Page 477 - Introduction to Information Optics

462 8. Information Storage with Optics

Fig. 8.8. Experimental results of wavefront and angular multiplexing. Two outputs from 36
patterns stored in (a) the first, (b) the second, and (c) the third angular position.

the Rayleigh criteria, as follows.

(8.11)

where Q is the diameter of the central spot of the Airy disk as given in Eq. (8.1),
Q/2 is the Rayleigh resolution limit, / is the focal length of lens, D is the
diameter of lens, and A is the wavelength of light. We cannot keep increasing
D to decrease Q/2 to zero, because, in practice, / and D of a lens are not
independent. When / is made small, D will be limited by the curvature of the
lens surface, which is, in turn, determined by /
The Rayleigh criteria are based on the diffraction pattern of a circular
aperture, which is commonly known as the Airy disk. Q/2 is actually the radius
of the first-zero ring of the Airy disk. We must not consider that the highest
1
spatial frequency passing through the optical system is (Q/2)" or D/1.22//L
which could be larger than I/A. Spatial frequencies higher than I/A. cannot
propagate far, as will be shown in the following paragraph.
We first look at the optical field /(x, y,z) provided that f(x, y, 0) is known.
The optical field f(x, v, z) satisfies the wave equation as follows [4]:
2
2
(V + k )f(x,y,z) = (8.12)