Keywords: astro-30m-emir-time-estimator

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# 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)