Page 67 - Introduction to Information Optics

1. Entropy Information and Optics

HIGH ACCURACY HIGH ACCURACY
HIGH RELIABILITY LOW RELIABILITY

LOW ACCURACY LOW ACCURACY
HIGH RELIABILITY LOW RELIABILITY
Fig. 1.17. Examples of accuracy and reliability of observation.

where A£ denotes the energy perturbation and At is the time-interval observa-
tion.
By reference to the preceding observation made by radiation, one can
compare the required energy AE with the mean-square thermal fluctuation of
the photodetector ykT, where y is the number of degrees of freedom, which is
essentially the number of low-frequency vibrations (hv«kT). Thus, if
AE < ykT, we have

h
Af »— . (1.181)
ykT

From this inequality we see that a larger time resolution At is required for
low-frequency observation. Since A£ is small, the perturbation within At is
very small and can by comparison be ignored.