Fresnel and Reticular Lenses

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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The array creates images ofany point onthe opposite side but only in cross-section. Two crossed arrays createimages

in 3D.


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Invertedimages areformedin front of thearray, without thedistortion effects of lenses.


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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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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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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

Fresnel and Reticular Lenses

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