Holography
Traditional imaging
Image, record intensity distribution in 2-d plane
Holography
From Gr, “holos”:
Record the interference pattern
(fringes) between coherent object
beam and reference beam. Then we
get phase and amplitude information.
Why does 3D look 3-D?
O
Holography
Coherence lengths
required for reference
beam?
Hologram recording
Simple example
Object wave can be made up by summing plane
waves. Imagine one of these coming at angle ob
vs the z axis. Put film at z = 0. Illuminate also with
reference beam along z.

E  Eref exp ik z z  Eob exp ik y y  ik z z
E  Eref  Eob exp ik sinob y
Spacing h of fringes on screen:
when k sinob y changes by 2p

hy 
sin ob

Hologram recording
Three different angles of plane waves
give three interference patterns, but
same angle to reference beam
I(y) depends on phase and amplitude of Eob . Expose a film
2
I  y   A  Eob  Eref

2


 2 Eob Eref cos k sinobj y 

Hologram reconstruction
The film becomes a grating of spacing hy . Send a reconstruction
beam along z: What diffraction angles do we get out?
For the first order, we get out exactly  ob !
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.
A zone plate is a crude hologram of a
point source of light!
Hologram reconstruction
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)
What
coherence
lengths are
needed for
reconstruction
beam?
Hologram as superposition
Film requirements
Resolution: 1000-2000 fringes/mm (almost down to )
Need a special nonlinear transparency of film:
2
T

I

E
Normal (linear) film: film
exposure
exposure so
Holography needs Etransmitted  I exposure
so
Tfilm  I 2 exposure  E 4exposure
Etransmitted 
I exposure
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 holograms
Recorded 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.