Page 418 - Introduction to Information Optics

7.7. Pattern Recognition with Photorefractive Optics 403
It is trivial the object beam can be written as

0(x, y) exp[i0(x, j') #i(x — b, y) exp[/c/> 1(x - />, y)]
(7.48)
+ 0 2(x + /?, y) expf>/> 2(x + b, y)],

where 0 15 0 2, 0 l5 and 4> 2 are the amplitude and phase distortion of the input
objects, respectively; b is the mean separation of the two input objects; and O t ,
0 2 are assumed positive real. At the image plane (i.e., the crystal), the object
beam is given by

(7.49)

where M represents the magnification factor of the imaging system; L = s ~ j\
where s is the image distance and / is the focal length of lens L^ and k =
27r//, where A is the wavelength of the light source.
Thus, the reconstructed beam emerging from the crystal is given by

A Z exp exp
M' M M' M

(7.50)

Notice that this expression does not represent the exact phase conjugation of
Eq. (7.49). The amplitude distribution of O'(x, y) deviates somewhat from,
0(x, y), which is primarily due to the nonlinearity of the crystal. However, a
phase shift 9(x, y) between the phase conjugation and the reconstructed beam
is also introduced, which is independent on the intensity ratio of the object
beam and the reference beam. The reconstructed beam, imaged back on the
object plane, can be written as

<9'(.x, y) exp[ — /Y/>(x, y)] exp[/0(x, y)].

After passing through the input objects, the complex light distribution becomes

0(x, y)0'(x, y) exp[/0(jc, y)], (7.5 1 )

which removes the phase distortion </>(x, y) of the input objects. By joint-
transforming the preceding equation, a phase-distortion free JTPS can be
captured by the CCD 2.
For demonstration, a pair of input objects, shown in Fig. 7.41a, has been
added with random phase noise (e.g., shower glass). Figure 7.41b shows the