Design Realization lecture 25

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Design Realization lecture 25

• John Canny
• 11/20/03

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Last time

• Improvisation application to circuits and
  real-time programming.
• Optics physics of light.

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This time

• Reflection, Scattering
• Refraction, TIR
• Retro-reflection
• Lenses

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Wavefronts and Rays

• EM waves propagate normal to the wavefront
  surface, and vice-versa.
• The ray description is most useful for describing
  the geometry of images.

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Reflection

• Most metals are excellent conductors.
• They reduce the E field to zero at the surface,
  causing reflection.
• If I, R, N unit vectors
• I?N R?N
• I?(N ? R) 0

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Ray-tracing

• By tracing rays back from the viewer, we can
  estimate what a reflected object would look like.
  Follow at least two rays at extremes of the
  object.

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Lambertian scattering

• For most non-metallic objects, the apparent
  brightness depends on surface orientation
  relative to the light source but not the viewer.
• i.e. brightness isproportional to I?N

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Refraction wave representation

• In transparent materials (plastic, glass), light
  propagates slower than in air.
• At the boundary, wavefronts bend

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Refractive index

• Refractive index measures how fast light
  propagates through a medium.
• Such media must be poor conductors and are
  usually called dielectric media.
• The refractive index of a dielectric medium
  iswhere c is the speed of light in vacuum,
  and v is the speed in the medium. Note that ? gt
  1.

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Refraction Snells law

• Incident and refracted rays satisfy

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Refraction ray representation

• In terms of rays, light bends toward the normal
  in the slower material.

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Refraction in triangular prisms

• For most media, refractive index varies with
  wavelength. This gives the familiar rainbow
  spectrum with white light in glass or water.

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Refractive index

• Refractive index as a function of wavelength for
  glass and
  water

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Refractive index

• High-quality optical glass is engineered to have
  a constant refractive index across the visible
  spectrum.
• Deviations are still possible. Such deviations
  are called chromatic aberration.

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Refractive indices

• Water is approximately 1.33
• Normal glass and acrylic plastic is about 1.5
• Polycarbonate is about 1.56
• Highest optical plastic index is 1.66
• Bismuth glass is over 2
• Diamond is 2.42

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Internal reflection

• Across a refractive index drop, there is an angle
  beyond which ray exit is impossible

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Total internal reflection (TIR)

• The critical angle is where the refracted ray
  would have 90? incidence.
• The internal reflection angle is therefore
• For glass/acrylic, this is 42?
• For diamond, it is 24? - light will make many
  internal reflections before leaving, creating the
  fire in the diamond.

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Penta-prisms

• Penta-prisms are used in SLR cameras to rotate an
  image without inverting it.
• They are equivalent to two conventional mirrors,
  and cause a 90? rotation of the image, without
  inversion.
• An even number of mirrors produce a
  non-inverted rotated image of the object.

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Retro-reflection Corner reflectors

• In 2D, two mirrors at right angles will
  retro-reflect light rays, i.e. send them back in
  the direction they came from.

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Retro-reflection Corner reflectors

• In 3D, you need 3 mirrors to do this
• Analysis each mirror inverts one of X,Y,Z

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Retro-reflection TIR spheres

• Consider a sphere and an incoming ray.
• Incoming and refracted ray angles are ?, ?.
• For the ray to hit the centerline, ? 2?.
• For retro-reflection, we want ? sin ? /sin ?
• For small angles, ? 2gives good results.

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Retro-reflective sheets

• Inexpensive retro-reflective tapes are available
  that use tiny corner reflectors or spheres
  embedded in clear plastic (3M Scotchlite)
• They come in many colors, including black.

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Retro-reflector gain

• The retro-reflection response of a screen is
  normally rated in terms of gain.
• Gain ratio of peak reflected light energy to
  the energy reflected by a Lambertian surface.
• Gains may be 1000 or more.
• Light source only needs 1/1000 of the light
  energy to illuminate the screen, as long as the
  viewer is close enough to the source.

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Application personal displays

• Each user has a personal projector (e.g. a PDA
  with a single lens in front of it), and projects
  on the same retro-reflective screen.

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Application Artificial backgrounds

• Projector and camera along same optical axis,
  project scene onto actors and retro-reflective
  background.
• Cameras sees background only on screen, not on
  the actors (3M received technical academy award
  for this in 1985).

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Convex Lenses

• A refractive disk with one or two convex
  spherical surfaces converges parallel light rays
  almost to a point.
• The distance to this point is the focal length of
  the lens.

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Lenses

• If light comes from a point source that is
  further away than the focal length, it will focus
  to another point on the other side.

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Lenses

• When there are two focal points f1 , f2
  (sometimes called conjugates), then they satisfy

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Spherical Lenses

• If the lens consists of spherical surfaces with
  radii r1 and r2, then the focal length
  satisfies 1/f (? - 1) (1/r1 -
  1/r2)

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Spherical aberration

• Spherical lenses cannot achieve perfect focus,
  and always have some aberration

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Spherical aberration

• Compound lenses, comprising convex, concave or
  hybrid elements, are used to minimize aberration.