1. Design Realization lecture 27 John Canny 12/2/03

2. Last time  Lenses reviewed: convex spherical lenses.  Ray diagrams. Real and virtual images.  More on lenses. Concave and aspheric lenses.  Fresnel optics:  Lenses

3. This time  More Fresnel optics:  Lenticular arrays/diffusers  Prisms  Diffusers  Holograms  Polarization

4. Fresnel lenses  Remove the thick- ness, but preserve power.  Some artifacts are introduced, but are invisible for large viewing areas (e.g. diplays).

5. Lenticular arrays  Many lenses printed on one sheet.  Simplest version: array of cylindrical lenses.  Used for budget 3D vision:

6. Lenticular arrays  Simplest version: array of cylindrical lenses.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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 

12. Lenticular arrays  Spherical arrays diffuse in both directions:  Large angle: 30-90   Homogeneous in all directions.

13. 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.

14. 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.

15. 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).

16. 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.

17. An improvisation with Fresnel prisms  Opposing prism arrays create an array of TIR mirrors:

18. 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.

19. An improvisation with Fresnel prisms  Inverted images are formed in front of the array, without the distortion effects of lenses.

20. An improvisation with Fresnel prisms  Two such pairs invert the image twice, producing a right-sided, displaced image.

21. 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…

22. Holography  E.g. white-light transmission hologram setup from www.3dimagery.comwww.3dimagery.com

23. 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.

24. 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.

25. 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 www.litiholographics.com

26. 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.

27. Polarization by reflection

28.  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.

29. 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.

30. 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.

31. Summary  More Fresnel optics:  Lenticular arrays/diffusers  Prisms  Diffusers  Holograms  Polarization