Classical Photography and Geometric Optics

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Classical Photographyand Geometric Optics

• Imaging Science Fundamentals

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Typical Imaging Chain for Photography
source (sun)
camera
object
image
collection (lens) exposure (aperture
shutter) detection (photographic film)
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Light
Ultraviolet Rays
Infrared (IR)
Gamma Rays
Radio wave
Microwave
X Rays
Light
750 nm
400 nm
Wavelength

• People detect visible wavelengths as colors
  the human eye is sensitive to that particular
  range of wavelengths.

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Sources Sun vs. light bulb

• Sun emits many different types of radiation,
  including X-rays, ultraviolet (UV), optical
  light, infrared (IR), and radio.
• Most harmful wavelengths (X-ray, UV) are blocked
  by the atmosphere.
• A light bulb -- like the Sun -- emits energy over
  a broad range of wavelengths most of its energy
  comes out in the IR, but a lot comes out in the
  optical.

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Object

• Energy from the source interacts with the object
  to be imaged.
• Some energy is absorbed, while some energy is
  reflected or scattered.
• The wavelengths that are scattered -- i.e., not
  absorbed -- are the ones which determine the
  color of the object.

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Collection

• For a camera to be efficient, the pinhole is
  replaced by a lens.
• The lens redirects light rays emanating from the
  object.

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Refraction

• Light slows down in materials.
• Imagine a line of marching Girl Scouts . . .

Direction of travel
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Girl Scouts in the Mud
Mud

• As the marching line steps into the mud, they
  will slow down, depending on how thick the mud is.

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Wavefronts at Normal Angle of Incidence
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Index of Refraction

• Index of Refraction (n) is the ratio between the
  speed of light in vacuum (c) and the speed of
  light in the medium (v).

n c/v
Medium Index of Refraction Vacuum 1
(exactly) Air 1.0003 Water 1.33
Glass 1.5 Diamond 2.4
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Girl Scouts in Mud at an Angle

• The direction of travel changes when the marching
  line hits the mud at a non-normal angle.

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Wavefront at Non-Normal Angle of Incidence
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Snells Law
normal
GLASS
AIR

• This change in direction is described by Snells
  Law

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Trigonometry Review
RULES THAT DEFINE SIN, COS, TAN of an ANGLE

• sin(?) y/r (opp/hyp)
• cos(?) x/r (adj/hyp)
• tan(?) y/x (opp/adj)

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Snells Law
?1
n1
n2
?2

• Snells Law n1sin?1 n2sin?2

(Or, if ?1 and ?2 are small, n1?1 n2?2)
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Refraction for Different Materials
light
45?
AIR
WATER
GLASS
DIAMOND
32?
28?
16?
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Flat to Curved Surface
A curved surface can be approximated with small
straight segments.
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Curved Interface
n
n
n
n

• Concave interface diverges rays.

• Convex interface converges rays.

Assuming n gt n
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Graphical Ray Tracing
Image side ()
Source side(-)
Light Rays
Axis of symmetry
Lens

• A way to analyze optical systems.
• Light rays always travel from left to right for
  analysis purposes.

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Convex Lens

• Positive Lens
• Burning Glass
• Magnifying lens

Plano-Convex
In real life
shorthand
Positive Meniscus
Double Convex
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Convex Lens
Image side
Object side
Light Rays
Axis of symmetry
F
F
Lens

• Image focal point, F, is half the distance to
  the effective center of curvature of the lens.
• Object focal point, F, is exactly the same
  distance on the object side of the lens.

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Convex Lens
f
f
F
F

• Image focal length, f, is the distance from the
  lens to the image focal point.
• Object focal length, f, is the distance from the
  lens to the object focal point.

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Ray Diagrams for a Positive (Convex) Lens
Object Location
Image Type and Location
??(infinity)
Real, at F
Real, at 2F
2F
Real, at ??(infinity)
F
Virtual
lt F
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Concave Lens

• Negative Lens
• Near-sighted corrective lens

In real life
shorthand
Plano- concave
Negative meniscus
Double concave
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Concave Lens
f
Light Rays
Axis of symmetry
F
Lens

• Image focal point, F, is on the object side
• Focal length, f, is negative.

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Ray Diagrams for a Negative (Concave) Lens
Object Location
Image Type and Location
Rays converging toward F
Virtual, at ??(infinity)
Virtual, at F
??(infinity)
Virtual, between F and the lens
Approaching the lens from ??(infinity)
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Dispersion

• Dispersion - Index of refraction, n, depends on
  the frequency (wavelength) of light.

Dispersion is responsible for the colors produced
by a prism red light bends less within the
prism, while blue light bends more.
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Chromatic Aberration

• Dispersion results in a lens having different
  focal points for different wavelengths - this
  effect is called chromatic aberration.
• Results in a halo of colors.
• Solution Use 2 lenses of different shape and
  material (achromatic doublet).

White light
FRed
FBlue
Object (small dot)
Image with chromatic aberration
.
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Spherical Aberration

• All the rays do not bend toward the focal point,
  resulting in a blurred spot.
• Solution use lenses with aspherical curvature,
  or use a compound lens.

F
Object (small dot)
Image with spherical aberration
.
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Other Aberrations

• Coma
• Off axis blur which looks like the coma of a
  comet.
• Astigmatism
• Different focal lengths for different planes.
• Distortion
• Images formed out of shape.

.
.
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Exposure
camera
Lens
Shutter
Aperture

• Exposure is defined as the total amount of light
  falling on the film.
• Exposure Illuminance Time

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Illuminance
Small aperture
Large aperture

• Illuminance is the rate of light falling on a
  given area (i.e. energy per unit time).
• Illuminance is controlled by aperture a larger
  aperture brings more light to the focus.

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Aperture and F number

• F (F number) is often used in photography to
  describe the aperture.
• F focal length of the system/diameter of
  aperture

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Exposure Time
Shutter Closed
Shutter Open

• Exposure time is controlled by the shutter when
  closed, the film is not exposed to light.
• Exposure time is simply the time interval between
  opening and closing the shutter.

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Types of Shutters
Simplified Camera
Between the Lens (BTL) Or Leaf Shutter
Focal Plane Shutter
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BTL or Leaf Shutter

• Made of overlapping leaves that slide out of
  the way when shutter opens.
• Located between the imaging lens elements.

CLOSED
OPEN
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BTL or Leaf Shutter

• Advantages
• Uniform illumination independent of film size.
• Entire film frame illuminated at once.
• Disadvantages
• Illumination of frame not constant over time.
• Limitations on shutter speed.

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Focal Plane Shutter

• Metal or fabric with a narrow slit opening which
  traverses the area to be exposed.
• Located just before the detector (film) at the
  focal plane.

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Focal Plane Shutter

• Advantages
• Cost effective (one shutter needed for all lenses
  - great for interchangeable lens systems)
• Can achieve very fast shutter speeds (1/10000
  sec)
• Disadvantages
• May cause time distortion if the film size is
  large (since the shutter slit must traverse the
  film)

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Why control exposure with aperture and shutter?

• Flexibility!
• Fast shutter speed for freezing action (e.g.
  sports photography).
• Slow shutter speed for low light levels (e.g.
  sunsets).
• Small aperture for bright scenes or to enable
  longer exposures.
• Large aperture for low light conditions (taking
  candle lit or moon lit pictures).