Page 651 - Introduction to Information Optics

11.3. 3-D Holographic Display

point object
reconstruction hologram
wave

observer

virtual
image

Fig. 11.15. Holographic reconstruction.

the zone defines the transverse location of the point object. For an arbitrary
3-D object, we can think of the object as a collection of points, and therefore
we can envision that we have a collection of zones on the hologram, with each
zone carrying the transverse location as well as the depth information of each
individual point. In fact, a hologram has been considered as a type of Fresnel
zone plate [21] and the holographic imaging process has been discussed in
terms of zone plates [22].
So far, we have discussed the transformation of a point object to a zone
plate on the hologram during holographic recording, and this corresponds to
a coding process. In order to decode it, we need to obtain the point object back
from the hologram. This can be done by simply illuminating the hologram with
a reconstruction wave, as shown in Fig. 11.15. Figure 11.15 corresponds to the
reconstruction of a hologram of the point object located on-axis; i.e., for the
simple case where x 0 = y 0 = 0.
Note that in practice, the reconstruction wave usually is identical to the
reference wave; therefore, we assume the reconstruction wave to have a field
distribution on the plane of the hologram given by \j/ rc(x, y) = a. Hence, the
field distribution of the transmitted wave immediately after the hologram is
ijs rct(x, y) = at(x, y) and the field at arbitrary distance of z away is according to
Eq. (11.18), given by the evaluation of at(x, y) * h(x, y; z). For the point-object
hologram given by Eq. (11.21), we have, after expanding the sine term of the
hologram r(x, v),

exp (y -

2
2
exp ( -j x 0) + (y - v 0) ] 11 .22)
V