3. Geometrical Optics

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3. Geometrical Optics
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• Geometric opticsprocess of light ray through
  lenses and mirrors to determine the location and
  size of the image from a given object .

Reflection and Mirror
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Image Formation by Reflection
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Application of Double Reflection-Periscope
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DIY Periscope
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DIY Periscope (Cont)
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• Law of reflection (Snells law)

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Types of Lenses
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Ray Tracing through Thin Lenses
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Image Formation by thin Lenses
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ABCD Matrix
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ABCD Matrix (Cont)
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ABCD Matrix (Cont)
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ABCD Matrix (Cont)
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ABCD Matrix (Cont)
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ABCD Matrix (Cont)
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ABCD Matrix (Cont)
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Aberrations of Lenses

• Primary Aberration ? image deviate from the
  original picture/the first-order approximation
• Monochromatic aberrations
• ? Spherical Aberration
• ? Coma
• ? Astigmatism
• ? Curvature of field
• ? Distortion
• Chromatic aberration

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General Method of Reducing Aberration in Optical
Systems-Multiple Lenses
United States Patent 6844972
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General Method of Reducing Aberration in Optical
Systems-Multiple Lenses (Cont)
United States Patent 6995908
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Chromatic Aberration
The focal lengths of lights with distinct
wavelengths are different.
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Solution of Chromatic Aberration-Using Doublet,
Triplet, or Diffractive Lens
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Spherical Aberration (SA)
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Spherical Aberration for Different Lenses
(a)  Simple biconvex lens (b)  Best-form
lens (c)  Two lenses (d)  Aspheric, almost
plano-convex lens
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Solutions of Spherical Aberration-Using
Aspherical Lens or Stop
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Coma
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Coma (Cont)
(a) Negative coma (b) Postive coma
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Astigmatism
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Astigmatism (Cont)
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Solutions of Astigmatism-Using Multiple Lenses
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Curvature of field
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Solutions of Curvature of field-Using Multiple
Lenses
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Distortion
Picture taken by a wide-angle camera in front of
graph paper with square grids
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Solution of Distortion-Using Multiple Lenses
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Nearsightedness (Myopia) and Farsightedness
(Hyperopia)
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Image Formation ? Camera
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Camera
F-number
Eg. 50 mm camera lens, aperture stop 6.25mm
F-number 8 (f/8)
Exposure
E energy collected by camera lens B brightness
of object A area of aperture d diameter of
aperture stop
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Camera Lenses

• Wide-angle Lenses-the Aviogon and the Zeiss
  Orthometer lenses
• Standard Lenses-the Tessar and the Biotar lenses
• Lens of reducing the 3rd-order aberration-the
  Cooke triplet lens

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Depth of Field (DOF)

• The distance between the nearest and farthest
  objects in a scene that appear acceptably sharp
  in an image.
• In cinematography, a large DOF is called deep
  focus, and a small DOF is often called shallow
  focus.
• For a given F-number, increasing the
  magnification decreases the DOF decreasing
  magnification increases DOF.
• For a given subject magnification, increasing the
  F-number increases the DOF decreasing F-number
  decreases DOF.

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Numerical Aperture (NA)

• The numerical aperture of an optical system is a
  dimensionless number that characterizes the range
  of angles over which the system can accept or
  emit light.
• Generally,
• For a multi-mode optical fiber,

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Telescope
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• Astronomical (Keplerian) Telescope

Magnification (magnifying power)
General Keplerian telescope dfofe
? angle subtended at input end in front of
objective ? angle subtended at output end
behind eyepiece
(inverted image)
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• Galileo Telescope

General Galileo telescope dfo-fe
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Terrestrial Telescope
All images are erecting
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Optical Microscope
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• Microscope Theory

Objective
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• Microscope Theory (Cont)

Eyepiece
(normal reading distance)
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• Simple Projection System

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Fresnel Lens and Plates

• Radius of the concentric circular rn
  (n?)22fn? ½ , n0, 1, 2,.
• Sapce between two adjacent circular
• zone ?rn rn1?rn

focusing point (in phase)