We consider a micro-scan lasting 
, consisting of
exposures on different pointings ( = 
for a raster scan of M points along N
lines). Each exposure is obtained by averaging 
successive elementary images with integration time 
.
Some area of the sky covered by the raster will be seen by 
different pixels:
where 
and 
are the displacements, in arc seconds, in each direction.
Assuming that an optimal micro-scan data reduction solution is obtained
simultaneously for the sky image and detector response, in areas seen
by different pixels, the rms uncertainty for a single
position in the final map is obtained as follows:
By definition:
where:
and:
Solving equations 
and :
where :
is the HF term of the detector noise.
The LF noise is as given above, but with the appropriate observing times:
