If the PI wants to reach the same rms noise (
) on
sources
(they must share the same calibrator sources), during a given elapsed
telescope time (
), we have

(2) |

The calibration time can be written as

(3) |

(4) |

The time spent per source (
) is linked to the integration time
(
) through the succession of
subscans, each subscan
having an on-source integration time of
and an overhead time of
. The
subscans are grouped into scans, with
an additional overhead time of
per scan. If one scan can
contain at most
subscans, the number of scans (
) and
the residual number of subcans (
) are computed through

(5) | |||

(6) |

We note that the actual number of scan is when and when . The time spent per source is thus given by

(7) | |||

(8) |