#### 5.2 Astrometric accuracy

The astrometric accuracy is derived in the same way as for the Wide survey. We refer to the beginning of Section
4.5 for a description of the method. The Deep analysis is however simpler than the Wide because there is only
one single position per field. The astrometric calibration of the Deep fields is detailed in Section 3.5, so we only
focus on the accuracy in this section.

The results of the internal and external error analysis are given in Tables 17 and 18. The internal errors have been
measured by SCAMP, from the astrometric solutions of each Deep field, for each filter separately. In contrast, the
external errors quoted in Tables 17 and 18 are not the values derived from the astrometric solutions. They are
computed separately as well, but after the production of the Deep images, in order to get the true astrometric
errors of sources in each stack. The reference external catalogue is 2MASS, and the external errors found are
very similar to the Wide survey.

On average, the mean internal astrometric rms errors in the Deep fields are

| (17) |

and the mean external errors

| (18) |

where, the dispersions are the rms errors. Since the four fields are calibrated independently, the values
quoted above are only rough estimates; the errors for D1, D2, D3 and D4 are given in Tables 17 and
18. The rather large scatter in the internal errors is due to the different ways each Deep field has
been calibrated (either using an internal catalogue based on the i band data, or using the external
2MASS catalogue, see Section 3.5). The external astrometric errors are similar to the Wide survey
and correspond to the expectations, considering the astrometric errors in the 2MASS reference
catalogue.