Optical systems

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Optical systems

• Hecht 5.7
• Wednesday October 2, 2002

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Field Stop
The aperture that controls the field of view by
limiting the solid angle formed by chief rays
As seen from the centre of the entrance pupil
(EnP), the field stop (or its image) subtends the
smallest angle.
In previous example, the lens is the field stop
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Entrance Window (EnW)
The image of the field stop in all elements
preceding it
Defines the lateral dimension of the object that
will be viewed
Example Camera
Where is the entrance window?
AS
FS
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Exit Window (ExW)
The image of the field stop in all elements
following it
Defines the lateral dimension of the image that
will be viewed
Example Camera
Where is the exit window?
AS
FS
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Entrance window and Angular field of view
Angular field of view in object plane angle
subtended by entrance window (EnW) at centre of
entrance pupil (EnP)
Exit window and Angular field of view
Angular field of view in image plane angle
subtended by exit window (ExW) at centre of exit
pupil (ExP)
Field Stop
That component whose entrance window (EnW)
subtends the smallest angle at the centre of the
entrance pupil (EnP)
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Field of a positive thin lens
FSEnW
P
Eye pupil
Image field
Q
Object field
a
a
F
Q
P
Object point must be within cone (to left of
lens) to be seen a field of view in object
space a field of view in image space
ASExP
Entrance pupil (small)
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Field of a positive thin lens
FSEnW
P
Q
F
Q
P
Full cone of rays received from all points on
object
ASExP
Entrance pupil (small)
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Stops, pupils and windows in an optical system
a
a
AS
FS
ExP
ExW
EnW
EnP
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Optical devices Camera
Multi-element lens
Film edges constitute field stop
ASIris Diaphragm
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Camera
Most common camera is the so-called 35 mm camera
( refers to the film size)
27 mm
34 mm
Multi element lens usually has a focal length of
f 50 mm
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Camera
Object s 1 m Image s 5.25 cm Object s 8
Image s 5.0 cm Thus to focus object
between s 1 m and infinity, we only have to
move the lens about 0.25 cm 2.5mm For most
cameras, this is about the limit and it is
difficult to focus on objects with s lt 1 m
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Camera
ASEnPExP Why?
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Camera Light Gathering Power
D diameter of entrance pupil L object
distance (Lgtgt d)
D
l
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Camera Brightness of image
Brightness of image is determined by the amount
of light falling on the film. Each point on the
film subtends a solid angle
D
D
Irradiance at any point on film is proportional
to (D/f)2
s f
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f-number of a lens
Define f-number,
This is a measure of the speed of the lens Small
f (big aperture) I large , t short Large f
(small aperture) I small, t long
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Standard settings on camera lenses
f f/D (f)2
1.2 1.5
1.8 3.2
2.8 7.8
4.0 16
5.6 31.5
8 64
11 121
16 256
22 484
Good lenses, f 1.2 or 1.8 (very fast)
Difficult to get f/1
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Total exposure on Film
Exposure time is varied by the shutter which has
settings, 1/1000, 1/500, 1/250, 1/100, 1/50 Again
in steps of factor of 2
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Photo imaging with a camera lens
In ordinary 35 mm camera, the image is very
small (i.e. reduced many times compared with the
object
An airplane 1000 m in the air will be imaged with
a magnification,
Thus a 30 m airplane will be a 2 mm speck on film
(same as a 2 m woman, 50 m)
Also, the lens is limited in the distance it can
move relative to the film
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Telephoto lens
L1
L2
50 mm
d
A larger image can be achieved with a telephoto
lens
Choose back focal length (bfl 50 mm) Then
lenses can be interchanged (easier to design)
The idea is to increase the effective focal
length (and hence image distance) of the camera
lens.
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Telephoto Lens, Example
Suppose d 9.0 cm, f2-1.25 cm f1 10 cm
Then for this telephoto lens
Choose f h bfl
Now the principal planes are located at
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Telephoto Lens, Example
H
h - 45 cm
9 cm
5 cm
f sTP 50 cm
Airplane now 1 cm long instead of 1 mm !!!!
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Depth of Field
s2
s2
s1
s1
d
x
x
so
so
If d is small enough (e.g. less than grain size
of film emulsion 1 µm) then the image of these
points will be acceptable
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Depth of Field (DOF)
d
a
a
D
x
x
so
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Depth of field
E.g. d 1 µm, f A 4, f 5 cm, so 6 m
DOF 0.114 m
i.e. so 6 0. 06 m
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Depth of field
Strongly dependent on the f of the lens
Suppose, so 4m, f 5 cm, d 40 µm
DOF s2 s1
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(No Transcript)
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Human Eye, Relaxed
20 mm
15 mm
n 1.33
F
H
H
F
3.6 mm
P 66.7 D
7.2 mm
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Accommodation

• Refers to changes undergone by lens to enable
  imaging of closer objects
• Power of lens must increase
• There is a limit to such accommodation however
  and objects inside ones near point cannot be
  imaged clearly
• Near point of normal eye 25 cm
• Fully accommodated eye P 70.7 for s 25 cm, s
  2 cm

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Myopia Near Sightedness
Eyeball too large ( or power of lens too large)