Maximization of the information capacity of measuring instruments

Conclusions

• 1. For a definite distribution function w(x) of the measured variable and a definite entropy error g(α) of the mechanism there is an optimum relationship between the angular deflectionα and the measured variable x such that the IC of the instrument attains the maximum value given by Eq. (6).

• 2. The maximum IC is equal to the resolving power of the instrument, Eq. (7).

• 3. From the physical point of view the optimal instrument realizes more precise measurements for more probable values of the measured variable, Eq. (9).

For equiprobable values of the measured variable the optimal instrument realizes more precise measurements for cases in which the angular errors of the mechanism are greater: Examples 3 and 4.

For nonuniform (nonflat) distributions of the measured variable the last two results are compatible: Examples 1 and 2.

• 4. The esign and use of an optimal instrument yield a positive result in every case. This result depends on the distribution of the measured variable and the entropy error of the mechanism.

For a hyperbolic distribution of the measured variable and a linear distribution of the entropy error of the mechanism the gain for linear and square-law instruments is appreciable: Examples 1 and 2.

For a flat distribution of the measured variable the optimization gain with respect to a linear instrument increases as the additive component of the entropy error decreases: Example 3.