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8/8/2019 Fresnel and Reticular Lenses
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Design Realization
lecture 27
John Canny
12/2/03
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Last time
Lenses reviewed: convex spherical lenses.
Ray diagrams. Real andvirtual images.
More on lenses. Concave and aspheric lenses.
Fresnel optics:
Lenses
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This time
More Fresnel optics:
Lenticular arrays/diffusers
Prisms
Diffusers
Holograms
Polarization
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Fresnel lenses
Remove the thick-ness, but preservepower.
Some artifacts areintroduced, butareinvisibleforlargeviewing areas(e.g. diplays).
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Lenticular arrays
Simplest version: array ofcylindrical lenses.
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Lenticular arrays
Lenticular screens are ratedin LPI for linesperinch. Typical rangeis 40-60 LPI, atabout $10 per squarefoot.
Budget color printers can achieve 4800 dpi.
At 40 LPI that gives 120 images in approx60r viewing range, or 0.5r perimage.
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Lenticular stereograms
By interleaving images from views ofascene spaced by 0.5r, you can achieve agood 3D image.
At 1m viewing distance, 0.5r translates to1cm spacing between images.
Eye spacing is about 6 cm.
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Diffusers
Diffusers spread collimated (parallel) lightover a specified range ofangles.
Can control viewing anglefor a display.
Gives sense of presencein partitionedspaces.
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Geometric diffusers
Arrays of tiny lenses (lenticular arrays).
Can be cylindrical (diffusion in onedirectiononly), usedin rear-projection screens.
Surfaceetching. Using in shower glass,anti-glare plastic coatings.
Holographic surfaceetching: providestightly-controlleddiffusion envelope.
Low-quality surfacefinish(!) on plasticsgives diffusion effect.
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Lenticular arrays
Cylindrical arrays
Diffusion in onedirection only, same as thearrays in lenticular stereograms.
Usedin rear-projection screens.
Large angle: 30-90r
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Lenticular arrays
Spherical arrays diffusein both directions:
Large angle: 30-90r
Homogeneous in all directions.
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Rough surfaces
Diffusion depends on the range ofangleson the surface. Surface should beirregularbut not too sharp.
Arbitrary range ofdiffusion angles. 2-4rtypical for anti-glare plastic coatings.
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Material diffusers
Tiny spheres embeddedin clear polymerwith different refractiveindex.
Can achievewide range ofdiffusion angles.
Simpler to manufacture than most surfacediffusers.
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Example: Rear projection screens
Combination of:
Rearfresnel lens - concentrates light towardcentral viewers
Front lenticular scr
een spr
eads l
ighthorizontally
Diffusing material spreads light vertically(by a smaller angle).
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Fresnel prisms
Similaridea to lenses. Remove thethickness of the prism and stagger thesurfacefacets.
Useful for bending light over a large area,e.g. fordeflecting daylight.
Also usedforvision correction.
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An improvisation withFresnel prisms
Opposing prism arrays create an array ofTIR mirrors:
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An improvisation withFresnel prisms
The array creates images ofany point onthe opposite side but only in cross-section. Two crossed arrays createimages
in 3D.
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An improvisation withFresnel prisms
Invertedimages areformedin front of thearray, without thedistortion effects of lenses.
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An improvisation withFresnel prisms
Two such pairs invert theimage twice, producing aright-sided, displaced
image.
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Holography
Holograms are based on interference patternscaused by thefine structure of the hologram.
Production methods are generally complicatedand require:
A coherent laser light source
Collimating optics
Careful film processing
Lots of trial anderror
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Holography
E.g. white-light transmission hologramsetup from www.3dimagery.com
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Computer-Generated Holography
Interestingly, there are many softwarepackages that can compute CGH holograms(most standard optical CAD packages can do
this).
One of the simplest and most robust types ofhologram is the Fraunhofer hologram. The
hologram is a kind ofFourier transform of theobject. It can be accelerated using efficientFFT software.
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Computer-Generated Holography
Current printers are at 4800 dpi, or about 5microns, and produce binary images.
Turning a printedimageinto a hologramrequires reduction down to opticalwavelengths (< 1 micron).
e.g. Photograph with SLR camera with Fujiminicopyfilm. The negativeis the hologram.
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Computer-Generated Holography
Some commercial vendors will printholograms from an image sequence (movie orpan-around a fixed object):e.g.
www.litiholographics.com
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Polarization
Remember that light is an electro-magneticwavewith both electric and magneticcomponents normal to its motion.
Normal light has E (electric) components in alldirections, but it can be polarized undercertain conditions.
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Polarization by reflection
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Polarization by reflection
This reflection profileistypical for othermaterials likewater or
metals. Reflected glareis
typically mostlyhorizontally polarized.
Vertical polarizedsunglasses eliminatemuch ofit.
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Polarization by absorption
Dichroicmaterials exhibit different absorptionfor transverse and parallel light polarizations.The (artificial) polaroid material typically
transmits 80% ofparallel light, but only 1% oftransverse light.
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Circular Polarization
Birefringentmaterials exhibit differentrefractiveindices (hencevelocity) for the twolight polarizations.
Ifa birefringent material is the right thickness,the slowerwave can bedelayedexactly wavelength.
Sending linearly polarized light into this layer
leads to elliptic polarization.
If the polarizer axis is at 45 to the birefrengentaxis, the light will becircularly polarized.
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Summary
More Fresnel optics:
Lenticular arrays/diffusers
Prisms
Diffusers Holograms
Polarization
Recommended