# Optimal number of ON per OFF measurements

This section is just a reformulation of the original demonstration by Ball (1976).

Let's assume that we are measuring independent on-positions for a single off. The same integration time ( ) is spent on each on-position and the off integration time is

(53)
where can be varied. Using eq. and , it can be shown than
(54)
Differenciating with respect to , we obtain
(55)
Setting the result to zero then gives that the minimum elapsed time to reach a given rms noise is obtained for
(56)