Optical systems: Cameras and the eye

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Optical systemsCameras and the eye

• Hecht 5.7
• Friday October 4, 2002

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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)
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Myopia Near Sightedness
Far point of the eye is much less than 8, e.g. lf
Must move object closer to eye to obtain a clear
image
Normal N.P.
Myopic F.P.
Myopic N.P.
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Myopia
e.g. lf 2m
How will the near point be affected?
0.5 66.7 67.2 D
is relaxed power of eye too large!
To move far point to 8, must decrease power to
66.7
Use negative lens with P -0.5 D
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Laser Eye surgery
Radial Keratotomy Introduce radial cuts to the
cornea of the elongated, myopic eyeball
Usually use the 10.6 µm line of a CO2 laser for
almost 100 absorption by the corneal tissue
Blurred vision
Front view
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Laser Eye surgery
Radial Keratotomy Introduce radial cuts to the
cornea of the elongated, myopic eyeball
Usually use the 10.6 µm line of a CO2 laser for
almost 100 absorption by the corneal tissue
Distinct vision
Front view
Flattening
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Hyperopia Far Sightedness
Eyeball too small or lens of eye cant fully
accommodate
Image of close objects formed behind retina
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Hyperopia Far Sightedness
Suppose near point 1m
Recall that for a near point of 25 cm, we need
70.7D
Use a positive lens with 3 D power to correct
this persons vision (e.g. to enable them to read)
Usually means they can no longer see distant
objects - Need bifocals
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Correction lenses for myopia and hyperopia
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