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:
where :
is the HF term of the detector noise.
The LF noise is as given above, but with the appropriate observing times: