## Decomposing the elapsed telescope time

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)
where is the time required to acquire the calibration information and the number of such calibration suits.

The calibration time can be written as

(3)
where , , and are respectively the typical times needed to perform a pointing, focus and skydip measurement and an OnOff measurement on a calibrator. is a multiplicative factor which takes into account the time to slew to the pointing and/or focus source as well as the possible need to do such calibrations twice in a row. The number of such calibrations is dictated by the fact that the maximum duration between two such calibration suits must be . This gives
(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)