C Holography
637
original reference wave used to make the recording, then the object will appear in
the same location it had been physically when the recording was made. The image
will be virtual, since the light appears to come from behind the hologram surface
where the object was, but no light need come from the image points.
C.2 Principles Behind Holography
Now, to understand holograms more deeply, we will introduce more of the physics
details. Consider a hologram made by light coming from a single laser illuminating
an object and photographic film. 1
As the vector character of the electric and magnetic field intensities is not
essential to the argument, we will use scalar waves. Also, since the wave travels
at the speed of light, we can neglect time delays for waves traveling between our
localized objects. At each fixed time, the amplitude of the light wave at the surface
of the film will be a superposition of the laser reference wave added to the wavelets
of incident laser light scattered from the object:
A = A r + A o .
(C.1)
The reference wave amplitude A r has a simple plane-wave behavior on the film.
The object wave amplitude varies over the film in a more complicated fashion, as it
is formed by the sum of all the scattering wavelets from every illuminated point on
the object that arrive at each point on the film. The film exposure is proportional to
the resultant intensity of light, which is proportional to
|A|
2
= |A r |
2
+ |A o |
2
+ A
∗
r A o + A r A
∗
o .
Now let’s see what happens when the film is developed and then put into a laser
beam in the same position as that of the reference wave in forming the hologram.
This procedure is called ‘holographic reconstruction’. The new reference wave
(which, we take also with amplitude A r ) will pass through the clear spots on the film,
while diffracting around the dark spots. Since the interference pattern recorded on
the film will have opacity variations with dimensions comparable to the wavelength
of the laser light, significant diffraction will occur, sending some light into noncolinear directions after passing through the film. Viewing the film from the side
opposite to where the object was originally, the light from the reference beam will
have passed through the film and enters the eye. Locations on the retina will have a
1 Negative photographic film can be made by a gel containing silver bromide crystals. When
exposed to light, electrons are released in the crystal which combine with the silver ions to make
metallic silver. Accumulated silver metal in the gel is opaque. Development of the film stabilizes
the remaining silver ions into a thiosulfate.
637
original reference wave used to make the recording, then the object will appear in
the same location it had been physically when the recording was made. The image
will be virtual, since the light appears to come from behind the hologram surface
where the object was, but no light need come from the image points.
C.2 Principles Behind Holography
Now, to understand holograms more deeply, we will introduce more of the physics
details. Consider a hologram made by light coming from a single laser illuminating
an object and photographic film. 1
As the vector character of the electric and magnetic field intensities is not
essential to the argument, we will use scalar waves. Also, since the wave travels
at the speed of light, we can neglect time delays for waves traveling between our
localized objects. At each fixed time, the amplitude of the light wave at the surface
of the film will be a superposition of the laser reference wave added to the wavelets
of incident laser light scattered from the object:
A = A r + A o .
(C.1)
The reference wave amplitude A r has a simple plane-wave behavior on the film.
The object wave amplitude varies over the film in a more complicated fashion, as it
is formed by the sum of all the scattering wavelets from every illuminated point on
the object that arrive at each point on the film. The film exposure is proportional to
the resultant intensity of light, which is proportional to
|A|
2
= |A r |
2
+ |A o |
2
+ A
∗
r A o + A r A
∗
o .
Now let’s see what happens when the film is developed and then put into a laser
beam in the same position as that of the reference wave in forming the hologram.
This procedure is called ‘holographic reconstruction’. The new reference wave
(which, we take also with amplitude A r ) will pass through the clear spots on the film,
while diffracting around the dark spots. Since the interference pattern recorded on
the film will have opacity variations with dimensions comparable to the wavelength
of the laser light, significant diffraction will occur, sending some light into noncolinear directions after passing through the film. Viewing the film from the side
opposite to where the object was originally, the light from the reference beam will
have passed through the film and enters the eye. Locations on the retina will have a
1 Negative photographic film can be made by a gel containing silver bromide crystals. When
exposed to light, electrons are released in the crystal which combine with the silver ions to make
metallic silver. Accumulated silver metal in the gel is opaque. Development of the film stabilizes
the remaining silver ions into a thiosulfate.