Image1 - Image Formation in Man and Machines Image...

Image formation - 1
Image Formation in Man and
Machines

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Overview
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Pinhole camera
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Refraction of light
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Thin-lens equation
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Optical power and accommodation
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Image irradiance and scene radiance
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Human eye
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Geometry of perspective imaging

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Lens-less Imaging Systems - Pinhole
Optics
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Pinhole optics
projects images
– without lens
– with infinite depth of
field
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Smaller the
pinhole
– better the focus
– less the light energy
from any single point
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Good for tracking
solar eclipses
Pinhole
Image
Scene
Blurred
Image

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Diffraction
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Two disadvantages to pinhole systems
– Low light collecting power
– diffraction
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Diffraction
– Light bends as it passes by the edge of a narrow aperture
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Human vision
– at high light levels, pupil (aperture) is small and blurring is
due to diffraction
– at low light levels, pupil is open and blurring is due to lens
imperfections
D
λ
θ =
D

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Diffraction and pinhole optics

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Lenses Collect More Light
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With a lens, diverging rays from a scene
point are converged back to an image point
Center of projection
Image plane
Scene
Lens

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incident ray
reflected ray
refracted ray
refracted ray
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If θ is the angle of incidence
and θ ’ is the angle of refraction
then
where n and n ’ are the
refractive indices of the two
media
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Refractive index is the ratio of
speed of light in a vacuum to
speed of light in the medium
Refraction: Snell’s law
Refractive indices
glass - 1.50
water - 1.333
air - 1.000
θ
' sin ' sin θ θ n n =

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Lens Equations

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Thin-Lens Equation
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Thin-lens equation
– relates the distance between the scene point being viewed and the lens
to the distance between the lens and the point’s image (where the rays
from that point are brought into focus by the lens)
– Let M be a point being viewed
u
p is the distance of M from the lens along the optical axis
u
The thin lens focuses all the rays from M onto the same point, the
image point m at distance q from the lens.
M
O
F
m
f q-f
p q
H
h
Q
S
s

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Thin-Lens Equation
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m can be determined by
intersecting two known
rays
– MQ is parallel to the optical
axis, so it must be refracted to
pass through F.
– MO passes through the lens
center, so it is not bent.
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Note two pairs of
similar triangles
– MSO and Osm (yellow)
– OQF and Fsm (green)
f q p
1 1 1
= +
q p
h H
q
h
p
H
+
+
= =
q
h H
f q
h
f
H +
=
−
=
q
q p
f
p +
=
M
O
F
m
f
q -f
p q
H
h
Q
S
s
q p
q p
f
+
=
1
Divide 2 equations:

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Thin-Lens Equation
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Notice that the distance behind the lens, q , at
which a point, M , is brought into focus
depends on p , the distance of that point from
the lens
– familiar to us from rotating the focus ring of any camera
f q p
1 1 1
= +
M
O
F
m
f
q-f
p q
H
h
Q
S
s

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Thin-Lens Equation
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As p gets large, q approaches f
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As q approaches f , p approaches infinity
f q p
1 1 1
= +
M
O
F
m
f
p q
Q
S
M’
S’
m’

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Optical Power and Accommodation
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