Page 79 - Introduction to Information Optics

64 1. Entropy Information and Optics

bits of the recorded information are considered to be in error, deter-
mine the entropy required for restoring the image.
1.16 For low-frequency observation, if the quantum stage g = m is selected as
the decision threshold, we will have an error probability of 50% per
observation. If we choose g = 5m calculate the probability of error per
observation.
1.17. In high-frequency observation, show that the cost of entropy per obser-
vation is greater. What is the minimum amount of entropy required per
observation? Compare this result with the low-frequency case and show
that the high-frequency case is more reliable.
1.18. For the problem of many simultaneous observations, if we assume that
an observation gives a positive (correct) result (i.e., any one of the a
photodetectors give rise to an energy level above £ 0 = ghv) and a 25%
chance of observation error is imposed, then calculate
a. the threshold energy level E 0 as a function of a and
b. the corresponding amount of entropy increase in the photodetectors.
1.19 In low-frequency simultaneous observations, if we obtain y simultaneous
correct observations out of a photodetectors (y < a), determine the
minimum cost of entropy required. Show that for the high-frequency case,
the minimum entropy required is even greater.
1.20 Given an imaging device; for example, a telescope, if the field of view at
a distant corner is denoted by A and the resolution of this imaging system
is limited to a small area A^4 over A, calculate the accuracy of this
imaging system and the amount of information provided by the observa-
tion.
1.21 With reference to the preceding problem,
a. Show that a high-accuracy observation requires a light source with a
shorter wavelength, and the reliability of this observation is inversely
proportional to the wavelength employed.
b. Determine the observation efficiency for higher-frequency observation.
1.22 The goal of a certain experiment is to measure the distance between two
reflecting walls. Assume that a plane monochromatic wave is to be
reflected back and forth between the two walls. The number of interfer-
ence fringes is determined to be 10 and the wavelength of the light
employed is 600nm. Calculate
a. the separation between the walls,
b. the amount of entropy increase in the photodetector (T= 300°K),
c. the amount of information required,
d. the corresponding energy threshold level of the photodetector if a
reliability 3% — 4 is required, where ?Jt = 1/probability of error, and
e. the efficiency of this observation.
1.23 Repeat the preceding problem for the higher-frequency observation.