Design Realization lecture 27

John Canny

12/2/03

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 thick-ness, but preservepower.

Some artifacts areintroduced, 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

Diffusers spread collimated (parallel) light over a specified range of angles.

Can control viewing angle for a display. Gives sense of “presence” in partitioned

spaces.

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

diffusers.

Example: Rear projection screens

Combination of: Rear fresnel lens - concentrates light toward

central viewers Front lenticular screen – spreads light

horizontally 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 cross-section. 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 image.

Holography

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…

Holography

E.g. white-light transmission hologram setup from www.3dimagery.com

Computer-Generated Holography

Interestingly, there are many software packages that can compute “CGH” holograms (most standard optical CAD packages can do this).

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. www.litiholographics.com

Polarization

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 metals.

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 wavelength.

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.

Summary

More Fresnel optics: Lenticular arrays/diffusers Prisms

Diffusers Holograms Polarization