Page 451 - Introduction to Information Optics

436 8. Information Storage with Optics

therefore, is dynamic. However, data, which is the formatted information, is
static. If the fluctuation of the energy is measured continuously and is
represented by a real number, it is an analog signal. On the contrary, if it is
measured in a discrete way and is represented by an integer, it is a digital
signal. In other words, a digital signal is sampled and quantized.
A signal is meaningful only after it is detected. The accuracy of the
interpretation of a received signal depends on the ability of the detector to
resolve two positions and also two values. In the context of optical information
processing and storage, energy is in the form of light intensity and the detector
is a photodetector that converts light intensity into an electric signal. The
resolving power for a given position is determined by the pixel size of the
detector, while the resolving power for intensity is determined by the sensitivity
of the detector. By taking both the smallest separable distance and the smallest
separable intensity as units, any analog signal is indeed converted into a digital
signal because it is unavoidably sampled and quantized by the detector.
Nevertheless, what is commonly called a digital signal is not the quantized
signal but the binarized signal. Quantized values are represented by integers
such as 0,1,2,3,...; however, binarized values are represented by binary
numbers; i.e., 0 and 1 only. Binary numbers use a base of 2 while decimal
numbers use a base of 10. For example, decimal 1 is 1 in binary, 2 is 10, 3 is
11, 4 is 100, 5 is 101, etc. The length of a binary number is represented in bits,
which stands for a binary unit. Thus, 1 is one bit, 10 and 11 are two bits, 100
and 101 are three bits, etc. Since there are only two states, 0 or 1, for binary
data, it is easy to restore the distorted binary data to the correct data by
applying a threshold at 0.5. Provided that information is stored in a binary
form in optical storage, the amount of stored information can be represented
in bits. For illustration, if a tiny photographic film can store just a picture of
a checkerboard with 64 black-and-white squares, the storage capacity is 64 bits.

8.2. UPPER LIMIT OF OPTICAL STORAGE DENSITY

It is well known from diffraction theory [2, 3] that a lens can focus light to
a spot that is limited by the diffraction. This spot is sometimes called an Airy
disk, which has a central bright spot surrounded with ring fringes. The
diameter of the central bright spot of the Airy disk is

0 = 2.44^ A, (8.1)

where / and D are the focal length and the diameter of the lens, and /, is the