Page 66 - Introduction to Information Optics

1.7. Accuracy and Reliability Observation 5 1

For y. » 1 the preceding equation can be written as

hv >kT(\noi + 0.367). (1.176)

Since the absorption of one quantum of light is adequate for a positive response,
the corresponding entropy increase is

AS - — > fc(ln a + 0.367). (1.177)

The amount of information obtained would be

7-log 2 abits. (1.178)

Thus we see that

AS-/fcln2>0.367fc>0. (1.179)

Except for the equality, this AS is identical to that of the low-frequency
observation of Eq. (1.162). However, the entropy increase is much higher, since
v is very high. Although fine observation can be obtained by using higher
frequency, there is a price to be paid; namely, higher cost of entropy.
We now come to the reliable observation. One must distinguish the basic
difference between accuracy and reliability in observations. A reliable observa-
tion is dependent on the chosen decision threshold level E 0; that is, the higher
the threshold level, the higher the reliability. However, accuracy in observation
is inversely related to the spread of the detected signal; the narrower the spread,
the higher the accuracy. These two issues are illustrated in Fig. 1.17. It is
evident that the higher threshold energy level E 0 chosen would have higher the
reliability. However, higher reliability also produces higher probability of
misses. On the other hand, if E 0 is set at a lower level, a less reliable observation
is expected. In other words, high probability of error (false alarms) may
produce, for example, due thermal noise fluctuation.

1.7.1. UNCERTAINTY OBSERVATION

All physical systems are ultimately restricted by some limitations. When
quantum conditions are in use, all limitations are essentially imposed by the
basic Heisenberg uncertainty principle:

AEAf^/T, (1.180)