Page 62 - Introduction to Information Optics

1.7. Accuracy and Reliability Observation 47

Fig. 1.16. A high-accuracy observation.

computer is

AA
A/ = Iog 2 — ^ , AA l« AA 0. (1.1 56)

Thus, we see that the minimum cost of entropy is

AA
(1.157)
ZA./I

where AA 0 and A^ are the initial and final observation errors.
In short, we have achieved a very fundamental conclusion: one cannot get
something from nothing — there is always a price to pay. Resolution beyond
the resolution limit is possible, but only through the increase of entropy from
a certain physical system (in our example, the computer). However, in practice,
the cost of entropy is very excessive. In fact, the additional information gain at
best can only approach the equivalent amount of entropy traded off:

(1.158)

1.7. ACCURACY AND RELIABILITY OBSERVATION

We discuss problems of observation within a space-and-time domain. This
involves observing a position on a spatial plane, at an instant in time, with a
certain observation error. Note that the spatial domain of observation must be