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Demo request 4/8 MondayPhysics 471 C285 ESC, 2 pm Hess call 2-2108 to confirm. Holography demo kit with laser, chess, cannon holograms in cylindrical plastic holders, and some flat holograms Horses blue/green reflection framed hologram (about 18” x 12”) that used to hang on the far west door of the demo area before remodeling. Hope you can find it…ask Clark
Bring: green laser
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Hologram of a point light source
Another simple example
Look familiar?
2 2
22 2
2 2 2 2
22O R O R
ik ikR R
O R O R
I z R E E E E kR
E E E E e e
( ) cos
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Announcements
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Why does 3D look 3-D?O
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Holography
Coherence lengths required for reference beam?
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Hologram recording
Simple exampleObject wave can be made up by summing plane waves. Imagine one of these coming at angle qob vs the z axis. Put film at z = 0. Illuminate also with reference beam along z.
ref ob obE E E ik y exp sin
Spacing of fringes on screen:when changes by 2p
yob
h
sin
obk ysin
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I(y) depends on phase and amplitude of Eob . Expose a film
The film becomes a grating of spacing . Send a reconstruction beam along z: What diffraction angles do we get out?
yh
Hologram reconstruction
222ob ref ob ref objI y A E E E E k y
cos sin
For the first order, we get out exactly ! ob
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A zone plate is a crude hologram of a point source of light!
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I(y) for two object waves (and reference)
Imagine infinite number of gratings superposed from all object angles...The reconstruction diffraction creates all the object angles again.
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When we shine the reference beam on the film, we get 1) undeflected part of the reconstruction beam, with no image information (m = 0)2) reconstructed object beam (m = 1)3) “conjugate” reconstruction beams that form a real “image” that is inside out! (m = -1)
Hologram reconstruction
What coherence lengths are needed for the reconstruction beam?
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Film requirements
Resolution: 1000-2000 fringes/mm (almost down to l)
Need a special nonlinear transparency of film:
Normal (linear) film: so film exposureT IexposuretransmittedE I
Holography needs exposuretransmittedE I
2 4film exposure exposureT I E
so
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Reflection holography
Object and reference beam come from opposite sides of holographic plate.
Reconstructing beam from same side as viewer: reflection
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Reflection holography
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White-light hologramsRecorded with coherent light. Reconstructed with incoherent light
15-20mm thick (“volume” hologram). Use “Bragg-plane” interference to give constructive interference for only a narrow band of wavelengths (like photonic crystal)
2d sin
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Rainbow thin reflecting holograms for white light exposure
Slit near object. 3-D appearance only along one axis. Rainbow in other direction.
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K-space Under-sampling
Jorge Jimenez
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Fully sampled k-space
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Low frequencies
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High Frequencies
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Vertical Image resolution
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Horizontal Image resolution