Page 652 - Introduction to Information Optics

636 11. Information Display with Optics
Therefore, we will have three terms resulting from the illumination of the
hologram by the reconstruction wave. These contributions, according to
Fresnel diffraction upon illumination of the hologram; i.e., at(x, y) * h(x, y; z ()),
are as follows:

First term: aA * h(x, y; z = z 0) = a A, (zero-order beam). (11.23a)
( k \
2
2
Second term: ~ exp I /-— [(.x — x 0) + (y — V 0) ] I * h(x, y,z =
" " / (11.23b)
\ 2z 0
~ S(x - x 0, y - y 0), (real image).
/ k 2 2 \
Third term: ~ exp -; ~- [(x - x 0) + (y - y 0) ] * h(x, y; z • o)
z
\ 2z 0 )
~ <5(x — x 0, y — y 0), (virtual image). (11.23c)

In the terminology of holography, the first term is the zero-order beam due to
the bias in the hologram. The result of the second term is called the real image
and the third term is the virtual image. Note that the real image and the virtual
image are located at a distance z 0 in front and back of the hologram,
respectively. This situation is shown in Fig. 11.15. The real image and the
virtual image are called the twin images in on-axis holography.
Figure 11.16(a) shows the holographic recording of a 3-point object and Fig.
11.16(b) shows the reconstruction of the hologram. Note that the virtual image
appears at the correct 3-D location of the original object, while the real image

wave

recording film

object
wmve

Fig. 11.16(a). Holographic recording.