When the stability of the system is long enough, we can share the same off for several independent on-positions measured in a row (e.g. ON-ON-ON-OFF-ON-ON-ON-OFF...). The first key point here is the fact that the on-positions must be independent. The OTF is an observing mode where the sharing of the off can be used because the goal is to map a given region of the sky made of independent positions or resolution elements. When sharing the off-position between several on, Ball (1976) showed that the optimal off integration time is
where
, we obtain
We thus see that the rms noise decreases when the number of independent on
per off increases. It seems tempting to have only one off for all the on
positions of the OTF map. However, the second key point of the method is
that the system must be stable between the first and last on
measurement. To take this point into account we must introduce
both in each individual coverage
and when averaging all the coverages.