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

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

Announcements

Why does 3D look 3-D?O

Holography

Coherence lengths required for reference beam?

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

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

A zone plate is a crude hologram of a point source of light!

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.

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?

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

Reflection holography

Object and reference beam come from opposite sides of holographic plate.

Reconstructing beam from same side as viewer: reflection

Reflection holography

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

Rainbow thin reflecting holograms for white light exposure

Slit near object. 3-D appearance only along one axis. Rainbow in other direction.

K-space Under-sampling

Jorge Jimenez

Fully sampled k-space

Low frequencies

High Frequencies

Vertical Image resolution

Horizontal Image resolution