Page 424 - Introduction to Information Optics

7.7. Pattern Recognition with Photorefractive Optics 409

vv r (fl v ,tf v ,/> v ,& } ,) can be written as

WJp, q) = ^jL= S r(p, q)H*(p, q). (7,65)

It is trivial that a conventional WT matched field (CMFW) is

CMF M,(p, q) = W*(p, q). (7.66)

If the wavelet signal w(a x,a y,b x,b y) is inserted in the FDP, the complex light
field behind the CMF W, can be written as

W(p, q)W*(p, q) = S,(p, g)WMF(p, q), (7.67)

where

WMF(p, q) = (l/a xa y)S*(p, q)\H a(p, q}\ 2 (7.68)
is defined as the wavelet matched filter. Thus, we see that WMF can be
synthesized by conventional interferometric technique with appropriate spectra
2
wavelet modulus \H a(p, q)\ .
The generation of WMFs is the key issue in the construction of a PR-based
WT correlator, as shown in Fig. 7.45. The scaled moduli of the wavelet spectra
can be sequentially generated by the SLM located at the back focal plane of
lens LI; the emerging light field can be synchronously imaged onto the crystal
by the imaging lens L2. Thus, a large number of WMFs can be recorded in the
PR crystal as a set of reflection holograms by means of angular multiplexing.
The light intensity within the crystal can be written as

2
2
/ = £ \S r\HJ + R n| , (7.69)
where S r and H n are the Fourier transforms of the reference signal and the
dilated analyzing wavelets, respectively; R n is the reference beam; and JV is the
total number of wavelets. If a target signal s is inserted at the input plane, as
shown in Fig. 7.45b, the reflected reconstructed light field from the crystal will
be

4
2
2
2
\H\ + |/g + S,S* £ \H\ R H + SfS r \H\ R*.
n = 1 n - 1 / n = 1 n = 1
(7.70)