplerian.
This is the advantage of the sign convention.
70

ECE 5616 OE System Design
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
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
Cassegrain
Replace first lens with combo of positive & negative mirrors.
Shorter throw.
Add refractive plate at entrance to correct aberrations, support secondary mirror without struts.
Schmidt-Cassegrain
Robert McLeod 71

ECE 5616 OE System Design
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
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
= D
NP
Infinite conjugate
Robert McLeod http://www.microscopyu.com/articles/optics/components.html
72

ECE 5616 OE System Design
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
Robert McLeod http://www.microscopyu.com/articles/optics/components.html
73

ECE 5616 OE System Design
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
Flat toward eye, cheap but bad eye relief.
Huygens
Common. Better eye relieve that Huygens.
Ramsden
Achromatic version of Ramsden. Wider field.
Kellner
74 Robert McLeod

ECE 5616 OE System Design
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
Better image quality,
±20° field.
Orthoscopic
Better image quality over large field.
Distortion worse than orthoscopic.
Plossl
Most common wide field eye piece.
Erfle
75 Robert McLeod

ECE 5616 OE System Design
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
Robert McLeod http://microscopy.berkeley.edu/courses/tlm/cmpd/cmpd.html
76

ECE 5616 OE System Design
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
f obj f eyepiece
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
  l tube f obj


D np f eyepiece
Note eq.s are approximate l tube
>> f obj
, D np
>> f eyepice
M obj
4
10
20
60
100 f obj
[mm]
30
16
8
3
1.8
Typical NA
0.10
0.25
0.40
0.85
1.3
Analysis the same for infinite conjugate objective, but replace objective with two-lens system with magnification M obj
Robert McLeod 77

ECE 5616 OE System Design
•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
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
Robert McLeod
Fresnel lens
Condenser lens
Platen
Illumination system gives uniform, directed, white illumination
78

•Design of ideal imaging systems with geometrical optics
–Single and compound lens systems
ECE 5616 OE System Design
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 Micro-
Nikkor 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

ECE 5616 OE System Design
•Design of ideal imaging systems with geometrical optics
–Paraxial ray-tracing
Matrix formulation of paraxial ray-tracing

 y u k
 k






1
 k
0
1



 y u k k


 R k

 y u k k



 y u k k

1

1





1
0 d
1 k
 


 y u k k



 T k

 y u k k



M
 k y
0

1 u

0 u
1 y
1
 u

1

K
Refraction equation u k
  u k
 y k
 k d

K y k
Transfer equation

1
 y k
 u
 k d
 k
-y
K+1 d
0 u
K

1
N

 y u
K

K


 R
K
T
K

1
R
K

1
 T
1
R
1

 y u
1
1


 M

 y u
1
1



 y u
K
K

1



1
 T
1
R
1
T
0

 u y
1
0



 N

 y u
0

0


Robert McLeod
System matrix
Conjugate matrix
80

ECE 5616 OE System Design
•Design of ideal imaging systems with geometrical optics
–Paraxial ray-tracing
M, N
M
R

 T
A
C
B
D
 M

AD

BC

1
 N 
1
Determinant = 1
Write out the matrix equation for N: y u
K
K

1

1


N
N
11
21 y y
0
0


N
N
12
22 u
0 u

0

If planes 0 and K+1 are conjugates, final ray height does not depend on initial ray angle:
N
12

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:
N
11

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 Afocal condition
Robert McLeod 81

ECE 5616 OE System Design
•Design of ideal imaging systems with geometrical optics
–Paraxial ray-tracing
M, N
Find image plane given object
M
 k y
0

1 u

0 u
1 y
1
 u

1
 d
1

K d

K
-y
K+1 u
K

1
N 

T
K

1
MT
0


1
0 d
1
K
 



A
C




A

C


A

C d
K

C d
K

C
B
D




1
0

1 d
1


B
 d

K
D
D

 d
1
( d
1
A
C
 d

K
C )


D

0 d
1
C

 Conjugate condition d

K
  d
1
A d
1
C


B
D
N
12

0 gives the image location d
K
  
E.g. single lens d
1 d
1
1
 

 
0

1

1 d

K

1 d
1
 
Robert McLeod 82

ECE 5616 OE System Design
•Design of ideal imaging systems with geometrical optics
–Paraxial ray-tracing
N
And EFL, first thick-lens concept
M
 y y
K
0

1
 N
11

A
 d

K
C N
12

0
N
11 is the magnification
N
22

1
M
F

1

 y
0
 u
K

1 u

0

0
Determinant = 1
Effective focal length & system power u
K

1 u
K

1
 N
21 y
0
 N
22 u

0
0
N
21
  
N 



M

1
0
M


Robert McLeod



1



 t

E.g. single lens
N  t t
T

1
R


1
1 t
1

T

0


1 t t
 

0






 t t

 t t

0



83