Biomedical Engineering Reference
In-Depth Information
I
o
5
1
r
6
4
2
3
4
4
1
5
6
Object
Plane
reference wave
FIgurE 9.1
Optical recording of a hologram in an off-axis configuration: a plane reference wave
r
interferes
with an object wave
o
to produce an intensity-only hologram
I
. This off-axis configuration takes its name from the
nonzero angle subtended by the direction of
r
with respect to that of
o
.
the object and reference waves exhibit perfect mutual coherence (
g
o,r
= 1), then
I
= |
o
|
2
+
or
*
+
ro
*
+ |
r
|
2
provides an ideal support for the holographic information, contained in the cross-terms that are referred
to as imaging terms. These terms produce an interference pattern, in which the successive dark and bright
fringes can be regarded as contour lines expressing the phase difference between the object and the refer-
ence waves.
Classically, a photo-sensitive plate is used to record the hologram. After exposure, the plate is photo-
chemically developed and only then is the hologram revealed as a plate of transmissivity proportional
to
I
. This process is, in itself, quite complicated. Indeed, exposure has to be rigorously controlled,
even more than with film photography, to ensure working in the linear regime of the photo-sensitive
medium. As if this is not enough, all development steps, requiring multiple chemical baths, also have to
be precisely controlled. Nevertheless, this art has been mastered both for scientific and artistic purposes
by the holographists of the time and has helped establish the foundations for the later digital holography.
It is not the purpose of this section to go into any more details concerning recording of holograms in
classical holography. Interested readers should refer to dedicated topics (Collier et al
.
, 1971; Hariharan,
1996).
9.2.4 Hologram Reconstruction
The hologram is a diffraction grating: its dark and bright fringes form a structure on which light can
diffract to restitute all the information about the amplitude and the phase of the object wavefront. This
is how the information contained in the hologram is classically revealed.
To understand how this works, let us assume that the photo-chemically developed hologram plate has
a transmissivity corresponding exactly to
I
, and is illuminated by a wave
u
. After expliciting
I
according
to Equation 9.2, the transmitted wave ψ can be expressed as
