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

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

- The concept of submap, which is a part of a map observed between two successive off measurements.
- , which is the area covered by the telescope in each submap.
- the number of such submaps needed to cover the whole map area.
- , the typical time where the system is stable. This time will be the maximum time between two off measurements, which is noted .
- , the number of coverages needed either to reach a given sensitivity or to exhaust the acquisition time.
- and are the times spent respectively on and off per independent measurement and per coverage.