The measurement procedure is then as follows. The telescope is first
corrected for coma at the center of the adapter.
With *B*'_{0}, *B*'_{1} and *B*'_{2} known, the values
for
and
could, in principle, be obtained from
one measurement of
and
somewhere in the
field of the telescope. But, in large telescopes field independent
astigmatism can easily be generated elastically. In addition, the
measurements are, for example due to local air effects, not free of
noise. Therefore, it will be necessary and more accurate to do
measurements at several
locations in the field and obtain the values for
and
with a least squares fit. We use typically eight
measurements at evenly distributed points at the edge of the field.
Such eight measurements would at least take fifteen minutes.
During this time the VLT optics changes, because of elastic
deformations due to changes of the zenith distance,
significantly. In particular, the aberrations decentering coma and
astigmatism are strongly affected. Therefore,
we had to do a closed loop active optics correction
at the center before each measurement at the edge and, in addition,
had to subtract the variation generated by the change of altitude
between the correction at the center and the measurement at the edge.

The expected change
of the angle between the axes of the
primary and secondary mirrors due to a rotation of the primary mirror
around its vertex can be deduced from Fig. 4. In an
initially perfectly aligned telescope first the primary mirror has
been rotated around its vertex by
.
Afterwards decentering coma has
been corrected by rotating the secondary mirror by
around its center of curvature. The axes of the primary and secondary
mirrors then intersect at the coma-free point
.
For small angles we get

The angle between the axes of the primary and secondary mirrors is then

The derivation of the change of the angle between the axes of the primary and secondary mirrors does, at least for small initial misalignments, not depend on the actual initial state of the telescope. Equation (84) is therefore always correct.

With the VLT parameters one gets

(85) |

For a rotation of the primary mirror around its vertex by 20'' one expects a change .

In addition, a rotation around the vertex will shift the whole pattern due to the tilt of the M1 axis, but the shift is only of the order of 0.5'' on the sky and therefore negligible.

The three mappings gave the following results for the *x*- and
*y*-components of
(all figures in arcseconds).

0 | 39.24 | 149.18 | |||

20 A | 38.52 | 285.23 | -0.72 | 136.05 | 136.05 |

20 B | 179.17 | 142.67 | 139.93 | -6.51 | 140.08 |

The total change of the misalignment is defined by . The average of the measured changes of the misalignment angles between the first and the second configuration on the one hand and the first and the third configuration on the other hand is . The difference to the expected value is only 5.3''. If, after a rotation of the secondary mirror around the coma free point a similar accuracy is achieved, the two nodes of the binodal field will only be 7'' apart. At the edge of the field of this would lead to an error in the coefficient of third order astigmatism of , which is negligible.

Copyright The European Southern Observatory (ESO)