638
C Holography
confluence of interfering wavelets coming from different locations on the film. The
eye sees the image produced by a diffraction pattern made by the film, a pattern
which itself was produced by diffracted light from an object. The eye should focus
not on the film, but rather where the object was originally placed.
For simplicity, let’s assume that the film is a positive linear recording, i.e. it
has a transmission at each location in proportion to the original light intensity,
and that the reference wave has the same amplitude as the original one. In this
case, the light transmitted by the film, just past the film’s surface, will have an
amplitude proportional to the intensity of the wave that occurred just past the film
as the recording was being made. We will express this observation in terms of the
diffracted wave amplitude, A D , just past the film:
A D ∝ |A r |
2 A o + A
2
r A
∗
o + (|A r |
2
+ |A o |
2 )A r .
(C.2)
The first term makes a virtual image of the object, seen at the same position the
object originally sat. The second term produces a ‘conjugate real image’ of the
object, seen in front of the film. The third term is seen as a light originating from
the position of the reference beam source and proportional to the intensity of that
reference beam. If the original object position and laser beam angles were not
colinear, then the images and reference light sources will not be seen in the same
direction (Fig. C.2).
C.3 Digital Holography
With present computational power, reconstructing a digitized image of an object
recorded on a hologram can be performed directly from the holographic recording
on a CCD or CMOS pixelated surface. Advantages to such a digital analysis include
the ability to program enhancements such as magnification, aberration correction,
noise reduction, low-pass (frequency) filtering, phase contrast enhancement, digital
color superposition from images made from various wavelength or by a multitude
Fig. C.2 Images for off-axis
hologram
Reference
beam
Virtual image
Hologram
Real image
Transmitted
beam
C Holography
confluence of interfering wavelets coming from different locations on the film. The
eye sees the image produced by a diffraction pattern made by the film, a pattern
which itself was produced by diffracted light from an object. The eye should focus
not on the film, but rather where the object was originally placed.
For simplicity, let’s assume that the film is a positive linear recording, i.e. it
has a transmission at each location in proportion to the original light intensity,
and that the reference wave has the same amplitude as the original one. In this
case, the light transmitted by the film, just past the film’s surface, will have an
amplitude proportional to the intensity of the wave that occurred just past the film
as the recording was being made. We will express this observation in terms of the
diffracted wave amplitude, A D , just past the film:
A D ∝ |A r |
2 A o + A
2
r A
∗
o + (|A r |
2
+ |A o |
2 )A r .
(C.2)
The first term makes a virtual image of the object, seen at the same position the
object originally sat. The second term produces a ‘conjugate real image’ of the
object, seen in front of the film. The third term is seen as a light originating from
the position of the reference beam source and proportional to the intensity of that
reference beam. If the original object position and laser beam angles were not
colinear, then the images and reference light sources will not be seen in the same
direction (Fig. C.2).
C.3 Digital Holography
With present computational power, reconstructing a digitized image of an object
recorded on a hologram can be performed directly from the holographic recording
on a CCD or CMOS pixelated surface. Advantages to such a digital analysis include
the ability to program enhancements such as magnification, aberration correction,
noise reduction, low-pass (frequency) filtering, phase contrast enhancement, digital
color superposition from images made from various wavelength or by a multitude
Fig. C.2 Images for off-axis
hologram
Reference
beam
Virtual image
Hologram
Real image
Transmitted
beam