Transcript Lecture 27

Design Realization
lecture 27
John Canny
Last time
Lenses reviewed: convex spherical lenses.
Ray diagrams. Real and virtual images.
More on lenses. Concave and aspheric lenses.
Fresnel optics:
 Lenses
This time
 More Fresnel optics:
 Lenticular arrays/diffusers
 Prisms
 Diffusers
 Holograms
 Polarization
Fresnel lenses
 Remove the thickness, but preserve
 Some artifacts are
introduced, but
are invisible for
large viewing areas
(e.g. diplays).
Lenticular arrays
 Many lenses printed on one sheet.
 Simplest version: array of cylindrical lenses.
 Used for budget 3D vision:
Lenticular arrays
 Simplest version: array of cylindrical lenses.
Lenticular arrays
 Lenticular screens are rated in LPI for lines
per inch. Typical range is 40-60 LPI, at
about $10 per square foot.
 Budget color printers can achieve 4800 dpi.
 At 40 LPI that gives 120 images in approx
60 viewing range, or 0.5 per image.
Lenticular stereograms
 By interleaving images from views of a
scene spaced by 0.5, you can achieve a
good 3D image.
 At 1m viewing distance, 0.5 translates to
1cm spacing between images.
 Eye spacing is about 6 cm.
 Diffusers spread collimated (parallel) light
over a specified range of angles.
 Can control viewing angle for a display.
 Gives sense of “presence” in partitioned
Geometric diffusers
 Arrays of tiny lenses (lenticular arrays).
 Can be cylindrical (diffusion in one direction
only), used in rear-projection screens.
 Surface etching. Using in shower glass,
anti-glare plastic coatings.
 Holographic surface etching: provides
tightly-controlled diffusion envelope.
 Low-quality surface finish(!) on plastics
gives diffusion effect.
Lenticular arrays
 Cylindrical arrays
 Diffusion in one direction only, same as the
arrays in lenticular stereograms.
 Used in rear-projection screens.
 Large angle: 30-90
Lenticular arrays
 Spherical arrays diffuse in both directions:
 Large angle: 30-90
 Homogeneous in all directions.
Rough surfaces
 Diffusion depends on the range of angles
on the surface. Surface should be irregular
but not too “sharp”.
 Arbitrary range of diffusion angles. 2-4
typical for anti-glare plastic coatings.
Material diffusers
 Tiny spheres embedded in clear polymer
with different refractive index.
 Can achieve wide range of diffusion angles.
 Simpler to manufacture than most surface
Example: Rear projection screens
 Combination of:
 Rear fresnel lens - concentrates light toward
central viewers
 Front lenticular screen – spreads light
 Diffusing material –
spreads light vertically
(by a smaller angle).
Fresnel prisms
 Similar idea to lenses. Remove the
thickness of the prism and stagger the
surface facets.
 Useful for bending light over a large area,
e.g. for deflecting daylight.
 Also used for vision correction.
An improvisation with Fresnel prisms
 Opposing prism arrays create an array of
TIR mirrors:
An improvisation with Fresnel prisms
 The array creates images of any point on
the opposite side – but only in crosssection. Two crossed arrays create images
in 3D.
An improvisation with Fresnel prisms
 Inverted images are formed in front of the
array, without the distortion effects of lenses.
An improvisation with Fresnel prisms
 Two such pairs invert the
image twice, producing a
right-sided, displaced
 Holograms are based on interference patterns
caused by the fine structure of the hologram.
 Production methods are generally complicated
and require:
A coherent laser light source
Collimating optics
Careful film processing
Lots of trial and error…
 E.g. white-light transmission hologram
setup from
Computer-Generated Holography
 Interestingly, there are many software
packages that can compute “CGH” holograms
(most standard optical CAD packages can do
 One of the simplest and most robust types of
hologram is the “Fraunhofer” hologram. The
hologram is a kind of Fourier transform of the
object. It can be accelerated using efficient
FFT software.
Computer-Generated Holography
 Current printers are at 4800 dpi, or about 5
microns, and produce binary images.
 Turning a printed image into a hologram
requires reduction down to optical
wavelengths (< 1 micron).
 e.g. Photograph with SLR camera with Fuji
“minicopy” film. The negative is the hologram.
Computer-Generated Holography
 Some commercial vendors will print
holograms from an image sequence (movie or
pan-around a fixed object): e.g.
 Remember that light is an electro-magnetic
wave with both electric and magnetic
components normal to its motion.
 Normal light has E (electric) components in all
directions, but it can be polarized under
certain conditions.
Polarization by reflection
Polarization by reflection
 This reflection profile is
typical for other
materials like water or
 Reflected “glare” is
typically mostly
horizontally polarized.
 Vertical polarized
sunglasses eliminate
much of it.
Polarization by absorption
 Dichroic materials exhibit different absorption
for transverse and parallel light polarizations.
The (artificial) polaroid material typically
transmits 80% of parallel light, but only 1% of
transverse light.
Circular Polarization
 Birefringent materials exhibit different
refractive indices (hence velocity) for the two
light polarizations.
 If a birefringent material is the right thickness,
the slower wave can be delayed exactly ¼
 Sending linearly polarized light into this layer
leads to elliptic polarization.
 If the polarizer axis is at 45 to the birefrengent
axis, the light will be circularly polarized.
 More Fresnel optics:
 Lenticular arrays/diffusers
 Prisms
 Diffusers
 Holograms
 Polarization